From 194c4541525e87b58f95d7a010d130b52ea6b663 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Mon, 23 Sep 2024 06:17:13 +0200 Subject: [PATCH] corrected week 39 --- .../_build/.doctrees/environment.pickle | Bin 379946 -> 380961 bytes .../_build/.doctrees/week39.doctree | Bin 356677 -> 1122470 bytes .../_build/html/_images/week39_153_1.png | Bin 0 -> 24275 bytes .../_build/html/_images/week39_166_1.png | Bin 0 -> 21406 bytes .../_build/html/_images/week39_169_1.png | Bin 0 -> 21647 bytes .../_build/html/_images/week39_171_1.png | Bin 0 -> 22057 bytes .../_build/html/_images/week39_193_1.png | Bin 0 -> 22257 bytes .../_build/html/_images/week39_236_0.png | Bin 0 -> 33538 bytes .../_build/html/_images/week39_265_1.png | Bin 0 -> 21520 bytes .../_build/html/_images/week39_271_1.png | Bin 0 -> 21893 bytes .../_build/html/_images/week39_82_1.png | Bin 0 -> 102653 bytes .../_build/html/_images/week39_84_0.png | Bin 0 -> 45273 bytes .../_build/html/_images/week39_90_1.png | Bin 0 -> 224710 bytes .../_build/html/_sources/week39.ipynb | 2447 ++++++++-------- doc/LectureNotes/_build/html/searchindex.js | 2 +- doc/LectureNotes/_build/html/week39.html | 431 ++- .../_build/jupyter_execute/week39.ipynb | 2477 +++++++++-------- .../_build/jupyter_execute/week39.py | 25 +- .../_build/jupyter_execute/week39_153_1.png | Bin 0 -> 24275 bytes .../_build/jupyter_execute/week39_166_1.png | Bin 0 -> 21406 bytes .../_build/jupyter_execute/week39_169_1.png | Bin 0 -> 21647 bytes .../_build/jupyter_execute/week39_171_1.png | Bin 0 -> 22057 bytes .../_build/jupyter_execute/week39_193_1.png | Bin 0 -> 22257 bytes .../_build/jupyter_execute/week39_236_0.png | Bin 0 -> 33538 bytes .../_build/jupyter_execute/week39_265_1.png | Bin 0 -> 21520 bytes .../_build/jupyter_execute/week39_271_1.png | Bin 0 -> 21893 bytes .../_build/jupyter_execute/week39_82_1.png | Bin 0 -> 102653 bytes .../_build/jupyter_execute/week39_84_0.png | Bin 0 -> 45273 bytes .../_build/jupyter_execute/week39_90_1.png | 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100644 --- a/doc/LectureNotes/_build/html/_sources/week39.ipynb +++ b/doc/LectureNotes/_build/html/_sources/week39.ipynb @@ -2,10 +2,8 @@ "cells": [ { "cell_type": "markdown", - "id": "918e6088", - "metadata": { - "editable": true - }, + "id": "0be56d20", + "metadata": {}, "source": [ "\n", @@ -14,10 +12,8 @@ }, { "cell_type": "markdown", - "id": "f6bdc2db", - "metadata": { - "editable": true - }, + "id": "41352012", + "metadata": {}, "source": [ "# Week 39: Optimization and Gradient Methods\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", @@ -27,20 +23,16 @@ }, { "cell_type": "markdown", - "id": "0fd73813", - "metadata": { - "editable": true - }, + "id": "471d9b17", + "metadata": {}, "source": [ "## Plan for week 39, September 23-27, 2024" ] }, { "cell_type": "markdown", - "id": "4659a144", - "metadata": { - "editable": true - }, + "id": "a3f843e5", + "metadata": {}, "source": [ "## Lecture Monday September 23\n", "\n", @@ -67,10 +59,8 @@ }, { "cell_type": "markdown", - "id": "fc1f68ca", - "metadata": { - "editable": true - }, + "id": "b611ff2d", + "metadata": {}, "source": [ "## Lab sessions week 39\n", "\n", @@ -94,10 +84,8 @@ }, { "cell_type": "markdown", - "id": "15869b1d", - "metadata": { - "editable": true - }, + "id": "126f7d60", + "metadata": {}, "source": [ "## Lecture Monday September 23, Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -115,10 +103,8 @@ }, { "cell_type": "markdown", - "id": "cfaf747a", - "metadata": { - "editable": true - }, + "id": "a2682f11", + "metadata": {}, "source": [ "## Revisiting our Logistic Regression case\n", "\n", @@ -132,10 +118,8 @@ }, { "cell_type": "markdown", - "id": "e2850b85", - "metadata": { - "editable": true - }, + "id": "d51c88b5", + "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", @@ -147,20 +131,16 @@ }, { "cell_type": "markdown", - "id": "a73f7a09", - "metadata": { - "editable": true - }, + "id": "4a135362", + "metadata": {}, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$." ] }, { "cell_type": "markdown", - "id": "eee9af50", - "metadata": { - "editable": true - }, + "id": "26444396", + "metadata": {}, "source": [ "## The equations to solve\n", "\n", @@ -173,10 +153,8 @@ }, { "cell_type": "markdown", - "id": "d8a40aeb", - "metadata": { - "editable": true - }, + "id": "9bc5702f", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -185,10 +163,8 @@ }, { "cell_type": "markdown", - "id": "7d24b6f4", - "metadata": { - "editable": true - }, + "id": "a857de8b", + "metadata": {}, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -196,10 +172,8 @@ }, { "cell_type": "markdown", - "id": "da0033f7", - "metadata": { - "editable": true - }, + "id": "dc870dc3", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -208,20 +182,16 @@ }, { "cell_type": "markdown", - "id": "eff96c8f", - "metadata": { - "editable": true - }, + "id": "4001c458", + "metadata": {}, "source": [ "This defines what is called the Hessian matrix." ] }, { "cell_type": "markdown", - "id": "bbf59e32", - "metadata": { - "editable": true - }, + "id": "4f3262b4", + "metadata": {}, "source": [ "## Solving using Newton-Raphson's method\n", "\n", @@ -232,10 +202,8 @@ }, { "cell_type": "markdown", - "id": "67e16976", - "metadata": { - "editable": true - }, + "id": "0d94cee2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -244,20 +212,16 @@ }, { "cell_type": "markdown", - "id": "374d66a6", - "metadata": { - "editable": true - }, + "id": "d92e7b5d", + "metadata": {}, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "id": "ed30dea2", - "metadata": { - "editable": true - }, + "id": "076acdca", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -266,10 +230,8 @@ }, { "cell_type": "markdown", - "id": "f098e947", - "metadata": { - "editable": true - }, + "id": "c37ab3fd", + "metadata": {}, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", @@ -278,10 +240,8 @@ }, { "cell_type": "markdown", - "id": "741d9a60", - "metadata": { - "editable": true - }, + "id": "4f771526", + "metadata": {}, "source": [ "## Brief reminder on Newton-Raphson's method\n", "\n", @@ -298,10 +258,8 @@ }, { "cell_type": "markdown", - "id": "dff616d1", - "metadata": { - "editable": true - }, + "id": "e13dad72", + "metadata": {}, "source": [ "## The equations\n", "\n", @@ -314,10 +272,8 @@ }, { "cell_type": "markdown", - "id": "5d37722e", - "metadata": { - "editable": true - }, + "id": "aff57d4b", + "metadata": {}, "source": [ "\n", "

\n", @@ -330,10 +286,8 @@ }, { "cell_type": "markdown", - "id": "6706784b", - "metadata": { - "editable": true - }, + "id": "38304c1d", + "metadata": {}, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -341,10 +295,8 @@ }, { "cell_type": "markdown", - "id": "3708fdef", - "metadata": { - "editable": true - }, + "id": "8da576a0", + "metadata": {}, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -353,20 +305,16 @@ }, { "cell_type": "markdown", - "id": "3f607de4", - "metadata": { - "editable": true - }, + "id": "46d9c588", + "metadata": {}, "source": [ "yielding" ] }, { "cell_type": "markdown", - "id": "bdb0ec30", - "metadata": { - "editable": true - }, + "id": "3a3ca58b", + "metadata": {}, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -375,20 +323,16 @@ }, { "cell_type": "markdown", - "id": "e941f0f2", - "metadata": { - "editable": true - }, + "id": "0c9c700f", + "metadata": {}, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "id": "2a7d9a7f", - "metadata": { - "editable": true - }, + "id": "b273b273", + "metadata": {}, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -397,10 +341,8 @@ }, { "cell_type": "markdown", - "id": "9c9bfa29", - "metadata": { - "editable": true - }, + "id": "3e0a875b", + "metadata": {}, "source": [ "## Simple geometric interpretation\n", "\n", @@ -419,10 +361,8 @@ }, { "cell_type": "markdown", - "id": "e6fecd57", - "metadata": { - "editable": true - }, + "id": "727cfd55", + "metadata": {}, "source": [ "## Extending to more than one variable\n", "\n", @@ -432,10 +372,8 @@ }, { "cell_type": "markdown", - "id": "250ae3be", - "metadata": { - "editable": true - }, + "id": "f78349b5", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -445,20 +383,16 @@ }, { "cell_type": "markdown", - "id": "13f76c19", - "metadata": { - "editable": true - }, + "id": "2ee16c9e", + "metadata": {}, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "id": "7c8dabb7", - "metadata": { - "editable": true - }, + "id": "f95fdb8b", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -473,20 +407,16 @@ }, { "cell_type": "markdown", - "id": "74eaf63d", - "metadata": { - "editable": true - }, + "id": "3f039432", + "metadata": {}, "source": [ "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have" ] }, { "cell_type": "markdown", - "id": "4a58d03d", - "metadata": { - "editable": true - }, + "id": "dbd20795", + "metadata": {}, "source": [ "$$\n", "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n", @@ -498,20 +428,16 @@ }, { "cell_type": "markdown", - "id": "ad5a8242", - "metadata": { - "editable": true - }, + "id": "98ba6676", + "metadata": {}, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "id": "2d1a3ad3", - "metadata": { - "editable": true - }, + "id": "ad52dad5", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -522,20 +448,16 @@ }, { "cell_type": "markdown", - "id": "3f664794", - "metadata": { - "editable": true - }, + "id": "cc09e475", + "metadata": {}, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "id": "2605bf0e", - "metadata": { - "editable": true - }, + "id": "7a1c0547", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -546,10 +468,8 @@ }, { "cell_type": "markdown", - "id": "01f6d82b", - "metadata": { - "editable": true - }, + "id": "9fe4208b", + "metadata": {}, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", @@ -561,10 +481,8 @@ }, { "cell_type": "markdown", - "id": "92fbc947", - "metadata": { - "editable": true - }, + "id": "2a81e02b", + "metadata": {}, "source": [ "## Steepest descent\n", "\n", @@ -578,10 +496,8 @@ }, { "cell_type": "markdown", - "id": "4456e346", - "metadata": { - "editable": true - }, + "id": "f90232dd", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -590,10 +506,8 @@ }, { "cell_type": "markdown", - "id": "98859a0d", - "metadata": { - "editable": true - }, + "id": "4fb8b51e", + "metadata": {}, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -604,10 +518,8 @@ }, { "cell_type": "markdown", - "id": "3249ff28", - "metadata": { - "editable": true - }, + "id": "81da0301", + "metadata": {}, "source": [ "## More on Steepest descent\n", "\n", @@ -619,10 +531,8 @@ }, { "cell_type": "markdown", - "id": "bc3514ae", - "metadata": { - "editable": true - }, + "id": "9b1a0014", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -631,10 +541,8 @@ }, { "cell_type": "markdown", - "id": "7dc046a6", - "metadata": { - "editable": true - }, + "id": "52e8d174", + "metadata": {}, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning." @@ -642,10 +550,8 @@ }, { "cell_type": "markdown", - "id": "0b885ad4", - "metadata": { - "editable": true - }, + "id": "be802e47", + "metadata": {}, "source": [ "## The ideal\n", "\n", @@ -670,10 +576,8 @@ }, { "cell_type": "markdown", - "id": "800ed299", - "metadata": { - "editable": true - }, + "id": "c2404539", + "metadata": {}, "source": [ "## The sensitiveness of the gradient descent\n", "\n", @@ -692,10 +596,8 @@ }, { "cell_type": "markdown", - "id": "bfd9b49f", - "metadata": { - "editable": true - }, + "id": "f96c6cdf", + "metadata": {}, "source": [ "## Convex functions\n", "\n", @@ -714,10 +616,8 @@ }, { "cell_type": "markdown", - "id": "7cc0574a", - "metadata": { - "editable": true - }, + "id": "0deb328b", + "metadata": {}, "source": [ "## Convex function\n", "\n", @@ -735,10 +635,8 @@ }, { "cell_type": "markdown", - "id": "a4a7e0d2", - "metadata": { - "editable": true - }, + "id": "74dc1b02", + "metadata": {}, "source": [ "## Conditions on convex functions\n", "\n", @@ -774,10 +672,8 @@ }, { "cell_type": "markdown", - "id": "4ac4f3dd", - "metadata": { - "editable": true - }, + "id": "bc8bc23c", + "metadata": {}, "source": [ "## More on convex functions\n", "\n", @@ -802,10 +698,8 @@ }, { "cell_type": "markdown", - "id": "e2c3e2b8", - "metadata": { - "editable": true - }, + "id": "b004d0d8", + "metadata": {}, "source": [ "## Some simple problems\n", "\n", @@ -832,10 +726,8 @@ }, { "cell_type": "markdown", - "id": "3cbf5677", - "metadata": { - "editable": true - }, + "id": "004c656f", + "metadata": {}, "source": [ "## Standard steepest descent\n", "\n", @@ -852,10 +744,8 @@ }, { "cell_type": "markdown", - "id": "8b46198f", - "metadata": { - "editable": true - }, + "id": "3055088e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -864,20 +754,16 @@ }, { "cell_type": "markdown", - "id": "87174dcb", - "metadata": { - "editable": true - }, + "id": "9d268d89", + "metadata": {}, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "id": "5af2eb1c", - "metadata": { - "editable": true - }, + "id": "c8dbe560", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -886,10 +772,8 @@ }, { "cell_type": "markdown", - "id": "977cfa69", - "metadata": { - "editable": true - }, + "id": "fd2de293", + "metadata": {}, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", @@ -898,10 +782,8 @@ }, { "cell_type": "markdown", - "id": "68fd5ea0", - "metadata": { - "editable": true - }, + "id": "25344346", + "metadata": {}, "source": [ "## Gradient method\n", "\n", @@ -910,10 +792,8 @@ }, { "cell_type": "markdown", - "id": "4e2bae9e", - "metadata": { - "editable": true - }, + "id": "c1b8855c", + "metadata": {}, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -922,10 +802,8 @@ }, { "cell_type": "markdown", - "id": "bcbbad7f", - "metadata": { - "editable": true - }, + "id": "506aceb6", + "metadata": {}, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite." @@ -933,10 +811,8 @@ }, { "cell_type": "markdown", - "id": "67d8e3f3", - "metadata": { - "editable": true - }, + "id": "53b26051", + "metadata": {}, "source": [ "## Steepest descent method\n", "\n", @@ -946,10 +822,8 @@ }, { "cell_type": "markdown", - "id": "7519f74e", - "metadata": { - "editable": true - }, + "id": "06b0db34", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -958,20 +832,16 @@ }, { "cell_type": "markdown", - "id": "f0b6000e", - "metadata": { - "editable": true - }, + "id": "0d9ddd86", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "0a5e83d1", - "metadata": { - "editable": true - }, + "id": "66dff86c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -980,20 +850,16 @@ }, { "cell_type": "markdown", - "id": "fff9b0be", - "metadata": { - "editable": true - }, + "id": "77c18c22", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "2be695a7", - "metadata": { - "editable": true - }, + "id": "9dfad29a", + "metadata": {}, "source": [ "## Steepest descent method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1001,10 +867,8 @@ }, { "cell_type": "markdown", - "id": "1bcf856f", - "metadata": { - "editable": true - }, + "id": "50edf2f9", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1013,10 +877,8 @@ }, { "cell_type": "markdown", - "id": "6dd2c43f", - "metadata": { - "editable": true - }, + "id": "51d84a77", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1025,10 +887,8 @@ }, { "cell_type": "markdown", - "id": "a4d7a932", - "metadata": { - "editable": true - }, + "id": "f3179c0a", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1037,10 +897,8 @@ }, { "cell_type": "markdown", - "id": "20db9bfe", - "metadata": { - "editable": true - }, + "id": "66bc0e76", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$." @@ -1048,10 +906,8 @@ }, { "cell_type": "markdown", - "id": "cde76790", - "metadata": { - "editable": true - }, + "id": "9be63d8b", + "metadata": {}, "source": [ "## Final expressions\n", "We can compute the residual iteratively as" @@ -1059,10 +915,8 @@ }, { "cell_type": "markdown", - "id": "c1ba27a3", - "metadata": { - "editable": true - }, + "id": "07294b6e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1071,20 +925,16 @@ }, { "cell_type": "markdown", - "id": "81525791", - "metadata": { - "editable": true - }, + "id": "5cb13e3a", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "42bd4217", - "metadata": { - "editable": true - }, + "id": "b95b4415", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -1093,20 +943,16 @@ }, { "cell_type": "markdown", - "id": "c1f6672f", - "metadata": { - "editable": true - }, + "id": "90956a95", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "df8c1efa", - "metadata": { - "editable": true - }, + "id": "d4675379", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -1115,20 +961,16 @@ }, { "cell_type": "markdown", - "id": "1b4bf5a8", - "metadata": { - "editable": true - }, + "id": "6e3a1c20", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "e2c3ad13", - "metadata": { - "editable": true - }, + "id": "e9b86a0a", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -1137,20 +979,16 @@ }, { "cell_type": "markdown", - "id": "333026af", - "metadata": { - "editable": true - }, + "id": "a1fd88cc", + "metadata": {}, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "id": "35825027", - "metadata": { - "editable": true - }, + "id": "39f090b1", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n", @@ -1159,10 +997,8 @@ }, { "cell_type": "markdown", - "id": "62866612", - "metadata": { - "editable": true - }, + "id": "0ad69506", + "metadata": {}, "source": [ "## Steepest descent example" ] @@ -1170,12 +1006,30 @@ { "cell_type": "code", "execution_count": 1, - "id": "ba11008c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "4a529fa4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%matplotlib inline\n", "\n", @@ -1194,7 +1048,7 @@ " return np.array([2*x[0], 6*x[1]])\n", "\n", "fig = pt.figure()\n", - "ax = fig.gca(projection=\"3d\")\n", + "ax = fig.add_subplot(projection = '3d')\n", "\n", "xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n", "fmesh = f(np.array([xmesh, ymesh]))\n", @@ -1203,10 +1057,8 @@ }, { "cell_type": "markdown", - "id": "d94f79ff", - "metadata": { - "editable": true - }, + "id": "949a0d1c", + "metadata": {}, "source": [ "And then as countor plot" ] @@ -1214,12 +1066,20 @@ { "cell_type": "code", "execution_count": 2, - "id": "8d03a29a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3b0698ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", @@ -1228,10 +1088,8 @@ }, { "cell_type": "markdown", - "id": "1560ce9e", - "metadata": { - "editable": true - }, + "id": "b3d4208f", + "metadata": {}, "source": [ "Find guesses" ] @@ -1239,11 +1097,8 @@ { "cell_type": "code", "execution_count": 3, - "id": "444dcac8", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "d7e4a182", + "metadata": {}, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -1252,10 +1107,8 @@ }, { "cell_type": "markdown", - "id": "6a3a8ba3", - "metadata": { - "editable": true - }, + "id": "fbc59d26", + "metadata": {}, "source": [ "Run it!" ] @@ -1263,12 +1116,17 @@ { "cell_type": "code", "execution_count": 4, - "id": "96921390", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "18be8fa1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.69230769 -0.38461539]\n" + ] + } + ], "source": [ "def f1d(alpha):\n", " return f(x + alpha*s)\n", @@ -1281,10 +1139,8 @@ }, { "cell_type": "markdown", - "id": "5090d289", - "metadata": { - "editable": true - }, + "id": "7f40f5f6", + "metadata": {}, "source": [ "What happened?" ] @@ -1292,12 +1148,30 @@ { "cell_type": "code", "execution_count": 5, - "id": "ac4b2a89", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "dbdb7d4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", @@ -1307,20 +1181,16 @@ }, { "cell_type": "markdown", - "id": "014335b8", - "metadata": { - "editable": true - }, + "id": "851db164", + "metadata": {}, "source": [ "Note that we did only one iteration here. We can easily add more using our previous guesses." ] }, { "cell_type": "markdown", - "id": "8f2fc479", - "metadata": { - "editable": true - }, + "id": "f1300342", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -1331,10 +1201,8 @@ }, { "cell_type": "markdown", - "id": "c12ed388", - "metadata": { - "editable": true - }, + "id": "15530c95", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -1343,10 +1211,8 @@ }, { "cell_type": "markdown", - "id": "525571bd", - "metadata": { - "editable": true - }, + "id": "35222dc4", + "metadata": {}, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -1354,10 +1220,8 @@ }, { "cell_type": "markdown", - "id": "16ea251e", - "metadata": { - "editable": true - }, + "id": "a5ab4e81", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -1366,10 +1230,8 @@ }, { "cell_type": "markdown", - "id": "bc20e247", - "metadata": { - "editable": true - }, + "id": "922a54c4", + "metadata": {}, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$." @@ -1377,10 +1239,8 @@ }, { "cell_type": "markdown", - "id": "7e393cfd", - "metadata": { - "editable": true - }, + "id": "606d1a71", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "An example is given by the eigenvectors of the matrix" @@ -1388,10 +1248,8 @@ }, { "cell_type": "markdown", - "id": "004102f6", - "metadata": { - "editable": true - }, + "id": "e46ac6fc", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -1400,20 +1258,16 @@ }, { "cell_type": "markdown", - "id": "842e93a3", - "metadata": { - "editable": true - }, + "id": "aec2962a", + "metadata": {}, "source": [ "which is zero unless $i=j$." ] }, { "cell_type": "markdown", - "id": "988aa113", - "metadata": { - "editable": true - }, + "id": "f62eeb16", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n", @@ -1422,10 +1276,8 @@ }, { "cell_type": "markdown", - "id": "6c460be1", - "metadata": { - "editable": true - }, + "id": "bde9cf46", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -1434,10 +1286,8 @@ }, { "cell_type": "markdown", - "id": "1694d645", - "metadata": { - "editable": true - }, + "id": "1b354afe", + "metadata": {}, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -1446,10 +1296,8 @@ }, { "cell_type": "markdown", - "id": "091ad567", - "metadata": { - "editable": true - }, + "id": "a3e7fc78", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -1458,10 +1306,8 @@ }, { "cell_type": "markdown", - "id": "dd3cf73c", - "metadata": { - "editable": true - }, + "id": "9608b5e1", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "The coefficients are given by" @@ -1469,10 +1315,8 @@ }, { "cell_type": "markdown", - "id": "13cf2ad9", - "metadata": { - "editable": true - }, + "id": "d667abb4", + "metadata": {}, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -1481,20 +1325,16 @@ }, { "cell_type": "markdown", - "id": "9bc1ee6e", - "metadata": { - "editable": true - }, + "id": "2b909963", + "metadata": {}, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "id": "05599b4f", - "metadata": { - "editable": true - }, + "id": "0e9960df", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -1503,20 +1343,16 @@ }, { "cell_type": "markdown", - "id": "48dce995", - "metadata": { - "editable": true - }, + "id": "4d334201", + "metadata": {}, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "id": "3ed1d31f", - "metadata": { - "editable": true - }, + "id": "f06c6496", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1525,10 +1361,8 @@ }, { "cell_type": "markdown", - "id": "d53065fb", - "metadata": { - "editable": true - }, + "id": "69adaefe", + "metadata": {}, "source": [ "## Conjugate gradient method and iterations\n", "\n", @@ -1545,10 +1379,8 @@ }, { "cell_type": "markdown", - "id": "1c9e8acd", - "metadata": { - "editable": true - }, + "id": "35cf8e92", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1557,20 +1389,16 @@ }, { "cell_type": "markdown", - "id": "b1ce7e22", - "metadata": { - "editable": true - }, + "id": "686fe37b", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "5a9d580f", - "metadata": { - "editable": true - }, + "id": "b6cdf1da", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1579,20 +1407,16 @@ }, { "cell_type": "markdown", - "id": "bd732814", - "metadata": { - "editable": true - }, + "id": "f03df570", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "a0b6ed43", - "metadata": { - "editable": true - }, + "id": "d2619eaa", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1600,10 +1424,8 @@ }, { "cell_type": "markdown", - "id": "0647b456", - "metadata": { - "editable": true - }, + "id": "7c99b348", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1612,10 +1434,8 @@ }, { "cell_type": "markdown", - "id": "39dd4393", - "metadata": { - "editable": true - }, + "id": "06107635", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1624,10 +1444,8 @@ }, { "cell_type": "markdown", - "id": "5d17f7b6", - "metadata": { - "editable": true - }, + "id": "7d57e70c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1636,10 +1454,8 @@ }, { "cell_type": "markdown", - "id": "7f0fbf0c", - "metadata": { - "editable": true - }, + "id": "d07728a4", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1649,10 +1465,8 @@ }, { "cell_type": "markdown", - "id": "f9d39a67", - "metadata": { - "editable": true - }, + "id": "64a6011d", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:" @@ -1660,10 +1474,8 @@ }, { "cell_type": "markdown", - "id": "75e12e7b", - "metadata": { - "editable": true - }, + "id": "395293fb", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1672,10 +1484,8 @@ }, { "cell_type": "markdown", - "id": "aec178fd", - "metadata": { - "editable": true - }, + "id": "2742cfb7", + "metadata": {}, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1688,10 +1498,8 @@ }, { "cell_type": "markdown", - "id": "d9c2ab58", - "metadata": { - "editable": true - }, + "id": "6bca98e3", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1700,10 +1508,8 @@ }, { "cell_type": "markdown", - "id": "cbe552ed", - "metadata": { - "editable": true - }, + "id": "0b38ac3f", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "We can also compute the residual iteratively as" @@ -1711,10 +1517,8 @@ }, { "cell_type": "markdown", - "id": "82a132bd", - "metadata": { - "editable": true - }, + "id": "0588ed16", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1723,20 +1527,16 @@ }, { "cell_type": "markdown", - "id": "0349d81c", - "metadata": { - "editable": true - }, + "id": "2f7bd339", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "7107cbd5", - "metadata": { - "editable": true - }, + "id": "5d46e7c8", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1745,20 +1545,16 @@ }, { "cell_type": "markdown", - "id": "3a56cd7c", - "metadata": { - "editable": true - }, + "id": "a6dfda96", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "63a24c09", - "metadata": { - "editable": true - }, + "id": "bea30687", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1767,20 +1563,16 @@ }, { "cell_type": "markdown", - "id": "6ef4ea63", - "metadata": { - "editable": true - }, + "id": "ec002ff0", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "c2357533", - "metadata": { - "editable": true - }, + "id": "a45514a5", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1789,10 +1581,8 @@ }, { "cell_type": "markdown", - "id": "61549c12", - "metadata": { - "editable": true - }, + "id": "60756713", + "metadata": {}, "source": [ "## Revisiting our first homework\n", "\n", @@ -1813,23 +1603,19 @@ { "cell_type": "code", "execution_count": 6, - "id": "2bbe00ae", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "9e6108fd", + "metadata": {}, "outputs": [], "source": [ + "m = 100\n", "x = 2*np.random.rand(m,1)\n", "y = 4+3*x+np.random.randn(m,1)" ] }, { "cell_type": "markdown", - "id": "2edbd94a", - "metadata": { - "editable": true - }, + "id": "146e4fe9", + "metadata": {}, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1837,10 +1623,8 @@ }, { "cell_type": "markdown", - "id": "97f601a1", - "metadata": { - "editable": true - }, + "id": "c5c0a7f1", + "metadata": {}, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1849,20 +1633,16 @@ }, { "cell_type": "markdown", - "id": "46f56da5", - "metadata": { - "editable": true - }, + "id": "f5f1aea6", + "metadata": {}, "source": [ "such that" ] }, { "cell_type": "markdown", - "id": "ea40d182", - "metadata": { - "editable": true - }, + "id": "76b1993f", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1871,10 +1651,8 @@ }, { "cell_type": "markdown", - "id": "f1529059", - "metadata": { - "editable": true - }, + "id": "b5a211bb", + "metadata": {}, "source": [ "## Gradient descent example\n", "\n", @@ -1885,10 +1663,8 @@ }, { "cell_type": "markdown", - "id": "ff686b79", - "metadata": { - "editable": true - }, + "id": "4b0b1b01", + "metadata": {}, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1901,20 +1677,16 @@ }, { "cell_type": "markdown", - "id": "e9072325", - "metadata": { - "editable": true - }, + "id": "c5751686", + "metadata": {}, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "id": "b039d2dd", - "metadata": { - "editable": true - }, + "id": "a2d6f6a6", + "metadata": {}, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1923,20 +1695,16 @@ }, { "cell_type": "markdown", - "id": "dc1285b8", - "metadata": { - "editable": true - }, + "id": "af74580d", + "metadata": {}, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized." ] }, { "cell_type": "markdown", - "id": "8d029669", - "metadata": { - "editable": true - }, + "id": "949f8aab", + "metadata": {}, "source": [ "## The derivative of the cost/loss function\n", "\n", @@ -1945,10 +1713,8 @@ }, { "cell_type": "markdown", - "id": "f2b0be18", - "metadata": { - "editable": true - }, + "id": "5e3860a4", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1959,20 +1725,16 @@ }, { "cell_type": "markdown", - "id": "72b959fa", - "metadata": { - "editable": true - }, + "id": "765febad", + "metadata": {}, "source": [ "where $X$ is the design matrix defined above." ] }, { "cell_type": "markdown", - "id": "53db546f", - "metadata": { - "editable": true - }, + "id": "65781e41", + "metadata": {}, "source": [ "## The Hessian matrix\n", "The Hessian matrix of $C(\\beta)$ is given by" @@ -1980,10 +1742,8 @@ }, { "cell_type": "markdown", - "id": "d9799e09", - "metadata": { - "editable": true - }, + "id": "7e1e9714", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -1995,20 +1755,16 @@ }, { "cell_type": "markdown", - "id": "433d7d4e", - "metadata": { - "editable": true - }, + "id": "9d48eebb", + "metadata": {}, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite." ] }, { "cell_type": "markdown", - "id": "8bcfa1d9", - "metadata": { - "editable": true - }, + "id": "fd88e7fd", + "metadata": {}, "source": [ "## Simple program\n", "\n", @@ -2017,10 +1773,8 @@ }, { "cell_type": "markdown", - "id": "9591273f", - "metadata": { - "editable": true - }, + "id": "e12fb5d1", + "metadata": {}, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -2029,10 +1783,8 @@ }, { "cell_type": "markdown", - "id": "ff30e5e6", - "metadata": { - "editable": true - }, + "id": "eeb13498", + "metadata": {}, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -2044,10 +1796,8 @@ }, { "cell_type": "markdown", - "id": "a58e0dda", - "metadata": { - "editable": true - }, + "id": "7ffca923", + "metadata": {}, "source": [ "## Gradient Descent Example\n", "\n", @@ -2057,12 +1807,31 @@ { "cell_type": "code", "execution_count": 7, - "id": "d6da2734", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9321710e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.30768763 4.39313488]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "# Importing various packages\n", @@ -2114,10 +1883,8 @@ }, { "cell_type": "markdown", - "id": "a2f94d89", - "metadata": { - "editable": true - }, + "id": "e65d5b5b", + "metadata": {}, "source": [ "## And a corresponding example using **scikit-learn**" ] @@ -2125,12 +1892,19 @@ { "cell_type": "code", "execution_count": 8, - "id": "f95809e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e73c4b82", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.94758046]\n", + " [2.92347862]]\n", + "[3.94453204] [2.94467121]\n" + ] + } + ], "source": [ "# Importing various packages\n", "from random import random, seed\n", @@ -2152,10 +1926,8 @@ }, { "cell_type": "markdown", - "id": "bcca1a86", - "metadata": { - "editable": true - }, + "id": "0cffa723", + "metadata": {}, "source": [ "## Gradient descent and Ridge\n", "\n", @@ -2164,10 +1936,8 @@ }, { "cell_type": "markdown", - "id": "3f8a3655", - "metadata": { - "editable": true - }, + "id": "e70974bf", + "metadata": {}, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -2176,20 +1946,16 @@ }, { "cell_type": "markdown", - "id": "fe1ae4c5", - "metadata": { - "editable": true - }, + "id": "8e2c0506", + "metadata": {}, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows" ] }, { "cell_type": "markdown", - "id": "75348007", - "metadata": { - "editable": true - }, + "id": "673104d6", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -2200,20 +1966,16 @@ }, { "cell_type": "markdown", - "id": "7b401e23", - "metadata": { - "editable": true - }, + "id": "f5d61a03", + "metadata": {}, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "id": "108955a9", - "metadata": { - "editable": true - }, + "id": "7e9aec7d", + "metadata": {}, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -2222,10 +1984,8 @@ }, { "cell_type": "markdown", - "id": "e81e374d", - "metadata": { - "editable": true - }, + "id": "54248fbe", + "metadata": {}, "source": [ "## The Hessian matrix for Ridge Regression\n", "The Hessian matrix of Ridge Regression for our simple example is given by" @@ -2233,10 +1993,8 @@ }, { "cell_type": "markdown", - "id": "5f670054", - "metadata": { - "editable": true - }, + "id": "0b57c03b", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -2248,10 +2006,8 @@ }, { "cell_type": "markdown", - "id": "44190400", - "metadata": { - "editable": true - }, + "id": "562d6a77", + "metadata": {}, "source": [ "This implies that the Hessian matrix is positive definite, hence the stationary point is a\n", "minimum.\n", @@ -2262,10 +2018,8 @@ }, { "cell_type": "markdown", - "id": "297e1218", - "metadata": { - "editable": true - }, + "id": "018079a6", + "metadata": {}, "source": [ "## Program example for gradient descent with Ridge Regression" ] @@ -2273,12 +2027,31 @@ { "cell_type": "code", "execution_count": 9, - "id": "f39e42bb", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "12f965e7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.32374405 4.06221646]\n", + "[[4.0585026]\n", + " [2.9999519]]\n", + "[[4.05843037]\n", + " [3.00001709]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from random import random, seed\n", "import numpy as np\n", @@ -2334,10 +2107,8 @@ }, { "cell_type": "markdown", - "id": "d84821a4", - "metadata": { - "editable": true - }, + "id": "06107436", + "metadata": {}, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -2356,10 +2127,8 @@ }, { "cell_type": "markdown", - "id": "386582c7", - "metadata": { - "editable": true - }, + "id": "bd3205c7", + "metadata": {}, "source": [ "## Improving gradient descent with momentum\n", "\n", @@ -2369,12 +2138,56 @@ { "cell_type": "code", "execution_count": 10, - "id": "bdd17d18", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "98ec014e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.59779819]) = 0.35736\n", + ">2 f([0.47823856]) = 0.22871\n", + ">3 f([0.38259084]) = 0.14638\n", + ">4 f([0.30607268]) = 0.09368\n", + ">5 f([0.24485814]) = 0.05996\n", + ">6 f([0.19588651]) = 0.03837\n", + ">7 f([0.15670921]) = 0.02456\n", + ">8 f([0.12536737]) = 0.01572\n", + ">9 f([0.10029389]) = 0.01006\n", + ">10 f([0.08023512]) = 0.00644\n", + ">11 f([0.06418809]) = 0.00412\n", + ">12 f([0.05135047]) = 0.00264\n", + ">13 f([0.04108038]) = 0.00169\n", + ">14 f([0.0328643]) = 0.00108\n", + ">15 f([0.02629144]) = 0.00069\n", + ">16 f([0.02103315]) = 0.00044\n", + ">17 f([0.01682652]) = 0.00028\n", + ">18 f([0.01346122]) = 0.00018\n", + ">19 f([0.01076897]) = 0.00012\n", + ">20 f([0.00861518]) = 0.00007\n", + ">21 f([0.00689214]) = 0.00005\n", + ">22 f([0.00551372]) = 0.00003\n", + ">23 f([0.00441097]) = 0.00002\n", + ">24 f([0.00352878]) = 0.00001\n", + ">25 f([0.00282302]) = 0.00001\n", + ">26 f([0.00225842]) = 0.00001\n", + ">27 f([0.00180673]) = 0.00000\n", + ">28 f([0.00144539]) = 0.00000\n", + ">29 f([0.00115631]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2435,10 +2248,8 @@ }, { "cell_type": "markdown", - "id": "6675456b", - "metadata": { - "editable": true - }, + "id": "35d2b3d9", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -2446,12 +2257,56 @@ { "cell_type": "code", "execution_count": 11, - "id": "5f7443ae", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ca391f17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.54175461]) = 0.29350\n", + ">2 f([0.37175575]) = 0.13820\n", + ">3 f([0.24640494]) = 0.06072\n", + ">4 f([0.15951871]) = 0.02545\n", + ">5 f([0.1015491]) = 0.01031\n", + ">6 f([0.0638484]) = 0.00408\n", + ">7 f([0.03976851]) = 0.00158\n", + ">8 f([0.02459084]) = 0.00060\n", + ">9 f([0.01511937]) = 0.00023\n", + ">10 f([0.00925406]) = 0.00009\n", + ">11 f([0.00564365]) = 0.00003\n", + ">12 f([0.0034318]) = 0.00001\n", + ">13 f([0.00208188]) = 0.00000\n", + ">14 f([0.00126053]) = 0.00000\n", + ">15 f([0.00076202]) = 0.00000\n", + ">16 f([0.00046006]) = 0.00000\n", + ">17 f([0.00027746]) = 0.00000\n", + ">18 f([0.00016719]) = 0.00000\n", + ">19 f([0.00010067]) = 0.00000\n", + ">20 f([6.05804744e-05]) = 0.00000\n", + ">21 f([3.64373635e-05]) = 0.00000\n", + ">22 f([2.19069576e-05]) = 0.00000\n", + ">23 f([1.31664443e-05]) = 0.00000\n", + ">24 f([7.91100141e-06]) = 0.00000\n", + ">25 f([4.75216828e-06]) = 0.00000\n", + ">26 f([2.85408468e-06]) = 0.00000\n", + ">27 f([1.71384267e-06]) = 0.00000\n", + ">28 f([1.02900153e-06]) = 0.00000\n", + ">29 f([6.17748881e-07]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2520,10 +2375,8 @@ }, { "cell_type": "markdown", - "id": "0c5c47e2", - "metadata": { - "editable": true - }, + "id": "181b30b4", + "metadata": {}, "source": [ "## Overview video on Stochastic Gradient Descent\n", "\n", @@ -2532,10 +2385,8 @@ }, { "cell_type": "markdown", - "id": "30d83150", - "metadata": { - "editable": true - }, + "id": "b51d1452", + "metadata": {}, "source": [ "## Batches and mini-batches\n", "\n", @@ -2553,10 +2404,8 @@ }, { "cell_type": "markdown", - "id": "310429e5", - "metadata": { - "editable": true - }, + "id": "85bbbc0c", + "metadata": {}, "source": [ "## Stochastic Gradient Descent (SGD)\n", "\n", @@ -2585,10 +2434,8 @@ }, { "cell_type": "markdown", - "id": "07ec38f2", - "metadata": { - "editable": true - }, + "id": "56b2b867", + "metadata": {}, "source": [ "## Stochastic Gradient Descent\n", "\n", @@ -2602,10 +2449,8 @@ }, { "cell_type": "markdown", - "id": "79d6fab8", - "metadata": { - "editable": true - }, + "id": "386e0c45", + "metadata": {}, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -2615,10 +2460,8 @@ }, { "cell_type": "markdown", - "id": "628eb747", - "metadata": { - "editable": true - }, + "id": "0f6d09dd", + "metadata": {}, "source": [ "## Computation of gradients\n", "\n", @@ -2628,10 +2471,8 @@ }, { "cell_type": "markdown", - "id": "e1133d46", - "metadata": { - "editable": true - }, + "id": "99541bf1", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2641,10 +2482,8 @@ }, { "cell_type": "markdown", - "id": "4f6e6b79", - "metadata": { - "editable": true - }, + "id": "a24ce1cc", + "metadata": {}, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -2655,10 +2494,8 @@ }, { "cell_type": "markdown", - "id": "4c3c9492", - "metadata": { - "editable": true - }, + "id": "d6c2eea5", + "metadata": {}, "source": [ "## SGD example\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", @@ -2677,10 +2514,8 @@ }, { "cell_type": "markdown", - "id": "8ef691b4", - "metadata": { - "editable": true - }, + "id": "b2561a99", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -2692,10 +2527,8 @@ }, { "cell_type": "markdown", - "id": "31bf40f3", - "metadata": { - "editable": true - }, + "id": "a0fb8d89", + "metadata": {}, "source": [ "## The gradient step\n", "\n", @@ -2704,10 +2537,8 @@ }, { "cell_type": "markdown", - "id": "526e5e7e", - "metadata": { - "editable": true - }, + "id": "71856a7b", + "metadata": {}, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2717,10 +2548,8 @@ }, { "cell_type": "markdown", - "id": "5022af9d", - "metadata": { - "editable": true - }, + "id": "9859ff14", + "metadata": {}, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -2731,10 +2560,8 @@ }, { "cell_type": "markdown", - "id": "19c6475e", - "metadata": { - "editable": true - }, + "id": "6558ed12", + "metadata": {}, "source": [ "## Simple example code" ] @@ -2742,11 +2569,8 @@ { "cell_type": "code", "execution_count": 12, - "id": "18c7a10f", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "f8cee4e8", + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2767,10 +2591,8 @@ }, { "cell_type": "markdown", - "id": "ad3f48f9", - "metadata": { - "editable": true - }, + "id": "aac3d48e", + "metadata": {}, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -2783,10 +2605,8 @@ }, { "cell_type": "markdown", - "id": "04e70295", - "metadata": { - "editable": true - }, + "id": "657c6870", + "metadata": {}, "source": [ "## When do we stop?\n", "\n", @@ -2804,10 +2624,8 @@ }, { "cell_type": "markdown", - "id": "2f10ae80", - "metadata": { - "editable": true - }, + "id": "5a8d8a8d", + "metadata": {}, "source": [ "## Slightly different approach\n", "\n", @@ -2824,10 +2642,8 @@ }, { "cell_type": "markdown", - "id": "88e4714d", - "metadata": { - "editable": true - }, + "id": "e0c75855", + "metadata": {}, "source": [ "## Time decay rate\n", "\n", @@ -2843,12 +2659,17 @@ { "cell_type": "code", "execution_count": 13, - "id": "4c882e5c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8368a998", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma_j after 500 epochs: 9.97108e-05\n" + ] + } + ], "source": [ "import numpy as np \n", "\n", @@ -2878,10 +2699,8 @@ }, { "cell_type": "markdown", - "id": "79963b9d", - "metadata": { - "editable": true - }, + "id": "a99e7227", + "metadata": {}, "source": [ "## Code with a Number of Minibatches which varies\n", "\n", @@ -2891,12 +2710,36 @@ { "cell_type": "code", "execution_count": 14, - "id": "b13f70e7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "b567ba9d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]\n", + "theta from own gd\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "theta from own sdg\n", + "[[4.014934 ]\n", + " [3.0042992]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Importing various packages\n", "from math import exp, sqrt\n", @@ -2968,10 +2811,8 @@ }, { "cell_type": "markdown", - "id": "8e833f35", - "metadata": { - "editable": true - }, + "id": "8ea309ee", + "metadata": {}, "source": [ "## Replace or not\n", "\n", @@ -2983,10 +2824,8 @@ }, { "cell_type": "markdown", - "id": "0312dcf2", - "metadata": { - "editable": true - }, + "id": "5573b607", + "metadata": {}, "source": [ "## Momentum based GD\n", "\n", @@ -2998,10 +2837,8 @@ }, { "cell_type": "markdown", - "id": "d4730af7", - "metadata": { - "editable": true - }, + "id": "5c393430", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -3010,10 +2847,8 @@ }, { "cell_type": "markdown", - "id": "3b041d81", - "metadata": { - "editable": true - }, + "id": "03d76b90", + "metadata": {}, "source": [ "\n", "
\n", @@ -3028,10 +2863,8 @@ }, { "cell_type": "markdown", - "id": "e05133d9", - "metadata": { - "editable": true - }, + "id": "c9de2175", + "metadata": {}, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -3047,10 +2880,8 @@ }, { "cell_type": "markdown", - "id": "4d90938e", - "metadata": { - "editable": true - }, + "id": "a493002b", + "metadata": {}, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -3059,20 +2890,16 @@ }, { "cell_type": "markdown", - "id": "519d60d5", - "metadata": { - "editable": true - }, + "id": "cb1d7212", + "metadata": {}, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$." ] }, { "cell_type": "markdown", - "id": "487a4624", - "metadata": { - "editable": true - }, + "id": "91135b7f", + "metadata": {}, "source": [ "## More on momentum based approaches\n", "\n", @@ -3085,10 +2912,8 @@ }, { "cell_type": "markdown", - "id": "58a8bcf7", - "metadata": { - "editable": true - }, + "id": "57c90f73", + "metadata": {}, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -3097,20 +2922,16 @@ }, { "cell_type": "markdown", - "id": "6a1c6dd4", - "metadata": { - "editable": true - }, + "id": "28fc8c64", + "metadata": {}, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "id": "d77b0f55", - "metadata": { - "editable": true - }, + "id": "9ea86afa", + "metadata": {}, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -3119,20 +2940,16 @@ }, { "cell_type": "markdown", - "id": "53e0b508", - "metadata": { - "editable": true - }, + "id": "259f8bd9", + "metadata": {}, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "id": "c7919a6b", - "metadata": { - "editable": true - }, + "id": "1b3b21b9", + "metadata": {}, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -3141,10 +2958,8 @@ }, { "cell_type": "markdown", - "id": "d658c8ac", - "metadata": { - "editable": true - }, + "id": "931ce41d", + "metadata": {}, "source": [ "## Momentum parameter\n", "\n", @@ -3157,10 +2972,8 @@ }, { "cell_type": "markdown", - "id": "93e53f3f", - "metadata": { - "editable": true - }, + "id": "d1d161a1", + "metadata": {}, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -3169,10 +2982,8 @@ }, { "cell_type": "markdown", - "id": "c0a79ce5", - "metadata": { - "editable": true - }, + "id": "4f3657ba", + "metadata": {}, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -3202,10 +3013,8 @@ }, { "cell_type": "markdown", - "id": "b43632bc", - "metadata": { - "editable": true - }, + "id": "81824da9", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -3214,10 +3023,8 @@ }, { "cell_type": "markdown", - "id": "efb8ea15", - "metadata": { - "editable": true - }, + "id": "6295bc9d", + "metadata": {}, "source": [ "\n", "
\n", @@ -3232,20 +3039,16 @@ }, { "cell_type": "markdown", - "id": "eb92118e", - "metadata": { - "editable": true - }, + "id": "7a094665", + "metadata": {}, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$." ] }, { "cell_type": "markdown", - "id": "6c9fb86f", - "metadata": { - "editable": true - }, + "id": "f0c6bb20", + "metadata": {}, "source": [ "## Second moment of the gradient\n", "\n", @@ -3273,10 +3076,8 @@ }, { "cell_type": "markdown", - "id": "a25c923d", - "metadata": { - "editable": true - }, + "id": "ce3b45b6", + "metadata": {}, "source": [ "## RMS prop\n", "\n", @@ -3288,10 +3089,8 @@ }, { "cell_type": "markdown", - "id": "24a3b8dd", - "metadata": { - "editable": true - }, + "id": "ee7e2069", + "metadata": {}, "source": [ "\n", "
\n", @@ -3306,10 +3105,8 @@ }, { "cell_type": "markdown", - "id": "2a4a4d3a", - "metadata": { - "editable": true - }, + "id": "ec4f73bb", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -3318,10 +3115,8 @@ }, { "cell_type": "markdown", - "id": "38b5c0c6", - "metadata": { - "editable": true - }, + "id": "fa5cb9a2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -3330,10 +3125,8 @@ }, { "cell_type": "markdown", - "id": "81dbe505", - "metadata": { - "editable": true - }, + "id": "eb93379a", + "metadata": {}, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -3348,10 +3141,8 @@ }, { "cell_type": "markdown", - "id": "fc1157b9", - "metadata": { - "editable": true - }, + "id": "b46162a4", + "metadata": {}, "source": [ "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n", "\n", @@ -3377,10 +3168,8 @@ }, { "cell_type": "markdown", - "id": "bf9b6954", - "metadata": { - "editable": true - }, + "id": "d103bc6a", + "metadata": {}, "source": [ "\n", "
\n", @@ -3395,10 +3184,8 @@ }, { "cell_type": "markdown", - "id": "20de7cae", - "metadata": { - "editable": true - }, + "id": "a0f031f6", + "metadata": {}, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -3407,10 +3194,8 @@ }, { "cell_type": "markdown", - "id": "3ce79d35", - "metadata": { - "editable": true - }, + "id": "2b384f75", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -3419,10 +3204,8 @@ }, { "cell_type": "markdown", - "id": "2830d104", - "metadata": { - "editable": true - }, + "id": "216435a6", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -3431,10 +3214,8 @@ }, { "cell_type": "markdown", - "id": "90e75ad2", - "metadata": { - "editable": true - }, + "id": "8b79e19e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -3443,10 +3224,8 @@ }, { "cell_type": "markdown", - "id": "99457a88", - "metadata": { - "editable": true - }, + "id": "ba777281", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -3455,10 +3234,8 @@ }, { "cell_type": "markdown", - "id": "d7aa5ab9", - "metadata": { - "editable": true - }, + "id": "f34eb136", + "metadata": {}, "source": [ "\n", "
\n", @@ -3472,10 +3249,8 @@ }, { "cell_type": "markdown", - "id": "26071aca", - "metadata": { - "editable": true - }, + "id": "695da6fd", + "metadata": {}, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -3491,10 +3266,8 @@ }, { "cell_type": "markdown", - "id": "09f63a9f", - "metadata": { - "editable": true - }, + "id": "8771f487", + "metadata": {}, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -3503,10 +3276,8 @@ }, { "cell_type": "markdown", - "id": "74b65884", - "metadata": { - "editable": true - }, + "id": "6b816830", + "metadata": {}, "source": [ "## Algorithms and codes for Adagrad, RMSprop and Adam\n", "\n", @@ -3517,10 +3288,8 @@ }, { "cell_type": "markdown", - "id": "0d5cee10", - "metadata": { - "editable": true - }, + "id": "4efb5cb8", + "metadata": {}, "source": [ "## Practical tips\n", "\n", @@ -3537,10 +3306,8 @@ }, { "cell_type": "markdown", - "id": "09734edc", - "metadata": { - "editable": true - }, + "id": "de7affbf", + "metadata": {}, "source": [ "## Automatic differentiation\n", "\n", @@ -3575,10 +3342,8 @@ }, { "cell_type": "markdown", - "id": "81d6131f", - "metadata": { - "editable": true - }, + "id": "3383da7c", + "metadata": {}, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -3587,20 +3352,16 @@ }, { "cell_type": "markdown", - "id": "0795db2e", - "metadata": { - "editable": true - }, + "id": "a8a03664", + "metadata": {}, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "id": "84ede40a", - "metadata": { - "editable": true - }, + "id": "da4e8c9e", + "metadata": {}, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -3609,10 +3370,8 @@ }, { "cell_type": "markdown", - "id": "3c0048b2", - "metadata": { - "editable": true - }, + "id": "b35c008d", + "metadata": {}, "source": [ "Using **autograd** we have" ] @@ -3620,12 +3379,27 @@ { "cell_type": "code", "execution_count": 15, - "id": "4f554ba9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9bb36858", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max absolute difference is: 1.77636e-15\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "\n", @@ -3665,10 +3439,8 @@ }, { "cell_type": "markdown", - "id": "dbb0af99", - "metadata": { - "editable": true - }, + "id": "9f8c7b5e", + "metadata": {}, "source": [ "## Using autograd\n", "\n", @@ -3682,12 +3454,18 @@ { "cell_type": "code", "execution_count": 16, - "id": "b44bbeac", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "65176228", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f1 evaluated at a = 1 using autograd is: 3\n", + "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3710,10 +3488,8 @@ }, { "cell_type": "markdown", - "id": "93f27878", - "metadata": { - "editable": true - }, + "id": "44375951", + "metadata": {}, "source": [ "## Autograd with more complicated functions\n", "\n", @@ -3725,12 +3501,23 @@ { "cell_type": "code", "execution_count": 17, - "id": "79de7d5e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "63ebdbaf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Evaluating at x1 = 1, x2 = 3\n", + "------------------------------\n", + "The derivative of f2 w.r.t x1: 12\n", + "The analytical derivative of f2 w.r.t x1: 12\n", + "\n", + "The derivative of f2 w.r.t x2: -4\n", + "The analytical derivative of f2 w.r.t x2: -4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3769,20 +3556,16 @@ }, { "cell_type": "markdown", - "id": "61ab2c3d", - "metadata": { - "editable": true - }, + "id": "ddef1f9a", + "metadata": {}, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] }, { "cell_type": "markdown", - "id": "b4784f66", - "metadata": { - "editable": true - }, + "id": "c6ff810b", + "metadata": {}, "source": [ "## More complicated functions using the elements of their arguments directly" ] @@ -3790,12 +3573,18 @@ { "cell_type": "code", "execution_count": 18, - "id": "73c1b6aa", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8c1ef66a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed gradient of f3 is: [ 2. 3. 5. 7. 88.]\n", + "The analytical gradient of f3 is: [ 2. 3. 5. 7. 88.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3818,10 +3607,8 @@ }, { "cell_type": "markdown", - "id": "c73c3739", - "metadata": { - "editable": true - }, + "id": "7ac0e490", + "metadata": {}, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -3833,10 +3620,8 @@ }, { "cell_type": "markdown", - "id": "94962c03", - "metadata": { - "editable": true - }, + "id": "f817a4b1", + "metadata": {}, "source": [ "## Functions using mathematical functions from Numpy" ] @@ -3844,12 +3629,18 @@ { "cell_type": "code", "execution_count": 19, - "id": "a48211f9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9950eceb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f4 at x = 2.7 is: 13.8759\n", + "The analytical gradient of f4 at x = 2.7 is: 13.8759\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3872,10 +3663,8 @@ }, { "cell_type": "markdown", - "id": "e8423919", - "metadata": { - "editable": true - }, + "id": "2d3597e1", + "metadata": {}, "source": [ "## More autograd" ] @@ -3883,12 +3672,17 @@ { "cell_type": "code", "execution_count": 20, - "id": "a3645e2a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a694b773", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f5 at x = 2.7 is: 5.4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3908,10 +3702,8 @@ }, { "cell_type": "markdown", - "id": "ef1a0f30", - "metadata": { - "editable": true - }, + "id": "63681987", + "metadata": {}, "source": [ "## And with loops" ] @@ -3919,12 +3711,18 @@ { "cell_type": "code", "execution_count": 21, - "id": "2bb96160", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ae061106", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f6_for at x = 0.5 is: 3.95703\n", + "The computed derivative of f6_while at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3955,12 +3753,17 @@ { "cell_type": "code", "execution_count": 22, - "id": "8434bcd7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a194eddc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The analytical derivative of f6 at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3975,10 +3778,8 @@ }, { "cell_type": "markdown", - "id": "df3fa84c", - "metadata": { - "editable": true - }, + "id": "8c21cf38", + "metadata": {}, "source": [ "## Using recursion" ] @@ -3986,12 +3787,18 @@ { "cell_type": "code", "execution_count": 23, - "id": "427c3a1f", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3eb55bad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f7 at n = 2 is: 1\n", + "The analytical derivative of f7 at n = 2 is: 1\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4024,20 +3831,16 @@ }, { "cell_type": "markdown", - "id": "6379139b", - "metadata": { - "editable": true - }, + "id": "12fbb13b", + "metadata": {}, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input." ] }, { "cell_type": "markdown", - "id": "82d727a4", - "metadata": { - "editable": true - }, + "id": "19ed9d51", + "metadata": {}, "source": [ "## Unsupported functions\n", "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", @@ -4048,11 +3851,8 @@ { "cell_type": "code", "execution_count": 24, - "id": "fce0115b", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "fb297a92", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4061,29 +3861,25 @@ " x[2] = 3\n", " return x*2\n", "\n", - "f8_grad = grad(f8)\n", + "#f8_grad = grad(f8)\n", "\n", - "x = 8.4\n", + "#x = 8.4\n", "\n", - "print(\"The derivative of f8 is:\",f8_grad(x))" + "#print(\"The derivative of f8 is:\",f8_grad(x))" ] }, { "cell_type": "markdown", - "id": "1dc97436", - "metadata": { - "editable": true - }, + "id": "06d0bc95", + "metadata": {}, "source": [ - "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." + "Here, running this code, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." ] }, { "cell_type": "markdown", - "id": "251cb0ff", - "metadata": { - "editable": true - }, + "id": "9974f300", + "metadata": {}, "source": [ "## The syntax a.dot(b) when finding the dot product" ] @@ -4091,11 +3887,8 @@ { "cell_type": "code", "execution_count": 25, - "id": "9b4aad8e", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "cbb0a202", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4104,19 +3897,17 @@ " b = np.array([1.0,2.0])\n", " return a.dot(b)\n", "\n", - "f9_grad = grad(f9)\n", + "#f9_grad = grad(f9)\n", "\n", - "x = np.array([1.0,0.0])\n", + "#x = np.array([1.0,0.0])\n", "\n", - "print(\"The derivative of f9 is:\",f9_grad(x))" + "#print(\"The derivative of f9 is:\",f9_grad(x))" ] }, { "cell_type": "markdown", - "id": "82401096", - "metadata": { - "editable": true - }, + "id": "7f08b96c", + "metadata": {}, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -4126,12 +3917,17 @@ { "cell_type": "code", "execution_count": 26, - "id": "11f68a91", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cba444cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f9 is: [1. 2.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4151,10 +3947,8 @@ }, { "cell_type": "markdown", - "id": "979bbeda", - "metadata": { - "editable": true - }, + "id": "18e2b174", + "metadata": {}, "source": [ "## Recommended to avoid\n", "The documentation recommends to avoid inplace operations such as" @@ -4163,12 +3957,21 @@ { "cell_type": "code", "execution_count": 27, - "id": "8b90b52c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "69c6914d", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'b' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[27], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[43mb\u001b[49m\n\u001b[1;32m 2\u001b[0m a \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m b\n\u001b[1;32m 3\u001b[0m a\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m b\n", + "\u001b[0;31mNameError\u001b[0m: name 'b' is not defined" + ] + } + ], "source": [ "a += b\n", "a -= b\n", @@ -4178,10 +3981,8 @@ }, { "cell_type": "markdown", - "id": "a88d50f6", - "metadata": { - "editable": true - }, + "id": "600cc052", + "metadata": {}, "source": [ "## Using Autograd with OLS\n", "\n", @@ -4193,12 +3994,33 @@ { "cell_type": "code", "execution_count": 28, - "id": "632ffb09", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cd18340b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.94499279]\n", + " [3.03306538]]\n", + "Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]\n", + "theta from own gd\n", + "[[3.94499279]\n", + " [3.03306538]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4253,10 +4075,8 @@ }, { "cell_type": "markdown", - "id": "77f1f250", - "metadata": { - "editable": true - }, + "id": "849de571", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4264,12 +4084,86 @@ { "cell_type": "code", "execution_count": 29, - "id": "ed5ad521", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ac458170", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.]\n", + " [3.]]\n", + "Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]\n", + "0 [-20.62275788] [-25.73690387]\n", + "1 [-0.03662823] [0.02925855]\n", + "2 [-0.0342458] [0.02735547]\n", + "3 [-0.03201832] [0.02557617]\n", + "4 [-0.02993573] [0.0239126]\n", + "5 [-0.0279886] [0.02235723]\n", + "6 [-0.02616812] [0.02090304]\n", + "7 [-0.02446604] [0.01954342]\n", + "8 [-0.02287468] [0.01827225]\n", + "9 [-0.02138683] [0.01708375]\n", + "10 [-0.01999575] [0.01597256]\n", + "11 [-0.01869515] [0.01493365]\n", + "12 [-0.01747915] [0.01396231]\n", + "13 [-0.01634224] [0.01305415]\n", + "14 [-0.01527928] [0.01220505]\n", + "15 [-0.01428546] [0.01141119]\n", + "16 [-0.01335628] [0.01066897]\n", + "17 [-0.01248754] [0.00997502]\n", + "18 [-0.0116753] [0.0093262]\n", + "19 [-0.01091589] [0.00871959]\n", + "20 [-0.01020588] [0.00815244]\n", + "21 [-0.00954206] [0.00762217]\n", + "22 [-0.0089214] [0.0071264]\n", + "23 [-0.00834112] [0.00666287]\n", + "24 [-0.00779859] [0.00622949]\n", + "25 [-0.00729134] [0.0058243]\n", + "26 [-0.00681708] [0.00544547]\n", + "27 [-0.00637367] [0.00509128]\n", + "28 [-0.0059591] [0.00476012]\n", + "29 [-0.0055715] [0.0044505]\n", + "theta from own gd\n", + "[[3.98281205]\n", + " [3.0137297 ]]\n", + "0 [-0.00520911] [0.00416103]\n", + "1 [-0.00487029] [0.00389038]\n", + "2 [-0.00445186] [0.00355614]\n", + "3 [-0.00403677] [0.00322456]\n", + "4 [-0.00364967] [0.00291535]\n", + "5 [-0.00329616] [0.00263296]\n", + "6 [-0.00297571] [0.00237699]\n", + "7 [-0.00268602] [0.00214559]\n", + "8 [-0.00242441] [0.00193661]\n", + "9 [-0.00218823] [0.00174795]\n", + "10 [-0.00197505] [0.00157766]\n", + "11 [-0.00178263] [0.00142396]\n", + "12 [-0.00160895] [0.00128523]\n", + "13 [-0.0014522] [0.00116001]\n", + "14 [-0.00131072] [0.001047]\n", + "15 [-0.00118302] [0.00094499]\n", + "16 [-0.00106776] [0.00085292]\n", + "17 [-0.00096373] [0.00076983]\n", + "18 [-0.00086984] [0.00069482]\n", + "19 [-0.00078509] [0.00062713]\n", + "20 [-0.0007086] [0.00056603]\n", + "21 [-0.00063957] [0.00051088]\n", + "22 [-0.00057726] [0.00046111]\n", + "23 [-0.00052102] [0.00041619]\n", + "24 [-0.00047025] [0.00037564]\n", + "25 [-0.00042444] [0.00033904]\n", + "26 [-0.00038309] [0.00030601]\n", + "27 [-0.00034576] [0.0002762]\n", + "28 [-0.00031208] [0.00024929]\n", + "29 [-0.00028167] [0.000225]\n", + "theta from own gd wth momentum\n", + "[[3.99916114]\n", + " [3.00067008]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4328,23 +4222,37 @@ }, { "cell_type": "markdown", - "id": "78643d49", - "metadata": { - "editable": true - }, + "id": "f33ed0dd", + "metadata": {}, "source": [ - "## But noen of these can compete with Newton's method" + "## But none of these can compete with Newton's method" ] }, { "cell_type": "code", "execution_count": 30, - "id": "b6031b96", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e6b06cdb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.26281735]\n", + " [2.84478178]]\n", + "Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]\n", + "0 [-14.67490857] [-18.08539155]\n", + "1 [-4.46170878e-15] [-1.45781905e-14]\n", + "2 [-1.21430643e-15] [-1.24768421e-15]\n", + "3 [4.92661467e-16] [4.50610071e-16]\n", + "4 [4.92661467e-16] [4.50610071e-16]\n", + "beta from own Newton code\n", + "[[4.26281735]\n", + " [2.84478178]]\n" + ] + } + ], "source": [ "# Using Newton's method\n", "from random import random, seed\n", @@ -4388,10 +4296,8 @@ }, { "cell_type": "markdown", - "id": "ac22e7a1", - "metadata": { - "editable": true - }, + "id": "90de8a04", + "metadata": {}, "source": [ "## Including Stochastic Gradient Descent with Autograd\n", "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." @@ -4400,12 +4306,42 @@ { "cell_type": "code", "execution_count": 31, - "id": "4852067a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a010a209", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.0586484]\n", + " [3.0718316]]\n", + "Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]\n", + "theta from own gd\n", + "[[4.0586484]\n", + " [3.0718316]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta from own sdg\n", + "[[4.02496085]\n", + " [3.12081773]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4484,10 +4420,8 @@ }, { "cell_type": "markdown", - "id": "ba1f3157", - "metadata": { - "editable": true - }, + "id": "18298e5e", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4495,12 +4429,26 @@ { "cell_type": "code", "execution_count": 32, - "id": "c06c4547", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3320d6c6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.96075051]\n", + " [3.02148021]]\n", + "Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]\n", + "theta from own gd\n", + "[[3.95906059]\n", + " [3.02296298]]\n", + "theta from own sdg with momentum\n", + "[[3.95611042]\n", + " [2.99475306]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4573,10 +4521,8 @@ }, { "cell_type": "markdown", - "id": "16b6b2c9", - "metadata": { - "editable": true - }, + "id": "f1411612", + "metadata": {}, "source": [ "## Similar (second order function now) problem but now with AdaGrad" ] @@ -4584,12 +4530,24 @@ { "cell_type": "code", "execution_count": 33, - "id": "d6d3a6ca", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "19414323", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own AdaGrad\n", + "[[2.00025662]\n", + " [2.99802696]\n", + " [4.00167329]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n", "# OLS example\n", @@ -4643,20 +4601,16 @@ }, { "cell_type": "markdown", - "id": "08925601", - "metadata": { - "editable": true - }, + "id": "a77cdfa4", + "metadata": {}, "source": [ "Running this code we note an almost perfect agreement with the results from matrix inversion." ] }, { "cell_type": "markdown", - "id": "cc62acf3", - "metadata": { - "editable": true - }, + "id": "9f488085", + "metadata": {}, "source": [ "## RMSprop for adaptive learning rate with Stochastic Gradient Descent" ] @@ -4664,12 +4618,24 @@ { "cell_type": "code", "execution_count": 34, - "id": "561a26b8", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "6724b3d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own RMSprop\n", + "[[1.99456598]\n", + " [2.99848815]\n", + " [3.99835783]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4729,10 +4695,8 @@ }, { "cell_type": "markdown", - "id": "f2c44a2a", - "metadata": { - "editable": true - }, + "id": "09728e4a", + "metadata": {}, "source": [ "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)" ] @@ -4740,12 +4704,24 @@ { "cell_type": "code", "execution_count": 35, - "id": "c32bd5e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "28aa6aad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own ADAM\n", + "[[1.99989103]\n", + " [3.00042093]\n", + " [3.99954925]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4810,10 +4786,8 @@ }, { "cell_type": "markdown", - "id": "4183d2b1", - "metadata": { - "editable": true - }, + "id": "70fc8bdd", + "metadata": {}, "source": [ "## And Logistic Regression" ] @@ -4821,12 +4795,18 @@ { "cell_type": "code", "execution_count": 36, - "id": "d1a76119", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "f3dde7c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss: 2.772588722239781\n", + "Trained loss: 1.067270675787016\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4865,10 +4845,8 @@ }, { "cell_type": "markdown", - "id": "68fef7c6", - "metadata": { - "editable": true - }, + "id": "b46c449b", + "metadata": {}, "source": [ "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n", "\n", @@ -4884,12 +4862,17 @@ { "cell_type": "code", "execution_count": 37, - "id": "d62a782e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "291c9b6d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.25 0.19661197 0.10499357]\n" + ] + } + ], "source": [ "import jax.numpy as jnp\n", "from jax import grad, jit, vmap\n", @@ -4901,9 +4884,35 @@ "derivative_fn = grad(sum_logistic)\n", "print(derivative_fn(x_small))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e201d58b", + "metadata": {}, + "outputs": [], + "source": [] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js index 3eb04852d..e17d39d5a 100644 --- a/doc/LectureNotes/_build/html/searchindex.js +++ b/doc/LectureNotes/_build/html/searchindex.js @@ -1 +1 @@ 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12,13,14,17,18,19,22,23,25,28,29,30,31,32,33],zeros_lik:4,zeroth:29,zfill:4,zip:[2,4,6],zm_h:[0,28],zn:0,zone:0,zoom:28,zx:[22,28],zy:[22,28],zz:[22,28]},titles:["3. Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and Gradient 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Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Exercises week 39","Applied Data Analysis and Machine Learning","2. Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 7 (midnight), 2024","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Regression and Statistical interpretations","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and Optimization","Week 39: Optimization and Gradient Methods"],titleterms:{"1":[0,15,16,17,18,23,28,29],"16":32,"2":[0,15,16,17,18,28,29,30],"2023":26,"2024":[23,33],"21":[],"23":33,"26":29,"27":33,"3":[0,15,16,28,29],"34":[15,28],"35":[16,29],"36":[17,30],"37":[18,31],"38":[19,32],"39":[20,33],"4":[0,29],"5":0,"7":23,"9":31,"case":[8,10,25,29,30,32,33],"class":32,"do":[1,30,31,33],"final":[12,29,30,33],"function":[0,1,6,7,8,10,11,12,13,23,25,28,29,30,31,32,33],"import":[5,22,28,29,30],"new":[4,30,31],A:[0,1,4,8,9,28,30,31,32],And:[28,29,30,32,33],But:33,For:29,In:26,Ising:6,The:[0,1,2,3,5,6,7,8,9,11,12,17,21,28,29,30,31,32,33],To:[28,29],With:[4,30],about:[28,29],abov:30,activ:[1,12,30],ad:[0,6,17,23,28,29],adaboost:10,adagrad:[13,33],adam:[13,33],adapt:[10,33],adjust:1,adversari:4,again:[3,9,32],ai:[23,28],aim:[8,9,17,18,19,20,28],aka:[28,29],algebra:[22,28],algorithm:[9,10,11,12,29,33],algortithm:[13,32,33],all:8,an:[0,4,10,28],analys:[5,29],analysi:[0,5,6,11,21,23,25,28,29,30,31],analyt:[0,16,17],ani:[13,32,33],anoth:[9,30,31],appli:21,approach:[0,8,14,28,31,33],approxim:12,architectur:1,argument:33,arrai:[22,28],assist:26,assumpt:[30,31],august:29,autocorrel:25,autograd:[2,13,33],automat:[13,33],avoid:33,b:[17,23,33],back:[1,11,12],background:[21,23,31],bag:10,base:[13,31,33],basic:[0,5,7,9,10,11,22,29,30,31,32],batch:[1,33],bay:[5,30,31],befor:11,beta:[30,31],better:8,bia:[6,23,31],binari:1,bind:28,bird:10,boldsymbol:[29,30,31],boost:10,bootstrap:[6,10,31],boston:0,breast:1,brief:[28,31,32,33],bring:12,build:[1,3,9],c:[23,28],calcul:29,can:[28,31,33],cancer:[1,7,9,11,32],cart:9,center:29,central:[13,21,25,31,32,33],chain:12,challeng:32,chang:10,channel:28,chi:[0,28],choos:1,cifar01:3,classic:11,classif:[1,9,10,32],classifi:[8,32],clip:1,cluster:14,cnn:3,code:[0,1,2,5,9,11,12,13,14,28,29,30,31,32,33],collect:[1,3],come:32,commun:28,compact:32,compar:[2,10],comparison:30,compet:33,complet:29,complex:[0,6,23,29],complic:[6,33],compon:11,comput:[9,33],computation:31,computerlab:28,con:9,concept:25,condit:[30,31,32,33],confid:31,conjug:[13,33],contn:28,convex:[8,13,32,33],convolut:[3,12],correctli:[30,31],correl:[11,29,32],correspond:[32,33],cost:[1,10,29,30,31,32,33],cours:[21,27,28],covari:[5,11,25,29],cover:28,cross:[6,23,31,32],cython:28,d:23,data:[0,1,3,6,7,9,11,15,16,21,23,25,28,29,30,32],dataset:[1,3],deadlin:[23,28],decai:[2,33],decis:[9,10],decomposit:[5,11,17,22,29],deep:[1,2,28,32],defin:[1,28],degre:[0,29],deliveri:23,delta:31,dens:[0,28],deriv:[5,12,29,30,31,32,33],descent:[2,10,13,32,33],descript:23,design:29,detail:[3,28],develop:1,diagon:11,differ:[8,33],differenti:[2,13,33],diffus:2,dimension:[2,3,8,23,29],directli:33,disadvantag:9,discret:25,discuss:32,distribut:[5,25,30,31],distrubut:31,doe:[29,30],domain:25,dot:33,down:1,dropout:1,e:23,each:32,economi:29,electron:23,element:[0,25,28,33],elimin:22,energi:28,ensembl:10,entropi:[9,32],environ:[0,15,28],equat:[0,2,12,28,29,30,32,33],error:[0,10,28,29,31],essenti:28,estim:[30,31],etc:28,euler:2,evalu:1,exampl:[0,1,2,3,4,6,7,8,9,10,28,29,30,31,32,33],exercis:[0,6,15,16,17,18,19,20,28,29],expect:[18,25,30,31],expens:31,experi:25,explor:[0,15,16,28],exponenti:2,express:[17,18,29,32,33],extend:[32,33],extrapol:4,extrem:[10,28],ey:10,f:23,fall:26,famili:[1,28,29],famou:22,fantast:29,featur:[9,22,29],feed:[1,12],find:[31,33],fine:1,first:[4,12,28,29,30,32,33],fit:[0,10,28,30],fix:29,fold:[31,32],forc:3,forest:10,format:[23,28],forward:[1,2,12],fourier:3,frank:[6,23,29],freedom:[0,29],frequent:29,frequentist:[0,28],fridai:[],from:[5,10,12,29,30,31,32,33],full:2,further:[3,5,29],g:23,gan:4,gaussian:22,gd:[13,33],gener:[4,9,28],geometr:[11,32,33],gini:9,good:[0,28],grade:[26,28],gradient:[1,2,10,13,32,33],grid:32,group:32,growth:2,ha:21,handl:[22,28,29],happen:[30,31],hessian:[29,32,33],hidden:2,histogram:31,homework:[32,33],hous:0,how:32,hyperparamet:1,hyperplan:8,i:1,id3:9,idea:11,ideal:[32,33],ident:[30,31],identifi:31,ii:28,iid:[30,31],illustr:30,implement:1,implic:[5,29],improv:[1,33],includ:[13,32,33],increment:11,independ:[30,31],index:9,inform:26,input:2,instal:[21,23,28],instructor:26,intercept:29,interpret:[5,11,28,29,30,31,32,33],interv:31,introduc:[11,13,29,33],introduct:[0,6,21,22,23,28],invers:[5,22,30],invert:29,iter:[10,33],its:29,jacobian:29,jax:[13,33],julia:28,jungl:10,k:[31,32],kera:[1,3],kernel:[8,11],lab:[31,32,33],lagrangian:8,lambda:32,lasso:[5,6,23,29,30,31,32],last:[29,32],later:[5,29],layer:[1,2,3,12],learn:[0,1,2,11,13,14,15,16,21,23,28,29,30,31,32,33],least:[5,6,18,23,28,29,30],lectur:[28,29,30,31,32,33],level:10,librari:[21,28],likelihood:[7,30,31,32],limit:[1,13,25,31,32,33],linear:[0,8,13,22,28,29,30,32],link:[5,11,24,27,29,30,31],literatur:23,logist:[7,28,32,33],loop:33,loss:[29,32,33],lu:22,machin:[0,8,13,21,23,28,32,33],made:[30,31],main:[25,28],make:[0,9,10,15,16,28,29],mani:[10,12],manipul:29,margin:[30,31],mass:28,materi:[23,24,28,29,30,31,32],math:[5,29],mathemat:[3,5,8,29,33],matric:[5,22,28,30],matrix:[1,5,11,12,22,28,29,30,32,33],matter:[0,28],max:29,maximum:[3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\ No newline at end of file diff --git a/doc/LectureNotes/_build/html/week39.html b/doc/LectureNotes/_build/html/week39.html index 9bc1ffe83..bd8990824 100644 --- a/doc/LectureNotes/_build/html/week39.html +++ b/doc/LectureNotes/_build/html/week39.html @@ -800,8 +800,8 @@ const thebe_selector_output = ".output, .cell_output"
  • - - But noen of these can compete with Newton’s method + + But none of these can compete with Newton’s method
  • @@ -1268,8 +1268,8 @@ const thebe_selector_output = ".output, .cell_output"
  • - - But noen of these can compete with Newton’s method + + But none of these can compete with Newton’s method
  • @@ -1788,7 +1788,7 @@ which equals

    return np.array([2*x[0], 6*x[1]]) fig = pt.figure() -ax = fig.gca(projection="3d") +ax = fig.add_subplot(projection = '3d') xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j] fmesh = f(np.array([xmesh, ymesh])) @@ -1797,21 +1797,10 @@ which equals

    -
    ---------------------------------------------------------------------------
    -TypeError                                 Traceback (most recent call last)
    -Cell In[1], line 18
    -     15     return np.array([2*x[0], 6*x[1]])
    -     17 fig = pt.figure()
    ----> 18 ax = fig.gca(projection="3d")
    -     20 xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]
    -     21 fmesh = f(np.array([xmesh, ymesh]))
    -
    -TypeError: gca() got an unexpected keyword argument 'projection'
    -
    -
    -
    <Figure size 640x480 with 0 Axes>
    +
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x1273ffac0>
     
    +_images/week39_82_1.png

    And then as countor plot

    @@ -1823,6 +1812,9 @@ which equals

    +
    +_images/week39_84_0.png +

    Find guesses

    @@ -1846,6 +1838,11 @@ which equals

    +
    +
    [ 0.69230769 -0.38461539]
    +
    +
    +

    What happened?

    @@ -1857,6 +1854,12 @@ which equals

    +
    +
    [<matplotlib.lines.Line2D at 0x1279bd460>]
    +
    +
    +_images/week39_90_1.png +

    Note that we did only one iteration here. We can easily add more using our previous guesses.

    @@ -2018,7 +2021,8 @@ desirable properties such as:

    We revisit an example similar to what we had in the first homework set. We had a function of the type

    -
    x = 2*np.random.rand(m,1)
    +
    m = 100
    +x = 2*np.random.rand(m,1)
     y = 4+3*x+np.random.randn(m,1)
     
    @@ -2144,6 +2148,16 @@ when \(||\nabla_\beta C(\beta_k) || \
    +
    +
    Eigenvalues of Hessian Matrix:[0.39517073 4.17377547]
    +[[3.7074705 ]
    + [3.25970297]]
    +[[3.7074705 ]
    + [3.25970297]]
    +
    +
    +_images/week39_153_1.png +
    @@ -2169,6 +2183,13 @@ when \(||\nabla_\beta C(\beta_k) || \
    +
    +
    [[3.95872127]
    + [3.20357736]]
    +[3.9712983] [3.26048873]
    +
    +
    +
    @@ -2264,6 +2285,16 @@ minimum of this function.

    +
    +
    Eigenvalues of Hessian Matrix:[0.25986026 4.46387965]
    +[[4.18118338]
    + [2.86240935]]
    +[[4.18234308]
    + [2.86143379]]
    +
    +
    +_images/week39_166_1.png +
    @@ -2340,6 +2371,41 @@ minimum of this function.

    +
    +
    >0 f([0.74724774]) = 0.55838
    +>1 f([0.59779819]) = 0.35736
    +>2 f([0.47823856]) = 0.22871
    +>3 f([0.38259084]) = 0.14638
    +>4 f([0.30607268]) = 0.09368
    +>5 f([0.24485814]) = 0.05996
    +>6 f([0.19588651]) = 0.03837
    +>7 f([0.15670921]) = 0.02456
    +>8 f([0.12536737]) = 0.01572
    +>9 f([0.10029389]) = 0.01006
    +>10 f([0.08023512]) = 0.00644
    +>11 f([0.06418809]) = 0.00412
    +>12 f([0.05135047]) = 0.00264
    +>13 f([0.04108038]) = 0.00169
    +>14 f([0.0328643]) = 0.00108
    +>15 f([0.02629144]) = 0.00069
    +>16 f([0.02103315]) = 0.00044
    +>17 f([0.01682652]) = 0.00028
    +>18 f([0.01346122]) = 0.00018
    +>19 f([0.01076897]) = 0.00012
    +>20 f([0.00861518]) = 0.00007
    +>21 f([0.00689214]) = 0.00005
    +>22 f([0.00551372]) = 0.00003
    +>23 f([0.00441097]) = 0.00002
    +>24 f([0.00352878]) = 0.00001
    +>25 f([0.00282302]) = 0.00001
    +>26 f([0.00225842]) = 0.00001
    +>27 f([0.00180673]) = 0.00000
    +>28 f([0.00144539]) = 0.00000
    +>29 f([0.00115631]) = 0.00000
    +
    +
    +_images/week39_169_1.png +
    @@ -2412,6 +2478,41 @@ minimum of this function.

    +
    +
    >0 f([0.74724774]) = 0.55838
    +>1 f([0.54175461]) = 0.29350
    +>2 f([0.37175575]) = 0.13820
    +>3 f([0.24640494]) = 0.06072
    +>4 f([0.15951871]) = 0.02545
    +>5 f([0.1015491]) = 0.01031
    +>6 f([0.0638484]) = 0.00408
    +>7 f([0.03976851]) = 0.00158
    +>8 f([0.02459084]) = 0.00060
    +>9 f([0.01511937]) = 0.00023
    +>10 f([0.00925406]) = 0.00009
    +>11 f([0.00564365]) = 0.00003
    +>12 f([0.0034318]) = 0.00001
    +>13 f([0.00208188]) = 0.00000
    +>14 f([0.00126053]) = 0.00000
    +>15 f([0.00076202]) = 0.00000
    +>16 f([0.00046006]) = 0.00000
    +>17 f([0.00027746]) = 0.00000
    +>18 f([0.00016719]) = 0.00000
    +>19 f([0.00010067]) = 0.00000
    +>20 f([6.05804744e-05]) = 0.00000
    +>21 f([3.64373635e-05]) = 0.00000
    +>22 f([2.19069576e-05]) = 0.00000
    +>23 f([1.31664443e-05]) = 0.00000
    +>24 f([7.91100141e-06]) = 0.00000
    +>25 f([4.75216828e-06]) = 0.00000
    +>26 f([2.85408468e-06]) = 0.00000
    +>27 f([1.71384267e-06]) = 0.00000
    +>28 f([1.02900153e-06]) = 0.00000
    +>29 f([6.17748881e-07]) = 0.00000
    +
    +
    +_images/week39_171_1.png +
    @@ -2607,6 +2708,11 @@ function.

    +
    +
    gamma_j after 500 epochs: 9.97108e-05
    +
    +
    +
    @@ -2683,6 +2789,21 @@ function.

    +
    +
    Own inversion
    +[[4.08687303]
    + [3.00141727]]
    +Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]
    +theta from own gd
    +[[4.08687303]
    + [3.00141727]]
    +theta from own sdg
    +[[4.014934 ]
    + [3.0042992]]
    +
    +
    +_images/week39_193_1.png +
    @@ -3011,6 +3132,12 @@ f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
    +
    +_images/week39_236_0.png +
    The max absolute difference is: 1.77636e-15
    +
    +
    +
    @@ -3042,6 +3169,12 @@ experiment with other, possibly more complicated, functions as well.

    +
    +
    The gradient of f1 evaluated at a = 1 using autograd is: 3
    +The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3
    +
    +
    +
    @@ -3087,6 +3220,17 @@ being differentiated with respect to.

    +
    +
    Evaluating at x1 = 1, x2 = 3
    +------------------------------
    +The derivative of f2 w.r.t x1: 12
    +The analytical derivative of f2 w.r.t x1: 12
    +
    +The derivative of f2 w.r.t x2: -4
    +The analytical derivative of f2 w.r.t x2: -4
    +
    +
    +

    Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.

    @@ -3114,6 +3258,12 @@ being differentiated with respect to.

    +
    +
    The computed gradient of f3 is:  [ 2.  3.  5.  7. 88.]
    +The analytical gradient of f3 is:  [ 2.  3.  5.  7. 88.]
    +
    +
    +

    Note that in this case, when sending an array as input argument, the output from Autograd is another array. This is the true gradient of @@ -3146,6 +3296,12 @@ could expect form a gradient-evaluting function.

    +
    +
    The computed derivative of f4 at x = 2.7 is: 13.8759
    +The analytical gradient of f4 at x = 2.7 is: 13.8759
    +
    +
    +
    @@ -3169,6 +3325,11 @@ could expect form a gradient-evaluting function.

    +
    +
    The computed derivative of f5 at x = 2.7 is: 5.4
    +
    +
    +
    @@ -3202,6 +3363,12 @@ could expect form a gradient-evaluting function.

    +
    +
    The computed derivative of f6_for at x = 0.5 is: 3.95703
    +The computed derivative of f6_while at x = 0.5 is: 3.95703
    +
    +
    +
    @@ -3217,6 +3384,11 @@ could expect form a gradient-evaluting function.

    +
    +
    The analytical derivative of f6 at x = 0.5 is: 3.95703
    +
    +
    +
    @@ -3253,6 +3425,12 @@ could expect form a gradient-evaluting function.

    +
    +
    The computed derivative of f7 at n = 2 is: 1
    +The analytical derivative of f7 at n = 2 is: 1
    +
    +
    +

    Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.

    @@ -3268,16 +3446,16 @@ could expect form a gradient-evaluting function.

    x[2] = 3 return x*2 -f8_grad = grad(f8) +#f8_grad = grad(f8) -x = 8.4 +#x = 8.4 -print("The derivative of f8 is:",f8_grad(x)) +#print("The derivative of f8 is:",f8_grad(x)) -

    Here, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.

    +

    Here, running this code, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.

    The syntax a.dot(b) when finding the dot product¶

    @@ -3289,11 +3467,11 @@ could expect form a gradient-evaluting function.

    b = np.array([1.0,2.0]) return a.dot(b) -f9_grad = grad(f9) +#f9_grad = grad(f9) -x = np.array([1.0,0.0]) +#x = np.array([1.0,0.0]) -print("The derivative of f9 is:",f9_grad(x)) +#print("The derivative of f9 is:",f9_grad(x))
    @@ -3320,6 +3498,11 @@ which also computed the dot product can be used:

    +
    +
    The gradient of f9 is: [1. 2.]
    +
    +
    +
    +
    +
    ---------------------------------------------------------------------------
    +NameError                                 Traceback (most recent call last)
    +Cell In[27], line 1
    +----> 1 a += b
    +      2 a -= b
    +      3 a*= b
    +
    +NameError: name 'b' is not defined
    +
    +
    +
    @@ -3395,6 +3590,18 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[3.94499279]
    + [3.03306538]]
    +Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]
    +theta from own gd
    +[[3.94499279]
    + [3.03306538]]
    +
    +
    +_images/week39_265_1.png +
    @@ -3457,10 +3664,84 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[4.]
    + [3.]]
    +Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]
    +0 [-20.62275788] [-25.73690387]
    +1 [-0.03662823] [0.02925855]
    +2 [-0.0342458] [0.02735547]
    +3 [-0.03201832] [0.02557617]
    +4 [-0.02993573] [0.0239126]
    +5 [-0.0279886] [0.02235723]
    +6 [-0.02616812] [0.02090304]
    +7 [-0.02446604] [0.01954342]
    +8 [-0.02287468] [0.01827225]
    +9 [-0.02138683] [0.01708375]
    +10 [-0.01999575] [0.01597256]
    +11 [-0.01869515] [0.01493365]
    +12 [-0.01747915] [0.01396231]
    +13 [-0.01634224] [0.01305415]
    +14 [-0.01527928] [0.01220505]
    +15 [-0.01428546] [0.01141119]
    +16 [-0.01335628] [0.01066897]
    +17 [-0.01248754] [0.00997502]
    +18 [-0.0116753] [0.0093262]
    +19 [-0.01091589] [0.00871959]
    +20 [-0.01020588] [0.00815244]
    +21 [-0.00954206] [0.00762217]
    +22 [-0.0089214] [0.0071264]
    +23 [-0.00834112] [0.00666287]
    +24 [-0.00779859] [0.00622949]
    +25 [-0.00729134] [0.0058243]
    +26 [-0.00681708] [0.00544547]
    +27 [-0.00637367] [0.00509128]
    +28 [-0.0059591] [0.00476012]
    +29 [-0.0055715] [0.0044505]
    +theta from own gd
    +[[3.98281205]
    + [3.0137297 ]]
    +0 [-0.00520911] [0.00416103]
    +1 [-0.00487029] [0.00389038]
    +2 [-0.00445186] [0.00355614]
    +3 [-0.00403677] [0.00322456]
    +4 [-0.00364967] [0.00291535]
    +5 [-0.00329616] [0.00263296]
    +6 [-0.00297571] [0.00237699]
    +7 [-0.00268602] [0.00214559]
    +8 [-0.00242441] [0.00193661]
    +9 [-0.00218823] [0.00174795]
    +10 [-0.00197505] [0.00157766]
    +11 [-0.00178263] [0.00142396]
    +12 [-0.00160895] [0.00128523]
    +13 [-0.0014522] [0.00116001]
    +14 [-0.00131072] [0.001047]
    +15 [-0.00118302] [0.00094499]
    +16 [-0.00106776] [0.00085292]
    +17 [-0.00096373] [0.00076983]
    +18 [-0.00086984] [0.00069482]
    +19 [-0.00078509] [0.00062713]
    +20 [-0.0007086] [0.00056603]
    +21 [-0.00063957] [0.00051088]
    +22 [-0.00057726] [0.00046111]
    +23 [-0.00052102] [0.00041619]
    +24 [-0.00047025] [0.00037564]
    +25 [-0.00042444] [0.00033904]
    +26 [-0.00038309] [0.00030601]
    +27 [-0.00034576] [0.0002762]
    +28 [-0.00031208] [0.00024929]
    +29 [-0.00028167] [0.000225]
    +theta from own gd wth momentum
    +[[3.99916114]
    + [3.00067008]]
    +
    -
    -

    But noen of these can compete with Newton’s method¶

    +
    + +
    +

    But none of these can compete with Newton’s method¶

    # Using Newton's method
    @@ -3504,6 +3785,22 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[4.26281735]
    + [2.84478178]]
    +Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]
    +0 [-14.67490857] [-18.08539155]
    +1 [-4.46170878e-15] [-1.45781905e-14]
    +2 [-1.21430643e-15] [-1.24768421e-15]
    +3 [4.92661467e-16] [4.50610071e-16]
    +4 [4.92661467e-16] [4.50610071e-16]
    +beta from own Newton code
    +[[4.26281735]
    + [2.84478178]]
    +
    +
    +
    @@ -3587,6 +3884,23 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[4.0586484]
    + [3.0718316]]
    +Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]
    +theta from own gd
    +[[4.0586484]
    + [3.0718316]]
    +
    +
    +_images/week39_271_1.png +
    theta from own sdg
    +[[4.02496085]
    + [3.12081773]]
    +
    +
    +
    @@ -3663,6 +3977,20 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[3.96075051]
    + [3.02148021]]
    +Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]
    +theta from own gd
    +[[3.95906059]
    + [3.02296298]]
    +theta from own sdg with momentum
    +[[3.95611042]
    + [2.99475306]]
    +
    +
    +
    @@ -3720,6 +4048,18 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[2.]
    + [3.]
    + [4.]]
    +theta from own AdaGrad
    +[[2.00025662]
    + [2.99802696]
    + [4.00167329]]
    +
    +
    +

    Running this code we note an almost perfect agreement with the results from matrix inversion.

    @@ -3784,6 +4124,18 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[2.]
    + [3.]
    + [4.]]
    +theta from own RMSprop
    +[[1.99456598]
    + [2.99848815]
    + [3.99835783]]
    +
    +
    +
    @@ -3852,6 +4204,18 @@ first example shows results with ordinary leats squares.

    +
    +
    Own inversion
    +[[2.]
    + [3.]
    + [4.]]
    +theta from own ADAM
    +[[1.99989103]
    + [3.00042093]
    + [3.99954925]]
    +
    +
    +
    @@ -3894,6 +4258,12 @@ first example shows results with ordinary leats squares.

    +
    +
    Initial loss: 2.772588722239781
    +Trained loss: 1.067270675787016
    +
    +
    +
    @@ -3917,6 +4287,11 @@ It provides composable transformations of Python+NumPy programs: differentiate,
    +
    +
    [0.25       0.19661197 0.10499357]
    +
    +
    +
    diff --git a/doc/LectureNotes/_build/jupyter_execute/week39.ipynb b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb index 9994db5a6..133dd2d9c 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week39.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb @@ -2,10 +2,8 @@ "cells": [ { "cell_type": "markdown", - "id": "918e6088", - "metadata": { - "editable": true - }, + "id": "0be56d20", + "metadata": {}, "source": [ "\n", @@ -14,10 +12,8 @@ }, { "cell_type": "markdown", - "id": "f6bdc2db", - "metadata": { - "editable": true - }, + "id": "41352012", + "metadata": {}, "source": [ "# Week 39: Optimization and Gradient Methods\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", @@ -27,20 +23,16 @@ }, { "cell_type": "markdown", - "id": "0fd73813", - "metadata": { - "editable": true - }, + "id": "471d9b17", + "metadata": {}, "source": [ "## Plan for week 39, September 23-27, 2024" ] }, { "cell_type": "markdown", - "id": "4659a144", - "metadata": { - "editable": true - }, + "id": "a3f843e5", + "metadata": {}, "source": [ "## Lecture Monday September 23\n", "\n", @@ -67,10 +59,8 @@ }, { "cell_type": "markdown", - "id": "fc1f68ca", - "metadata": { - "editable": true - }, + "id": "b611ff2d", + "metadata": {}, "source": [ "## Lab sessions week 39\n", "\n", @@ -94,10 +84,8 @@ }, { "cell_type": "markdown", - "id": "15869b1d", - "metadata": { - "editable": true - }, + "id": "126f7d60", + "metadata": {}, "source": [ "## Lecture Monday September 23, Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -115,10 +103,8 @@ }, { "cell_type": "markdown", - "id": "cfaf747a", - "metadata": { - "editable": true - }, + "id": "a2682f11", + "metadata": {}, "source": [ "## Revisiting our Logistic Regression case\n", "\n", @@ -132,10 +118,8 @@ }, { "cell_type": "markdown", - "id": "e2850b85", - "metadata": { - "editable": true - }, + "id": "d51c88b5", + "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", @@ -147,20 +131,16 @@ }, { "cell_type": "markdown", - "id": "a73f7a09", - "metadata": { - "editable": true - }, + "id": "4a135362", + "metadata": {}, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$." ] }, { "cell_type": "markdown", - "id": "eee9af50", - "metadata": { - "editable": true - }, + "id": "26444396", + "metadata": {}, "source": [ "## The equations to solve\n", "\n", @@ -173,10 +153,8 @@ }, { "cell_type": "markdown", - "id": "d8a40aeb", - "metadata": { - "editable": true - }, + "id": "9bc5702f", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -185,10 +163,8 @@ }, { "cell_type": "markdown", - "id": "7d24b6f4", - "metadata": { - "editable": true - }, + "id": "a857de8b", + "metadata": {}, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -196,10 +172,8 @@ }, { "cell_type": "markdown", - "id": "da0033f7", - "metadata": { - "editable": true - }, + "id": "dc870dc3", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -208,20 +182,16 @@ }, { "cell_type": "markdown", - "id": "eff96c8f", - "metadata": { - "editable": true - }, + "id": "4001c458", + "metadata": {}, "source": [ "This defines what is called the Hessian matrix." ] }, { "cell_type": "markdown", - "id": "bbf59e32", - "metadata": { - "editable": true - }, + "id": "4f3262b4", + "metadata": {}, "source": [ "## Solving using Newton-Raphson's method\n", "\n", @@ -232,10 +202,8 @@ }, { "cell_type": "markdown", - "id": "67e16976", - "metadata": { - "editable": true - }, + "id": "0d94cee2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -244,20 +212,16 @@ }, { "cell_type": "markdown", - "id": "374d66a6", - "metadata": { - "editable": true - }, + "id": "d92e7b5d", + "metadata": {}, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "id": "ed30dea2", - "metadata": { - "editable": true - }, + "id": "076acdca", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -266,10 +230,8 @@ }, { "cell_type": "markdown", - "id": "f098e947", - "metadata": { - "editable": true - }, + "id": "c37ab3fd", + "metadata": {}, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", @@ -278,10 +240,8 @@ }, { "cell_type": "markdown", - "id": "741d9a60", - "metadata": { - "editable": true - }, + "id": "4f771526", + "metadata": {}, "source": [ "## Brief reminder on Newton-Raphson's method\n", "\n", @@ -298,10 +258,8 @@ }, { "cell_type": "markdown", - "id": "dff616d1", - "metadata": { - "editable": true - }, + "id": "e13dad72", + "metadata": {}, "source": [ "## The equations\n", "\n", @@ -314,10 +272,8 @@ }, { "cell_type": "markdown", - "id": "5d37722e", - "metadata": { - "editable": true - }, + "id": "aff57d4b", + "metadata": {}, "source": [ "\n", "
    \n", @@ -330,10 +286,8 @@ }, { "cell_type": "markdown", - "id": "6706784b", - "metadata": { - "editable": true - }, + "id": "38304c1d", + "metadata": {}, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -341,10 +295,8 @@ }, { "cell_type": "markdown", - "id": "3708fdef", - "metadata": { - "editable": true - }, + "id": "8da576a0", + "metadata": {}, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -353,20 +305,16 @@ }, { "cell_type": "markdown", - "id": "3f607de4", - "metadata": { - "editable": true - }, + "id": "46d9c588", + "metadata": {}, "source": [ "yielding" ] }, { "cell_type": "markdown", - "id": "bdb0ec30", - "metadata": { - "editable": true - }, + "id": "3a3ca58b", + "metadata": {}, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -375,20 +323,16 @@ }, { "cell_type": "markdown", - "id": "e941f0f2", - "metadata": { - "editable": true - }, + "id": "0c9c700f", + "metadata": {}, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "id": "2a7d9a7f", - "metadata": { - "editable": true - }, + "id": "b273b273", + "metadata": {}, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -397,10 +341,8 @@ }, { "cell_type": "markdown", - "id": "9c9bfa29", - "metadata": { - "editable": true - }, + "id": "3e0a875b", + "metadata": {}, "source": [ "## Simple geometric interpretation\n", "\n", @@ -419,10 +361,8 @@ }, { "cell_type": "markdown", - "id": "e6fecd57", - "metadata": { - "editable": true - }, + "id": "727cfd55", + "metadata": {}, "source": [ "## Extending to more than one variable\n", "\n", @@ -432,10 +372,8 @@ }, { "cell_type": "markdown", - "id": "250ae3be", - "metadata": { - "editable": true - }, + "id": "f78349b5", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -445,20 +383,16 @@ }, { "cell_type": "markdown", - "id": "13f76c19", - "metadata": { - "editable": true - }, + "id": "2ee16c9e", + "metadata": {}, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "id": "7c8dabb7", - "metadata": { - "editable": true - }, + "id": "f95fdb8b", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -473,20 +407,16 @@ }, { "cell_type": "markdown", - "id": "74eaf63d", - "metadata": { - "editable": true - }, + "id": "3f039432", + "metadata": {}, "source": [ "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have" ] }, { "cell_type": "markdown", - "id": "4a58d03d", - "metadata": { - "editable": true - }, + "id": "dbd20795", + "metadata": {}, "source": [ "$$\n", "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n", @@ -498,20 +428,16 @@ }, { "cell_type": "markdown", - "id": "ad5a8242", - "metadata": { - "editable": true - }, + "id": "98ba6676", + "metadata": {}, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "id": "2d1a3ad3", - "metadata": { - "editable": true - }, + "id": "ad52dad5", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -522,20 +448,16 @@ }, { "cell_type": "markdown", - "id": "3f664794", - "metadata": { - "editable": true - }, + "id": "cc09e475", + "metadata": {}, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "id": "2605bf0e", - "metadata": { - "editable": true - }, + "id": "7a1c0547", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -546,10 +468,8 @@ }, { "cell_type": "markdown", - "id": "01f6d82b", - "metadata": { - "editable": true - }, + "id": "9fe4208b", + "metadata": {}, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", @@ -561,10 +481,8 @@ }, { "cell_type": "markdown", - "id": "92fbc947", - "metadata": { - "editable": true - }, + "id": "2a81e02b", + "metadata": {}, "source": [ "## Steepest descent\n", "\n", @@ -578,10 +496,8 @@ }, { "cell_type": "markdown", - "id": "4456e346", - "metadata": { - "editable": true - }, + "id": "f90232dd", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -590,10 +506,8 @@ }, { "cell_type": "markdown", - "id": "98859a0d", - "metadata": { - "editable": true - }, + "id": "4fb8b51e", + "metadata": {}, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -604,10 +518,8 @@ }, { "cell_type": "markdown", - "id": "3249ff28", - "metadata": { - "editable": true - }, + "id": "81da0301", + "metadata": {}, "source": [ "## More on Steepest descent\n", "\n", @@ -619,10 +531,8 @@ }, { "cell_type": "markdown", - "id": "bc3514ae", - "metadata": { - "editable": true - }, + "id": "9b1a0014", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -631,10 +541,8 @@ }, { "cell_type": "markdown", - "id": "7dc046a6", - "metadata": { - "editable": true - }, + "id": "52e8d174", + "metadata": {}, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning." @@ -642,10 +550,8 @@ }, { "cell_type": "markdown", - "id": "0b885ad4", - "metadata": { - "editable": true - }, + "id": "be802e47", + "metadata": {}, "source": [ "## The ideal\n", "\n", @@ -670,10 +576,8 @@ }, { "cell_type": "markdown", - "id": "800ed299", - "metadata": { - "editable": true - }, + "id": "c2404539", + "metadata": {}, "source": [ "## The sensitiveness of the gradient descent\n", "\n", @@ -692,10 +596,8 @@ }, { "cell_type": "markdown", - "id": "bfd9b49f", - "metadata": { - "editable": true - }, + "id": "f96c6cdf", + "metadata": {}, "source": [ "## Convex functions\n", "\n", @@ -714,10 +616,8 @@ }, { "cell_type": "markdown", - "id": "7cc0574a", - "metadata": { - "editable": true - }, + "id": "0deb328b", + "metadata": {}, "source": [ "## Convex function\n", "\n", @@ -735,10 +635,8 @@ }, { "cell_type": "markdown", - "id": "a4a7e0d2", - "metadata": { - "editable": true - }, + "id": "74dc1b02", + "metadata": {}, "source": [ "## Conditions on convex functions\n", "\n", @@ -774,10 +672,8 @@ }, { "cell_type": "markdown", - "id": "4ac4f3dd", - "metadata": { - "editable": true - }, + "id": "bc8bc23c", + "metadata": {}, "source": [ "## More on convex functions\n", "\n", @@ -802,10 +698,8 @@ }, { "cell_type": "markdown", - "id": "e2c3e2b8", - "metadata": { - "editable": true - }, + "id": "b004d0d8", + "metadata": {}, "source": [ "## Some simple problems\n", "\n", @@ -832,10 +726,8 @@ }, { "cell_type": "markdown", - "id": "3cbf5677", - "metadata": { - "editable": true - }, + "id": "004c656f", + "metadata": {}, "source": [ "## Standard steepest descent\n", "\n", @@ -852,10 +744,8 @@ }, { "cell_type": "markdown", - "id": "8b46198f", - "metadata": { - "editable": true - }, + "id": "3055088e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -864,20 +754,16 @@ }, { "cell_type": "markdown", - "id": "87174dcb", - "metadata": { - "editable": true - }, + "id": "9d268d89", + "metadata": {}, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "id": "5af2eb1c", - "metadata": { - "editable": true - }, + "id": "c8dbe560", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -886,10 +772,8 @@ }, { "cell_type": "markdown", - "id": "977cfa69", - "metadata": { - "editable": true - }, + "id": "fd2de293", + "metadata": {}, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", @@ -898,10 +782,8 @@ }, { "cell_type": "markdown", - "id": "68fd5ea0", - "metadata": { - "editable": true - }, + "id": "25344346", + "metadata": {}, "source": [ "## Gradient method\n", "\n", @@ -910,10 +792,8 @@ }, { "cell_type": "markdown", - "id": "4e2bae9e", - "metadata": { - "editable": true - }, + "id": "c1b8855c", + "metadata": {}, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -922,10 +802,8 @@ }, { "cell_type": "markdown", - "id": "bcbbad7f", - "metadata": { - "editable": true - }, + "id": "506aceb6", + "metadata": {}, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite." @@ -933,10 +811,8 @@ }, { "cell_type": "markdown", - "id": "67d8e3f3", - "metadata": { - "editable": true - }, + "id": "53b26051", + "metadata": {}, "source": [ "## Steepest descent method\n", "\n", @@ -946,10 +822,8 @@ }, { "cell_type": "markdown", - "id": "7519f74e", - "metadata": { - "editable": true - }, + "id": "06b0db34", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -958,20 +832,16 @@ }, { "cell_type": "markdown", - "id": "f0b6000e", - "metadata": { - "editable": true - }, + "id": "0d9ddd86", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "0a5e83d1", - "metadata": { - "editable": true - }, + "id": "66dff86c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -980,20 +850,16 @@ }, { "cell_type": "markdown", - "id": "fff9b0be", - "metadata": { - "editable": true - }, + "id": "77c18c22", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "2be695a7", - "metadata": { - "editable": true - }, + "id": "9dfad29a", + "metadata": {}, "source": [ "## Steepest descent method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1001,10 +867,8 @@ }, { "cell_type": "markdown", - "id": "1bcf856f", - "metadata": { - "editable": true - }, + "id": "50edf2f9", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1013,10 +877,8 @@ }, { "cell_type": "markdown", - "id": "6dd2c43f", - "metadata": { - "editable": true - }, + "id": "51d84a77", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1025,10 +887,8 @@ }, { "cell_type": "markdown", - "id": "a4d7a932", - "metadata": { - "editable": true - }, + "id": "f3179c0a", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1037,10 +897,8 @@ }, { "cell_type": "markdown", - "id": "20db9bfe", - "metadata": { - "editable": true - }, + "id": "66bc0e76", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$." @@ -1048,10 +906,8 @@ }, { "cell_type": "markdown", - "id": "cde76790", - "metadata": { - "editable": true - }, + "id": "9be63d8b", + "metadata": {}, "source": [ "## Final expressions\n", "We can compute the residual iteratively as" @@ -1059,10 +915,8 @@ }, { "cell_type": "markdown", - "id": "c1ba27a3", - "metadata": { - "editable": true - }, + "id": "07294b6e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1071,20 +925,16 @@ }, { "cell_type": "markdown", - "id": "81525791", - "metadata": { - "editable": true - }, + "id": "5cb13e3a", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "42bd4217", - "metadata": { - "editable": true - }, + "id": "b95b4415", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -1093,20 +943,16 @@ }, { "cell_type": "markdown", - "id": "c1f6672f", - "metadata": { - "editable": true - }, + "id": "90956a95", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "df8c1efa", - "metadata": { - "editable": true - }, + "id": "d4675379", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -1115,20 +961,16 @@ }, { "cell_type": "markdown", - "id": "1b4bf5a8", - "metadata": { - "editable": true - }, + "id": "6e3a1c20", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "e2c3ad13", - "metadata": { - "editable": true - }, + "id": "e9b86a0a", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -1137,20 +979,16 @@ }, { "cell_type": "markdown", - "id": "333026af", - "metadata": { - "editable": true - }, + "id": "a1fd88cc", + "metadata": {}, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "id": "35825027", - "metadata": { - "editable": true - }, + "id": "39f090b1", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n", @@ -1159,10 +997,8 @@ }, { "cell_type": "markdown", - "id": "62866612", - "metadata": { - "editable": true - }, + "id": "0ad69506", + "metadata": {}, "source": [ "## Steepest descent example" ] @@ -1170,30 +1006,31 @@ { "cell_type": "code", "execution_count": 1, - "id": "ba11008c", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "4a529fa4", + "metadata": {}, "outputs": [ - { - "ename": "TypeError", - "evalue": "gca() got an unexpected keyword argument 'projection'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[1], line 18\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mx[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;241m6\u001b[39m\u001b[38;5;241m*\u001b[39mx[\u001b[38;5;241m1\u001b[39m]])\n\u001b[1;32m 17\u001b[0m fig \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[0;32m---> 18\u001b[0m ax \u001b[38;5;241m=\u001b[39m \u001b[43mfig\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgca\u001b[49m\u001b[43m(\u001b[49m\u001b[43mprojection\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43m3d\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m 20\u001b[0m xmesh, ymesh \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mmgrid[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m3\u001b[39m:\u001b[38;5;241m3\u001b[39m:\u001b[38;5;241m50\u001b[39mj,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m3\u001b[39m:\u001b[38;5;241m3\u001b[39m:\u001b[38;5;241m50\u001b[39mj]\n\u001b[1;32m 21\u001b[0m fmesh \u001b[38;5;241m=\u001b[39m f(np\u001b[38;5;241m.\u001b[39marray([xmesh, ymesh]))\n", - "\u001b[0;31mTypeError\u001b[0m: gca() got an unexpected keyword argument 'projection'" - ] - }, { "data": { "text/plain": [ - "
    " + "" ] }, + "execution_count": 1, "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_82_1.png" + } + }, "output_type": "display_data" } ], @@ -1215,7 +1052,7 @@ " return np.array([2*x[0], 6*x[1]])\n", "\n", "fig = pt.figure()\n", - "ax = fig.gca(projection=\"3d\")\n", + "ax = fig.add_subplot(projection = '3d')\n", "\n", "xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n", "fmesh = f(np.array([xmesh, ymesh]))\n", @@ -1224,10 +1061,8 @@ }, { "cell_type": "markdown", - "id": "d94f79ff", - "metadata": { - "editable": true - }, + "id": "949a0d1c", + "metadata": {}, "source": [ "And then as countor plot" ] @@ -1235,12 +1070,24 @@ { "cell_type": "code", "execution_count": 2, - "id": "8d03a29a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3b0698ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_84_0.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", @@ -1249,10 +1096,8 @@ }, { "cell_type": "markdown", - "id": "1560ce9e", - "metadata": { - "editable": true - }, + "id": "b3d4208f", + "metadata": {}, "source": [ "Find guesses" ] @@ -1260,11 +1105,8 @@ { "cell_type": "code", "execution_count": 3, - "id": "444dcac8", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "d7e4a182", + "metadata": {}, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -1273,10 +1115,8 @@ }, { "cell_type": "markdown", - "id": "6a3a8ba3", - "metadata": { - "editable": true - }, + "id": "fbc59d26", + "metadata": {}, "source": [ "Run it!" ] @@ -1284,12 +1124,17 @@ { "cell_type": "code", "execution_count": 4, - "id": "96921390", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "18be8fa1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.69230769 -0.38461539]\n" + ] + } + ], "source": [ "def f1d(alpha):\n", " return f(x + alpha*s)\n", @@ -1302,10 +1147,8 @@ }, { "cell_type": "markdown", - "id": "5090d289", - "metadata": { - "editable": true - }, + "id": "7f40f5f6", + "metadata": {}, "source": [ "What happened?" ] @@ -1313,12 +1156,34 @@ { "cell_type": "code", "execution_count": 5, - "id": "ac4b2a89", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "dbdb7d4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_90_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", @@ -1328,20 +1193,16 @@ }, { "cell_type": "markdown", - "id": "014335b8", - "metadata": { - "editable": true - }, + "id": "851db164", + "metadata": {}, "source": [ "Note that we did only one iteration here. We can easily add more using our previous guesses." ] }, { "cell_type": "markdown", - "id": "8f2fc479", - "metadata": { - "editable": true - }, + "id": "f1300342", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -1352,10 +1213,8 @@ }, { "cell_type": "markdown", - "id": "c12ed388", - "metadata": { - "editable": true - }, + "id": "15530c95", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -1364,10 +1223,8 @@ }, { "cell_type": "markdown", - "id": "525571bd", - "metadata": { - "editable": true - }, + "id": "35222dc4", + "metadata": {}, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -1375,10 +1232,8 @@ }, { "cell_type": "markdown", - "id": "16ea251e", - "metadata": { - "editable": true - }, + "id": "a5ab4e81", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -1387,10 +1242,8 @@ }, { "cell_type": "markdown", - "id": "bc20e247", - "metadata": { - "editable": true - }, + "id": "922a54c4", + "metadata": {}, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$." @@ -1398,10 +1251,8 @@ }, { "cell_type": "markdown", - "id": "7e393cfd", - "metadata": { - "editable": true - }, + "id": "606d1a71", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "An example is given by the eigenvectors of the matrix" @@ -1409,10 +1260,8 @@ }, { "cell_type": "markdown", - "id": "004102f6", - "metadata": { - "editable": true - }, + "id": "e46ac6fc", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -1421,20 +1270,16 @@ }, { "cell_type": "markdown", - "id": "842e93a3", - "metadata": { - "editable": true - }, + "id": "aec2962a", + "metadata": {}, "source": [ "which is zero unless $i=j$." ] }, { "cell_type": "markdown", - "id": "988aa113", - "metadata": { - "editable": true - }, + "id": "f62eeb16", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n", @@ -1443,10 +1288,8 @@ }, { "cell_type": "markdown", - "id": "6c460be1", - "metadata": { - "editable": true - }, + "id": "bde9cf46", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -1455,10 +1298,8 @@ }, { "cell_type": "markdown", - "id": "1694d645", - "metadata": { - "editable": true - }, + "id": "1b354afe", + "metadata": {}, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -1467,10 +1308,8 @@ }, { "cell_type": "markdown", - "id": "091ad567", - "metadata": { - "editable": true - }, + "id": "a3e7fc78", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -1479,10 +1318,8 @@ }, { "cell_type": "markdown", - "id": "dd3cf73c", - "metadata": { - "editable": true - }, + "id": "9608b5e1", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "The coefficients are given by" @@ -1490,10 +1327,8 @@ }, { "cell_type": "markdown", - "id": "13cf2ad9", - "metadata": { - "editable": true - }, + "id": "d667abb4", + "metadata": {}, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -1502,20 +1337,16 @@ }, { "cell_type": "markdown", - "id": "9bc1ee6e", - "metadata": { - "editable": true - }, + "id": "2b909963", + "metadata": {}, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "id": "05599b4f", - "metadata": { - "editable": true - }, + "id": "0e9960df", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -1524,20 +1355,16 @@ }, { "cell_type": "markdown", - "id": "48dce995", - "metadata": { - "editable": true - }, + "id": "4d334201", + "metadata": {}, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "id": "3ed1d31f", - "metadata": { - "editable": true - }, + "id": "f06c6496", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1546,10 +1373,8 @@ }, { "cell_type": "markdown", - "id": "d53065fb", - "metadata": { - "editable": true - }, + "id": "69adaefe", + "metadata": {}, "source": [ "## Conjugate gradient method and iterations\n", "\n", @@ -1566,10 +1391,8 @@ }, { "cell_type": "markdown", - "id": "1c9e8acd", - "metadata": { - "editable": true - }, + "id": "35cf8e92", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1578,20 +1401,16 @@ }, { "cell_type": "markdown", - "id": "b1ce7e22", - "metadata": { - "editable": true - }, + "id": "686fe37b", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "5a9d580f", - "metadata": { - "editable": true - }, + "id": "b6cdf1da", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1600,20 +1419,16 @@ }, { "cell_type": "markdown", - "id": "bd732814", - "metadata": { - "editable": true - }, + "id": "f03df570", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "a0b6ed43", - "metadata": { - "editable": true - }, + "id": "d2619eaa", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1621,10 +1436,8 @@ }, { "cell_type": "markdown", - "id": "0647b456", - "metadata": { - "editable": true - }, + "id": "7c99b348", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1633,10 +1446,8 @@ }, { "cell_type": "markdown", - "id": "39dd4393", - "metadata": { - "editable": true - }, + "id": "06107635", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1645,10 +1456,8 @@ }, { "cell_type": "markdown", - "id": "5d17f7b6", - "metadata": { - "editable": true - }, + "id": "7d57e70c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1657,10 +1466,8 @@ }, { "cell_type": "markdown", - "id": "7f0fbf0c", - "metadata": { - "editable": true - }, + "id": "d07728a4", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1670,10 +1477,8 @@ }, { "cell_type": "markdown", - "id": "f9d39a67", - "metadata": { - "editable": true - }, + "id": "64a6011d", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:" @@ -1681,10 +1486,8 @@ }, { "cell_type": "markdown", - "id": "75e12e7b", - "metadata": { - "editable": true - }, + "id": "395293fb", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1693,10 +1496,8 @@ }, { "cell_type": "markdown", - "id": "aec178fd", - "metadata": { - "editable": true - }, + "id": "2742cfb7", + "metadata": {}, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1709,10 +1510,8 @@ }, { "cell_type": "markdown", - "id": "d9c2ab58", - "metadata": { - "editable": true - }, + "id": "6bca98e3", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1721,10 +1520,8 @@ }, { "cell_type": "markdown", - "id": "cbe552ed", - "metadata": { - "editable": true - }, + "id": "0b38ac3f", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "We can also compute the residual iteratively as" @@ -1732,10 +1529,8 @@ }, { "cell_type": "markdown", - "id": "82a132bd", - "metadata": { - "editable": true - }, + "id": "0588ed16", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1744,20 +1539,16 @@ }, { "cell_type": "markdown", - "id": "0349d81c", - "metadata": { - "editable": true - }, + "id": "2f7bd339", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "7107cbd5", - "metadata": { - "editable": true - }, + "id": "5d46e7c8", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1766,20 +1557,16 @@ }, { "cell_type": "markdown", - "id": "3a56cd7c", - "metadata": { - "editable": true - }, + "id": "a6dfda96", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "63a24c09", - "metadata": { - "editable": true - }, + "id": "bea30687", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1788,20 +1575,16 @@ }, { "cell_type": "markdown", - "id": "6ef4ea63", - "metadata": { - "editable": true - }, + "id": "ec002ff0", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "c2357533", - "metadata": { - "editable": true - }, + "id": "a45514a5", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1810,10 +1593,8 @@ }, { "cell_type": "markdown", - "id": "61549c12", - "metadata": { - "editable": true - }, + "id": "60756713", + "metadata": {}, "source": [ "## Revisiting our first homework\n", "\n", @@ -1834,23 +1615,19 @@ { "cell_type": "code", "execution_count": 6, - "id": "2bbe00ae", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "9e6108fd", + "metadata": {}, "outputs": [], "source": [ + "m = 100\n", "x = 2*np.random.rand(m,1)\n", "y = 4+3*x+np.random.randn(m,1)" ] }, { "cell_type": "markdown", - "id": "2edbd94a", - "metadata": { - "editable": true - }, + "id": "146e4fe9", + "metadata": {}, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1858,10 +1635,8 @@ }, { "cell_type": "markdown", - "id": "97f601a1", - "metadata": { - "editable": true - }, + "id": "c5c0a7f1", + "metadata": {}, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1870,20 +1645,16 @@ }, { "cell_type": "markdown", - "id": "46f56da5", - "metadata": { - "editable": true - }, + "id": "f5f1aea6", + "metadata": {}, "source": [ "such that" ] }, { "cell_type": "markdown", - "id": "ea40d182", - "metadata": { - "editable": true - }, + "id": "76b1993f", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1892,10 +1663,8 @@ }, { "cell_type": "markdown", - "id": "f1529059", - "metadata": { - "editable": true - }, + "id": "b5a211bb", + "metadata": {}, "source": [ "## Gradient descent example\n", "\n", @@ -1906,10 +1675,8 @@ }, { "cell_type": "markdown", - "id": "ff686b79", - "metadata": { - "editable": true - }, + "id": "4b0b1b01", + "metadata": {}, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1922,20 +1689,16 @@ }, { "cell_type": "markdown", - "id": "e9072325", - "metadata": { - "editable": true - }, + "id": "c5751686", + "metadata": {}, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "id": "b039d2dd", - "metadata": { - "editable": true - }, + "id": "a2d6f6a6", + "metadata": {}, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1944,20 +1707,16 @@ }, { "cell_type": "markdown", - "id": "dc1285b8", - "metadata": { - "editable": true - }, + "id": "af74580d", + "metadata": {}, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized." ] }, { "cell_type": "markdown", - "id": "8d029669", - "metadata": { - "editable": true - }, + "id": "949f8aab", + "metadata": {}, "source": [ "## The derivative of the cost/loss function\n", "\n", @@ -1966,10 +1725,8 @@ }, { "cell_type": "markdown", - "id": "f2b0be18", - "metadata": { - "editable": true - }, + "id": "5e3860a4", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1980,20 +1737,16 @@ }, { "cell_type": "markdown", - "id": "72b959fa", - "metadata": { - "editable": true - }, + "id": "765febad", + "metadata": {}, "source": [ "where $X$ is the design matrix defined above." ] }, { "cell_type": "markdown", - "id": "53db546f", - "metadata": { - "editable": true - }, + "id": "65781e41", + "metadata": {}, "source": [ "## The Hessian matrix\n", "The Hessian matrix of $C(\\beta)$ is given by" @@ -2001,10 +1754,8 @@ }, { "cell_type": "markdown", - "id": "d9799e09", - "metadata": { - "editable": true - }, + "id": "7e1e9714", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -2016,20 +1767,16 @@ }, { "cell_type": "markdown", - "id": "433d7d4e", - "metadata": { - "editable": true - }, + "id": "9d48eebb", + "metadata": {}, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite." ] }, { "cell_type": "markdown", - "id": "8bcfa1d9", - "metadata": { - "editable": true - }, + "id": "fd88e7fd", + "metadata": {}, "source": [ "## Simple program\n", "\n", @@ -2038,10 +1785,8 @@ }, { "cell_type": "markdown", - "id": "9591273f", - "metadata": { - "editable": true - }, + "id": "e12fb5d1", + "metadata": {}, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -2050,10 +1795,8 @@ }, { "cell_type": "markdown", - "id": "ff30e5e6", - "metadata": { - "editable": true - }, + "id": "eeb13498", + "metadata": {}, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -2065,10 +1808,8 @@ }, { "cell_type": "markdown", - "id": "a58e0dda", - "metadata": { - "editable": true - }, + "id": "7ffca923", + "metadata": {}, "source": [ "## Gradient Descent Example\n", "\n", @@ -2078,12 +1819,35 @@ { "cell_type": "code", "execution_count": 7, - "id": "d6da2734", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9321710e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.39517073 4.17377547]\n", + "[[3.7074705 ]\n", + " [3.25970297]]\n", + "[[3.7074705 ]\n", + " [3.25970297]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_153_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "\n", "# Importing various packages\n", @@ -2135,10 +1899,8 @@ }, { "cell_type": "markdown", - "id": "a2f94d89", - "metadata": { - "editable": true - }, + "id": "e65d5b5b", + "metadata": {}, "source": [ "## And a corresponding example using **scikit-learn**" ] @@ -2146,12 +1908,19 @@ { "cell_type": "code", "execution_count": 8, - "id": "f95809e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e73c4b82", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.95872127]\n", + " [3.20357736]]\n", + "[3.9712983] [3.26048873]\n" + ] + } + ], "source": [ "# Importing various packages\n", "from random import random, seed\n", @@ -2173,10 +1942,8 @@ }, { "cell_type": "markdown", - "id": "bcca1a86", - "metadata": { - "editable": true - }, + "id": "0cffa723", + "metadata": {}, "source": [ "## Gradient descent and Ridge\n", "\n", @@ -2185,10 +1952,8 @@ }, { "cell_type": "markdown", - "id": "3f8a3655", - "metadata": { - "editable": true - }, + "id": "e70974bf", + "metadata": {}, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -2197,20 +1962,16 @@ }, { "cell_type": "markdown", - "id": "fe1ae4c5", - "metadata": { - "editable": true - }, + "id": "8e2c0506", + "metadata": {}, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows" ] }, { "cell_type": "markdown", - "id": "75348007", - "metadata": { - "editable": true - }, + "id": "673104d6", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -2221,20 +1982,16 @@ }, { "cell_type": "markdown", - "id": "7b401e23", - "metadata": { - "editable": true - }, + "id": "f5d61a03", + "metadata": {}, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "id": "108955a9", - "metadata": { - "editable": true - }, + "id": "7e9aec7d", + "metadata": {}, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -2243,10 +2000,8 @@ }, { "cell_type": "markdown", - "id": "e81e374d", - "metadata": { - "editable": true - }, + "id": "54248fbe", + "metadata": {}, "source": [ "## The Hessian matrix for Ridge Regression\n", "The Hessian matrix of Ridge Regression for our simple example is given by" @@ -2254,10 +2009,8 @@ }, { "cell_type": "markdown", - "id": "5f670054", - "metadata": { - "editable": true - }, + "id": "0b57c03b", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -2269,10 +2022,8 @@ }, { "cell_type": "markdown", - "id": "44190400", - "metadata": { - "editable": true - }, + "id": "562d6a77", + "metadata": {}, "source": [ "This implies that the Hessian matrix is positive definite, hence the stationary point is a\n", "minimum.\n", @@ -2283,10 +2034,8 @@ }, { "cell_type": "markdown", - "id": "297e1218", - "metadata": { - "editable": true - }, + "id": "018079a6", + "metadata": {}, "source": [ "## Program example for gradient descent with Ridge Regression" ] @@ -2294,12 +2043,35 @@ { "cell_type": "code", "execution_count": 9, - "id": "f39e42bb", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "12f965e7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.25986026 4.46387965]\n", + "[[4.18118338]\n", + " [2.86240935]]\n", + "[[4.18234308]\n", + " [2.86143379]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_166_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "from random import random, seed\n", "import numpy as np\n", @@ -2355,10 +2127,8 @@ }, { "cell_type": "markdown", - "id": "d84821a4", - "metadata": { - "editable": true - }, + "id": "06107436", + "metadata": {}, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -2377,10 +2147,8 @@ }, { "cell_type": "markdown", - "id": "386582c7", - "metadata": { - "editable": true - }, + "id": "bd3205c7", + "metadata": {}, "source": [ "## Improving gradient descent with momentum\n", "\n", @@ -2390,12 +2158,60 @@ { "cell_type": "code", "execution_count": 10, - "id": "bdd17d18", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "98ec014e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.59779819]) = 0.35736\n", + ">2 f([0.47823856]) = 0.22871\n", + ">3 f([0.38259084]) = 0.14638\n", + ">4 f([0.30607268]) = 0.09368\n", + ">5 f([0.24485814]) = 0.05996\n", + ">6 f([0.19588651]) = 0.03837\n", + ">7 f([0.15670921]) = 0.02456\n", + ">8 f([0.12536737]) = 0.01572\n", + ">9 f([0.10029389]) = 0.01006\n", + ">10 f([0.08023512]) = 0.00644\n", + ">11 f([0.06418809]) = 0.00412\n", + ">12 f([0.05135047]) = 0.00264\n", + ">13 f([0.04108038]) = 0.00169\n", + ">14 f([0.0328643]) = 0.00108\n", + ">15 f([0.02629144]) = 0.00069\n", + ">16 f([0.02103315]) = 0.00044\n", + ">17 f([0.01682652]) = 0.00028\n", + ">18 f([0.01346122]) = 0.00018\n", + ">19 f([0.01076897]) = 0.00012\n", + ">20 f([0.00861518]) = 0.00007\n", + ">21 f([0.00689214]) = 0.00005\n", + ">22 f([0.00551372]) = 0.00003\n", + ">23 f([0.00441097]) = 0.00002\n", + ">24 f([0.00352878]) = 0.00001\n", + ">25 f([0.00282302]) = 0.00001\n", + ">26 f([0.00225842]) = 0.00001\n", + ">27 f([0.00180673]) = 0.00000\n", + ">28 f([0.00144539]) = 0.00000\n", + ">29 f([0.00115631]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_169_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2456,10 +2272,8 @@ }, { "cell_type": "markdown", - "id": "6675456b", - "metadata": { - "editable": true - }, + "id": "35d2b3d9", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -2467,12 +2281,60 @@ { "cell_type": "code", "execution_count": 11, - "id": "5f7443ae", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ca391f17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.54175461]) = 0.29350\n", + ">2 f([0.37175575]) = 0.13820\n", + ">3 f([0.24640494]) = 0.06072\n", + ">4 f([0.15951871]) = 0.02545\n", + ">5 f([0.1015491]) = 0.01031\n", + ">6 f([0.0638484]) = 0.00408\n", + ">7 f([0.03976851]) = 0.00158\n", + ">8 f([0.02459084]) = 0.00060\n", + ">9 f([0.01511937]) = 0.00023\n", + ">10 f([0.00925406]) = 0.00009\n", + ">11 f([0.00564365]) = 0.00003\n", + ">12 f([0.0034318]) = 0.00001\n", + ">13 f([0.00208188]) = 0.00000\n", + ">14 f([0.00126053]) = 0.00000\n", + ">15 f([0.00076202]) = 0.00000\n", + ">16 f([0.00046006]) = 0.00000\n", + ">17 f([0.00027746]) = 0.00000\n", + ">18 f([0.00016719]) = 0.00000\n", + ">19 f([0.00010067]) = 0.00000\n", + ">20 f([6.05804744e-05]) = 0.00000\n", + ">21 f([3.64373635e-05]) = 0.00000\n", + ">22 f([2.19069576e-05]) = 0.00000\n", + ">23 f([1.31664443e-05]) = 0.00000\n", + ">24 f([7.91100141e-06]) = 0.00000\n", + ">25 f([4.75216828e-06]) = 0.00000\n", + ">26 f([2.85408468e-06]) = 0.00000\n", + ">27 f([1.71384267e-06]) = 0.00000\n", + ">28 f([1.02900153e-06]) = 0.00000\n", + ">29 f([6.17748881e-07]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_171_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2541,10 +2403,8 @@ }, { "cell_type": "markdown", - "id": "0c5c47e2", - "metadata": { - "editable": true - }, + "id": "181b30b4", + "metadata": {}, "source": [ "## Overview video on Stochastic Gradient Descent\n", "\n", @@ -2553,10 +2413,8 @@ }, { "cell_type": "markdown", - "id": "30d83150", - "metadata": { - "editable": true - }, + "id": "b51d1452", + "metadata": {}, "source": [ "## Batches and mini-batches\n", "\n", @@ -2574,10 +2432,8 @@ }, { "cell_type": "markdown", - "id": "310429e5", - "metadata": { - "editable": true - }, + "id": "85bbbc0c", + "metadata": {}, "source": [ "## Stochastic Gradient Descent (SGD)\n", "\n", @@ -2606,10 +2462,8 @@ }, { "cell_type": "markdown", - "id": "07ec38f2", - "metadata": { - "editable": true - }, + "id": "56b2b867", + "metadata": {}, "source": [ "## Stochastic Gradient Descent\n", "\n", @@ -2623,10 +2477,8 @@ }, { "cell_type": "markdown", - "id": "79d6fab8", - "metadata": { - "editable": true - }, + "id": "386e0c45", + "metadata": {}, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -2636,10 +2488,8 @@ }, { "cell_type": "markdown", - "id": "628eb747", - "metadata": { - "editable": true - }, + "id": "0f6d09dd", + "metadata": {}, "source": [ "## Computation of gradients\n", "\n", @@ -2649,10 +2499,8 @@ }, { "cell_type": "markdown", - "id": "e1133d46", - "metadata": { - "editable": true - }, + "id": "99541bf1", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2662,10 +2510,8 @@ }, { "cell_type": "markdown", - "id": "4f6e6b79", - "metadata": { - "editable": true - }, + "id": "a24ce1cc", + "metadata": {}, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -2676,10 +2522,8 @@ }, { "cell_type": "markdown", - "id": "4c3c9492", - "metadata": { - "editable": true - }, + "id": "d6c2eea5", + "metadata": {}, "source": [ "## SGD example\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", @@ -2698,10 +2542,8 @@ }, { "cell_type": "markdown", - "id": "8ef691b4", - "metadata": { - "editable": true - }, + "id": "b2561a99", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -2713,10 +2555,8 @@ }, { "cell_type": "markdown", - "id": "31bf40f3", - "metadata": { - "editable": true - }, + "id": "a0fb8d89", + "metadata": {}, "source": [ "## The gradient step\n", "\n", @@ -2725,10 +2565,8 @@ }, { "cell_type": "markdown", - "id": "526e5e7e", - "metadata": { - "editable": true - }, + "id": "71856a7b", + "metadata": {}, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2738,10 +2576,8 @@ }, { "cell_type": "markdown", - "id": "5022af9d", - "metadata": { - "editable": true - }, + "id": "9859ff14", + "metadata": {}, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -2752,10 +2588,8 @@ }, { "cell_type": "markdown", - "id": "19c6475e", - "metadata": { - "editable": true - }, + "id": "6558ed12", + "metadata": {}, "source": [ "## Simple example code" ] @@ -2763,11 +2597,8 @@ { "cell_type": "code", "execution_count": 12, - "id": "18c7a10f", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "f8cee4e8", + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2788,10 +2619,8 @@ }, { "cell_type": "markdown", - "id": "ad3f48f9", - "metadata": { - "editable": true - }, + "id": "aac3d48e", + "metadata": {}, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -2804,10 +2633,8 @@ }, { "cell_type": "markdown", - "id": "04e70295", - "metadata": { - "editable": true - }, + "id": "657c6870", + "metadata": {}, "source": [ "## When do we stop?\n", "\n", @@ -2825,10 +2652,8 @@ }, { "cell_type": "markdown", - "id": "2f10ae80", - "metadata": { - "editable": true - }, + "id": "5a8d8a8d", + "metadata": {}, "source": [ "## Slightly different approach\n", "\n", @@ -2845,10 +2670,8 @@ }, { "cell_type": "markdown", - "id": "88e4714d", - "metadata": { - "editable": true - }, + "id": "e0c75855", + "metadata": {}, "source": [ "## Time decay rate\n", "\n", @@ -2864,12 +2687,17 @@ { "cell_type": "code", "execution_count": 13, - "id": "4c882e5c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8368a998", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma_j after 500 epochs: 9.97108e-05\n" + ] + } + ], "source": [ "import numpy as np \n", "\n", @@ -2899,10 +2727,8 @@ }, { "cell_type": "markdown", - "id": "79963b9d", - "metadata": { - "editable": true - }, + "id": "a99e7227", + "metadata": {}, "source": [ "## Code with a Number of Minibatches which varies\n", "\n", @@ -2912,12 +2738,40 @@ { "cell_type": "code", "execution_count": 14, - "id": "b13f70e7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "b567ba9d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]\n", + "theta from own gd\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "theta from own sdg\n", + "[[4.014934 ]\n", + " [3.0042992]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_193_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "# Importing various packages\n", "from math import exp, sqrt\n", @@ -2989,10 +2843,8 @@ }, { "cell_type": "markdown", - "id": "8e833f35", - "metadata": { - "editable": true - }, + "id": "8ea309ee", + "metadata": {}, "source": [ "## Replace or not\n", "\n", @@ -3004,10 +2856,8 @@ }, { "cell_type": "markdown", - "id": "0312dcf2", - "metadata": { - "editable": true - }, + "id": "5573b607", + "metadata": {}, "source": [ "## Momentum based GD\n", "\n", @@ -3019,10 +2869,8 @@ }, { "cell_type": "markdown", - "id": "d4730af7", - "metadata": { - "editable": true - }, + "id": "5c393430", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -3031,10 +2879,8 @@ }, { "cell_type": "markdown", - "id": "3b041d81", - "metadata": { - "editable": true - }, + "id": "03d76b90", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3049,10 +2895,8 @@ }, { "cell_type": "markdown", - "id": "e05133d9", - "metadata": { - "editable": true - }, + "id": "c9de2175", + "metadata": {}, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -3068,10 +2912,8 @@ }, { "cell_type": "markdown", - "id": "4d90938e", - "metadata": { - "editable": true - }, + "id": "a493002b", + "metadata": {}, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -3080,20 +2922,16 @@ }, { "cell_type": "markdown", - "id": "519d60d5", - "metadata": { - "editable": true - }, + "id": "cb1d7212", + "metadata": {}, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$." ] }, { "cell_type": "markdown", - "id": "487a4624", - "metadata": { - "editable": true - }, + "id": "91135b7f", + "metadata": {}, "source": [ "## More on momentum based approaches\n", "\n", @@ -3106,10 +2944,8 @@ }, { "cell_type": "markdown", - "id": "58a8bcf7", - "metadata": { - "editable": true - }, + "id": "57c90f73", + "metadata": {}, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -3118,20 +2954,16 @@ }, { "cell_type": "markdown", - "id": "6a1c6dd4", - "metadata": { - "editable": true - }, + "id": "28fc8c64", + "metadata": {}, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "id": "d77b0f55", - "metadata": { - "editable": true - }, + "id": "9ea86afa", + "metadata": {}, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -3140,20 +2972,16 @@ }, { "cell_type": "markdown", - "id": "53e0b508", - "metadata": { - "editable": true - }, + "id": "259f8bd9", + "metadata": {}, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "id": "c7919a6b", - "metadata": { - "editable": true - }, + "id": "1b3b21b9", + "metadata": {}, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -3162,10 +2990,8 @@ }, { "cell_type": "markdown", - "id": "d658c8ac", - "metadata": { - "editable": true - }, + "id": "931ce41d", + "metadata": {}, "source": [ "## Momentum parameter\n", "\n", @@ -3178,10 +3004,8 @@ }, { "cell_type": "markdown", - "id": "93e53f3f", - "metadata": { - "editable": true - }, + "id": "d1d161a1", + "metadata": {}, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -3190,10 +3014,8 @@ }, { "cell_type": "markdown", - "id": "c0a79ce5", - "metadata": { - "editable": true - }, + "id": "4f3657ba", + "metadata": {}, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -3223,10 +3045,8 @@ }, { "cell_type": "markdown", - "id": "b43632bc", - "metadata": { - "editable": true - }, + "id": "81824da9", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -3235,10 +3055,8 @@ }, { "cell_type": "markdown", - "id": "efb8ea15", - "metadata": { - "editable": true - }, + "id": "6295bc9d", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3253,20 +3071,16 @@ }, { "cell_type": "markdown", - "id": "eb92118e", - "metadata": { - "editable": true - }, + "id": "7a094665", + "metadata": {}, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$." ] }, { "cell_type": "markdown", - "id": "6c9fb86f", - "metadata": { - "editable": true - }, + "id": "f0c6bb20", + "metadata": {}, "source": [ "## Second moment of the gradient\n", "\n", @@ -3294,10 +3108,8 @@ }, { "cell_type": "markdown", - "id": "a25c923d", - "metadata": { - "editable": true - }, + "id": "ce3b45b6", + "metadata": {}, "source": [ "## RMS prop\n", "\n", @@ -3309,10 +3121,8 @@ }, { "cell_type": "markdown", - "id": "24a3b8dd", - "metadata": { - "editable": true - }, + "id": "ee7e2069", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3327,10 +3137,8 @@ }, { "cell_type": "markdown", - "id": "2a4a4d3a", - "metadata": { - "editable": true - }, + "id": "ec4f73bb", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -3339,10 +3147,8 @@ }, { "cell_type": "markdown", - "id": "38b5c0c6", - "metadata": { - "editable": true - }, + "id": "fa5cb9a2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -3351,10 +3157,8 @@ }, { "cell_type": "markdown", - "id": "81dbe505", - "metadata": { - "editable": true - }, + "id": "eb93379a", + "metadata": {}, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -3369,10 +3173,8 @@ }, { "cell_type": "markdown", - "id": "fc1157b9", - "metadata": { - "editable": true - }, + "id": "b46162a4", + "metadata": {}, "source": [ "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n", "\n", @@ -3398,10 +3200,8 @@ }, { "cell_type": "markdown", - "id": "bf9b6954", - "metadata": { - "editable": true - }, + "id": "d103bc6a", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3416,10 +3216,8 @@ }, { "cell_type": "markdown", - "id": "20de7cae", - "metadata": { - "editable": true - }, + "id": "a0f031f6", + "metadata": {}, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -3428,10 +3226,8 @@ }, { "cell_type": "markdown", - "id": "3ce79d35", - "metadata": { - "editable": true - }, + "id": "2b384f75", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -3440,10 +3236,8 @@ }, { "cell_type": "markdown", - "id": "2830d104", - "metadata": { - "editable": true - }, + "id": "216435a6", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -3452,10 +3246,8 @@ }, { "cell_type": "markdown", - "id": "90e75ad2", - "metadata": { - "editable": true - }, + "id": "8b79e19e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -3464,10 +3256,8 @@ }, { "cell_type": "markdown", - "id": "99457a88", - "metadata": { - "editable": true - }, + "id": "ba777281", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -3476,10 +3266,8 @@ }, { "cell_type": "markdown", - "id": "d7aa5ab9", - "metadata": { - "editable": true - }, + "id": "f34eb136", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3493,10 +3281,8 @@ }, { "cell_type": "markdown", - "id": "26071aca", - "metadata": { - "editable": true - }, + "id": "695da6fd", + "metadata": {}, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -3512,10 +3298,8 @@ }, { "cell_type": "markdown", - "id": "09f63a9f", - "metadata": { - "editable": true - }, + "id": "8771f487", + "metadata": {}, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -3524,10 +3308,8 @@ }, { "cell_type": "markdown", - "id": "74b65884", - "metadata": { - "editable": true - }, + "id": "6b816830", + "metadata": {}, "source": [ "## Algorithms and codes for Adagrad, RMSprop and Adam\n", "\n", @@ -3538,10 +3320,8 @@ }, { "cell_type": "markdown", - "id": "0d5cee10", - "metadata": { - "editable": true - }, + "id": "4efb5cb8", + "metadata": {}, "source": [ "## Practical tips\n", "\n", @@ -3558,10 +3338,8 @@ }, { "cell_type": "markdown", - "id": "09734edc", - "metadata": { - "editable": true - }, + "id": "de7affbf", + "metadata": {}, "source": [ "## Automatic differentiation\n", "\n", @@ -3596,10 +3374,8 @@ }, { "cell_type": "markdown", - "id": "81d6131f", - "metadata": { - "editable": true - }, + "id": "3383da7c", + "metadata": {}, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -3608,20 +3384,16 @@ }, { "cell_type": "markdown", - "id": "0795db2e", - "metadata": { - "editable": true - }, + "id": "a8a03664", + "metadata": {}, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "id": "84ede40a", - "metadata": { - "editable": true - }, + "id": "da4e8c9e", + "metadata": {}, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -3630,10 +3402,8 @@ }, { "cell_type": "markdown", - "id": "3c0048b2", - "metadata": { - "editable": true - }, + "id": "b35c008d", + "metadata": {}, "source": [ "Using **autograd** we have" ] @@ -3641,12 +3411,31 @@ { "cell_type": "code", "execution_count": 15, - "id": "4f554ba9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9bb36858", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_236_0.png" + } + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max absolute difference is: 1.77636e-15\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "\n", @@ -3686,10 +3475,8 @@ }, { "cell_type": "markdown", - "id": "dbb0af99", - "metadata": { - "editable": true - }, + "id": "9f8c7b5e", + "metadata": {}, "source": [ "## Using autograd\n", "\n", @@ -3703,12 +3490,18 @@ { "cell_type": "code", "execution_count": 16, - "id": "b44bbeac", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "65176228", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f1 evaluated at a = 1 using autograd is: 3\n", + "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3731,10 +3524,8 @@ }, { "cell_type": "markdown", - "id": "93f27878", - "metadata": { - "editable": true - }, + "id": "44375951", + "metadata": {}, "source": [ "## Autograd with more complicated functions\n", "\n", @@ -3746,12 +3537,23 @@ { "cell_type": "code", "execution_count": 17, - "id": "79de7d5e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "63ebdbaf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Evaluating at x1 = 1, x2 = 3\n", + "------------------------------\n", + "The derivative of f2 w.r.t x1: 12\n", + "The analytical derivative of f2 w.r.t x1: 12\n", + "\n", + "The derivative of f2 w.r.t x2: -4\n", + "The analytical derivative of f2 w.r.t x2: -4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3790,20 +3592,16 @@ }, { "cell_type": "markdown", - "id": "61ab2c3d", - "metadata": { - "editable": true - }, + "id": "ddef1f9a", + "metadata": {}, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] }, { "cell_type": "markdown", - "id": "b4784f66", - "metadata": { - "editable": true - }, + "id": "c6ff810b", + "metadata": {}, "source": [ "## More complicated functions using the elements of their arguments directly" ] @@ -3811,12 +3609,18 @@ { "cell_type": "code", "execution_count": 18, - "id": "73c1b6aa", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8c1ef66a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed gradient of f3 is: [ 2. 3. 5. 7. 88.]\n", + "The analytical gradient of f3 is: [ 2. 3. 5. 7. 88.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3839,10 +3643,8 @@ }, { "cell_type": "markdown", - "id": "c73c3739", - "metadata": { - "editable": true - }, + "id": "7ac0e490", + "metadata": {}, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -3854,10 +3656,8 @@ }, { "cell_type": "markdown", - "id": "94962c03", - "metadata": { - "editable": true - }, + "id": "f817a4b1", + "metadata": {}, "source": [ "## Functions using mathematical functions from Numpy" ] @@ -3865,12 +3665,18 @@ { "cell_type": "code", "execution_count": 19, - "id": "a48211f9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9950eceb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f4 at x = 2.7 is: 13.8759\n", + "The analytical gradient of f4 at x = 2.7 is: 13.8759\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3893,10 +3699,8 @@ }, { "cell_type": "markdown", - "id": "e8423919", - "metadata": { - "editable": true - }, + "id": "2d3597e1", + "metadata": {}, "source": [ "## More autograd" ] @@ -3904,12 +3708,17 @@ { "cell_type": "code", "execution_count": 20, - "id": "a3645e2a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a694b773", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f5 at x = 2.7 is: 5.4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3929,10 +3738,8 @@ }, { "cell_type": "markdown", - "id": "ef1a0f30", - "metadata": { - "editable": true - }, + "id": "63681987", + "metadata": {}, "source": [ "## And with loops" ] @@ -3940,12 +3747,18 @@ { "cell_type": "code", "execution_count": 21, - "id": "2bb96160", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ae061106", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f6_for at x = 0.5 is: 3.95703\n", + "The computed derivative of f6_while at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3976,12 +3789,17 @@ { "cell_type": "code", "execution_count": 22, - "id": "8434bcd7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a194eddc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The analytical derivative of f6 at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3996,10 +3814,8 @@ }, { "cell_type": "markdown", - "id": "df3fa84c", - "metadata": { - "editable": true - }, + "id": "8c21cf38", + "metadata": {}, "source": [ "## Using recursion" ] @@ -4007,12 +3823,18 @@ { "cell_type": "code", "execution_count": 23, - "id": "427c3a1f", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3eb55bad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f7 at n = 2 is: 1\n", + "The analytical derivative of f7 at n = 2 is: 1\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4045,20 +3867,16 @@ }, { "cell_type": "markdown", - "id": "6379139b", - "metadata": { - "editable": true - }, + "id": "12fbb13b", + "metadata": {}, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input." ] }, { "cell_type": "markdown", - "id": "82d727a4", - "metadata": { - "editable": true - }, + "id": "19ed9d51", + "metadata": {}, "source": [ "## Unsupported functions\n", "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", @@ -4069,11 +3887,8 @@ { "cell_type": "code", "execution_count": 24, - "id": "fce0115b", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "fb297a92", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4082,29 +3897,25 @@ " x[2] = 3\n", " return x*2\n", "\n", - "f8_grad = grad(f8)\n", + "#f8_grad = grad(f8)\n", "\n", - "x = 8.4\n", + "#x = 8.4\n", "\n", - "print(\"The derivative of f8 is:\",f8_grad(x))" + "#print(\"The derivative of f8 is:\",f8_grad(x))" ] }, { "cell_type": "markdown", - "id": "1dc97436", - "metadata": { - "editable": true - }, + "id": "06d0bc95", + "metadata": {}, "source": [ - "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." + "Here, running this code, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." ] }, { "cell_type": "markdown", - "id": "251cb0ff", - "metadata": { - "editable": true - }, + "id": "9974f300", + "metadata": {}, "source": [ "## The syntax a.dot(b) when finding the dot product" ] @@ -4112,11 +3923,8 @@ { "cell_type": "code", "execution_count": 25, - "id": "9b4aad8e", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "cbb0a202", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4125,19 +3933,17 @@ " b = np.array([1.0,2.0])\n", " return a.dot(b)\n", "\n", - "f9_grad = grad(f9)\n", + "#f9_grad = grad(f9)\n", "\n", - "x = np.array([1.0,0.0])\n", + "#x = np.array([1.0,0.0])\n", "\n", - "print(\"The derivative of f9 is:\",f9_grad(x))" + "#print(\"The derivative of f9 is:\",f9_grad(x))" ] }, { "cell_type": "markdown", - "id": "82401096", - "metadata": { - "editable": true - }, + "id": "7f08b96c", + "metadata": {}, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -4147,12 +3953,17 @@ { "cell_type": "code", "execution_count": 26, - "id": "11f68a91", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cba444cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f9 is: [1. 2.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4172,10 +3983,8 @@ }, { "cell_type": "markdown", - "id": "979bbeda", - "metadata": { - "editable": true - }, + "id": "18e2b174", + "metadata": {}, "source": [ "## Recommended to avoid\n", "The documentation recommends to avoid inplace operations such as" @@ -4184,12 +3993,21 @@ { "cell_type": "code", "execution_count": 27, - "id": "8b90b52c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "69c6914d", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'b' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[27], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[43mb\u001b[49m\n\u001b[1;32m 2\u001b[0m a \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m b\n\u001b[1;32m 3\u001b[0m a\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m b\n", + "\u001b[0;31mNameError\u001b[0m: name 'b' is not defined" + ] + } + ], "source": [ "a += b\n", "a -= b\n", @@ -4199,10 +4017,8 @@ }, { "cell_type": "markdown", - "id": "a88d50f6", - "metadata": { - "editable": true - }, + "id": "600cc052", + "metadata": {}, "source": [ "## Using Autograd with OLS\n", "\n", @@ -4214,12 +4030,37 @@ { "cell_type": "code", "execution_count": 28, - "id": "632ffb09", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cd18340b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.94499279]\n", + " [3.03306538]]\n", + "Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]\n", + "theta from own gd\n", + "[[3.94499279]\n", + " [3.03306538]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_265_1.png" + } + }, + "output_type": "display_data" + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4274,10 +4115,8 @@ }, { "cell_type": "markdown", - "id": "77f1f250", - "metadata": { - "editable": true - }, + "id": "849de571", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4285,12 +4124,86 @@ { "cell_type": "code", "execution_count": 29, - "id": "ed5ad521", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ac458170", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.]\n", + " [3.]]\n", + "Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]\n", + "0 [-20.62275788] [-25.73690387]\n", + "1 [-0.03662823] [0.02925855]\n", + "2 [-0.0342458] [0.02735547]\n", + "3 [-0.03201832] [0.02557617]\n", + "4 [-0.02993573] [0.0239126]\n", + "5 [-0.0279886] [0.02235723]\n", + "6 [-0.02616812] [0.02090304]\n", + "7 [-0.02446604] [0.01954342]\n", + "8 [-0.02287468] [0.01827225]\n", + "9 [-0.02138683] [0.01708375]\n", + "10 [-0.01999575] [0.01597256]\n", + "11 [-0.01869515] [0.01493365]\n", + "12 [-0.01747915] [0.01396231]\n", + "13 [-0.01634224] [0.01305415]\n", + "14 [-0.01527928] [0.01220505]\n", + "15 [-0.01428546] [0.01141119]\n", + "16 [-0.01335628] [0.01066897]\n", + "17 [-0.01248754] [0.00997502]\n", + "18 [-0.0116753] [0.0093262]\n", + "19 [-0.01091589] [0.00871959]\n", + "20 [-0.01020588] [0.00815244]\n", + "21 [-0.00954206] [0.00762217]\n", + "22 [-0.0089214] [0.0071264]\n", + "23 [-0.00834112] [0.00666287]\n", + "24 [-0.00779859] [0.00622949]\n", + "25 [-0.00729134] [0.0058243]\n", + "26 [-0.00681708] [0.00544547]\n", + "27 [-0.00637367] [0.00509128]\n", + "28 [-0.0059591] [0.00476012]\n", + "29 [-0.0055715] [0.0044505]\n", + "theta from own gd\n", + "[[3.98281205]\n", + " [3.0137297 ]]\n", + "0 [-0.00520911] [0.00416103]\n", + "1 [-0.00487029] [0.00389038]\n", + "2 [-0.00445186] [0.00355614]\n", + "3 [-0.00403677] [0.00322456]\n", + "4 [-0.00364967] [0.00291535]\n", + "5 [-0.00329616] [0.00263296]\n", + "6 [-0.00297571] [0.00237699]\n", + "7 [-0.00268602] [0.00214559]\n", + "8 [-0.00242441] [0.00193661]\n", + "9 [-0.00218823] [0.00174795]\n", + "10 [-0.00197505] [0.00157766]\n", + "11 [-0.00178263] [0.00142396]\n", + "12 [-0.00160895] [0.00128523]\n", + "13 [-0.0014522] [0.00116001]\n", + "14 [-0.00131072] [0.001047]\n", + "15 [-0.00118302] [0.00094499]\n", + "16 [-0.00106776] [0.00085292]\n", + "17 [-0.00096373] [0.00076983]\n", + "18 [-0.00086984] [0.00069482]\n", + "19 [-0.00078509] [0.00062713]\n", + "20 [-0.0007086] [0.00056603]\n", + "21 [-0.00063957] [0.00051088]\n", + "22 [-0.00057726] [0.00046111]\n", + "23 [-0.00052102] [0.00041619]\n", + "24 [-0.00047025] [0.00037564]\n", + "25 [-0.00042444] [0.00033904]\n", + "26 [-0.00038309] [0.00030601]\n", + "27 [-0.00034576] [0.0002762]\n", + "28 [-0.00031208] [0.00024929]\n", + "29 [-0.00028167] [0.000225]\n", + "theta from own gd wth momentum\n", + "[[3.99916114]\n", + " [3.00067008]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4349,23 +4262,37 @@ }, { "cell_type": "markdown", - "id": "78643d49", - "metadata": { - "editable": true - }, + "id": "f33ed0dd", + "metadata": {}, "source": [ - "## But noen of these can compete with Newton's method" + "## But none of these can compete with Newton's method" ] }, { "cell_type": "code", "execution_count": 30, - "id": "b6031b96", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e6b06cdb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.26281735]\n", + " [2.84478178]]\n", + "Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]\n", + "0 [-14.67490857] [-18.08539155]\n", + "1 [-4.46170878e-15] [-1.45781905e-14]\n", + "2 [-1.21430643e-15] [-1.24768421e-15]\n", + "3 [4.92661467e-16] [4.50610071e-16]\n", + "4 [4.92661467e-16] [4.50610071e-16]\n", + "beta from own Newton code\n", + "[[4.26281735]\n", + " [2.84478178]]\n" + ] + } + ], "source": [ "# Using Newton's method\n", "from random import random, seed\n", @@ -4409,10 +4336,8 @@ }, { "cell_type": "markdown", - "id": "ac22e7a1", - "metadata": { - "editable": true - }, + "id": "90de8a04", + "metadata": {}, "source": [ "## Including Stochastic Gradient Descent with Autograd\n", "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." @@ -4421,12 +4346,46 @@ { "cell_type": "code", "execution_count": 31, - "id": "4852067a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a010a209", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.0586484]\n", + " [3.0718316]]\n", + "Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]\n", + "theta from own gd\n", + "[[4.0586484]\n", + " [3.0718316]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week39_271_1.png" + } + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta from own sdg\n", + "[[4.02496085]\n", + " [3.12081773]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4505,10 +4464,8 @@ }, { "cell_type": "markdown", - "id": "ba1f3157", - "metadata": { - "editable": true - }, + "id": "18298e5e", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4516,12 +4473,26 @@ { "cell_type": "code", "execution_count": 32, - "id": "c06c4547", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3320d6c6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.96075051]\n", + " [3.02148021]]\n", + "Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]\n", + "theta from own gd\n", + "[[3.95906059]\n", + " [3.02296298]]\n", + "theta from own sdg with momentum\n", + "[[3.95611042]\n", + " [2.99475306]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4594,10 +4565,8 @@ }, { "cell_type": "markdown", - "id": "16b6b2c9", - "metadata": { - "editable": true - }, + "id": "f1411612", + "metadata": {}, "source": [ "## Similar (second order function now) problem but now with AdaGrad" ] @@ -4605,12 +4574,24 @@ { "cell_type": "code", "execution_count": 33, - "id": "d6d3a6ca", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "19414323", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own AdaGrad\n", + "[[2.00025662]\n", + " [2.99802696]\n", + " [4.00167329]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n", "# OLS example\n", @@ -4664,20 +4645,16 @@ }, { "cell_type": "markdown", - "id": "08925601", - "metadata": { - "editable": true - }, + "id": "a77cdfa4", + "metadata": {}, "source": [ "Running this code we note an almost perfect agreement with the results from matrix inversion." ] }, { "cell_type": "markdown", - "id": "cc62acf3", - "metadata": { - "editable": true - }, + "id": "9f488085", + "metadata": {}, "source": [ "## RMSprop for adaptive learning rate with Stochastic Gradient Descent" ] @@ -4685,12 +4662,24 @@ { "cell_type": "code", "execution_count": 34, - "id": "561a26b8", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "6724b3d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own RMSprop\n", + "[[1.99456598]\n", + " [2.99848815]\n", + " [3.99835783]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4750,10 +4739,8 @@ }, { "cell_type": "markdown", - "id": "f2c44a2a", - "metadata": { - "editable": true - }, + "id": "09728e4a", + "metadata": {}, "source": [ "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)" ] @@ -4761,12 +4748,24 @@ { "cell_type": "code", "execution_count": 35, - "id": "c32bd5e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "28aa6aad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own ADAM\n", + "[[1.99989103]\n", + " [3.00042093]\n", + " [3.99954925]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4831,10 +4830,8 @@ }, { "cell_type": "markdown", - "id": "4183d2b1", - "metadata": { - "editable": true - }, + "id": "70fc8bdd", + "metadata": {}, "source": [ "## And Logistic Regression" ] @@ -4842,12 +4839,18 @@ { "cell_type": "code", "execution_count": 36, - "id": "d1a76119", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "f3dde7c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss: 2.772588722239781\n", + "Trained loss: 1.067270675787016\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4886,10 +4889,8 @@ }, { "cell_type": "markdown", - "id": "68fef7c6", - "metadata": { - "editable": true - }, + "id": "b46c449b", + "metadata": {}, "source": [ "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n", "\n", @@ -4905,12 +4906,17 @@ { "cell_type": "code", "execution_count": 37, - "id": "d62a782e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "291c9b6d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.25 0.19661197 0.10499357]\n" + ] + } + ], "source": [ "import jax.numpy as jnp\n", "from jax import grad, jit, vmap\n", @@ -4922,9 +4928,22 @@ "derivative_fn = grad(sum_logistic)\n", "print(derivative_fn(x_small))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e201d58b", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, "language_info": { "codemirror_mode": { "name": "ipython", diff --git a/doc/LectureNotes/_build/jupyter_execute/week39.py b/doc/LectureNotes/_build/jupyter_execute/week39.py index eb85dda4e..c5e936e73 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week39.py +++ b/doc/LectureNotes/_build/jupyter_execute/week39.py @@ -532,7 +532,7 @@ def df(x): return np.array([2*x[0], 6*x[1]]) fig = pt.figure() -ax = fig.gca(projection="3d") +ax = fig.add_subplot(projection = '3d') xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j] fmesh = f(np.array([xmesh, ymesh])) @@ -755,6 +755,7 @@ pt.plot(it_array.T[0], it_array.T[1], "x-") # In[6]: +m = 100 x = 2*np.random.rand(m,1) y = 4+3*x+np.random.randn(m,1) @@ -2029,14 +2030,14 @@ def f8(x): # Assume x is an array x[2] = 3 return x*2 -f8_grad = grad(f8) +#f8_grad = grad(f8) -x = 8.4 +#x = 8.4 -print("The derivative of f8 is:",f8_grad(x)) +#print("The derivative of f8 is:",f8_grad(x)) -# Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible. +# Here, running this code, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible. # ## The syntax a.dot(b) when finding the dot product @@ -2049,11 +2050,11 @@ def f9(a): # Assume a is an array with 2 elements b = np.array([1.0,2.0]) return a.dot(b) -f9_grad = grad(f9) +#f9_grad = grad(f9) -x = np.array([1.0,0.0]) +#x = np.array([1.0,0.0]) -print("The derivative of f9 is:",f9_grad(x)) +#print("The derivative of f9 is:",f9_grad(x)) # Here we are told that the 'dot' function does not belong to Autograd's @@ -2211,7 +2212,7 @@ print("theta from own gd wth momentum") print(theta) -# ## But noen of these can compete with Newton's method +# ## But none of these can compete with Newton's method # In[30]: @@ -2658,3 +2659,9 @@ x_small = jnp.arange(3.) derivative_fn = grad(sum_logistic) print(derivative_fn(x_small)) + +# In[ ]: + + + + diff --git a/doc/LectureNotes/_build/jupyter_execute/week39_153_1.png b/doc/LectureNotes/_build/jupyter_execute/week39_153_1.png new 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b/doc/LectureNotes/week39.ipynb @@ -2,10 +2,8 @@ "cells": [ { "cell_type": "markdown", - "id": "918e6088", - "metadata": { - "editable": true - }, + "id": "0be56d20", + "metadata": {}, "source": [ "\n", @@ -14,10 +12,8 @@ }, { "cell_type": "markdown", - "id": "f6bdc2db", - "metadata": { - "editable": true - }, + "id": "41352012", + "metadata": {}, "source": [ "# Week 39: Optimization and Gradient Methods\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", @@ -27,20 +23,16 @@ }, { "cell_type": "markdown", - "id": "0fd73813", - "metadata": { - "editable": true - }, + "id": "471d9b17", + "metadata": {}, "source": [ "## Plan for week 39, September 23-27, 2024" ] }, { "cell_type": "markdown", - "id": "4659a144", - "metadata": { - "editable": true - }, + "id": "a3f843e5", + "metadata": {}, "source": [ "## Lecture Monday September 23\n", "\n", @@ -67,10 +59,8 @@ }, { "cell_type": "markdown", - "id": "fc1f68ca", - "metadata": { - "editable": true - }, + "id": "b611ff2d", + "metadata": {}, "source": [ "## Lab sessions week 39\n", "\n", @@ -94,10 +84,8 @@ }, { "cell_type": "markdown", - "id": "15869b1d", - "metadata": { - "editable": true - }, + "id": "126f7d60", + "metadata": {}, "source": [ "## Lecture Monday September 23, Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -115,10 +103,8 @@ }, { "cell_type": "markdown", - "id": "cfaf747a", - "metadata": { - "editable": true - }, + "id": "a2682f11", + "metadata": {}, "source": [ "## Revisiting our Logistic Regression case\n", "\n", @@ -132,10 +118,8 @@ }, { "cell_type": "markdown", - "id": "e2850b85", - "metadata": { - "editable": true - }, + "id": "d51c88b5", + "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", @@ -147,20 +131,16 @@ }, { "cell_type": "markdown", - "id": "a73f7a09", - "metadata": { - "editable": true - }, + "id": "4a135362", + "metadata": {}, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$." ] }, { "cell_type": "markdown", - "id": "eee9af50", - "metadata": { - "editable": true - }, + "id": "26444396", + "metadata": {}, "source": [ "## The equations to solve\n", "\n", @@ -173,10 +153,8 @@ }, { "cell_type": "markdown", - "id": "d8a40aeb", - "metadata": { - "editable": true - }, + "id": "9bc5702f", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -185,10 +163,8 @@ }, { "cell_type": "markdown", - "id": "7d24b6f4", - "metadata": { - "editable": true - }, + "id": "a857de8b", + "metadata": {}, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -196,10 +172,8 @@ }, { "cell_type": "markdown", - "id": "da0033f7", - "metadata": { - "editable": true - }, + "id": "dc870dc3", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -208,20 +182,16 @@ }, { "cell_type": "markdown", - "id": "eff96c8f", - "metadata": { - "editable": true - }, + "id": "4001c458", + "metadata": {}, "source": [ "This defines what is called the Hessian matrix." ] }, { "cell_type": "markdown", - "id": "bbf59e32", - "metadata": { - "editable": true - }, + "id": "4f3262b4", + "metadata": {}, "source": [ "## Solving using Newton-Raphson's method\n", "\n", @@ -232,10 +202,8 @@ }, { "cell_type": "markdown", - "id": "67e16976", - "metadata": { - "editable": true - }, + "id": "0d94cee2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -244,20 +212,16 @@ }, { "cell_type": "markdown", - "id": "374d66a6", - "metadata": { - "editable": true - }, + "id": "d92e7b5d", + "metadata": {}, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "id": "ed30dea2", - "metadata": { - "editable": true - }, + "id": "076acdca", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -266,10 +230,8 @@ }, { "cell_type": "markdown", - "id": "f098e947", - "metadata": { - "editable": true - }, + "id": "c37ab3fd", + "metadata": {}, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", @@ -278,10 +240,8 @@ }, { "cell_type": "markdown", - "id": "741d9a60", - "metadata": { - "editable": true - }, + "id": "4f771526", + "metadata": {}, "source": [ "## Brief reminder on Newton-Raphson's method\n", "\n", @@ -298,10 +258,8 @@ }, { "cell_type": "markdown", - "id": "dff616d1", - "metadata": { - "editable": true - }, + "id": "e13dad72", + "metadata": {}, "source": [ "## The equations\n", "\n", @@ -314,10 +272,8 @@ }, { "cell_type": "markdown", - "id": "5d37722e", - "metadata": { - "editable": true - }, + "id": "aff57d4b", + "metadata": {}, "source": [ "\n", "

    \n", @@ -330,10 +286,8 @@ }, { "cell_type": "markdown", - "id": "6706784b", - "metadata": { - "editable": true - }, + "id": "38304c1d", + "metadata": {}, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -341,10 +295,8 @@ }, { "cell_type": "markdown", - "id": "3708fdef", - "metadata": { - "editable": true - }, + "id": "8da576a0", + "metadata": {}, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -353,20 +305,16 @@ }, { "cell_type": "markdown", - "id": "3f607de4", - "metadata": { - "editable": true - }, + "id": "46d9c588", + "metadata": {}, "source": [ "yielding" ] }, { "cell_type": "markdown", - "id": "bdb0ec30", - "metadata": { - "editable": true - }, + "id": "3a3ca58b", + "metadata": {}, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -375,20 +323,16 @@ }, { "cell_type": "markdown", - "id": "e941f0f2", - "metadata": { - "editable": true - }, + "id": "0c9c700f", + "metadata": {}, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "id": "2a7d9a7f", - "metadata": { - "editable": true - }, + "id": "b273b273", + "metadata": {}, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -397,10 +341,8 @@ }, { "cell_type": "markdown", - "id": "9c9bfa29", - "metadata": { - "editable": true - }, + "id": "3e0a875b", + "metadata": {}, "source": [ "## Simple geometric interpretation\n", "\n", @@ -419,10 +361,8 @@ }, { "cell_type": "markdown", - "id": "e6fecd57", - "metadata": { - "editable": true - }, + "id": "727cfd55", + "metadata": {}, "source": [ "## Extending to more than one variable\n", "\n", @@ -432,10 +372,8 @@ }, { "cell_type": "markdown", - "id": "250ae3be", - "metadata": { - "editable": true - }, + "id": "f78349b5", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -445,20 +383,16 @@ }, { "cell_type": "markdown", - "id": "13f76c19", - "metadata": { - "editable": true - }, + "id": "2ee16c9e", + "metadata": {}, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "id": "7c8dabb7", - "metadata": { - "editable": true - }, + "id": "f95fdb8b", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -473,20 +407,16 @@ }, { "cell_type": "markdown", - "id": "74eaf63d", - "metadata": { - "editable": true - }, + "id": "3f039432", + "metadata": {}, "source": [ "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have" ] }, { "cell_type": "markdown", - "id": "4a58d03d", - "metadata": { - "editable": true - }, + "id": "dbd20795", + "metadata": {}, "source": [ "$$\n", "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n", @@ -498,20 +428,16 @@ }, { "cell_type": "markdown", - "id": "ad5a8242", - "metadata": { - "editable": true - }, + "id": "98ba6676", + "metadata": {}, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "id": "2d1a3ad3", - "metadata": { - "editable": true - }, + "id": "ad52dad5", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -522,20 +448,16 @@ }, { "cell_type": "markdown", - "id": "3f664794", - "metadata": { - "editable": true - }, + "id": "cc09e475", + "metadata": {}, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "id": "2605bf0e", - "metadata": { - "editable": true - }, + "id": "7a1c0547", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -546,10 +468,8 @@ }, { "cell_type": "markdown", - "id": "01f6d82b", - "metadata": { - "editable": true - }, + "id": "9fe4208b", + "metadata": {}, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", @@ -561,10 +481,8 @@ }, { "cell_type": "markdown", - "id": "92fbc947", - "metadata": { - "editable": true - }, + "id": "2a81e02b", + "metadata": {}, "source": [ "## Steepest descent\n", "\n", @@ -578,10 +496,8 @@ }, { "cell_type": "markdown", - "id": "4456e346", - "metadata": { - "editable": true - }, + "id": "f90232dd", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -590,10 +506,8 @@ }, { "cell_type": "markdown", - "id": "98859a0d", - "metadata": { - "editable": true - }, + "id": "4fb8b51e", + "metadata": {}, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -604,10 +518,8 @@ }, { "cell_type": "markdown", - "id": "3249ff28", - "metadata": { - "editable": true - }, + "id": "81da0301", + "metadata": {}, "source": [ "## More on Steepest descent\n", "\n", @@ -619,10 +531,8 @@ }, { "cell_type": "markdown", - "id": "bc3514ae", - "metadata": { - "editable": true - }, + "id": "9b1a0014", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -631,10 +541,8 @@ }, { "cell_type": "markdown", - "id": "7dc046a6", - "metadata": { - "editable": true - }, + "id": "52e8d174", + "metadata": {}, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning." @@ -642,10 +550,8 @@ }, { "cell_type": "markdown", - "id": "0b885ad4", - "metadata": { - "editable": true - }, + "id": "be802e47", + "metadata": {}, "source": [ "## The ideal\n", "\n", @@ -670,10 +576,8 @@ }, { "cell_type": "markdown", - "id": "800ed299", - "metadata": { - "editable": true - }, + "id": "c2404539", + "metadata": {}, "source": [ "## The sensitiveness of the gradient descent\n", "\n", @@ -692,10 +596,8 @@ }, { "cell_type": "markdown", - "id": "bfd9b49f", - "metadata": { - "editable": true - }, + "id": "f96c6cdf", + "metadata": {}, "source": [ "## Convex functions\n", "\n", @@ -714,10 +616,8 @@ }, { "cell_type": "markdown", - "id": "7cc0574a", - "metadata": { - "editable": true - }, + "id": "0deb328b", + "metadata": {}, "source": [ "## Convex function\n", "\n", @@ -735,10 +635,8 @@ }, { "cell_type": "markdown", - "id": "a4a7e0d2", - "metadata": { - "editable": true - }, + "id": "74dc1b02", + "metadata": {}, "source": [ "## Conditions on convex functions\n", "\n", @@ -774,10 +672,8 @@ }, { "cell_type": "markdown", - "id": "4ac4f3dd", - "metadata": { - "editable": true - }, + "id": "bc8bc23c", + "metadata": {}, "source": [ "## More on convex functions\n", "\n", @@ -802,10 +698,8 @@ }, { "cell_type": "markdown", - "id": "e2c3e2b8", - "metadata": { - "editable": true - }, + "id": "b004d0d8", + "metadata": {}, "source": [ "## Some simple problems\n", "\n", @@ -832,10 +726,8 @@ }, { "cell_type": "markdown", - "id": "3cbf5677", - "metadata": { - "editable": true - }, + "id": "004c656f", + "metadata": {}, "source": [ "## Standard steepest descent\n", "\n", @@ -852,10 +744,8 @@ }, { "cell_type": "markdown", - "id": "8b46198f", - "metadata": { - "editable": true - }, + "id": "3055088e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -864,20 +754,16 @@ }, { "cell_type": "markdown", - "id": "87174dcb", - "metadata": { - "editable": true - }, + "id": "9d268d89", + "metadata": {}, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "id": "5af2eb1c", - "metadata": { - "editable": true - }, + "id": "c8dbe560", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -886,10 +772,8 @@ }, { "cell_type": "markdown", - "id": "977cfa69", - "metadata": { - "editable": true - }, + "id": "fd2de293", + "metadata": {}, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", @@ -898,10 +782,8 @@ }, { "cell_type": "markdown", - "id": "68fd5ea0", - "metadata": { - "editable": true - }, + "id": "25344346", + "metadata": {}, "source": [ "## Gradient method\n", "\n", @@ -910,10 +792,8 @@ }, { "cell_type": "markdown", - "id": "4e2bae9e", - "metadata": { - "editable": true - }, + "id": "c1b8855c", + "metadata": {}, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -922,10 +802,8 @@ }, { "cell_type": "markdown", - "id": "bcbbad7f", - "metadata": { - "editable": true - }, + "id": "506aceb6", + "metadata": {}, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite." @@ -933,10 +811,8 @@ }, { "cell_type": "markdown", - "id": "67d8e3f3", - "metadata": { - "editable": true - }, + "id": "53b26051", + "metadata": {}, "source": [ "## Steepest descent method\n", "\n", @@ -946,10 +822,8 @@ }, { "cell_type": "markdown", - "id": "7519f74e", - "metadata": { - "editable": true - }, + "id": "06b0db34", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -958,20 +832,16 @@ }, { "cell_type": "markdown", - "id": "f0b6000e", - "metadata": { - "editable": true - }, + "id": "0d9ddd86", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "0a5e83d1", - "metadata": { - "editable": true - }, + "id": "66dff86c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -980,20 +850,16 @@ }, { "cell_type": "markdown", - "id": "fff9b0be", - "metadata": { - "editable": true - }, + "id": "77c18c22", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "2be695a7", - "metadata": { - "editable": true - }, + "id": "9dfad29a", + "metadata": {}, "source": [ "## Steepest descent method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1001,10 +867,8 @@ }, { "cell_type": "markdown", - "id": "1bcf856f", - "metadata": { - "editable": true - }, + "id": "50edf2f9", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1013,10 +877,8 @@ }, { "cell_type": "markdown", - "id": "6dd2c43f", - "metadata": { - "editable": true - }, + "id": "51d84a77", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1025,10 +887,8 @@ }, { "cell_type": "markdown", - "id": "a4d7a932", - "metadata": { - "editable": true - }, + "id": "f3179c0a", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1037,10 +897,8 @@ }, { "cell_type": "markdown", - "id": "20db9bfe", - "metadata": { - "editable": true - }, + "id": "66bc0e76", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$." @@ -1048,10 +906,8 @@ }, { "cell_type": "markdown", - "id": "cde76790", - "metadata": { - "editable": true - }, + "id": "9be63d8b", + "metadata": {}, "source": [ "## Final expressions\n", "We can compute the residual iteratively as" @@ -1059,10 +915,8 @@ }, { "cell_type": "markdown", - "id": "c1ba27a3", - "metadata": { - "editable": true - }, + "id": "07294b6e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1071,20 +925,16 @@ }, { "cell_type": "markdown", - "id": "81525791", - "metadata": { - "editable": true - }, + "id": "5cb13e3a", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "42bd4217", - "metadata": { - "editable": true - }, + "id": "b95b4415", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -1093,20 +943,16 @@ }, { "cell_type": "markdown", - "id": "c1f6672f", - "metadata": { - "editable": true - }, + "id": "90956a95", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "df8c1efa", - "metadata": { - "editable": true - }, + "id": "d4675379", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -1115,20 +961,16 @@ }, { "cell_type": "markdown", - "id": "1b4bf5a8", - "metadata": { - "editable": true - }, + "id": "6e3a1c20", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "e2c3ad13", - "metadata": { - "editable": true - }, + "id": "e9b86a0a", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -1137,20 +979,16 @@ }, { "cell_type": "markdown", - "id": "333026af", - "metadata": { - "editable": true - }, + "id": "a1fd88cc", + "metadata": {}, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "id": "35825027", - "metadata": { - "editable": true - }, + "id": "39f090b1", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n", @@ -1159,10 +997,8 @@ }, { "cell_type": "markdown", - "id": "62866612", - "metadata": { - "editable": true - }, + "id": "0ad69506", + "metadata": {}, "source": [ "## Steepest descent example" ] @@ -1170,12 +1006,30 @@ { "cell_type": "code", "execution_count": 1, - "id": "ba11008c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "4a529fa4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%matplotlib inline\n", "\n", @@ -1194,7 +1048,7 @@ " return np.array([2*x[0], 6*x[1]])\n", "\n", "fig = pt.figure()\n", - "ax = fig.gca(projection=\"3d\")\n", + "ax = fig.add_subplot(projection = '3d')\n", "\n", "xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n", "fmesh = f(np.array([xmesh, ymesh]))\n", @@ -1203,10 +1057,8 @@ }, { "cell_type": "markdown", - "id": "d94f79ff", - "metadata": { - "editable": true - }, + "id": "949a0d1c", + "metadata": {}, "source": [ "And then as countor plot" ] @@ -1214,12 +1066,20 @@ { "cell_type": "code", "execution_count": 2, - "id": "8d03a29a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3b0698ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", @@ -1228,10 +1088,8 @@ }, { "cell_type": "markdown", - "id": "1560ce9e", - "metadata": { - "editable": true - }, + "id": "b3d4208f", + "metadata": {}, "source": [ "Find guesses" ] @@ -1239,11 +1097,8 @@ { "cell_type": "code", "execution_count": 3, - "id": "444dcac8", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "d7e4a182", + "metadata": {}, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -1252,10 +1107,8 @@ }, { "cell_type": "markdown", - "id": "6a3a8ba3", - "metadata": { - "editable": true - }, + "id": "fbc59d26", + "metadata": {}, "source": [ "Run it!" ] @@ -1263,12 +1116,17 @@ { "cell_type": "code", "execution_count": 4, - "id": "96921390", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "18be8fa1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.69230769 -0.38461539]\n" + ] + } + ], "source": [ "def f1d(alpha):\n", " return f(x + alpha*s)\n", @@ -1281,10 +1139,8 @@ }, { "cell_type": "markdown", - "id": "5090d289", - "metadata": { - "editable": true - }, + "id": "7f40f5f6", + "metadata": {}, "source": [ "What happened?" ] @@ -1292,12 +1148,30 @@ { "cell_type": "code", "execution_count": 5, - "id": "ac4b2a89", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "dbdb7d4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", @@ -1307,20 +1181,16 @@ }, { "cell_type": "markdown", - "id": "014335b8", - "metadata": { - "editable": true - }, + "id": "851db164", + "metadata": {}, "source": [ "Note that we did only one iteration here. We can easily add more using our previous guesses." ] }, { "cell_type": "markdown", - "id": "8f2fc479", - "metadata": { - "editable": true - }, + "id": "f1300342", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -1331,10 +1201,8 @@ }, { "cell_type": "markdown", - "id": "c12ed388", - "metadata": { - "editable": true - }, + "id": "15530c95", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -1343,10 +1211,8 @@ }, { "cell_type": "markdown", - "id": "525571bd", - "metadata": { - "editable": true - }, + "id": "35222dc4", + "metadata": {}, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -1354,10 +1220,8 @@ }, { "cell_type": "markdown", - "id": "16ea251e", - "metadata": { - "editable": true - }, + "id": "a5ab4e81", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -1366,10 +1230,8 @@ }, { "cell_type": "markdown", - "id": "bc20e247", - "metadata": { - "editable": true - }, + "id": "922a54c4", + "metadata": {}, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$." @@ -1377,10 +1239,8 @@ }, { "cell_type": "markdown", - "id": "7e393cfd", - "metadata": { - "editable": true - }, + "id": "606d1a71", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "An example is given by the eigenvectors of the matrix" @@ -1388,10 +1248,8 @@ }, { "cell_type": "markdown", - "id": "004102f6", - "metadata": { - "editable": true - }, + "id": "e46ac6fc", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -1400,20 +1258,16 @@ }, { "cell_type": "markdown", - "id": "842e93a3", - "metadata": { - "editable": true - }, + "id": "aec2962a", + "metadata": {}, "source": [ "which is zero unless $i=j$." ] }, { "cell_type": "markdown", - "id": "988aa113", - "metadata": { - "editable": true - }, + "id": "f62eeb16", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n", @@ -1422,10 +1276,8 @@ }, { "cell_type": "markdown", - "id": "6c460be1", - "metadata": { - "editable": true - }, + "id": "bde9cf46", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -1434,10 +1286,8 @@ }, { "cell_type": "markdown", - "id": "1694d645", - "metadata": { - "editable": true - }, + "id": "1b354afe", + "metadata": {}, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -1446,10 +1296,8 @@ }, { "cell_type": "markdown", - "id": "091ad567", - "metadata": { - "editable": true - }, + "id": "a3e7fc78", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -1458,10 +1306,8 @@ }, { "cell_type": "markdown", - "id": "dd3cf73c", - "metadata": { - "editable": true - }, + "id": "9608b5e1", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "The coefficients are given by" @@ -1469,10 +1315,8 @@ }, { "cell_type": "markdown", - "id": "13cf2ad9", - "metadata": { - "editable": true - }, + "id": "d667abb4", + "metadata": {}, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -1481,20 +1325,16 @@ }, { "cell_type": "markdown", - "id": "9bc1ee6e", - "metadata": { - "editable": true - }, + "id": "2b909963", + "metadata": {}, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "id": "05599b4f", - "metadata": { - "editable": true - }, + "id": "0e9960df", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -1503,20 +1343,16 @@ }, { "cell_type": "markdown", - "id": "48dce995", - "metadata": { - "editable": true - }, + "id": "4d334201", + "metadata": {}, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "id": "3ed1d31f", - "metadata": { - "editable": true - }, + "id": "f06c6496", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1525,10 +1361,8 @@ }, { "cell_type": "markdown", - "id": "d53065fb", - "metadata": { - "editable": true - }, + "id": "69adaefe", + "metadata": {}, "source": [ "## Conjugate gradient method and iterations\n", "\n", @@ -1545,10 +1379,8 @@ }, { "cell_type": "markdown", - "id": "1c9e8acd", - "metadata": { - "editable": true - }, + "id": "35cf8e92", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1557,20 +1389,16 @@ }, { "cell_type": "markdown", - "id": "b1ce7e22", - "metadata": { - "editable": true - }, + "id": "686fe37b", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "5a9d580f", - "metadata": { - "editable": true - }, + "id": "b6cdf1da", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1579,20 +1407,16 @@ }, { "cell_type": "markdown", - "id": "bd732814", - "metadata": { - "editable": true - }, + "id": "f03df570", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "a0b6ed43", - "metadata": { - "editable": true - }, + "id": "d2619eaa", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1600,10 +1424,8 @@ }, { "cell_type": "markdown", - "id": "0647b456", - "metadata": { - "editable": true - }, + "id": "7c99b348", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1612,10 +1434,8 @@ }, { "cell_type": "markdown", - "id": "39dd4393", - "metadata": { - "editable": true - }, + "id": "06107635", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1624,10 +1444,8 @@ }, { "cell_type": "markdown", - "id": "5d17f7b6", - "metadata": { - "editable": true - }, + "id": "7d57e70c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1636,10 +1454,8 @@ }, { "cell_type": "markdown", - "id": "7f0fbf0c", - "metadata": { - "editable": true - }, + "id": "d07728a4", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1649,10 +1465,8 @@ }, { "cell_type": "markdown", - "id": "f9d39a67", - "metadata": { - "editable": true - }, + "id": "64a6011d", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:" @@ -1660,10 +1474,8 @@ }, { "cell_type": "markdown", - "id": "75e12e7b", - "metadata": { - "editable": true - }, + "id": "395293fb", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1672,10 +1484,8 @@ }, { "cell_type": "markdown", - "id": "aec178fd", - "metadata": { - "editable": true - }, + "id": "2742cfb7", + "metadata": {}, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1688,10 +1498,8 @@ }, { "cell_type": "markdown", - "id": "d9c2ab58", - "metadata": { - "editable": true - }, + "id": "6bca98e3", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1700,10 +1508,8 @@ }, { "cell_type": "markdown", - "id": "cbe552ed", - "metadata": { - "editable": true - }, + "id": "0b38ac3f", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "We can also compute the residual iteratively as" @@ -1711,10 +1517,8 @@ }, { "cell_type": "markdown", - "id": "82a132bd", - "metadata": { - "editable": true - }, + "id": "0588ed16", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1723,20 +1527,16 @@ }, { "cell_type": "markdown", - "id": "0349d81c", - "metadata": { - "editable": true - }, + "id": "2f7bd339", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "7107cbd5", - "metadata": { - "editable": true - }, + "id": "5d46e7c8", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1745,20 +1545,16 @@ }, { "cell_type": "markdown", - "id": "3a56cd7c", - "metadata": { - "editable": true - }, + "id": "a6dfda96", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "63a24c09", - "metadata": { - "editable": true - }, + "id": "bea30687", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1767,20 +1563,16 @@ }, { "cell_type": "markdown", - "id": "6ef4ea63", - "metadata": { - "editable": true - }, + "id": "ec002ff0", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "c2357533", - "metadata": { - "editable": true - }, + "id": "a45514a5", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1789,10 +1581,8 @@ }, { "cell_type": "markdown", - "id": "61549c12", - "metadata": { - "editable": true - }, + "id": "60756713", + "metadata": {}, "source": [ "## Revisiting our first homework\n", "\n", @@ -1813,23 +1603,19 @@ { "cell_type": "code", "execution_count": 6, - "id": "2bbe00ae", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "9e6108fd", + "metadata": {}, "outputs": [], "source": [ + "m = 100\n", "x = 2*np.random.rand(m,1)\n", "y = 4+3*x+np.random.randn(m,1)" ] }, { "cell_type": "markdown", - "id": "2edbd94a", - "metadata": { - "editable": true - }, + "id": "146e4fe9", + "metadata": {}, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1837,10 +1623,8 @@ }, { "cell_type": "markdown", - "id": "97f601a1", - "metadata": { - "editable": true - }, + "id": "c5c0a7f1", + "metadata": {}, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1849,20 +1633,16 @@ }, { "cell_type": "markdown", - "id": "46f56da5", - "metadata": { - "editable": true - }, + "id": "f5f1aea6", + "metadata": {}, "source": [ "such that" ] }, { "cell_type": "markdown", - "id": "ea40d182", - "metadata": { - "editable": true - }, + "id": "76b1993f", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1871,10 +1651,8 @@ }, { "cell_type": "markdown", - "id": "f1529059", - "metadata": { - "editable": true - }, + "id": "b5a211bb", + "metadata": {}, "source": [ "## Gradient descent example\n", "\n", @@ -1885,10 +1663,8 @@ }, { "cell_type": "markdown", - "id": "ff686b79", - "metadata": { - "editable": true - }, + "id": "4b0b1b01", + "metadata": {}, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1901,20 +1677,16 @@ }, { "cell_type": "markdown", - "id": "e9072325", - "metadata": { - "editable": true - }, + "id": "c5751686", + "metadata": {}, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "id": "b039d2dd", - "metadata": { - "editable": true - }, + "id": "a2d6f6a6", + "metadata": {}, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1923,20 +1695,16 @@ }, { "cell_type": "markdown", - "id": "dc1285b8", - "metadata": { - "editable": true - }, + "id": "af74580d", + "metadata": {}, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized." ] }, { "cell_type": "markdown", - "id": "8d029669", - "metadata": { - "editable": true - }, + "id": "949f8aab", + "metadata": {}, "source": [ "## The derivative of the cost/loss function\n", "\n", @@ -1945,10 +1713,8 @@ }, { "cell_type": "markdown", - "id": "f2b0be18", - "metadata": { - "editable": true - }, + "id": "5e3860a4", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1959,20 +1725,16 @@ }, { "cell_type": "markdown", - "id": "72b959fa", - "metadata": { - "editable": true - }, + "id": "765febad", + "metadata": {}, "source": [ "where $X$ is the design matrix defined above." ] }, { "cell_type": "markdown", - "id": "53db546f", - "metadata": { - "editable": true - }, + "id": "65781e41", + "metadata": {}, "source": [ "## The Hessian matrix\n", "The Hessian matrix of $C(\\beta)$ is given by" @@ -1980,10 +1742,8 @@ }, { "cell_type": "markdown", - "id": "d9799e09", - "metadata": { - "editable": true - }, + "id": "7e1e9714", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -1995,20 +1755,16 @@ }, { "cell_type": "markdown", - "id": "433d7d4e", - "metadata": { - "editable": true - }, + "id": "9d48eebb", + "metadata": {}, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite." ] }, { "cell_type": "markdown", - "id": "8bcfa1d9", - "metadata": { - "editable": true - }, + "id": "fd88e7fd", + "metadata": {}, "source": [ "## Simple program\n", "\n", @@ -2017,10 +1773,8 @@ }, { "cell_type": "markdown", - "id": "9591273f", - "metadata": { - "editable": true - }, + "id": "e12fb5d1", + "metadata": {}, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -2029,10 +1783,8 @@ }, { "cell_type": "markdown", - "id": "ff30e5e6", - "metadata": { - "editable": true - }, + "id": "eeb13498", + "metadata": {}, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -2044,10 +1796,8 @@ }, { "cell_type": "markdown", - "id": "a58e0dda", - "metadata": { - "editable": true - }, + "id": "7ffca923", + "metadata": {}, "source": [ "## Gradient Descent Example\n", "\n", @@ -2057,12 +1807,31 @@ { "cell_type": "code", "execution_count": 7, - "id": "d6da2734", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9321710e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.30768763 4.39313488]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "# Importing various packages\n", @@ -2114,10 +1883,8 @@ }, { "cell_type": "markdown", - "id": "a2f94d89", - "metadata": { - "editable": true - }, + "id": "e65d5b5b", + "metadata": {}, "source": [ "## And a corresponding example using **scikit-learn**" ] @@ -2125,12 +1892,19 @@ { "cell_type": "code", "execution_count": 8, - "id": "f95809e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e73c4b82", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.94758046]\n", + " [2.92347862]]\n", + "[3.94453204] [2.94467121]\n" + ] + } + ], "source": [ "# Importing various packages\n", "from random import random, seed\n", @@ -2152,10 +1926,8 @@ }, { "cell_type": "markdown", - "id": "bcca1a86", - "metadata": { - "editable": true - }, + "id": "0cffa723", + "metadata": {}, "source": [ "## Gradient descent and Ridge\n", "\n", @@ -2164,10 +1936,8 @@ }, { "cell_type": "markdown", - "id": "3f8a3655", - "metadata": { - "editable": true - }, + "id": "e70974bf", + "metadata": {}, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -2176,20 +1946,16 @@ }, { "cell_type": "markdown", - "id": "fe1ae4c5", - "metadata": { - "editable": true - }, + "id": "8e2c0506", + "metadata": {}, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows" ] }, { "cell_type": "markdown", - "id": "75348007", - "metadata": { - "editable": true - }, + "id": "673104d6", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -2200,20 +1966,16 @@ }, { "cell_type": "markdown", - "id": "7b401e23", - "metadata": { - "editable": true - }, + "id": "f5d61a03", + "metadata": {}, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "id": "108955a9", - "metadata": { - "editable": true - }, + "id": "7e9aec7d", + "metadata": {}, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -2222,10 +1984,8 @@ }, { "cell_type": "markdown", - "id": "e81e374d", - "metadata": { - "editable": true - }, + "id": "54248fbe", + "metadata": {}, "source": [ "## The Hessian matrix for Ridge Regression\n", "The Hessian matrix of Ridge Regression for our simple example is given by" @@ -2233,10 +1993,8 @@ }, { "cell_type": "markdown", - "id": "5f670054", - "metadata": { - "editable": true - }, + "id": "0b57c03b", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -2248,10 +2006,8 @@ }, { "cell_type": "markdown", - "id": "44190400", - "metadata": { - "editable": true - }, + "id": "562d6a77", + "metadata": {}, "source": [ "This implies that the Hessian matrix is positive definite, hence the stationary point is a\n", "minimum.\n", @@ -2262,10 +2018,8 @@ }, { "cell_type": "markdown", - "id": "297e1218", - "metadata": { - "editable": true - }, + "id": "018079a6", + "metadata": {}, "source": [ "## Program example for gradient descent with Ridge Regression" ] @@ -2273,12 +2027,31 @@ { "cell_type": "code", "execution_count": 9, - "id": "f39e42bb", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "12f965e7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.32374405 4.06221646]\n", + "[[4.0585026]\n", + " [2.9999519]]\n", + "[[4.05843037]\n", + " [3.00001709]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from random import random, seed\n", "import numpy as np\n", @@ -2334,10 +2107,8 @@ }, { "cell_type": "markdown", - "id": "d84821a4", - "metadata": { - "editable": true - }, + "id": "06107436", + "metadata": {}, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -2356,10 +2127,8 @@ }, { "cell_type": "markdown", - "id": "386582c7", - "metadata": { - "editable": true - }, + "id": "bd3205c7", + "metadata": {}, "source": [ "## Improving gradient descent with momentum\n", "\n", @@ -2369,12 +2138,56 @@ { "cell_type": "code", "execution_count": 10, - "id": "bdd17d18", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "98ec014e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.59779819]) = 0.35736\n", + ">2 f([0.47823856]) = 0.22871\n", + ">3 f([0.38259084]) = 0.14638\n", + ">4 f([0.30607268]) = 0.09368\n", + ">5 f([0.24485814]) = 0.05996\n", + ">6 f([0.19588651]) = 0.03837\n", + ">7 f([0.15670921]) = 0.02456\n", + ">8 f([0.12536737]) = 0.01572\n", + ">9 f([0.10029389]) = 0.01006\n", + ">10 f([0.08023512]) = 0.00644\n", + ">11 f([0.06418809]) = 0.00412\n", + ">12 f([0.05135047]) = 0.00264\n", + ">13 f([0.04108038]) = 0.00169\n", + ">14 f([0.0328643]) = 0.00108\n", + ">15 f([0.02629144]) = 0.00069\n", + ">16 f([0.02103315]) = 0.00044\n", + ">17 f([0.01682652]) = 0.00028\n", + ">18 f([0.01346122]) = 0.00018\n", + ">19 f([0.01076897]) = 0.00012\n", + ">20 f([0.00861518]) = 0.00007\n", + ">21 f([0.00689214]) = 0.00005\n", + ">22 f([0.00551372]) = 0.00003\n", + ">23 f([0.00441097]) = 0.00002\n", + ">24 f([0.00352878]) = 0.00001\n", + ">25 f([0.00282302]) = 0.00001\n", + ">26 f([0.00225842]) = 0.00001\n", + ">27 f([0.00180673]) = 0.00000\n", + ">28 f([0.00144539]) = 0.00000\n", + ">29 f([0.00115631]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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/P78Kr7Gzs4OdnZ050SxSsKcTejR3x57zl/HDvgRMH9xadiQiIrISQgis/tc4sv7ArU1tbm2Rq5k1MqLT6RAaGorIyMhy2yMjI9GrV69KX5OXlweVqvy3UauNjzwWQpjz7a3Sg6XDamv2J0BvsP3jJSKi2nH0QiZOJGdBp1Hhnq6284Teyph9mWbGjBlYunQpli9fjujoaEyfPh3x8fGmyy6zZs3CuHHjTPsPHz4c69atw+LFi3H+/Hns3LkTzzzzDLp16wZ/f9ucFXy1Ie194eaoRVJmAf45fUl2HCIishJlE1eHhfjCzVEnOU3dMusyDQCMGTMG6enpmD9/PpKTkxESEoKNGzciKCgIAJCcnFxuzZEJEyYgOzsbn376KZ577jm4ublh4MCBeOedd2rvKCyYvVaNu7s0wVc7Y7F6bzwGtPWWHYmIiCxcbmEJNpSu4l02/9CWKcIKrpVkZWXB1dUVmZmZcHFxkR3HbKcvZiP8w3+gVinYPXMgvF3sZUciIiILFrEvHi+tPYpgTyf8/Vw/q50vUt33bz6bph609nFG16Zu0BsE1kQlyo5DREQWruwSzZhbA622iJiDZaSelN0fHrEvAQZOZCUioiqcTMnCoYQMaFQK7u0aIDtOvWAZqSd3dfSDs50G8ZfzsPu87T4kkIiIbs73paMig2/xgZez9S9zUR0sI/XEUafBiNJnCqzmiqxERFSJgmI91h0wXs635RVXr8UyUo/K1hz54/hFXM4tkpyGiIgsze/HkpFVUIImbg7o29JTdpx6wzJSj0KauCKkiQuK9AZT8yUiIipz9cRVlcr2J66WYRmpZ2X3i6/eG98gVqAlIqLqOXcpB3tjLkOlAPeHNYyJq2VYRurZyM7+cNCqce5SLvbHXZEdh4iILETEPuOoyIA23vBzdZCcpn6xjNQzZ3st7upofDggJ7ISEREAFJUYsDaq4U1cLcMyIkHZD9rGo8nIzC+WnIaIiGSLPHER6blF8HGxw4A2XrLj1DuWEQm6NnVDGx9nFBQbsL702QNERNRwfb/POFJ+f2ggNOqG99bc8I7YAiiKgge6BQIwzpzmRFYiooYr4XIetp9JA2C8i6YhYhmR5O4uTaDTqBCdnIUjiZmy4xARkSRlE1f7tvJEoLuj5DRysIxI4uaowx0hvgD+G54jIqKGpURvwJooYxkpW/qhIWIZkahsIuuGQ0nILSyRnIaIiOrbllOXcDGrEB5OOgy+xUd2HGlYRiTqHuyO5p5OyC3S45fDSbLjEBFRPfu+dImHe0MDoNM03LfkhnvkFkBRFNNkJa45QkTUsCRn5mPLqVQADXfiahmWEcnuDQ2AVq3gcGImTiRlyY5DRET15Id9iTAIoFuwO1p4NZIdRyqWEck8G9mZrhNyIisRUcOgNwj8sN84cfXBbg17VARgGbEIZTOofzp4AflFeslpiIiorm0/cwkXMvLhYq/BsBA/2XGkYxmxAH1aeiKgsQOyC0qw8Wiy7DhERFTHvt9rHBW5p2sA7LVqyWnkYxmxACqVgjFhxmE6XqohIrJtl7IL8Wf0RQAwrcbd0LGMWIj7wwKhUoB9sVdwNjVbdhwiIqojP0YlosQg0KWpG9r6usiOYxFYRiyEr6s9Brb1BvDf8B0REdkWIQQiSkfAH2zAK65ei2XEgpRNZF17IBGFJZzISkRka3afT0dseh4a2WlwVydOXC3DMmJB+rfxgo+LHa7kFeOP4xdlxyEiolpWNvI9orM/HHUayWksB8uIBdGoVRjNiaxERDbpSm4RNh1LAcBLNNdiGbEwo8MCoSjAzrPpiEvPlR2HiIhqybqDF1CkN6C9vws6BLjKjmNRWEYsTKC7I/q09AQAROzjRFYiIlsghDA9FK/sie30H5YRC/Rg6Q/qmqhEFOsNktMQEdHNOhB/BWdSc+CgVWNkZ3/ZcSwOy4gFGtTOBx5OOlzKLsTfJ1NlxyEiopu0unTi6p0d/eBir5WcxvKwjFggnUaF+8ICAMA0rEdERNYpq6AYvx5JAsCH4lWFZcRCla05su30JSRl5EtOQ0RENbX+UBIKig1o5d0IXZs2lh3HIrGMWKhgTyf0aO4Og4DpMdNERGR9rp64qiiK5DSWiWXEgpVNZP1hXwL0BiE5DRERmetoYiaOJ2VBp1bhni5NZMexWCwjFmxIe1+4OWqRlFmAf85ckh2HiIjMtLp0AcuhIb5o7KSTnMZysYxYMHutGneXNmlOZCUisi65hSXYcMg4cfUBTly9LpYRC1d2qebP6FSkZhVITkNERNX165Ek5BSWoJmHI3o295Adx6KxjFi41j7O6NrUDXqDwJqoRNlxiIiomsrWFhlzKyeu3gjLiBUoWzo4Yl8CDJzISkRk8U6mZOFQQgY0KgX3hQbIjmPxWEaswF0d/eBsp0H85TzsPp8uOw4REd3A96WjIoPa+cDL2U5yGsvHMmIFHHUajCh9lsFqTmQlIrJoBcV6rDtgvKzOiavVwzJiJcomsv5x/CIu5xZJTkNERFX5/VgysgpK0MTNAX1becmOYxVYRqxESBNXhDRxQZHeYGrcRERkecomro4OC4RaxYmr1cEyYkXKnlezem88hOBEViIiS3PuUg72xlyGSgFG38qJq9XFMmJFRnb2h4NWjXOXcrE/7orsOEREdI2IfcZRkf5tvOHn6iA5jfVgGbEizvZaDO/kBwD4Znec5DRERHS1/CI91pQ+2PSBWzlx1RwsI1ZmfK9mAICNR5NxISNfbhgiIjL58UAiruQVI9DdAbe385Edx6qwjFiZ9v6u6NXCA3qDwIqdMbLjEBERAINBYPkO47/Jj/UO5sRVM7GMWKFJfYMBGBfVyS4olpyGiIj+OpmKmLRcONtrcH8YL9GYi2XECvVv7Y0WXk7ILiwxTZYiIiJ5lm4/DwB4qHtTNLLTSE5jfVhGrJBKpWBin+YAgK92xqJEb5CciIio4TqamIl/Yy5Do1IwoXReH5mHZcRK3dO1CTycdLiQkY9Nx1NkxyEiarCW7jCOitzV0Y+389YQy4iVsteq8UiPIADAl9tjuAgaEZEESRn5+PVIMgBgUt/mktNYL5YRKza2ZxB0GhUOJ2QgiougERHVu693xUJvEOjR3B0hTVxlx7FaLCNWzLORHe7p0gQA8GXp5CkiIqofOYUlWFX6JPXJHBW5KTUqI4sWLUJwcDDs7e0RGhqK7du3X3f/wsJCzJ49G0FBQbCzs0OLFi2wfPnyGgWm8ib2Md7m+8eJi4hLz5Wchoio4fhhXwKyC0rQ3MsJA9p4y45j1cwuIxEREXj22Wcxe/ZsHDx4EH379sWwYcMQHx9f5WtGjx6Nv/76C8uWLcOpU6ewevVqtG3b9qaCk1ErH2f0b+MFIWBacIeIiOpWid6A5aULT07sEwwVFzm7KYowc+Zj9+7d0bVrVyxevNi0rV27dhg1ahQWLFhQYf9NmzbhgQcewPnz5+Hu7l6jkFlZWXB1dUVmZiZcXFxq9DVs2Y4zaXhk2b9w0KqxZ9btcHXUyo5ERGTTNh5Nxv9WHkBjRy12zbwdDjq17EgWqbrv32aNjBQVFSEqKgrh4eHltoeHh2PXrl2VvmbDhg0ICwvD//3f/6FJkyZo3bo1nn/+eeTnV/1clcLCQmRlZZX7oKr1bumBtr7OyC/WY+VePkCPiKiulc3TG9sjiEWkFphVRtLS0qDX6+HjU/4BQD4+PkhJqXyti/Pnz2PHjh04duwYfvrpJyxcuBA//vgjnnzyySq/z4IFC+Dq6mr6CAzk0rrXoyiK6Zayr3fFoqiEi6AREdWVqLgrOBifAZ1ahUd6BsmOYxNqNIFVUcpfGxNCVNhWxmAwQFEUrFy5Et26dcMdd9yBDz74ACtWrKhydGTWrFnIzMw0fSQkcMnzGxnRyR/ezna4mFWIX48kyY5DRGSzypZ+H9XFH97O9pLT2AazyoinpyfUanWFUZDU1NQKoyVl/Pz80KRJE7i6/nf/dbt27SCEQGJiYqWvsbOzg4uLS7kPuj6dRoXxpcsQL+UiaEREdSI+PQ+bS1e9LnssB908s8qITqdDaGgoIiMjy22PjIxEr169Kn1N7969kZSUhJycHNO206dPQ6VSISAgoAaRqSoPd28KB60aJ5KzsPtcuuw4REQ2Z/nOGBgEcFtrL7TxdZYdx2aYfZlmxowZWLp0KZYvX47o6GhMnz4d8fHxmDp1KgDjJZZx48aZ9n/ooYfg4eGBRx99FCdOnMA///yDF154AY899hgcHLiGf21yc9ThvlBjwVvK23yJiGpVZn4xfthvnDYwqXSNJ6odZj/neMyYMUhPT8f8+fORnJyMkJAQbNy4EUFBxkk8ycnJ5dYcadSoESIjI/H0008jLCwMHh4eGD16NN54443aOwoyeaxPML77Nw5/n0zF2dRstPRmcyciqg2r98Yjr0iPNj7O6NvKU3Ycm2L2OiMycJ0R80z+Zj8iT1zEg92aYsE9HWTHISKyesV6A/q+swUpWQX4v/s6YnQY7/KsjjpZZ4SsQ9kzEtYdSER6TqHkNERE1u+3I8lIySqAZyM7jOzsLzuOzWEZsUG3NmuMjgGuKCwx4Ls9VS/TT0RENyaEwNIdxtt5x/cMgp2Gi5zVNpYRG3T1Imjf7olFQbFeciIiIuu15/xlHLuQBXutCg/34CJndYFlxEYNC/GFv6s90nKKsP7QBdlxiIis1rLSUZF7uwbA3UknOY1tYhmxUVq1Co/2Nt56xkXQiIhqJvbwKeRu+hO+WWmYyNt56wzLiA0b0y0Qjew0OJOag22nL8mOQ0RkXZYtQ9Mu7bD6+5ex6/PH0HxDhOxENotlxIa52Gsx5lbj7WdLt3MRNCKiaktMhHj8cahKR5VVwgBMmQJU8RgTujksIzZuQq9mUCnAjrNpiE7Okh2HiMg6nDkDxXDNE9D1euDsWTl5bBzLiI0LdHfEsA5+ADg6QkRUXQXNmqPCTDu1GmjZUkYcm8cy0gCUPUNhw+ELSM0qkJyGiMjybf33DJSrN6jVwJIlAB/wWidYRhqALk0bIyyoMYr1Al/vjpUdh4jIogkh4Pj2mwCA2B79gS1bgNhYYOJEqblsGctIA1G2CNrKf+ORV1QiOQ0RkeWK+m07+hzeBgDw+Ph9oH9/jojUMZaRBmLwLT4I8nBERl4x1kZxNjgRUVVK5s2HCgLHe4XD+dausuM0CCwjDYRapeCx0kXQlu2IgcHARdCIiK4Vs/VfdNv/NwDA453XJadpOFhGGpD7QgPgYq9BbHoe/oy+KDsOEZHFyXx5DlQQONDtdvj26SY7ToPBMtKAONlpTA954m2+RETlpe89gI67IwEA9q/Pk5ymYWEZaWDG92wGjUrB3tjLOJyQITsOEZHFuPTiq1BBYHfn/rglvLfsOA0Ky0gD4+tqjxGd/AEAS3dwdISICAAKDh9F639+BwDoX3lFcpqGh2WkAZrY1ziRdePRZFzIyJechohIvpQXZkMlBLaG9EXPuwfKjtPgsIw0QO39XdGrhQf0BoEVOzk6QkQNm+HYcTT981cAQMZzM6FWKTd4BdU2lpEGalLp6Mj3exOQXVAsOQ0RkTypL74ClRCIbNcbgx4Mlx2nQWIZaaD6t/ZGCy8nZBeWIGJfguw4RERyREfDe9N6AED8k8+hkZ1GcqCGiWWkgVKpFEzsY1wi/qudsSjRG27wCiIi25Mxaw5UQmBz656445GhsuM0WCwjDdg9XZvA3UmHCxn52HQ8RXYcIqL6FR0Nlw1rAQBHHn0Gfq4OkgM1XCwjDZi9Vo1HShdB+3J7DITgEvFE1HDkvToXKiGwqXVPDBs7THacBo1lpIEb2yMIOo0KhxMyEBV3RXYcIqL6cfIkHNatAQBsGT0FIU1cJQdq2FhGGjgvZzvc3bkJAC4RT0QNR/HceVCEwOZWPTD4Qc4VkY1lhEyLoG0+kYK49FzJaYiI6tjJk9D8EAEAWHvnYxjY1ltyIGIZIbT2cUa/1l4QwnhnDRGRLTO8/oZpVOS2MeFQcZEz6VhGCAAwua/xNt8f9icgPadQchoiojpy8iSU71cDAL66fSzu7RogORABLCNUqndLD4Q0cUFekR5L/jkvOw4RUZ0wvP46FIMBf7TqgR73DoKDTi07EoFlhEopioLnBrcBAHy9KxapWQWSExER1bJTp6B8/z0AYNntYzGxT7DkQFSGZYRM+rfxQmhQYxSWGPDZlrOy4xAR1aqyUZHIlt0x4IEhcLbXyo5EpVhGyERRFDwX3hoAsGpvPBKv5ElORERUS06dAlYb54qsGDwe43oGSQ5EV2MZoXJ6tfBErxYeKNYLfPo3R0eIyDbo578OVemoyKCHh8JRxwfiWRKWEaqgbHRkTVQiYtO47ggRWbnTp0130Hw3ZAIe7NZUciC6FssIVRAa5I4BbbygNwgs/PO07DhERDelZP780lGRbhgy9g7Ya3kHjaVhGaFKzSi9s2b94SScvpgtOQ0RUQ2dPg1V6VyRiGGP4f4writiiVhGqFIdAlwxtL0vhAA+jOToCBFZpyLTXJFuGDb+TmjVfNuzRDwrVKUZ4a2hKMDvx1Jw7EKm7DhEROY5cwaa1asAAGvvegyjujSRHIiqwjJCVWrt44yRnfwBAB9wdISIrEzhXONckT9b3Irhj46Ams+gsVgsI3Rd0wa1hlql4O+TqYiKuyI7DhFR9Zw5A+33xlGRDSMnY1iIr+RAdD0sI3RdwZ5OuK/0QVIfRJ6SnIaIqHoKrhoVGTFxBJ/Ma+FYRuiGnr69JbRqBTvPpmPXuTTZcYiIru/sWehK1xX5/Z4puL2dt+RAdCMsI3RDAY0dTYsEvf/HaQghJCciIqpa3px5UBn0+KvFrRg1eQQUhaMilo5lhKrlyQEtYadRISruCraeviQ7DhFR5c6ehV2EcVTkr/unoE9LT8mBqDpYRqhafFzsTQ+Wev+PUxwdISKLlDNnHtQGPf5uHoZRj9/NURErwTJC1Ta1Xws46dQ4diELm49flB2HiKi8s2fhUDoq8s+D/0O3YHfJgai6WEao2jwa2eGxPsEAjHfW6A0cHSEiy5H16lzTqMjdU+6WHYfMwDJCZpnUtzlc7DU4fTEHvx5Jkh2HiMjo3Dk4/fA9AGD3I0+hU6Cb3DxkFpYRMourgxaP39YcALDwzzMo0RskJyIiAjJmG0dFtjQPxT1TOSpibVhGyGwTegfD3UmHmLRcrDtwQXYcImrozp2D8xrjXJH9459GOz8XyYHIXCwjZLZGdho80a8FAOCjv86gsEQvORERNWTppaMiW5uH4p4n7pUdh2qAZYRq5JEeQfB2tsOFjHz8sC9BdhwiaqjOn4db6ajIkYnPooVXI8mBqCZYRqhGHHRqPDWwJQDgk7/PoqCYoyNEVP9SZ86B2qDHtuahuHvqPbLjUA2xjFCNjbk1EE3cHJCaXYjv9sTJjkNEDYw4dw4ea4130ERPfhaB7o6SE1FN1aiMLFq0CMHBwbC3t0doaCi2b99erdft3LkTGo0GnTt3rsm3JQtjp1Fj2u2tAACLtp5DbmGJ5ERE1JBcnPka1AY9/mkeipGcK2LVzC4jERERePbZZzF79mwcPHgQffv2xbBhwxAfH3/d12VmZmLcuHG4/fbbaxyWLM89XZugmYcjLucWYcWuWNlxiKiBEOfOwXOdcVTkzNTn4OfqIDkR3Qyzy8gHH3yAiRMnYtKkSWjXrh0WLlyIwMBALF68+LqvmzJlCh566CH07NmzxmHJ8mjUKkwf3BoAsGTbOWTmF0tOREQNQdJLc6Ax6LG9eShGcK6I1TOrjBQVFSEqKgrh4eHltoeHh2PXrl1Vvu6rr77CuXPn8Nprr1Xr+xQWFiIrK6vcB1muuzr6o7VPI2QVlGDp9vOy4xCRjTOcOw+fnyIAAHFPPQcvZzvJiehmmVVG0tLSoNfr4ePjU267j48PUlJSKn3NmTNnMHPmTKxcuRIajaZa32fBggVwdXU1fQQGBpoTk+qZWqVgRunoyPIdMUjPKZSciIhsWeKLr0Jj0GNn8664awrnitiCGk1gvfaRzEKISh/TrNfr8dBDD2HevHlo3bp1tb/+rFmzkJmZafpISOA6FpZuSHtftPd3QW6RHkv+4egIEdWNknPn4f+zcVTkwjMvws1RJzkR1QazyoinpyfUanWFUZDU1NQKoyUAkJ2djf379+Opp56CRqOBRqPB/PnzcfjwYWg0Gvz999+Vfh87Ozu4uLiU+yDLpigKng9vAwD4elcsUrMKJCciIluU8IJxVGRXi1AMm8K5IrbCrDKi0+kQGhqKyMjIctsjIyPRq1evCvu7uLjg6NGjOHTokOlj6tSpaNOmDQ4dOoTu3bvfXHqyKP3beKFrUzcUlhjw2ZazsuMQkY0pPncegeuNoyIXp78EZ3ut5ERUW6o3ieMqM2bMwNixYxEWFoaePXviiy++QHx8PKZOnQrAeInlwoUL+Oabb6BSqRASElLu9d7e3rC3t6+wnayfoih4fkgbPPTlv1i1Nx6Tb2uOgMZchIiIakfcc6+gpUGPPS26YshkPpnXlphdRsaMGYP09HTMnz8fycnJCAkJwcaNGxEUFAQASE5OvuGaI2S7erXwRK8WHth1Lh2f/HUW79zXUXYkIrIBhWfOodkvPwAALj83E446s9++yIIpQgghO8SNZGVlwdXVFZmZmZw/YgWi4i7j3sW7oVYp+HNGPwR7OsmORERW7uTIh9B2w2rsbRmKTtH/wk6jlh2JqqG67998Ng3VutAgdwxo4wW9QeCjP0/LjkNEVi7/zDm0/NU4KpL54iwWERvEMkJ1YsZg45016w8n4fTFbMlpiMianZ/xCjQGPfa1DEX/xzhXxBaxjFCd6BDgiqHtfSEE8GEkR0eIqGayT51F640/AgDyZr4MrZpvW7aIZ5XqzIzw1lAU4PdjKTh2IVN2HCKyQjHPvQKtoQRRrULR51GOitgqlhGqM619nDGykz8A4AOOjhCRmbK2bMctG9cAAApffgVqVcWVvsk2sIxQnZo2qDXUKgV/n0xFVNwV2XGIyFosWwbngbdBIwwQAHoUp8lORHWIZYTqVLCnE+7rGgAAeP3XEzAYLP5OciKSLTER4vHHUTYOogBQPTEVSEyUmYrqEMsI1bnpg1vDSafGoYQMROznQw+J6PrE6dNQDIbyG/V64CwfM2GrWEaozvm62mP6YONTm9/+/STScwolJyIiS3Z097GKG9VqoGXL+g9D9YJlhOrFhF7N0NbXGZn5xXhn00nZcYjIQuVdyYTXe28BAIRSeqFGrQaWLAECAiQmo7rEMkL1QqNW4c27jQ9H/GF/IvbHXpaciIgs0ZHHn4NfxkWkuHmj4MhxYMsWIDYWmDhRdjSqQywjVG9Cg9wxJiwQAPDKz8dQojfc4BVE1JDEbdmNsLVfAQBS3noPDiHtgP79OSLSALCMUL16aVhbuDlqcTIlGyt2xcqOQ0QWQuj1KJw4GRphQFTYQHR+YqzsSFSPWEaoXrk76TBzaFsAxmXikzPzJSciIktw6NX/Q+uY48jROcBvxRLZcaiesYxQvRsdFoiuTd2QW6THG79Gy45DRJJlnYtHyw/fBAAcnPI8/NvzrpmGhmWE6p1KpeCNUR2gUoDfjiZj2+lLsiMRkURxE6bAuSAXpwLboPu7r8qOQxKwjJAUt/i7YEKvYADAa+uPoaBYLzkREclw/tsf0WHHJugVFQo/WQSdnVZ2JJKAZYSkmT64Fbyd7RCbnocl287LjkNE9UyfkwvH6c8AALYPexAdRw6UnIhkYRkhaZzttXj1rlsAAJ9tPYu49FzJiYioPkX/7wX4picjxcUT7ZculB2HJGIZIanu6uiHPi09UVRiwJz1xyEEH6RH1BBc/vcA2qz8AgAQ/fKb8PLzlJyIZGIZIakURcH8ke2hU6uw7fQlbDqWIjsSEdU1gwGZ4x6D1qDH7o59cdsLk2UnIslYRki65l6NMLVfcwDAvF9OIKewRHIiIqpL5xcsRPDpw8jROcDli0VQqxTZkUgylhGyCP8b0BKB7g5IySrAx3+dkR2HiOpI0YVkeL35GgBg28NPoX33EMmJyBKwjJBFsNeqMX+E8R+lZTticColW3IiIqoLcROmwjk/B9F+LdFn4TzZcchCsIyQxRjQ1htD2vtAbxB45eejnMxKZGPSfvoVrf7cAL2iQtI7C+Hq4iA7ElkIlhGyKHOGt4eDVo19sVew9sAF2XGIqLbk58Mw9QkAwOb+92LgI3dIDkSWhGWELEoTNwdMG9QKAPDWxmhk5BVJTkREtSF2+svwTk1EirMHWi35EIrCSav0H5YRsjgT+wSjlXcjXM4twv9tPiU7DhHdpILDR9Fk6acAgJ1Pz0GrVk0kJyJLwzJCFkerVuGNUcbJrKv3xuNg/BXJiYioxgwGpD38KLT6Emxv2xNDX31CdiKyQCwjZJG6N/fAPV2bQAjglZ+PQW/gZFYia5T68WIEHI9CrtYe+o8/gpM9H4RHFbGMkMWaNawdXOw1OJ6Uhe/2xMmOQ0RmEhcvwnH2ywCAX+5+HP0GhUlORJaKZYQslpezHV4Y2hYA8N7mU0jNLpCciIjMkTjpSTTKy0K0d3P0+vh1TlqlKrGMkEV7qFtTdAxwRXZhCd76LVp2HCKqprzfNyPw17UwQMGROe+gqY+L7EhkwVhGyKKpVQreHNUBigL8fCgJu86myY5ERDdSUID8SVMAAOt7jcTIx++WHIgsHcsIWbwOAa4Y2yMIAPDK+mMoKjFITkRE15P68mvwSIrDxUbu8P74Pdhr1bIjkYVjGSGr8Fx4G3g20uH8pVx8uf287DhEVAXDiWg0/vgDAMAvj72I3qEtJCcia8AyQlbB1UGL2Xe2AwB88vcZJFzOk5yIiCoQAmljH4NWX4JtLW/FXfOekZ2IrATLCFmNUZ2boHuwOwqKDZj3ywnZcYjoGjlfLIP3gT3I19gh+c334OvGB+FR9bCMkNVQFAVvjAqBRqXgz+iLiDxxUXYkIiqTlgblhRcAACuHTsB99/aRHIisCcsIWZVWPs6YfFtzAMDcDceRV1QiORERAUDaE8/AKTsD0V7N0OXDedCo+fZC1cefFrI6Tw9siSZuDriQkY9P/z4rOw5Rg6f/6294/rgaBij4e9p8hLb0kR2JrAzLCFkdR50Grw2/BQDw5fbzOJuaLTkRUQNWWIjsRycBAH4MuwMPPjtGciCyRiwjZJUG3+KD29t6o1gv8OrPxyEEH6RHJEP2vDfhlhCDS05uUL+9AO5OOtmRyAqxjJBVUhQFc0e0h51Ghd3n0/HVzljZkYgaHP3JU7B/920AwNdjpuPuASGSE5G1YhkhqxXo7oiX7zCuPbLg92gcTsiQG4ioIRECSQ9NgLakGNubh2LUW89CpeKD8KhmWEbIqo3rGYSh7X1RrBd4avUBZOYXy45E1CCc/eBzBB7cgwKNDrkffISWfBAe3QSWEbJqiqLgnfs6ItDdAQmX8zFz7RHOHyGqY+lxSfCYMwsA8NfoqRg6srfkRGTtWEbI6rk6aPHpg12hVSv4/VgKvt0TJzsSkc0yGASOPTIVjfMyEePbDAO+eFt2JLIBLCNkEzoFumHmMOP8kTd+jcaxC5mSExHZps3zP0W/Hb8AANRffAFHJy75TjePZYRsxmO9m2FQOx8U6Q14ctUBZBdw/ghRbYp9830MLX34nQDQNDVebiCyGSwjZDMURcF793dEEzcHxKXnYda6o5w/QlRLrpw+j6BXnkfZ/TIKAEyZAiQmSkxFtoJlhGyKm6MOHz/YBRqVgl+PJGP13gTZkYisnsEg8M8Lb6HCjbt6PXCWj2Sgm8cyQjYnNKgxXhjSBgAw75fjiE7OkpyIyLr9+N1mDN74XcVPqNVAy5b1H4hsDssI2aTJfZtjQBsvFJYY54/kFvLpvkQ1ceh4HEKnT4ZjSSEyg1oYCwhg/HPJEiAgQG5AsgksI2STVCoF74/uDF8Xe5y/lItXfj7G+SNEZsrILcSVB8aixeVEXHH3gcu/O4HYWGDLFuOfEyfKjkg2gmWEbJa7kw6fPNQFapWCnw5ewJr9nGhHVF1CCPwx8UUMOLYdxWoNdD+theLjYxwJ6d+fIyJUq2pURhYtWoTg4GDY29sjNDQU27dvr3LfdevWYfDgwfDy8oKLiwt69uyJzZs31zgwkTlubeaOGYNbAwDmbDiG0xezJScisg4bP/0e9/7wKQDg0uvvwOk2rrJKdcfsMhIREYFnn30Ws2fPxsGDB9G3b18MGzYM8fGV32/+zz//YPDgwdi4cSOioqIwYMAADB8+HAcPHrzp8ETV8US/FujbyhMFxQY8ufIA8oo4f4Toeo7vO4HuM/8HtTDg3NC74T9zuuxIZOMUYeaF9O7du6Nr165YvHixaVu7du0watQoLFiwoFpfo3379hgzZgzmzJlTrf2zsrLg6uqKzMxMuLjwYUxkvrScQtzx0XakZhfi/tAAvHt/J9mRiCxSZmYu4jt2Q4f4E0gMbIUm0QehODnJjkVWqrrv32aNjBQVFSEqKgrh4eHltoeHh2PXrl3V+hoGgwHZ2dlwd3evcp/CwkJkZWWV+yC6GZ6N7PDRA12gUoA1UYlYd4DzR4iuJYTAgfsnokP8CWTbO8H19w0sIlQvzCojaWlp0Ov18PHxKbfdx8cHKSkp1foa77//PnJzczF69Ogq91mwYAFcXV1NH4GBgebEJKpUzxYemHa7cf7IKz8fw9nUHMmJiCzLjnkfYUBkBAAg7bMv4dy+reRE1FDUaAKropRfh08IUWFbZVavXo25c+ciIiIC3t7eVe43a9YsZGZmmj4SEriKJtWOpwa2RK8WHsgr0uOpVQdQUKyXHYnIIpz5cxdC35oJADg07kkEP/ag5ETUkJhVRjw9PaFWqyuMgqSmplYYLblWREQEJk6ciB9++AGDBg267r52dnZwcXEp90FUG9QqBQsf6AzPRnY4mZKNeb8clx2JSLrsi2lweGA0HIsLcbx9d3RatlB2JGpgzCojOp0OoaGhiIyMLLc9MjISvXr1qvJ1q1evxoQJE7Bq1SrceeedNUtKVEu8ne3x0QOdoSjA6r0JWH/oguxIRNIIvR7n77wPAekXkOLmjYCN66BoNLJjUQNj9mWaGTNmYOnSpVi+fDmio6Mxffp0xMfHY+rUqQCMl1jGjRtn2n/16tUYN24c3n//ffTo0QMpKSlISUlBZmZm7R0FkZl6t/TE0wOMz9R4ed1RxKTlSk5EJMfhZ2ajU9Q2FKk1yPhmFVyb+suORA2Q2WVkzJgxWLhwIebPn4/OnTvjn3/+wcaNGxEUFAQASE5OLrfmyJIlS1BSUoInn3wSfn5+po9p06bV3lEQ1cC0Qa3RPdgduUV6PLmS80eo4Yn7YQM6LH4XALDn2bloO/x2yYmooTJ7nREZuM4I1ZWLWQUY9tF2XM4twtgeQXh9VIjsSET1Iu9sDIo6d4Fbbia29xmO3lt/hkrNJ4RQ7aqTdUaIbI2Piz0+GG1cAO3bPXHYeDRZciKiuicKCpA6bCTccjNxyq8l2v/0LYsIScWfPmrw+rfxxhP9WwAAXvrxCOLSOX+EbNu5Rx5Hs7NHkWHfCIXfR8Dd01V2JGrgWEaIADw3uDXCghoju7AET606iMISzh8h25T8yRK0XPstDFCwY86H6HhbV9mRiFhGiABAo1bh4we7wM1Ri6MXMrFg40nZkYhqXf6+/XCf8QwAYP2IibjjpYmSExEZsYwQlfJ3czDNH1mxKxabj1fvEQdEVuHKFeQNvxt2JUXY1epW9P32Y6hUN145m6g+sIwQXWVgWx88fltzAMALaw4j4XKe5EREtcBgQPLI0fC4mIgEVx9ov18FTxcH2amITFhGiK7xwpA26NLUDVkFJZj49T5cyS2SHYnopiQ8/wr8tv+JQrUWO97+HLd2bSk7ElE5LCNE19CqVfj0oa7wcbHD6Ys5GLv8X2TmF8uORVQjZ75biyYfvg0AWDX+JYx+fKTkREQVsYwQVaKJmwNWTuoBDycdjl3IwqNf7UVuYYnsWETVl5iI+EXL4D15PFQQ2NJ3BB78fC7UnCdCFohlhKgKLb0b4duJ3eHqoMWB+AxM+no/l4wn67BsGURQEJo+OQmuBblIdfdB919Xwl6rlp2MqFIsI0TXcYu/C75+rBsa2Wmw+3w6pn4XxTVIyLIlJkI8/jgUg8G0ySvjEhyzMuRlIroBlhGiG+gc6IblE26FvVaFracuYdrqQyjRG278QiIJLkUdKVdEABj/fvaspEREN8YyQlQN3YLd8eW4MOjUKmw6noLn1hyG3mDxz5ikBuZiZj62v72k4ifUaqAl76Ahy8UyQlRNfVt5YdHDXaFRKVh/KAmzfzoKK3joNTUQ6TmF2Hz/E7hnzwYAgFBKJ6qq1cCSJUBAgMR0RNfHMkJkhkG3+OCjB7pApQDf70vAvF9OsJCQdJl5xfjlgacxLvJrAMCVN9+BEh8PbNkCxMYCE7nsO1k2jewARNbmzo5+yC/uhOfXHMaKXbFw0Knx4pA2UBTeMkn1L7ugGOsefhaP/vYlACD91fnwePlF4yc5GkJWgiMjRDVwX2gA3hgVAgBYvPUcPv2bkwOp/uUX6fHjuBfx6M+LAABpL8yGx/xXJaciMh/LCFENPdIjCK/c2Q4A8H7kaSzdfl5yImpICor1WD1pNh5dsxAAkDrteXj+3xtyQxHVEMsI0U2Y1Lc5nhvcGgDwxm/R+G5PnORE1BAU6w1YPXUuHvv2HQBAypSn4f3h/0lORVRzLCNEN+mpgS3xRP8WAIBXfj6GH6MSJSciW6Y3CKx8+i2MX/4mACBpwuPwXfwRwDlLZMVYRohukqIoeHFIG0zo1QwA8OKPh/HrkSS5ocgmGQwCK597F2M/fw0qCFx4cAL8l3/OIkJWj2WEqBYoioI5d92CB24NhEEAz35/CH+euCg7FtkQIQRWv/wRHvpoFtTCgIR7HkKT75axiJBNYBkhqiUqlYI37+6AkZ39UWIQ+N/KA9h+5pLsWGQDhBD4Ye5i3P/uC9AIAxLuvBeBa74FVPwnnGwDf5KJapFapeD9+zthSHsfFOkNmPzNfuyNuSw7Flm5dW8vx6g3p0FnKEFc+AgEro9gESGbwp9molqmUavw8YNd0L+NFwqKDXhsxT4cSsiQHYus1IYPvsOdc/4HO30JYvsNQdCvPxqXeCeyISwjRHXATqPG54+EomdzD+QUlmDcsn9xIilLdiyyMhsXRWDQzEmwLylCbK+BaPbHBkCrlR2LqNaxjBDVEXutGkvHh6FrUzdkFZRg7LJ/cTY1W3YssgaJiTjwwuvo9+wEOBYXIiasL5r9vRHQ6WQnI6oTLCNEdcjJToMVj3VDSBMXpOcW4eGl/yIuPVd2LLJky5ZBNG2Kru/NgVNxAS4FNEezbZsAOzvZyYjqDMsIUR1zsdfim8e6o7VPI1zMKsRDX/6LCxn5smORJUpMhJg8GcpVT4L2TI6DcpmToMm2sYwQ1QN3Jx2+m9QdwZ5OuJCRj4e/3INzl3JkxyJLIgTOvTS3XBEBAEWvB87yQYxk21hGiOqJt7M9Vk7qjoDGDohNz8PwT3bgp4NcOp6Agtx87B06Bi1WLav4SbUaaNmy/kMR1SOWEaJ65O/mgHVP9ELP5h7IK9JjesRhvPjjYeQX6WVHI0lio2NwplNPdPtjDQxQcLLPEIiyW3fVamDJEiAgQG5IojrGMkJUz7xd7PHdpO6YdnsrKArww/5EjPxsB85c5J02Dc3fEZHQ9uyBDucOI8fOEce/WIm22zdBiY0FtmwBYmOBiRNlxySqc4oQ11ygtEBZWVlwdXVFZmYmXFxcZMchqjW7zqZhWsQhXMouhL1WhddHhuD+sEDZsaiO5RfpsWb2R7j3o9lwKi5AsncAtL/+As9bO8uORlSrqvv+zZERIol6tfTExmf6ok9LTxQUG/DCj0cw44dDyC0skR2N6sjZlEysGTEZ4957Dk7FBYjt2hveJw6ziFCDxjJCJJmXsx2+eawbng9vDZUCrDtwASM+3YHoZK7Yamt+2nEaZwfehXGbvwIAJE2Ygmb/boXaw11yMiK5WEaILIBKpeCpga2wenIP+LjY4dylXIz6bCdW/RsPK7iSSjeQW1iC+Yt+R+t7h2Fo9A6UqDXI+uxz+H/1OaDRyI5HJB3njBBZmPScQsz44TC2nb4EABjeyR9v3R0CZ3s+k8TqJCYi/t9DWPrLATyz5gN45mUiz80Ddht+hrpvH9npiOpcdd+/WUaILJDBIPDF9vN4d/Mp6A0CzTwc8elDXRHSxFV2NKomsXQpMGUKFIMBAoACIPeWDnD6/VegaVPZ8YjqBcsIkQ2IiruMp1cdRFJmAXRqFV69qx0e6REERVFkR6PryD0XC4dWLaASBtM2oShQTp4EWreWmIyofvFuGiIbEBrkjt+e6YtB7bxRpDfg1fXH8eSqA8gqKJYdjapwPCkTX01/t1wRAWBc5j0pSVIqIsvGMkJk4Ro76fDluDC8cmc7aFQKNh5NwZ0fb8fhhAzZ0egqQgis/vMYDg1/GE/9sqjiDlzWnahKLCNEVkBRFEzq2xw/PtELAY0dkHA5H/d9vgvLd8TwbhsLkFVQjE9nLULfewfi4QO/AQCK+/Q1FhCAy7oT3QDnjBBZmcz8Yrz442FsPn4RADD4Fh+8e19HuDnqJCdrmI4dj0PchCdw5/7fAQBZfoFw/mY5lEGDgMRE4xN3W7ZkEaEGiRNYiWyYEALf7I7Dm79Fo0hvQBM3B3zyUBd0bdpYdrQGQwiBP/9vGTq8MRO+OekwKArSJkyG98fvA40ayY5HZBFYRogagKOJmXhq9QHEpedBo1Lw4tA2mNSnOVQq3m1TZxITkbtjD06/+ym6HNgGAEjxbYpG336NRoP6y81GZGFYRogaiKyCYsxadxS/HUkGAHQOdMPjtzXHkPa+ULOU1Kq8RUvg8NQTxjtjABig4PhDkxHy5YdQHB0lpyOyPCwjRA2IEAKr9sZj/i8nUFhivKU00N0Bj/YKxuhbA9HIjkuO34y4tBzsf+sz3PPhTFxd74RKBSUujvNBiKrAMkLUAKVmF+Db3XH4bk8cruQZ1yJxttfgoW5NMaF3M/i5OkhOaD2EEIiKu4K/l/+M21Z8iB4JxyrfccsWoH//es1GZC1YRogasPwiPdYeSMTyHTE4n5YLANCoFNzZ0Q+T+zbnsvJVSUyE/uQpbBGu+GXLcQz/4TMMOrcPAFCk1kJrKDFdogFgvGU3NpYjI0RVYBkhIhgMAn+fTMXSHeex5/xl0/buwe6Y3Lc5Brb15mTXUgWffwHdk09AVfosGQHjQkx6lRrZD42F21vzgT/+AKZMAfT6/9YOmThRcnIiy8UyQkTlHE3MxLId5/HrkWSUGIy/9s09nfBYn2Dc2zUADjq15IRyXMjIx9r1u/HUo4Oguuafw4Jhd8J+4QflnyfDtUOIqo1lhIgqlZyZjxW7YrHq33hkF5QAABo7avFIjyCM7RkEb2d7yQnrWGIicOYMTjh548uTOVB+XIMndv6AVpcTKu7L+SBEN4VlhIiuK6ewBGv2J2D5zhgkXM4HAOjUKozs7I+JfYPR1tf2ftcMXy6FMnUKFIMBBgC5Ogc4FxmPXQDl7pThfBCim8cyQkTVojcI/HE8BV9uP48D8Rmm7X1beWJS3+a4rZUnFMUK55WUjoCgVSvkefsi8sctGP7wEKhQ/p+8Ym9faJ95CnB0BF54gfNBiGoRywgRmS0q7gqW7TiPTcdSUDqtBK19GmFSn+YY0dkf9loLnldyVfnA5s3A448DBgOEouCUTzCap8ZCZzBUfN2ffwK33/7f1+B8EKJaU6dlZNGiRXj33XeRnJyM9u3bY+HChejbt2+V+2/btg0zZszA8ePH4e/vjxdffBFTp06t9vdjGSGqXwmX87B8Zwx+2JeA3CI9AMDFXoO2vi4I9nRCsJcTgj2d0MLLCYHujrDTSCgpV5WP/F83wv7JJ6CUlg8IgcrGcngphqh+1VkZiYiIwNixY7Fo0SL07t0bS5YswdKlS3HixAk0bdq0wv4xMTEICQnB5MmTMWXKFOzcuRP/+9//sHr1atx77721ejBEVLsy84vx/d54rNgVi+TMgkr3USlAQGNHY0nxdEJzr7I/G8HPxf7Gtw5/8AGwaJHx8kiHDkCPHkDjqx745+EBBAejKDMTKSUaXExOR8nefei+5F2ohAEGKAAEVDc4Fv3SZVALAzB1Ki/FENWTOisj3bt3R9euXbF48WLTtnbt2mHUqFFYsGBBhf1feuklbNiwAdHR0aZtU6dOxeHDh7F79+5qfU+WESK5ivUGnEzOxvm0HMSk5SImLRfnLxn/zCksqfJ1dhqVqaT8V1YaobmnExo76QBvb+DSpRt+/7IRjWv/rLarR0B4KYao3lT3/dusB1YUFRUhKioKM2fOLLc9PDwcu3btqvQ1u3fvRnh4eLltQ4YMwbJly1BcXAytVlvhNYWFhSgsLCx3MEQkj1atQocAV3QIKL9yqxACl3IKEVNaTGLScnE+LRfnL+Ug/nIeCksMOJmSjZMp2RW+5v8OrscLly5Vq1QoVfxZJVXpOInB8N8ISFnxCAhgCSGyMGaVkbS0NOj1evj4+JTb7uPjg5SUlEpfk5KSUun+JSUlSEtLg5+fX4XXLFiwAPPmzTMnGhFJoCgKvJ3t4e1sj+7NPcp9rkRvwIWMfJxPyy1fVi7lICmzAAOObTdvdON6KisfQ4ZwBITIStToUZ7X3uYnhLjurX+V7V/Z9jKzZs3CjBkzTH/PyspCYGBgTaISkSQatQpBHk4I8nDCgDblP5dfpEeG/WGIebNvvpBcr3ywhBBZBbPKiKenJ9RqdYVRkNTU1AqjH2V8fX0r3V+j0cDDw6PS19jZ2cHOzs6caERkRRx0ajjMfRlYtLBac0YqUKuBt98GwsJYPohsgFllRKfTITQ0FJGRkbj77rtN2yMjIzFy5MhKX9OzZ0/88ssv5bb98ccfCAsLq3S+CBE1IKmpxrtpFi8GSkqATp2A7t0r3k3TrBmQmws4ORn/5KUXIptS41t7P//8c/Ts2RNffPEFvvzySxw/fhxBQUGYNWsWLly4gG+++QbAf7f2TpkyBZMnT8bu3bsxdepU3tpLRERk4+rkbhoAGDNmDNLT0zF//nwkJycjJCQEGzduRFBQEAAgOTkZ8fHxpv2Dg4OxceNGTJ8+HZ999hn8/f3x8ccfV7uIEBERkW3jcvBERERUJ6r7/n2jRQuJiIiI6hTLCBEREUnFMkJERERSsYwQERGRVCwjREREJBXLCBEREUnFMkJERERSsYwQERGRVCwjREREJJXZy8HLULZIbFZWluQkREREVF1l79s3WuzdKspIdnY2ACAwMFByEiIiIjJXdnY2XF1dq/y8VTybxmAwICkpCc7OzlAUpda+blZWFgIDA5GQkGCzz7yx9WPk8Vk/Wz9GWz8+wPaPkcdXc0IIZGdnw9/fHypV1TNDrGJkRKVSISAgoM6+vouLi03+gF3N1o+Rx2f9bP0Ybf34ANs/Rh5fzVxvRKQMJ7ASERGRVCwjREREJFWDLiN2dnZ47bXXYGdnJztKnbH1Y+TxWT9bP0ZbPz7A9o+Rx1f3rGICKxEREdmuBj0yQkRERPKxjBAREZFULCNEREQkFcsIERERSWXzZeTNN99Er1694OjoCDc3t2q9RgiBuXPnwt/fHw4ODujfvz+OHz9ebp/CwkI8/fTT8PT0hJOTE0aMGIHExMQ6OILru3LlCsaOHQtXV1e4urpi7NixyMjIuO5rFEWp9OPdd9817dO/f/8Kn3/ggQfq+GgqqsnxTZgwoUL2Hj16lNvHUs4fYP4xFhcX46WXXkKHDh3g5OQEf39/jBs3DklJSeX2k3UOFy1ahODgYNjb2yM0NBTbt2+/7v7btm1DaGgo7O3t0bx5c3z++ecV9lm7di1uueUW2NnZ4ZZbbsFPP/1UV/GrxZxjXLduHQYPHgwvLy+4uLigZ8+e2Lx5c7l9VqxYUenvZEFBQV0fSqXMOb6tW7dWmv3kyZPl9rOkc2jO8VX274miKGjfvr1pH0s6f//88w+GDx8Of39/KIqCn3/++YavsYjfQWHj5syZIz744AMxY8YM4erqWq3XvP3228LZ2VmsXbtWHD16VIwZM0b4+fmJrKws0z5Tp04VTZo0EZGRkeLAgQNiwIABolOnTqKkpKSOjqRyQ4cOFSEhIWLXrl1i165dIiQkRNx1113XfU1ycnK5j+XLlwtFUcS5c+dM+/Tr109Mnjy53H4ZGRl1fTgV1OT4xo8fL4YOHVoue3p6erl9LOX8CWH+MWZkZIhBgwaJiIgIcfLkSbF7927RvXt3ERoaWm4/Gefw+++/F1qtVnz55ZfixIkTYtq0acLJyUnExcVVuv/58+eFo6OjmDZtmjhx4oT48ssvhVarFT/++KNpn127dgm1Wi3eeustER0dLd566y2h0WjEnj176vRYqmLuMU6bNk288847Yu/eveL06dNi1qxZQqvVigMHDpj2+eqrr4SLi0uF300ZzD2+LVu2CADi1KlT5bJf/btkSefQ3OPLyMgod1wJCQnC3d1dvPbaa6Z9LOn8bdy4UcyePVusXbtWABA//fTTdfe3lN9Bmy8jZb766qtqlRGDwSB8fX3F22+/bdpWUFAgXF1dxeeffy6EMP5warVa8f3335v2uXDhglCpVGLTpk21nr0qJ06cEADK/UDs3r1bABAnT56s9tcZOXKkGDhwYLlt/fr1E9OmTautqDVS0+MbP368GDlyZJWft5TzJ0TtncO9e/cKAOX+QZVxDrt16yamTp1ablvbtm3FzJkzK93/xRdfFG3bti23bcqUKaJHjx6mv48ePVoMHTq03D5DhgwRDzzwQC2lNo+5x1iZW265RcybN8/09+r++1QfzD2+sjJy5cqVKr+mJZ3Dmz1/P/30k1AURcTGxpq2WdL5u1p1yoil/A7a/GUac8XExCAlJQXh4eGmbXZ2dujXrx927doFAIiKikJxcXG5ffz9/RESEmLapz7s3r0brq6u6N69u2lbjx494OrqWu0cFy9exG+//YaJEydW+NzKlSvh6emJ9u3b4/nnnzc9Pbm+3Mzxbd26Fd7e3mjdujUmT56M1NRU0+cs5fwBtXMOASAzMxOKolS4FFmf57CoqAhRUVHl/n8FgPDw8CqPZffu3RX2HzJkCPbv34/i4uLr7lPf5wqo2TFey2AwIDs7G+7u7uW25+TkICgoCAEBAbjrrrtw8ODBWstdXTdzfF26dIGfnx9uv/12bNmypdznLOUc1sb5W7ZsGQYNGoSgoKBy2y3h/NWEpfwOWsWD8upTSkoKAMDHx6fcdh8fH8TFxZn20el0aNy4cYV9yl5fH1JSUuDt7V1hu7e3d7VzfP3113B2dsY999xTbvvDDz+M4OBg+Pr64tixY5g1axYOHz6MyMjIWsleHTU9vmHDhuH+++9HUFAQYmJi8Oqrr2LgwIGIioqCnZ2dxZw/oHbOYUFBAWbOnImHHnqo3EOu6vscpqWlQa/XV/q7U9WxpKSkVLp/SUkJ0tLS4OfnV+U+9X2ugJod47Xef/995ObmYvTo0aZtbdu2xYoVK9ChQwdkZWXho48+Qu/evXH48GG0atWqVo/hempyfH5+fvjiiy8QGhqKwsJCfPvtt7j99tuxdetW3HbbbQCqPs/1fQ5v9vwlJyfj999/x6pVq8ptt5TzVxOW8jtolWVk7ty5mDdv3nX32bdvH8LCwmr8PRRFKfd3IUSFbdeqzj7VUd3jAyrmNDfH8uXL8fDDD8Pe3r7c9smTJ5v+d0hICFq1aoWwsDAcOHAAXbt2rdbXrkpdH9+YMWNM/zskJARhYWEICgrCb7/9VqF0mfN1zVFf57C4uBgPPPAADAYDFi1aVO5zdXkOr8fc353K9r92e01+H+tSTfOsXr0ac+fOxfr168uV0B49epSbZN27d2907doVn3zyCT7++OPaC15N5hxfmzZt0KZNG9Pfe/bsiYSEBLz33numMmLu16xrNc2yYsUKuLm5YdSoUeW2W9r5M5cl/A5aZRl56qmnbnhXQLNmzWr0tX19fQEY26Kfn59pe2pqqqkZ+vr6oqioCFeuXCn3X9epqano1atXjb7v1ap7fEeOHMHFixcrfO7SpUsVWmxltm/fjlOnTiEiIuKG+3bt2hVarRZnzpy56Tey+jq+Mn5+fggKCsKZM2cA1P35A+rnGIuLizF69GjExMTg77//vuGjv2vzHFbG09MTarW6wn8tXf27cy1fX99K99doNPDw8LjuPub8DNSWmhxjmYiICEycOBFr1qzBoEGDrruvSqXCrbfeavqZrS83c3xX69GjB7777jvT3y3lHN7M8QkhsHz5cowdOxY6ne66+8o6fzVhMb+DtTb7xMKZO4H1nXfeMW0rLCysdAJrRESEaZ+kpCRpE1j//fdf07Y9e/ZUe/Lj+PHjK9yBUZWjR48KAGLbtm01zmuumz2+MmlpacLOzk58/fXXQgjLOX9C1PwYi4qKxKhRo0T79u1Fampqtb5XfZzDbt26iSeeeKLctnbt2l13Amu7du3KbZs6dWqFyXPDhg0rt8/QoUOlTmA15xiFEGLVqlXC3t7+hpMJyxgMBhEWFiYeffTRm4laIzU5vmvde++9YsCAAaa/W9I5rOnxlU3UPXr06A2/h8zzdzVUcwKrJfwO2nwZiYuLEwcPHhTz5s0TjRo1EgcPHhQHDx4U2dnZpn3atGkj1q1bZ/r722+/LVxdXcW6devE0aNHxYMPPljprb0BAQHizz//FAcOHBADBw6Udmtvx44dxe7du8Xu3btFhw4dKtwWeu3xCSFEZmamcHR0FIsXL67wNc+ePSvmzZsn9u3bJ2JiYsRvv/0m2rZtK7p06WLxx5ednS2ee+45sWvXLhETEyO2bNkievbsKZo0aWKR508I84+xuLhYjBgxQgQEBIhDhw6Vu5WwsLBQCCHvHJbdNrls2TJx4sQJ8eyzzwonJyfTnQczZ84UY8eONe1fdlvh9OnTxYkTJ8SyZcsq3Fa4c+dOoVarxdtvvy2io6PF22+/bRG39lb3GFetWiU0Go347LPPqrzNeu7cuWLTpk3i3Llz4uDBg+LRRx8VGo2mXEm11OP78MMPxU8//SROnz4tjh07JmbOnCkAiLVr15r2saRzaO7xlXnkkUdE9+7dK/2alnT+srOzTe9zAMQHH3wgDh48aLrTzlJ/B22+jIwfP14AqPCxZcsW0z4AxFdffWX6u8FgEK+99prw9fUVdnZ24rbbbqvQhvPz88VTTz0l3N3dhYODg7jrrrtEfHx8PR3Vf9LT08XDDz8snJ2dhbOzs3j44Ycr3GJ37fEJIcSSJUuEg4NDpetOxMfHi9tuu024u7sLnU4nWrRoIZ555pkKa3XUB3OPLy8vT4SHhwsvLy+h1WpF06ZNxfjx4yucG0s5f0KYf4wxMTGV/kxf/XMt8xx+9tlnIigoSOh0OtG1a9dyIzHjx48X/fr1K7f/1q1bRZcuXYROpxPNmjWrtCCvWbNGtGnTRmi1WtG2bdtyb3QymHOM/fr1q/RcjR8/3rTPs88+K5o2bSp0Op3w8vIS4eHhYteuXfV4ROWZc3zvvPOOaNGihbC3txeNGzcWffr0Eb/99luFr2lJ59Dcn9GMjAzh4OAgvvjii0q/niWdv7IRnKp+3iz1d1ARonSmChEREZEEXGeEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKS6v8B0CYa08e5UzUAAAAASUVORK5CYII=", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2435,10 +2248,8 @@ }, { "cell_type": "markdown", - "id": "6675456b", - "metadata": { - "editable": true - }, + "id": "35d2b3d9", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -2446,12 +2257,56 @@ { "cell_type": "code", "execution_count": 11, - "id": "5f7443ae", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ca391f17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.54175461]) = 0.29350\n", + ">2 f([0.37175575]) = 0.13820\n", + ">3 f([0.24640494]) = 0.06072\n", + ">4 f([0.15951871]) = 0.02545\n", + ">5 f([0.1015491]) = 0.01031\n", + ">6 f([0.0638484]) = 0.00408\n", + ">7 f([0.03976851]) = 0.00158\n", + ">8 f([0.02459084]) = 0.00060\n", + ">9 f([0.01511937]) = 0.00023\n", + ">10 f([0.00925406]) = 0.00009\n", + ">11 f([0.00564365]) = 0.00003\n", + ">12 f([0.0034318]) = 0.00001\n", + ">13 f([0.00208188]) = 0.00000\n", + ">14 f([0.00126053]) = 0.00000\n", + ">15 f([0.00076202]) = 0.00000\n", + ">16 f([0.00046006]) = 0.00000\n", + ">17 f([0.00027746]) = 0.00000\n", + ">18 f([0.00016719]) = 0.00000\n", + ">19 f([0.00010067]) = 0.00000\n", + ">20 f([6.05804744e-05]) = 0.00000\n", + ">21 f([3.64373635e-05]) = 0.00000\n", + ">22 f([2.19069576e-05]) = 0.00000\n", + ">23 f([1.31664443e-05]) = 0.00000\n", + ">24 f([7.91100141e-06]) = 0.00000\n", + ">25 f([4.75216828e-06]) = 0.00000\n", + ">26 f([2.85408468e-06]) = 0.00000\n", + ">27 f([1.71384267e-06]) = 0.00000\n", + ">28 f([1.02900153e-06]) = 0.00000\n", + ">29 f([6.17748881e-07]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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GHx+fCq/R6XTQ6XSmRDNLge4O6NncDfsvXcOGg7F4amhr2ZGIiMhCCCGw7u+SkfWJ3Zpa3doiNzJpZESr1SIkJAQRERHltkdERKB3796VviY3NxcqVflvo1aXPPJYCGHKt7dIk0qH1TYeioXeYP3HS0REteN4fAZOJWZCq1Hhnq7W84Teyph8mWbevHlYtWoV1qxZg9OnT+Opp55CTEyM8bLL/PnzMXXqVOP+o0aNwubNm7FixQpcunQJe/bswZNPPonu3bvD19c6ZwXfaFh7b7ja2yAhIx87z12VHYeIiCxE2cTVEcHecLXXSk5Tt0y6TAMAEyZMQFpaGhYvXozExEQEBwdj27ZtCAgIAAAkJiaWW3PkwQcfRFZWFj788EM8/fTTcHV1xaBBg/Dmm2/W3lGYMVsbNf6vSxN8tucy1h2IwcA2nrIjERGRmcspKMYPpat4l80/tGaKsIBrJZmZmXBxcUFGRgacnZ1lxzHZueQshP93J9QqBfteGARPZ1vZkYiIyIytPxiD5zcdR6C7A/58ur/Fzhep7vs3n01TD1p7OaFrU1foDQIbI+NkxyEiIjNXdolmQjd/iy0ipmAZqSdl94evPxgLAyeyEhFRFc4kZeJIbDo0KgXjuvrJjlMvWEbqyciOPnDSaRBzLRf7LlnvQwKJiOjOfFM6KjK0nRc8nCx/mYvqYBmpJ/ZaDUaXPlNgHVdkJSKiSuQX6bH5cMnlfGtecfVmLCP1qGzNkd9OJuNaTqHkNEREZG5+PpGIzPxiNHG1Q1hLd9lx6g3LSD0KbuKC4CbOKNQbjM2XiIiozI0TV1Uq65+4WoZlpJ6V3S++7kBMg1iBloiIqufi1WwciL4GlQLcF9owJq6WYRmpZ2M6+8LORo2LV3Nw6Mp12XGIiMhMrD9YMioyMMgTPi52ktPUL5aReuZka4ORHUseDsiJrEREBACFxQZsimx4E1fLsIxIUPaDtu14IjLyiiSnISIi2SJOJSMtpxBezjoMDPKQHafesYxI0LWpK4K8nJBfZMCW0mcPEBFRw/XNwZKR8vtC/KFRN7y35oZ3xGZAURRM7O4PoGTmNCeyEhE1XLHXcrHrfCqAkrtoGiKWEUn+r0sTaDUqnE7MxLG4DNlxiIhIkrKJq2Gt3OHvZi85jRwsI5K42mtxV7A3gH+G54iIqGEp1huwMbKkjJQt/dAQsYxIVDaR9YcjCcgpKJachoiI6tv2s1eRnFmAxg5aDG3nJTuONCwjEvUIdENzdwfkFOrx49EE2XGIiKiefVO6xMO4ED9oNQ33LbnhHrkZUBTFOFmJa44QETUsiRl52H42BUDDnbhahmVEsnEhfrBRKzgal4FTCZmy4xARUT3ZcDAOBgF0D3RDCw9H2XGkYhmRzN1RZ7xOyImsREQNg94gsOFQycTVSd0b9qgIwDJiFspmUH8XFY+8Qr3kNEREVNd2nb+K+PQ8ONtqMCLYR3Yc6VhGzEDflu7wa2SHrPxibDueKDsOERHVsW8OlIyK3NPVD7Y2aslp5GMZMQMqlYIJoSXDdLxUQ0Rk3a5mFeD308kAYFyNu6FjGTET94X6Q6UABy9fx4WULNlxiIiojnwbGYdig0CXpq5o4+0sO45ZYBkxE94uthjUxhPAP8N3RERkXYQQWF86Aj6pAa+4ejOWETNSNpF10+E4FBRzIisRkbXZdykNl9Ny4ajTYGQnTlwtwzJiRgYEecDLWYfruUX47WSy7DhERFTLyka+R3f2hb1WIzmN+WAZMSMatQrjOZGViMgqXc8pxC8nkgDwEs3NWEbMzPhQfygKsOdCGq6k5ciOQ0REtWRzVDwK9Qa093VGBz8X2XHMCsuImfF3s0fflu4AgPUHOZGViMgaCCGMD8Ure2I7/YNlxAxNKv1B3RgZhyK9QXIaIiK6U4djruN8SjbsbNQY09lXdhyzwzJihoa09UJjBy2uZhXgzzMpsuMQEdEdWlc6cfXujj5wtrWRnMb8sIyYIa1GhXtD/QDAOKxHRESWKTO/CD8dSwDAh+JVhWXETJWtOfLXuatISM+TnIaIiGpqy5EE5BcZ0MrTEV2bNpIdxyyxjJipQHcH9GzuBoOA8THTRERkeW6cuKooiuQ05ollxIyVTWTdcDAWeoOQnIaIiEx1PC4DJxMyoVWrcE+XJrLjmC2WETM2rL03XO1tkJCRj53nr8qOQ0REJlpXuoDl8GBvNHLQSk5jvlhGzJitjRr/V9qkOZGViMiy5BQU44cjJRNXJ3Li6i2xjJi5sks1v59OQUpmvuQ0RERUXT8dS0B2QTGaNbZHr+aNZccxaywjZq61lxO6NnWF3iCwMTJOdhwiIqqmsrVFJnTjxNXbYRmxAGVLB68/GAsDJ7ISEZm9M0mZOBKbDo1Kwb0hfrLjmD2WEQswsqMPnHQaxFzLxb5LabLjEBHRbXxTOioypK0XPJx0ktOYP5YRC2Cv1WB06bMM1nEiKxGRWcsv0mPz4ZLL6py4Wj0sIxaibCLrbyeTcS2nUHIaIiKqys8nEpGZX4wmrnYIa+UhO45FYBmxEMFNXBDcxBmFeoOxcRMRkfkpm7g6PtQfahUnrlYHy4gFKXtezboDMRCCE1mJiMzNxavZOBB9DSoFGN+NE1eri2XEgozp7As7GzUuXs3BoSvXZcchIqKbrD9YMioyIMgTPi52ktNYDpYRC+Jka4NRnXwAAF/uuyI5DRER3SivUI+NpQ82ndiNE1dNwTJiYab1bgYA2HY8EfHpeXLDEBGR0beH43A9twj+bnYY3NZLdhyLwjJiYdr7uqB3i8bQGwQ+3xMtOw4REQEwGATW7C75O3l6n0BOXDURy4gFmhkWCKBkUZ2s/CLJaYiI6I8zKYhOzYGTrQb3hfISjalYRizQgNaeaOHhgKyCYuNkKSIikmfVrksAgMk9msJRp5GcxvKwjFgglUrBjL7NAQCf7bmMYr1BciIioobreFwG/o6+Bo1KwYOl8/rINCwjFuqerk3Q2EGL+PQ8/HIySXYcIqIGa9XuklGRkR19eDtvDbGMWChbGzUe6BkAAPh0VzQXQSMikiAhPQ8/HUsEAMwMay45jeViGbFgU3oFQKtR4WhsOiK5CBoRUb37Yu9l6A0CPZu7IbiJi+w4FotlxIK5O+pwT5cmAIBPSydPERFR/cguKMbXpU9Sn8VRkTtSozKyfPlyBAYGwtbWFiEhIdi1a9ct9y8oKMCCBQsQEBAAnU6HFi1aYM2aNTUKTOXN6Ftym+9vp5JxJS1HchoiooZjw8FYZOUXo7mHAwYGecqOY9FMLiPr16/H3LlzsWDBAkRFRSEsLAwjRoxATExMla8ZP348/vjjD6xevRpnz57FunXr0KZNmzsKTiVaeTlhQJAHhIBxwR0iIqpbxXoD1pQuPDmjbyBUXOTsjijCxJmPPXr0QNeuXbFixQrjtrZt22Ls2LFYsmRJhf1/+eUXTJw4EZcuXYKbm1uNQmZmZsLFxQUZGRlwdnau0dewZrvPp+KB1X/DzkaN/fMHw8XeRnYkIiKrtu14Ih5dexiN7G2w94XBsNOqZUcyS9V9/zZpZKSwsBCRkZEIDw8vtz08PBx79+6t9DU//PADQkND8dZbb6FJkyZo3bo1nnnmGeTlVf1clYKCAmRmZpb7oKr1adkYbbydkFekx9oDfIAeEVFdK5unN6VnAItILTCpjKSmpkKv18PLq/wDgLy8vJCUVPlaF5cuXcLu3btx4sQJfPfdd1i2bBm+/fZbPPbYY1V+nyVLlsDFxcX44e/PpXVvRVEU4y1lX+y9jMJiLoJGRFRXIq9cR1RMOrRqFR7oFSA7jlWo0QRWRSl/bUwIUWFbGYPBAEVRsHbtWnTv3h133XUXli5dis8//7zK0ZH58+cjIyPD+BEbyyXPb2d0J194OumQnFmAn44lyI5DRGS1ypZ+H9vFF55OtpLTWAeTyoi7uzvUanWFUZCUlJQKoyVlfHx80KRJE7i4/HP/ddu2bSGEQFxcXKWv0el0cHZ2LvdBt6bVqDCtdBniVVwEjYioTsSk5eLX0lWvyx7LQXfOpDKi1WoREhKCiIiIctsjIiLQu3fvSl/Tp08fJCQkIDs727jt3LlzUKlU8PPzq0Fkqsr9PZrCzkaNU4mZ2HcxTXYcIiKrs2ZPNAwC6NfaA0HeTrLjWA2TL9PMmzcPq1atwpo1a3D69Gk89dRTiImJwezZswGUXGKZOnWqcf/JkyejcePGeOihh3Dq1Cns3LkTzz77LKZPnw47O67hX5tc7bW4N6Sk4K3ibb5ERLUqI68IGw6VTBuYWbrGE9UOk59zPGHCBKSlpWHx4sVITExEcHAwtm3bhoCAkkk8iYmJ5dYccXR0REREBJ544gmEhoaicePGGD9+PF577bXaOwoymt43EF/9fQV/nknBhZQstPRkcyciqg3rDsQgt1CPIC8nhLVylx3Hqpi8zogMXGfENLO+PISIU8mY1L0pltzTQXYcIiKLV6Q3IOzN7UjKzMdb93bE+FDe5VkddbLOCFmGsmckbD4ch7TsAslpiIgs39ZjiUjKzIe7ow5jOvvKjmN1WEasULdmjdDRzwUFxQZ8tb/qZfqJiOj2hBBYtbvkdt5pvQKg03CRs9rGMmKFblwE7X/7LyO/SC85ERGR5dp/6RpOxGfC1kaF+3tykbO6wDJipUYEe8PXxRap2YXYciRedhwiIou1unRUZFxXP7g5aCWnsU4sI1bKRq3CQ31Kbj3jImhERDVz+ehZ5PzyO7wzUzGDt/PWGZYRKzahuz8cdRqcT8nGX+euyo5DRGRZVq9G0y5tse6bf2Pvx9PR/If1shNZLZYRK+Zsa4MJ3UpuP1u1i4ugERFVW1wcxL/+BVXpqLJKGICHHwaqeIwJ3RmWESv3YO9mUCnA7gupOJ2YKTsOEZFlOH8eiuGmJ6Dr9cCFC3LyWDmWESvn72aPER18AHB0hIiouvKbNUeFmXZqNdCypYw4Vo9lpAEoe4bCD0fjkZKZLzkNEZH52/vHISjAP4VErQZWrgT4gNc6wTLSAHRp2gihAY1QpBf4Yt9l2XGIiMyaMBjgvuRVAMD5IaOB7duBy5eBGTPkBrNiLCMNRNkiaGv/jkFuYbHkNERE5uvE59+i46WjKFDbwHv5MmDAAI6I1DGWkQZiaDsvBDS2R3puETZFcjY4EVGlhIDDqwsBAIdHToJzK64tUh9YRhoItUrB9NJF0FbvjobBwEXQiIhuFv/ZOjS/fBo5NrZo+uYi2XEaDJaRBuTeED8422pwOS0Xv59Olh2HiMi86PVQL3wZALDzrsloEtRMbp4GhGWkAXHQaYwPeeJtvkRE5WV89iW8Yy8iQ+cA31dfkh2nQWEZaWCm9WoGjUrBgcvXcDQ2XXYcIiLzUFQE8fIrAIAfhz2ATh2ayc3TwLCMNDDeLrYY3ckXALBqN0dHiIgAoPDT1XBNjMVVe1d4/vtZ2XEaHJaRBmhGWMlE1m3HExGfnic5DRGRZPn5KFq0GADw9eDJGNytueRADQ/LSAPU3tcFvVs0ht4g8Pkejo4QUcNmWLECDimJSHByR6O5T0CtUmRHanBYRhqomaWjI98ciEVWfpHkNEREkmRno/i1/wAAVg64H/f04bNnZGAZaaAGtPZECw8HZBUUY/3BWNlxiIjkeO89aK+lIbqRD+xnTYejTiM7UYPEMtJAqVQKZvQtuS762Z7LKNYbbvMKIiIrc/069G+9BQB4P+wBTO3XSnKghotlpAG7p2sTuDloEZ+eh19OJsmOQ0RUv955B+rMTJxxDwAmTICPi53sRA0Wy0gDZmujxgOli6B9uisaQnCJeCJqIJKTYVi2DADwbr8pmNGfc0VkYhlp4Kb0DIBWo8LR2HREXrkuOw4RUf1YsgSq3Fwc8WmNrPARCG7iIjtRg8Yy0sB5OOnwf52bAOAS8UTUQMTGQqxYAQB4J2wKZoa1kByIWEbIuAjar6eScCUtR3IaIqI69uqrUAoLsd8/GAmhfTCojafsRA0eywihtZcT+rf2gBAld9YQEVmt8+ch1qwBALzdbyqmhzWHioucSccyQgCAWWElt/luOBSLtOwCyWmIiOrIwoVQ9Hr82TwUl1p3wriufrITEVhGqFSflo0R3MQZuYV6rNx5SXYcIqLad+IExLp1AEruoJnWuxnstGrJoQhgGaFSiqLg6aFBAIAv9l5GSma+5ERERLXspZegCIGtQX0QH9gGM/oGyk5EpVhGyGhAkAdCAhqhoNiAj7ZfkB2HiKj2HDgAfP899IoKS/s+gNn9W8DJ1kZ2KirFMkJGiqLg6fDWAICvD8Qg7nqu5ERERLXkxRcBAN+1H4iMZi0xtVeA5EB0I5YRKqd3C3f0btEYRXqBD//k6AgRWYEdO4CICBSpNVjWZxIeG9gC9lo+EM+csIxQBWWjIxsj43A5leuOEJEFEwJYsAAA8E3HcOgDmmFS96aSQ9HNWEaogpAANwwM8oDeILDs93Oy4xAR1dzPPwN79yJfo8UHvSbgiUGtYGvDO2jMDcsIVWpe6Z01W44m4FxyluQ0REQ1YDAY54p80XUkbAP8cV8o1xUxRywjVKkOfi4Y3t4bQgD/jeDoCBFZoM2bgagoZGvt8XGPcZgzuBVs1HzbM0c8K1SleeGtoSjAzyeScCI+Q3YcIqLq0+uBl14CAKwOHQO3AF+M7dJEciiqCssIVam1lxPGdPIFACzl6AgRWZKvvgLOnEG6nRNWdR+LeUODoOYzaMwWywjd0pwhraFWKfjzTAoir1yXHYeI6PYKC4GFCwEAK3qMg18zH4wI9pabiW6JZYRuKdDdAfeWPkhqacRZyWmIiKph9Wrg8mVcdWyEL7qOxNNDW/PJvGaOZYRu64nBLWGjVrDnQhr2XkyVHYeIqGq5ucCrrwIAPug5HkHNvTG4rafkUHQ7LCN0W36N7I2LBL372zkIISQnIiKqwvLlQGIi4lw88U2n4XgmvDUUhaMi5o5lhKrlsYEtodOoEHnlOnacuyo7DhFRRZmZwBtvAADe6z0JXVp5oW9Ld8mhqDpYRqhavJxtjQ+Weve3sxwdISLzs2wZkJaGi25+2Bw8CE+HB3FUxEKwjFC1ze7fAg5aNU7EZ+LXk8my4xAR/SMtDXjnHQDAf/tORp823uge6CY5FFUXywhVW2NHHab3DQRQcmeN3sDRESIyE2+9BWRl4ZRnILa26Yunh7aWnYhMwDJCJpkZ1hzOthqcS87GT8cSZMchIgISE4EPPgAAvBM2BUPa+6CTv6vcTGQSlhEyiYudDf7VrzkAYNnv51GsN0hOREQN3uuvA3l5OOwbhD9bdMM8jopYHJYRMtmDfQLh5qBFdGoONh+Olx2HiBqyy5eBlSsBAG/3m4aRnXzR1sdZbiYyGcsImcxRp8Ej/VsAAN774zwKivWSExFRg7V4MVBUhN0BnfB3s454iqMiFollhGrkgZ4B8HTSIT49DxsOxsqOQ0QN0dmzwBdfAADe6TcV93T1QwsPR8mhqCZYRqhG7LRqPD6oJQDggz8vIL+IoyNEVM9efhkwGBDRsjtO+LXBnMGtZCeiGmIZoRqb0M0fTVztkJJVgK/2X5Edh4gakiNHgA0bAADvhk3BhG7+8Hezl5uJaqxGZWT58uUIDAyEra0tQkJCsGvXrmq9bs+ePdBoNOjcuXNNvi2ZGZ1GbfyXyPIdF5FTUCw5ERE1GC+9BAD4oW0/XPJtYRypJctkchlZv3495s6diwULFiAqKgphYWEYMWIEYmJibvm6jIwMTJ06FYMHD65xWDI/93RtgmaN7XEtpxCf770sOw4RNQT79gE//QS9So3/9r0fD/QIgI+LnexUdAdMLiNLly7FjBkzMHPmTLRt2xbLli2Dv78/VqxYccvXPfzww5g8eTJ69epV47BkfjRqlXH2+sq/LiIjr0hyIiKyegsWAAC+bT8ISV5N8ciAFpID0Z0yqYwUFhYiMjIS4eHh5baHh4dj7969Vb7us88+w8WLF/HKK69U6/sUFBQgMzOz3AeZr5EdfdHayxGZ+cVYteuS7DhEZM3++APYvh2Fahu832cSHurTDB5OOtmp6A6ZVEZSU1Oh1+vh5eVVbruXlxeSkpIqfc358+fxwgsvYO3atdBoNNX6PkuWLIGLi4vxw9/f35SYVM/UKsW44uGa3dFIyy6QnIiIrJIQxlGRtZ2HI9PT17giNFm2Gk1gvfmRzEKISh/TrNfrMXnyZCxatAitW1d/IZr58+cjIyPD+BEby3UszN2w9t5o7+uMnEI9Vu7k6AgR1YGffgL+/hv5Njos7zkeM8Oaw9VeKzsV1QKTyoi7uzvUanWFUZCUlJQKoyUAkJWVhUOHDuHxxx+HRqOBRqPB4sWLcfToUWg0Gvz555+Vfh+dTgdnZ+dyH2TeFEXBM+FBAIAv9l5GSma+5EREZFUMBuDFFwEAn3UdhSJPT0zv20xuJqo1JpURrVaLkJAQRERElNseERGB3r17V9jf2dkZx48fx5EjR4wfs2fPRlBQEI4cOYIePXrcWXoyKwOCPNC1qSsKig34aPsF2XGIyJps2AAcO4ZsnQM+7jEOs/u3gJOtjexUVEuqN4njBvPmzcOUKVMQGhqKXr164ZNPPkFMTAxmz54NoOQSS3x8PL788kuoVCoEBweXe72npydsbW0rbCfLpygKnhkWhMmf/o2vD8RgVr/m8GvERYiI6A4VFwOlN0Cs7DYWNh7umNorQHIoqk0ml5EJEyYgLS0NixcvRmJiIoKDg7Ft2zYEBJT8YCQmJt52zRGyXr1buKN3i8bYezENH/xxAW/e21F2JCKydF9+CZw7h+v2LlgTOgbPDmwBe63Jb19kxhQhhJAd4nYyMzPh4uKCjIwMzh+xAJFXrmHcin1QqxT8Pq8/At0dZEciIktVUAC0bg3ExOC1gdOxbehkbH92AHQatexkVA3Vff/ms2mo1oUEuGFgkAf0BoH3fj8nOw4RWbJPPgFiYpDi1Bj/63I3nhjcikXECrGMUJ2YN7TkzpotRxNwLjlLchoiskg5OcB//gMAeK/XBHh5NcK9IX6SQ1FdYBmhOtHBzwXD23tDCOC/ERwdIaIa+OADIDkZca7e2NBxKOYOaQUbNd+2rBHPKtWZeeGtoSjAzyeScCI+Q3YcIrIk6enAW28BAJb2mYSm3q4Y07mJ3ExUZ1hGqM609nLCmE6+AIClHB0hIlMsXQpcv46L7k3xfbsBmDc0CGpVxZW+yTqwjFCdmjOkNdQqBX+eSUHkleuy4xCRJbh6FfjvfwEAb/e9H22aNMKIYG/JoagusYxQnQp0d8C9XUsmnL360ykYDGZ/JzkRyfbGG0B2Nk54t8QvrXvj6fDWUHFUxKqxjFCde2poazho1TgSm471h/jQQyK6hfh4iI8+AgC80/cB9G7pjkFtPCWHorrGMkJ1ztvFFk8NLXlq8xs/n0FadoHkRERktl57DUpBAQ74tcOeVqFYPCa40qfCk3VhGaF68WDvZmjj7YSMvCK8+csZ2XGIyBxdugSxahUA4J1+U/Fw/5Zo6ekoORTVB5YRqhcatQr/+b+ShyNuOBSHQ5evSU5ERGZn4UIoxcXY2awLEjp2w2MDW8pORPWEZYTqTUiAGyaE+gMAXvz+BIr1BsmJiMhsnDoF8dVXAIB3+k3BotHtYaflsu8NBcsI1avnR7SBq70NziRl4fO9l2XHISIzIV5+GYoQ+KV1L3gNDsPgtl6yI1E9YhmheuXmoMULw9sAKFkmPjEjT3IiIpIuMhLKpk0wQMGHA6filVHtZCeiesYyQvVufKg/ujZ1RU6hHq/9dFp2HCKSrGj+AgDAlnb9cdfEIfBrZC85EdU3lhGqdyqVgtfGdoBKAbYeT8Rf567KjkREsuzeDZuIX1GsqPDdmJmY2be57EQkAcsISdHO1xkP9g4EALyy5QTyi/SSExFRvRMC2c88DwDY0DEcj8wYDq2Gb0sNEc86SfPU0FbwdNLhclouVv51SXYcIqpn+l9/g+Pfe1GgtsG5f81FrxaNZUciSVhGSBonWxu8NLJkotpHOy7gSlqO5EREVG+EwPV5zwEANoSOxKNT+ksORDKxjJBUIzv6oG9LdxQWG/DylpMQgg/SI2oIMtZthPvpY8ixsYXupX/D08lWdiSSiGWEpFIUBYvHtIdWrcJf567ilxNJsiMRUV3T65H7/L8BAD8OvA/jRoRIDkSysYyQdM09HDG7f8kM+kU/nkJ2QbHkRERUly689wl84i4iQ+eA9u++CrWKD8Jr6FhGyCw8OrAl/N3skJSZj/f/OC87DhHVkcK8Ati//hoA4O9x09EhOEByIjIHLCNkFmxt1Fg8uuRBeqt3R+NsUpbkRERUF/a99A580xKQ5uCKHv9dJDsOmQmWETIbA9t4Ylh7L+gNAi9+f5yTWYmsTHzSdQR98l8AQNzsuXDxbCQ5EZkLlhEyKy+Pag87GzUOXr6OTYfjZccholq05+lX4Z2VhtRGnuj46nOy45AZYRkhs9LE1Q5zhrQCALy+7TTScwslJyKi2rBv2x4M2/QJAKD43y9CsbOTnIjMCcsImZ0ZfQPRytMR13IK8davZ2XHIaI7VLjyU/S4OwwuBTkQALyddbIjkZlhGSGzY6NW4bWxJZNZ1x2IQVTMdcmJiKjG4uKgeWQ2VCiZA6YAwKOPAnFxUmOReWEZIbPUo3lj3NO1CYQAXvz+BPQGTmYlskTx+6OgEobyG/V64MIFOYHILLGMkNmaP6ItnG01OJmQia/2X5Edh4hMJITA8RVfVfyEWg20bFn/gchssYyQ2fJw0uHZ4W0AAO/8ehYpWfmSExGRKfat2ojwPzcCAISq9O1GrQZWrgT8/CQmI3PDMkJmbXL3pujo54KsgmK8vvW07DhEVE3ZMfFoPe8RqCBwcsS9UK5cAbZvBy5fBmbMkB2PzAzLCJk1tUrBf8Z2gKIA3x9JwN4LqbIjEdHtGAxIvGcS3LOv4bJnAFp8vbpkJGTAAI6IUKVYRsjsdfBzwZSeJc+veHHLCRQWG27zCiKSKWnh62gVuQsFahukrvoCtq7OsiORmWMZIYvwdHgQ3B21uHQ1B5/uuiQ7DhFVwfD3Abj/ZyEAYPPUZxA6qr/cQGQRWEbIIrjY2WDB3W0BAB/8eR6x13IlJyKiCjIykDvuPmgMevzWpg8GLn1JdiKyECwjZDHGdm6CHoFuyC8yYNGPp2THIaIbCYGCGbPgGB+DOGdPJL37IbxdueQ7VQ/LCFkMRVHw2thgaFQKfj+djIhTybIjEVGZNWug27QRxYoK7zy0EJOHdZSdiCwIywhZlFZeTpjVrzkAYOEPJ5FbWCw5ERHh1CnoH38CAPBOv6mY8tQEaNR8e6Hq408LWZwnBrVEE1c7xKfn4cM/uaQ0kVR5eRATJkCdn4edzbog/dE5CAlwk52KLAzLCFkce60Gr4xqBwD4dNclXEjJkpyIqAGbNw/KiRO46uCKhfc9j+fubic7EVkglhGySEPbeWFwG08U6QVe+v4khOCD9Ijq3bffAh9/DAB46u6n8a97e8HNQSs5FFkilhGySIqiYOHo9tBpVNh3KQ2f7bksOxJRw3L5MsTMmQCA5T3vRU7/gRgf6i85FFkqlhGyWP5u9vj3XSVrjyz5+TSOxqbLDUTUUBQVAZMmQcnIwGHfIKwYOA1v39sRKpUiOxlZKJYRsmhTewVgeHtvFOkFHl93GBl5RbIjEVm/l18G9u9Hps4BT45+DgvHdUZLTyfZqciCsYyQRVMUBW/e2xH+bnaIvZaHFzYd4/wRorr022/AG28AAJ4f/gR6DgrBuBA+/I7uDMsIWTwXOxt8OKkrbNQKfj6RhP/tvyI7EpF1SkqCmDIFAPBV5xG40G84Fo9pLzkUWQOWEbIKnfxd8cKIkvkjr/10GifiMyQnIrIyBgMwdSqUlBSccQ/A28P+hY/u7wp7rUZ2MrICLCNkNab3aYYhbb1QqDfgsa8PIyuf80eIas3bbwMREcjT6PD4mOexYFwIWntxngjVDpYRshqKouCd+zqiiasdrqTlYv7m45w/QlQb9u2DWLAAAPDKkIcRPKQn7gvlPBGqPSwjZFVc7bV4f1IXaFQKfjqWiHUHYmVHIrJs6ekQkyZB0evxQ9t+ODRoLF77vw5QFN7GS7WHZYSsTkhAIzw7LAgAsOjHkzidmCk5EZGFEgKYORPKlSu44uqNhXc9gQ/vD4GjjvNEqHaxjJBVmhXWHAODPFBQXDJ/JKeAT/clMtknnwCbNqFIpcYTo5/D0/d1QztfZ9mpyAqxjJBVUqkUvDu+M7ydbXHpag5e/P4E548QmeL4cYi5cwEAb/afhqbD+mNy96ZyM5HVYhkhq+XmoMUHk7tArVLwXVQ8Nh6Kkx2JyDLk5EBMmAAlPx/bm4fgj2GTseQezhOhulOjMrJ8+XIEBgbC1tYWISEh2LVrV5X7bt68GUOHDoWHhwecnZ3Rq1cv/PrrrzUOTGSKbs3cMG9oawDAyz+cwLnkLMmJiCzA3LlQTp9GsqMb5o96Gh88EAonWxvZqciKmVxG1q9fj7lz52LBggWIiopCWFgYRowYgZiYmEr337lzJ4YOHYpt27YhMjISAwcOxKhRoxAVFXXH4Ymq45H+LRDWyh35RQY8tvYwcgs5f4SoSt98A6xaBQMUzB35NB6d0AvBTVxkpyIrpwgTL6T36NEDXbt2xYoVK4zb2rZti7Fjx2LJkiXV+hrt27fHhAkT8PLLL1dr/8zMTLi4uCAjIwPOzpw8RaZLzS7AXe/tQkpWAe4L8cPb93WSHYnI/Fy6BNG5M5SsLLzfawJOPfIsVjzQlZdnqMaq+/5t0shIYWEhIiMjER4eXm57eHg49u7dW62vYTAYkJWVBTc3tyr3KSgoQGZmZrkPojvh7qjDexO7QKUAGyPjsPkw548QlVNYCDFxIpSsLBxs0g6bR83Am/d2ZBGhemFSGUlNTYVer4eXl1e57V5eXkhKSqrW13j33XeRk5OD8ePHV7nPkiVL4OLiYvzw9/c3JSZRpXq1aIw5g0vmj7z4/QlcSMmWnIjIjCxYAOXgQaTbOuLpsc/ivQe6wcWO80SoftRoAuvNTVkIUa32vG7dOixcuBDr16+Hp6dnlfvNnz8fGRkZxo/YWK6iSbXj8UEt0btFY+QW6vH414eRX6SXHYlIvp9/Bt55BwDw7F1zMW1if3Tyd5WbiRoUk8qIu7s71Gp1hVGQlJSUCqMlN1u/fj1mzJiBDRs2YMiQIbfcV6fTwdnZudwHUW1QqxQsm9gZ7o46nEnKwqIfT8qORCRXQgIMU6cCAD4LGQWMGYPpfZrJzUQNjkllRKvVIiQkBBEREeW2R0REoHfv3lW+bt26dXjwwQfx9ddf4+67765ZUqJa4ulki/cmdoaiAOsOxGLLkXjZkYjk0OshpkyBKjUVJz2b48sxj+JtzhMhCUy+TDNv3jysWrUKa9aswenTp/HUU08hJiYGs2fPBlByiWVqacsGSorI1KlT8e6776Jnz55ISkpCUlISMjIyau8oiEzUp6U7nhjYEgDw783HEZ2aIzkRkQRvvAHlzz+RY2OLuWOfx7vTesDVXis7FTVAJpeRCRMmYNmyZVi8eDE6d+6MnTt3Ytu2bQgICAAAJCYmlltzZOXKlSguLsZjjz0GHx8f48ecOXNq7yiIamDOkNboEeiGnEI9HlvL+SPUwOzeDfHKKwCAl8IfwX33D0bXpo0kh6KGyuR1RmTgOiNUV5Iz8zHivV24llOIKT0D8OrYYNmRiOretWswdOoMVVwsNrUfiK3PvIlVU0OhUvHyDNWuOllnhMjaeDnbYun4kgXQ/rf/CrYdT5SciKiOCQExfTpUcbG41MgXH417Cu/c14lFhKRiGaEGb0CQJx4Z0AIA8Py3x3AljfNHyIp99BGULVtQoNZg7tjn8eZDfeDmwHkiJBfLCBGAp4e2RmhAI2QVFOPxr6NQUMz5I2SFjhyB4emnAQBLBkzHsCl3oVuzqlfDJqovLCNEADRqFd6f1AWu9jY4Hp+BJdvOyI5EVLuys2EYPwGqwkJEtOyOS5Om45H+LWSnIgLAMkJk5OtqZ5w/8vney/j1ZPUecUBkER5/HKrz55Do2BhvjX8eSyd05jwRMhssI0Q3GNTGC//q1xwA8OzGo4i9lis5EVEt+N//gC++gF5RYe7oZ/HqjP5wd9TJTkVkxDJCdJNnhwWhS1NXZOYXY8YXB3E9p1B2JKKaO3cO+tmPAADe6zMJfabfg57NG0sORVQeywjRTWzUKnw4uSu8nHU4l5yNKWv+RkZekexYRKYrKEDuPfdBnZuD/f7BOD39cTxWuvIwkTlhGSGqRBNXO6yd2RONHbQ4EZ+Jhz47gJyCYtmxiEyS+thc2J88hmt2zlj7xOv44IFuUHOeCJkhlhGiKrT0dMT/ZvSAi50NDsekY+YXh7hkPFmM+C/Xw331xwCAlQ+9hDfnjICtjVpyKqLKsYwQ3UI7X2d8Mb07HHUa7LuUhtlfRXINEjJ7McfOwWH2LADAloHj8fi7c2Cv1UhORVQ1lhGi2+js74o1D3aDrY0KO85exZx1R1CsN8iORVSpxKOnURg+HK55WTjnF4T+m1bBydZGdiyiW2IZIaqG7oFu+HRqKLRqFX45mYSnNx6F3mD2z5ikBibjw4/h1bk9WiZHQwDwnXE/XBs5yY5FdFssI0TVFNbKA8vv7wqNSsGWIwlY8N1xWMBDr6mBuH72IpyefBQqlPxMKgAcX1sExMXJDUZUDSwjRCYY0s4L703sApUCfHMwFot+PMVCQtJl5Bbhj9kLoLr5Z1GvBy5ckBOKyAQsI0QmurujD966959l49/69SwLCUmTlVeI7yc/iXt3rK/4SbUaaMl1Rcj8sYwQ1cC9IX54bWwwAGDFjov48E/+65PqX15BMbaPfgjTtpTcwps9aGhJAQFK/rtyJeDnJzEhUfXwXi+iGnqgZwDyi/R4betpvBtxDnZaNWaGNZcdixqI/LwCHBh6L0bv+QkAkPjSq/BZ/GLJHJELF0pGRFhEyEKwjBDdgZlhzZFXqMe7Eefw2tbTsLVR44GeAbJjkZUrysnF6bAR6B+1E8WKCnFvvY9mzzxW8kk/P5YQsji8TEN0hx4f1BKPDGgBAHjx+xP4NpJ3L1Dd0V9PR3S3fugStRMFahucX/75P0WEyEKxjBDdIUVR8NywIDzYuxkA4Llvj+KnYwlyQ5FVMiQlI7FrL7Q+HYlsrR1OfbYBbWdPkR2L6I6xjBDVAkVR8PLIdpjYzR8GAcz95gh+P5UsOxZZEREdjWtde8Dv8hmk2rvi6Fdb0GXKWNmxiGoFywhRLVGpFPzn/zpgTGdfFBsEHl17GLvOX5Udi6yAOHEC2aE94Z54BXHOnjjy9Q/oc99Q2bGIag3LCFEtUqsUvHtfJwxr74VCvQGzvjyEA9HXZMciS7Z/Pwp694XTtRScdW+Kw1//iCFjwmSnIqpVLCNEtUyjVuH9SV0wIMgD+UUGTP/8II7EpsuORZbo119RNHAQbLMycNg3CJFffo/Rd3eXnYqo1rGMENUBnUaNjx8IQa/mjZFdUIypq//GqYRM2bHIkqxfD/3IUbDJz8OOwBBErtqIySO6yE5FVCdYRojqiK2NGqumhaJrU1dk5hdjyuq/cSElS3YssgQrVkBMmgR1cRF+aNsPRz74DLNGdJCdiqjOsIwQ1SEHnQafT++O4CbOSMspxP2r/saVtBzZschcCQG8+irw6KNQhMCXXe7GiTc+xJy7gmUnI6pTLCNEdczZ1gZfTu+B1l6OSM4swORP/0Z8ep7sWGRuDAZg7lzg5ZcBAO/1noRzL72O+aOCoSiK3GxEdYxlhKgeuDlo8dXMHgh0d0B8eh7u/3Q/Ll7Nlh2LzEVRETB1KvD++wCAV4Y8jJg5z2PxmA4sItQgsIwQ1RNPJ1usndkDfo3scDktF6M+2I3vorh0fIOXmwv9mDHA2rUoUqkxZ+TTSH3oX3jr3o5QqVhEqGFgGSGqR76udtj8SG/0at4YuYV6PLX+KJ779ijyCvWyo5EM6enIHzgY6p9/Rp5Gh1n3vIgmj83EexM6Q80iQg0IywhRPfN0tsVXM3tgzuBWUBRgw6E4jPloN84n806bBiUxERnde8P2wH5k6Bzw2LQ38NB/HsNzw9tAo+ZfzdSw8CeeSAK1SsFTQ1tj7Ywe8HDS4VxyNkZ9uBsbD8XKjkb1IP/0OaR16Q6X86eR7OiG157/GEuWzkb/1h6yoxFJwTJCJFHvlu7Y9mQY+rZ0R36RAc9+ewzzNhxBTkGx7GhUR2K270Vuj15onByHy64++OmjDXjjlfvh5WwrOxqRNCwjRJJ5OOnw5fTueCa8NVQKsPlwPEZ/uBunE7liq7XZvnozXEeEwy3rGs56N0fKtgjMmDqY80OowWMZITIDKpWCxwe1wrpZPeHlrMPFqzkY+9EefP13DIQQsuPRHcopKManL3yAXrMnwbkgB2dadoLbgT3o3qu97GhEZkERFvA3XWZmJlxcXJCRkQFnZ2fZcYjqVFp2AeZtOIq/zl0FAIzq5IvX/y8YTrY2kpORyeLiEPP3Efzwv18x+4fl0AgDonsORNOIH6F2dJCdjqjOVff9m2WEyAwZDAKf7LqEt389C71BoFlje3w4uSuCm7jIjkbVJFatAh5+GIrBYNx2dex4eGz4CrBhsaSGgWWEyApEXrmGJ76OQkJGPrRqFV4a2RYP9AzgqpxmLufiZdi1agGV+KeICEWBcvky0LSpvGBE9ay679+cM0JkxkIC3LD1yTAMaeuJQr0BL205ice+PozM/CLZ0agKJ+Ou48cZz5crIgCgCAFcuiQpFZF5YxkhMnONHLT4dGooXry7LTQqBduOJ+Hu93fhaGy67Gh0AyEEfvp8Kwp79sbEvzZU3EGtBlq2rP9gRBaAZYTIAiiKgplhzfHtI73h18gOsdfycO/He7FmdzTvtjEDmUlX8dewiRgxfTS6xJ9Bvq09Cu4ZV1JAgJL/rlwJ+PnJDUpkplhGiCxIZ39XbH0yDMPae6FIL7D4p1P41/8ikZ5bKDtawyQEYt77GEWtgjAgYgPUwoCLg+6G7vxZ6DZ9C1y+DGzfXvLfGTNkpyUyW5zASmSBhBD4ct8V/GfraRTqDWjiaocPJndB16aNZEdrMMTx40ieMgPeRw8CAK54+KNw2ftoNXms3GBEZoQTWImsmKIomNa7GTY90hsBje0Rn56H8R/vwyc7L8JgMPt/X1i2rCwUPPkUDJ27wPvoQeTa6LD5vsfgeu40iwhRDXFkhMjCZeYXYf7m49h6LBFAyaWcf/VrjmHtvbnMeG0SArlfroXhmWfgmJoMAPitdW9kvP4m7r2nD2+3JqoE1xkhakCEEPj6QAwW/3gKBcUlt5T6u9nhod6BGN/NH446jeSEli1+/2EUPPwYmh/bDwC47OqD5fc8iSmLHkEHPy5ER1QVlhGiBiglKx//23cFX+2/guu5JWuRONlqMLl7UzzYpxl8XOwkJ7QcQghEnY5DyvMvY9C2r6A1FKNAbYP1Qx+A40v/xt3dA6HTqGXHJDJrLCNEDVheoR6bDsdhze5oXErNAQBoVAru7uiDWWHNuaz8LRRficHBiP2I/DMSY7d+Br/MkmcEHenYB0VLlyF0UAgvyRBVE8sIEcFgEPjzTApW7b6E/ZeuGbf3CHTDrLDmGNTGEyrOKwEAZOUXIeqVd9H37X9DdcNfi9c8fJH39rtoMnUCwBJCZBKWESIq53hcBlbvvoSfjiWiuPSOm+buDpjeNxDjuvrBTtswLznEp+fhi53nkbP6C7z2w1LcWDeEokA5exZo1UpaPiJLxjJCRJVKzMjD53sv4+u/Y5CVXwwAaGRvgwd6BmBKrwB4OtlKTlg/jsam47tNu+CxcS3GHYuAd/a1ynfcvh0YMKBesxFZC5YRIrql7IJibDwUizV7ohF7LQ8AoFWrMKazL2aEBaKNt/X9rukNAn8euYJTH32B0D82o8+VY8bPFTq7wiYro+SBdmXU6pLVU7mMO1GNsIwQUbXoDQK/nUzCp7su4XBMunF7WCt3zAxrjn6t3C13wmZcHHD+PPICAvH7ntMoXPkpBkdGwDU/GwBgUBTk9hsIx8dmA6NHA199BTz8MKDX//M8GS7jTlRjLCNEZLLIK9exevcl/HIiCWULubb2csTMvs0xurMvbG0saF7J6tUQ//oXFIMBAig3FyTTwweq6dPh+MgsICCg/Ovi4oALF0qesMsREaI7UqdlZPny5Xj77beRmJiI9u3bY9myZQgLC6ty/7/++gvz5s3DyZMn4evri+eeew6zZ8+u9vdjGSGqX7HXcrFmTzQ2HIxFTqEeAOBsq0Ebb2cEujsg0MMBge4OaOHhAH83eznrbZSOeqBVK2S6eyH6ag5iYlORv3sP3P/8BQN+/ab8ZFQAcb0GwOPfz8J2xLB/nqhLRHWmzsrI+vXrMWXKFCxfvhx9+vTBypUrsWrVKpw6dQpNmzatsH90dDSCg4Mxa9YsPPzww9izZw8effRRrFu3DuPGjavVgyGi2pWRV4RvDsTg872XkZiRX+k+KgXwa2RfUlLcHdDco+y/jvBxtr39rcOBgSXzMpydgeefLxmRCAwEsrNL7mLx8wPi4lB45gziG/vhnNYVui8+Q793XoRKGGBQFOwIDIFzQQ46Jp6H1lBc9ffiZFSielVnZaRHjx7o2rUrVqxYYdzWtm1bjB07FkuWLKmw//PPP48ffvgBp0+fNm6bPXs2jh49in379lXre7KMEMlVpDfgTGIWLqVmIzo1B9GpObh0teS/2QVVv/nrNCpjSfmnrDiiubsDGjloq1y3o+yyikFRYXev4ei772eohIABCvY1DUbvmOOoquKku3vjetuOaLY7gpNRiSSr7vu3SQ+sKCwsRGRkJF544YVy28PDw7F3795KX7Nv3z6Eh4eX2zZs2DCsXr0aRUVFsLGxqfCagoICFBQUlDsYIpLHRq1CBz+XCs9hEULganYBokuLSXRqDi6l5uDS1WzEXMtFQbEBZ5KycCYpq8LX3L7iITQDKi0VZdtUwoCwvdv++TME+sQcrzzkc88Bs2fDtVkzuCoKsHp1xcmoLCJEZsmkMpKamgq9Xg8vL69y2728vJCUlFTpa5KSkirdv7i4GKmpqfDx8anwmiVLlmDRokWmRCMiCRRFgaeTLTydbNGjeeNynyvWGxCfnodLqTnly8rVbCRk5KNp5tUqRzfKfY/qBFGrgSeeKF82ZswAhg3jZFQiC1CjR3nefJufEOKWt/5Vtn9l28vMnz8f8+bNM/45MzMT/v7+NYlKRJJo1CoENHZAQGMHDAwq/7m8Qj0K1/rDNi62emXjRmo1sGQJMH/+7Uc9/PxYQogsgEllxN3dHWq1usIoSEpKSoXRjzLe3t6V7q/RaNC4ceNKX6PT6aDT6UyJRkQWxE6rBmJjbv+sF7UaeOCBkvU/bl77Y9IkjnoQWQmTyohWq0VISAgiIiLwf//3f8btERERGDNmTKWv6dWrF3788cdy23777TeEhoZWOl+EiBoQIcrfTfPCCyXlolkzICfnn6Lx2msViwdHPYishsmXaebNm4cpU6YgNDQUvXr1wieffIKYmBjjuiHz589HfHw8vvzySwAld858+OGHmDdvHmbNmoV9+/Zh9erVWLduXe0eCRFZpujo2+/D4kFk1UwuIxMmTEBaWhoWL16MxMREBAcHY9u2bQgoXcUwMTERMTExxv0DAwOxbds2PPXUU/joo4/g6+uL999/v9prjBAREZF143LwREREVCeq+/6tqsdMRERERBWwjBAREZFULCNEREQkFcsIERERScUyQkRERFKxjBAREZFULCNEREQkFcsIERERScUyQkRERFKZvBy8DGWLxGZmZkpOQkRERNVV9r59u8XeLaKMZGVlAQD8/f0lJyEiIiJTZWVlwcXFpcrPW8SzaQwGAxISEuDk5ARFUWrt62ZmZsLf3x+xsbFW+8wbaz9GHp/ls/ZjtPbjA6z/GHl8NSeEQFZWFnx9faFSVT0zxCJGRlQqFfzq8PHhzs7OVvkDdiNrP0Yen+Wz9mO09uMDrP8YeXw1c6sRkTKcwEpERERSsYwQERGRVA26jOh0OrzyyivQ6XSyo9QZaz9GHp/ls/ZjtPbjA6z/GHl8dc8iJrASERGR9WrQIyNEREQkH8sIERERScUyQkRERFKxjBAREZFUVl9G/vOf/6B3796wt7eHq6trtV4jhMDChQvh6+sLOzs7DBgwACdPniy3T0FBAZ544gm4u7vDwcEBo0ePRlxcXB0cwa1dv34dU6ZMgYuLC1xcXDBlyhSkp6ff8jWKolT68fbbbxv3GTBgQIXPT5w4sY6PpqKaHN+DDz5YIXvPnj3L7WMu5w8w/RiLiorw/PPPo0OHDnBwcICvry+mTp2KhISEcvvJOofLly9HYGAgbG1tERISgl27dt1y/7/++gshISGwtbVF8+bN8fHHH1fYZ9OmTWjXrh10Oh3atWuH7777rq7iV4spx7h582YMHToUHh4ecHZ2Rq9evfDrr7+W2+fzzz+v9HcyPz+/rg+lUqYc344dOyrNfubMmXL7mdM5NOX4Kvv7RFEUtG/f3riPOZ2/nTt3YtSoUfD19YWiKPj+++9v+xqz+B0UVu7ll18WS5cuFfPmzRMuLi7Ves0bb7whnJycxKZNm8Tx48fFhAkThI+Pj8jMzDTuM3v2bNGkSRMREREhDh8+LAYOHCg6deokiouL6+hIKjd8+HARHBws9u7dK/bu3SuCg4PFyJEjb/maxMTEch9r1qwRiqKIixcvGvfp37+/mDVrVrn90tPT6/pwKqjJ8U2bNk0MHz68XPa0tLRy+5jL+RPC9GNMT08XQ4YMEevXrxdnzpwR+/btEz169BAhISHl9pNxDr/55hthY2MjPv30U3Hq1CkxZ84c4eDgIK5cuVLp/pcuXRL29vZizpw54tSpU+LTTz8VNjY24ttvvzXus3fvXqFWq8Xrr78uTp8+LV5//XWh0WjE/v376/RYqmLqMc6ZM0e8+eab4sCBA+LcuXNi/vz5wsbGRhw+fNi4z2effSacnZ0r/G7KYOrxbd++XQAQZ8+eLZf9xt8lczqHph5fenp6ueOKjY0Vbm5u4pVXXjHuY07nb9u2bWLBggVi06ZNAoD47rvvbrm/ufwOWn0ZKfPZZ59Vq4wYDAbh7e0t3njjDeO2/Px84eLiIj7++GMhRMkPp42Njfjmm2+M+8THxwuVSiV++eWXWs9elVOnTgkA5X4g9u3bJwCIM2fOVPvrjBkzRgwaNKjctv79+4s5c+bUVtQaqenxTZs2TYwZM6bKz5vL+ROi9s7hgQMHBIByf6HKOIfdu3cXs2fPLretTZs24oUXXqh0/+eee060adOm3LaHH35Y9OzZ0/jn8ePHi+HDh5fbZ9iwYWLixIm1lNo0ph5jZdq1aycWLVpk/HN1/36qD6YeX1kZuX79epVf05zO4Z2ev++++04oiiIuX75s3GZO5+9G1Skj5vI7aPWXaUwVHR2NpKQkhIeHG7fpdDr0798fe/fuBQBERkaiqKio3D6+vr4IDg427lMf9u3bBxcXF/To0cO4rWfPnnBxcal2juTkZGzduhUzZsyo8Lm1a9fC3d0d7du3xzPPPGN8enJ9uZPj27FjBzw9PdG6dWvMmjULKSkpxs+Zy/kDauccAkBGRgYURalwKbI+z2FhYSEiIyPL/f8KAOHh4VUey759+yrsP2zYMBw6dAhFRUW33Ke+zxVQs2O8mcFgQFZWFtzc3Mptz87ORkBAAPz8/DBy5EhERUXVWu7qupPj69KlC3x8fDB48GBs37693OfM5RzWxvlbvXo1hgwZgoCAgHLbzeH81YS5/A5axIPy6lNSUhIAwMvLq9x2Ly8vXLlyxbiPVqtFo0aNKuxT9vr6kJSUBE9PzwrbPT09q53jiy++gJOTE+65555y2++//34EBgbC29sbJ06cwPz583H06FFERETUSvbqqOnxjRgxAvfddx8CAgIQHR2Nl156CYMGDUJkZCR0Op3ZnD+gds5hfn4+XnjhBUyePLncQ67q+xympqZCr9dX+rtT1bEkJSVVun9xcTFSU1Ph4+NT5T71fa6Amh3jzd59913k5ORg/Pjxxm1t2rTB559/jg4dOiAzMxPvvfce+vTpg6NHj6JVq1a1egy3UpPj8/HxwSeffIKQkBAUFBTgf//7HwYPHowdO3agX79+AKo+z/V9Du/0/CUmJuLnn3/G119/XW67uZy/mjCX30GLLCMLFy7EokWLbrnPwYMHERoaWuPvoShKuT8LISpsu1l19qmO6h4fUDGnqTnWrFmD+++/H7a2tuW2z5o1y/i/g4OD0apVK4SGhuLw4cPo2rVrtb52Ver6+CZMmGD838HBwQgNDUVAQAC2bt1aoXSZ8nVNUV/nsKioCBMnToTBYMDy5cvLfa4uz+GtmPq7U9n+N2+vye9jXappnnXr1mHhwoXYsmVLuRLas2fPcpOs+/Tpg65du+KDDz7A+++/X3vBq8mU4wsKCkJQUJDxz7169UJsbCzeeecdYxkx9WvWtZpm+fzzz+Hq6oqxY8eW225u589U5vA7aJFl5PHHH7/tXQHNmjWr0df29vYGUNIWfXx8jNtTUlKMzdDb2xuFhYW4fv16uX9dp6SkoHfv3jX6vjeq7vEdO3YMycnJFT539erVCi22Mrt27cLZs2exfv362+7btWtX2NjY4Pz583f8RlZfx1fGx8cHAQEBOH/+PIC6P39A/RxjUVERxo8fj+joaPz555+3ffR3bZ7Dyri7u0OtVlf419KNvzs38/b2rnR/jUaDxo0b33IfU34GaktNjrHM+vXrMWPGDGzcuBFDhgy55b4qlQrdunUz/szWlzs5vhv17NkTX331lfHP5nIO7+T4hBBYs2YNpkyZAq1We8t9ZZ2/mjCb38Fam31i5kydwPrmm28atxUUFFQ6gXX9+vXGfRISEqRNYP3777+N2/bv31/tyY/Tpk2rcAdGVY4fPy4AiL/++qvGeU11p8dXJjU1Veh0OvHFF18IIczn/AlR82MsLCwUY8eOFe3btxcpKSnV+l71cQ67d+8uHnnkkXLb2rZte8sJrG3bti23bfbs2RUmz40YMaLcPsOHD5c6gdWUYxRCiK+//lrY2tredjJhGYPBIEJDQ8VDDz10J1FrpCbHd7Nx48aJgQMHGv9sTuewpsdXNlH3+PHjt/0eMs/fjVDNCazm8Dto9WXkypUrIioqSixatEg4OjqKqKgoERUVJbKysoz7BAUFic2bNxv//MYbbwgXFxexefNmcfz4cTFp0qRKb+318/MTv//+uzh8+LAYNGiQtFt7O3bsKPbt2yf27dsnOnToUOG20JuPTwghMjIyhL29vVixYkWFr3nhwgWxaNEicfDgQREdHS22bt0q2rRpI7p06WL2x5eVlSWefvppsXfvXhEdHS22b98uevXqJZo0aWKW508I04+xqKhIjB49Wvj5+YkjR46Uu5WwoKBACCHvHJbdNrl69Wpx6tQpMXfuXOHg4GC88+CFF14QU6ZMMe5fdlvhU089JU6dOiVWr15d4bbCPXv2CLVaLd544w1x+vRp8cYbb5jFrb3VPcavv/5aaDQa8dFHH1V5m/XChQvFL7/8Ii5evCiioqLEQw89JDQaTbmSaq7H99///ld899134ty5c+LEiRPihRdeEADEpk2bjPuY0zk09fjKPPDAA6JHjx6Vfk1zOn9ZWVnG9zkAYunSpSIqKsp4p525/g5afRmZNm2aAFDhY/v27cZ9AIjPPvvM+GeDwSBeeeUV4e3tLXQ6nejXr1+FNpyXlycef/xx4ebmJuzs7MTIkSNFTExMPR3VP9LS0sT9998vnJychJOTk7j//vsr3GJ38/EJIcTKlSuFnZ1dpetOxMTEiH79+gk3Nzeh1WpFixYtxJNPPllhrY76YOrx5ebmivDwcOHh4SFsbGxE06ZNxbRp0yqcG3M5f0KYfozR0dGV/kzf+HMt8xx+9NFHIiAgQGi1WtG1a9dyIzHTpk0T/fv3L7f/jh07RJcuXYRWqxXNmjWrtCBv3LhRBAUFCRsbG9GmTZtyb3QymHKM/fv3r/RcTZs2zbjP3LlzRdOmTYVWqxUeHh4iPDxc7N27tx6PqDxTju/NN98ULVq0ELa2tqJRo0aib9++YuvWrRW+pjmdQ1N/RtPT04WdnZ345JNPKv165nT+ykZwqvp5M9ffQUWI0pkqRERERBJwnREiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEiq/wclH+JFCiVgUAAAAABJRU5ErkJggg==", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2520,10 +2375,8 @@ }, { "cell_type": "markdown", - "id": "0c5c47e2", - "metadata": { - "editable": true - }, + "id": "181b30b4", + "metadata": {}, "source": [ "## Overview video on Stochastic Gradient Descent\n", "\n", @@ -2532,10 +2385,8 @@ }, { "cell_type": "markdown", - "id": "30d83150", - "metadata": { - "editable": true - }, + "id": "b51d1452", + "metadata": {}, "source": [ "## Batches and mini-batches\n", "\n", @@ -2553,10 +2404,8 @@ }, { "cell_type": "markdown", - "id": "310429e5", - "metadata": { - "editable": true - }, + "id": "85bbbc0c", + "metadata": {}, "source": [ "## Stochastic Gradient Descent (SGD)\n", "\n", @@ -2585,10 +2434,8 @@ }, { "cell_type": "markdown", - "id": "07ec38f2", - "metadata": { - "editable": true - }, + "id": "56b2b867", + "metadata": {}, "source": [ "## Stochastic Gradient Descent\n", "\n", @@ -2602,10 +2449,8 @@ }, { "cell_type": "markdown", - "id": "79d6fab8", - "metadata": { - "editable": true - }, + "id": "386e0c45", + "metadata": {}, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -2615,10 +2460,8 @@ }, { "cell_type": "markdown", - "id": "628eb747", - "metadata": { - "editable": true - }, + "id": "0f6d09dd", + "metadata": {}, "source": [ "## Computation of gradients\n", "\n", @@ -2628,10 +2471,8 @@ }, { "cell_type": "markdown", - "id": "e1133d46", - "metadata": { - "editable": true - }, + "id": "99541bf1", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2641,10 +2482,8 @@ }, { "cell_type": "markdown", - "id": "4f6e6b79", - "metadata": { - "editable": true - }, + "id": "a24ce1cc", + "metadata": {}, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -2655,10 +2494,8 @@ }, { "cell_type": "markdown", - "id": "4c3c9492", - "metadata": { - "editable": true - }, + "id": "d6c2eea5", + "metadata": {}, "source": [ "## SGD example\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", @@ -2677,10 +2514,8 @@ }, { "cell_type": "markdown", - "id": "8ef691b4", - "metadata": { - "editable": true - }, + "id": "b2561a99", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -2692,10 +2527,8 @@ }, { "cell_type": "markdown", - "id": "31bf40f3", - "metadata": { - "editable": true - }, + "id": "a0fb8d89", + "metadata": {}, "source": [ "## The gradient step\n", "\n", @@ -2704,10 +2537,8 @@ }, { "cell_type": "markdown", - "id": "526e5e7e", - "metadata": { - "editable": true - }, + "id": "71856a7b", + "metadata": {}, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2717,10 +2548,8 @@ }, { "cell_type": "markdown", - "id": "5022af9d", - "metadata": { - "editable": true - }, + "id": "9859ff14", + "metadata": {}, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -2731,10 +2560,8 @@ }, { "cell_type": "markdown", - "id": "19c6475e", - "metadata": { - "editable": true - }, + "id": "6558ed12", + "metadata": {}, "source": [ "## Simple example code" ] @@ -2742,11 +2569,8 @@ { "cell_type": "code", "execution_count": 12, - "id": "18c7a10f", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "f8cee4e8", + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2767,10 +2591,8 @@ }, { "cell_type": "markdown", - "id": "ad3f48f9", - "metadata": { - "editable": true - }, + "id": "aac3d48e", + "metadata": {}, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -2783,10 +2605,8 @@ }, { "cell_type": "markdown", - "id": "04e70295", - "metadata": { - "editable": true - }, + "id": "657c6870", + "metadata": {}, "source": [ "## When do we stop?\n", "\n", @@ -2804,10 +2624,8 @@ }, { "cell_type": "markdown", - "id": "2f10ae80", - "metadata": { - "editable": true - }, + "id": "5a8d8a8d", + "metadata": {}, "source": [ "## Slightly different approach\n", "\n", @@ -2824,10 +2642,8 @@ }, { "cell_type": "markdown", - "id": "88e4714d", - "metadata": { - "editable": true - }, + "id": "e0c75855", + "metadata": {}, "source": [ "## Time decay rate\n", "\n", @@ -2843,12 +2659,17 @@ { "cell_type": "code", "execution_count": 13, - "id": "4c882e5c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8368a998", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma_j after 500 epochs: 9.97108e-05\n" + ] + } + ], "source": [ "import numpy as np \n", "\n", @@ -2878,10 +2699,8 @@ }, { "cell_type": "markdown", - "id": "79963b9d", - "metadata": { - "editable": true - }, + "id": "a99e7227", + "metadata": {}, "source": [ "## Code with a Number of Minibatches which varies\n", "\n", @@ -2891,12 +2710,36 @@ { "cell_type": "code", "execution_count": 14, - "id": "b13f70e7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "b567ba9d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]\n", + "theta from own gd\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "theta from own sdg\n", + "[[4.014934 ]\n", + " [3.0042992]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Importing various packages\n", "from math import exp, sqrt\n", @@ -2968,10 +2811,8 @@ }, { "cell_type": "markdown", - "id": "8e833f35", - "metadata": { - "editable": true - }, + "id": "8ea309ee", + "metadata": {}, "source": [ "## Replace or not\n", "\n", @@ -2983,10 +2824,8 @@ }, { "cell_type": "markdown", - "id": "0312dcf2", - "metadata": { - "editable": true - }, + "id": "5573b607", + "metadata": {}, "source": [ "## Momentum based GD\n", "\n", @@ -2998,10 +2837,8 @@ }, { "cell_type": "markdown", - "id": "d4730af7", - "metadata": { - "editable": true - }, + "id": "5c393430", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -3010,10 +2847,8 @@ }, { "cell_type": "markdown", - "id": "3b041d81", - "metadata": { - "editable": true - }, + "id": "03d76b90", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3028,10 +2863,8 @@ }, { "cell_type": "markdown", - "id": "e05133d9", - "metadata": { - "editable": true - }, + "id": "c9de2175", + "metadata": {}, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -3047,10 +2880,8 @@ }, { "cell_type": "markdown", - "id": "4d90938e", - "metadata": { - "editable": true - }, + "id": "a493002b", + "metadata": {}, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -3059,20 +2890,16 @@ }, { "cell_type": "markdown", - "id": "519d60d5", - "metadata": { - "editable": true - }, + "id": "cb1d7212", + "metadata": {}, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$." ] }, { "cell_type": "markdown", - "id": "487a4624", - "metadata": { - "editable": true - }, + "id": "91135b7f", + "metadata": {}, "source": [ "## More on momentum based approaches\n", "\n", @@ -3085,10 +2912,8 @@ }, { "cell_type": "markdown", - "id": "58a8bcf7", - "metadata": { - "editable": true - }, + "id": "57c90f73", + "metadata": {}, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -3097,20 +2922,16 @@ }, { "cell_type": "markdown", - "id": "6a1c6dd4", - "metadata": { - "editable": true - }, + "id": "28fc8c64", + "metadata": {}, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "id": "d77b0f55", - "metadata": { - "editable": true - }, + "id": "9ea86afa", + "metadata": {}, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -3119,20 +2940,16 @@ }, { "cell_type": "markdown", - "id": "53e0b508", - "metadata": { - "editable": true - }, + "id": "259f8bd9", + "metadata": {}, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "id": "c7919a6b", - "metadata": { - "editable": true - }, + "id": "1b3b21b9", + "metadata": {}, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -3141,10 +2958,8 @@ }, { "cell_type": "markdown", - "id": "d658c8ac", - "metadata": { - "editable": true - }, + "id": "931ce41d", + "metadata": {}, "source": [ "## Momentum parameter\n", "\n", @@ -3157,10 +2972,8 @@ }, { "cell_type": "markdown", - "id": "93e53f3f", - "metadata": { - "editable": true - }, + "id": "d1d161a1", + "metadata": {}, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -3169,10 +2982,8 @@ }, { "cell_type": "markdown", - "id": "c0a79ce5", - "metadata": { - "editable": true - }, + "id": "4f3657ba", + "metadata": {}, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -3202,10 +3013,8 @@ }, { "cell_type": "markdown", - "id": "b43632bc", - "metadata": { - "editable": true - }, + "id": "81824da9", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -3214,10 +3023,8 @@ }, { "cell_type": "markdown", - "id": "efb8ea15", - "metadata": { - "editable": true - }, + "id": "6295bc9d", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3232,20 +3039,16 @@ }, { "cell_type": "markdown", - "id": "eb92118e", - "metadata": { - "editable": true - }, + "id": "7a094665", + "metadata": {}, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$." ] }, { "cell_type": "markdown", - "id": "6c9fb86f", - "metadata": { - "editable": true - }, + "id": "f0c6bb20", + "metadata": {}, "source": [ "## Second moment of the gradient\n", "\n", @@ -3273,10 +3076,8 @@ }, { "cell_type": "markdown", - "id": "a25c923d", - "metadata": { - "editable": true - }, + "id": "ce3b45b6", + "metadata": {}, "source": [ "## RMS prop\n", "\n", @@ -3288,10 +3089,8 @@ }, { "cell_type": "markdown", - "id": "24a3b8dd", - "metadata": { - "editable": true - }, + "id": "ee7e2069", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3306,10 +3105,8 @@ }, { "cell_type": "markdown", - "id": "2a4a4d3a", - "metadata": { - "editable": true - }, + "id": "ec4f73bb", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -3318,10 +3115,8 @@ }, { "cell_type": "markdown", - "id": "38b5c0c6", - "metadata": { - "editable": true - }, + "id": "fa5cb9a2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -3330,10 +3125,8 @@ }, { "cell_type": "markdown", - "id": "81dbe505", - "metadata": { - "editable": true - }, + "id": "eb93379a", + "metadata": {}, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -3348,10 +3141,8 @@ }, { "cell_type": "markdown", - "id": "fc1157b9", - "metadata": { - "editable": true - }, + "id": "b46162a4", + "metadata": {}, "source": [ "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n", "\n", @@ -3377,10 +3168,8 @@ }, { "cell_type": "markdown", - "id": "bf9b6954", - "metadata": { - "editable": true - }, + "id": "d103bc6a", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3395,10 +3184,8 @@ }, { "cell_type": "markdown", - "id": "20de7cae", - "metadata": { - "editable": true - }, + "id": "a0f031f6", + "metadata": {}, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -3407,10 +3194,8 @@ }, { "cell_type": "markdown", - "id": "3ce79d35", - "metadata": { - "editable": true - }, + "id": "2b384f75", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -3419,10 +3204,8 @@ }, { "cell_type": "markdown", - "id": "2830d104", - "metadata": { - "editable": true - }, + "id": "216435a6", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -3431,10 +3214,8 @@ }, { "cell_type": "markdown", - "id": "90e75ad2", - "metadata": { - "editable": true - }, + "id": "8b79e19e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -3443,10 +3224,8 @@ }, { "cell_type": "markdown", - "id": "99457a88", - "metadata": { - "editable": true - }, + "id": "ba777281", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -3455,10 +3234,8 @@ }, { "cell_type": "markdown", - "id": "d7aa5ab9", - "metadata": { - "editable": true - }, + "id": "f34eb136", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3472,10 +3249,8 @@ }, { "cell_type": "markdown", - "id": "26071aca", - "metadata": { - "editable": true - }, + "id": "695da6fd", + "metadata": {}, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -3491,10 +3266,8 @@ }, { "cell_type": "markdown", - "id": "09f63a9f", - "metadata": { - "editable": true - }, + "id": "8771f487", + "metadata": {}, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -3503,10 +3276,8 @@ }, { "cell_type": "markdown", - "id": "74b65884", - "metadata": { - "editable": true - }, + "id": "6b816830", + "metadata": {}, "source": [ "## Algorithms and codes for Adagrad, RMSprop and Adam\n", "\n", @@ -3517,10 +3288,8 @@ }, { "cell_type": "markdown", - "id": "0d5cee10", - "metadata": { - "editable": true - }, + "id": "4efb5cb8", + "metadata": {}, "source": [ "## Practical tips\n", "\n", @@ -3537,10 +3306,8 @@ }, { "cell_type": "markdown", - "id": "09734edc", - "metadata": { - "editable": true - }, + "id": "de7affbf", + "metadata": {}, "source": [ "## Automatic differentiation\n", "\n", @@ -3575,10 +3342,8 @@ }, { "cell_type": "markdown", - "id": "81d6131f", - "metadata": { - "editable": true - }, + "id": "3383da7c", + "metadata": {}, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -3587,20 +3352,16 @@ }, { "cell_type": "markdown", - "id": "0795db2e", - "metadata": { - "editable": true - }, + "id": "a8a03664", + "metadata": {}, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "id": "84ede40a", - "metadata": { - "editable": true - }, + "id": "da4e8c9e", + "metadata": {}, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -3609,10 +3370,8 @@ }, { "cell_type": "markdown", - "id": "3c0048b2", - "metadata": { - "editable": true - }, + "id": "b35c008d", + "metadata": {}, "source": [ "Using **autograd** we have" ] @@ -3620,12 +3379,27 @@ { "cell_type": "code", "execution_count": 15, - "id": "4f554ba9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9bb36858", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max absolute difference is: 1.77636e-15\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "\n", @@ -3665,10 +3439,8 @@ }, { "cell_type": "markdown", - "id": "dbb0af99", - "metadata": { - "editable": true - }, + "id": "9f8c7b5e", + "metadata": {}, "source": [ "## Using autograd\n", "\n", @@ -3682,12 +3454,18 @@ { "cell_type": "code", "execution_count": 16, - "id": "b44bbeac", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "65176228", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f1 evaluated at a = 1 using autograd is: 3\n", + "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3710,10 +3488,8 @@ }, { "cell_type": "markdown", - "id": "93f27878", - "metadata": { - "editable": true - }, + "id": "44375951", + "metadata": {}, "source": [ "## Autograd with more complicated functions\n", "\n", @@ -3725,12 +3501,23 @@ { "cell_type": "code", "execution_count": 17, - "id": "79de7d5e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "63ebdbaf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Evaluating at x1 = 1, x2 = 3\n", + "------------------------------\n", + "The derivative of f2 w.r.t x1: 12\n", + "The analytical derivative of f2 w.r.t x1: 12\n", + "\n", + "The derivative of f2 w.r.t x2: -4\n", + "The analytical derivative of f2 w.r.t x2: -4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3769,20 +3556,16 @@ }, { "cell_type": "markdown", - "id": "61ab2c3d", - "metadata": { - "editable": true - }, + "id": "ddef1f9a", + "metadata": {}, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] }, { "cell_type": "markdown", - "id": "b4784f66", - "metadata": { - "editable": true - }, + "id": "c6ff810b", + "metadata": {}, "source": [ "## More complicated functions using the elements of their arguments directly" ] @@ -3790,12 +3573,18 @@ { "cell_type": "code", "execution_count": 18, - "id": "73c1b6aa", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8c1ef66a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed gradient of f3 is: [ 2. 3. 5. 7. 88.]\n", + "The analytical gradient of f3 is: [ 2. 3. 5. 7. 88.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3818,10 +3607,8 @@ }, { "cell_type": "markdown", - "id": "c73c3739", - "metadata": { - "editable": true - }, + "id": "7ac0e490", + "metadata": {}, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -3833,10 +3620,8 @@ }, { "cell_type": "markdown", - "id": "94962c03", - "metadata": { - "editable": true - }, + "id": "f817a4b1", + "metadata": {}, "source": [ "## Functions using mathematical functions from Numpy" ] @@ -3844,12 +3629,18 @@ { "cell_type": "code", "execution_count": 19, - "id": "a48211f9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9950eceb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f4 at x = 2.7 is: 13.8759\n", + "The analytical gradient of f4 at x = 2.7 is: 13.8759\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3872,10 +3663,8 @@ }, { "cell_type": "markdown", - "id": "e8423919", - "metadata": { - "editable": true - }, + "id": "2d3597e1", + "metadata": {}, "source": [ "## More autograd" ] @@ -3883,12 +3672,17 @@ { "cell_type": "code", "execution_count": 20, - "id": "a3645e2a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a694b773", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f5 at x = 2.7 is: 5.4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3908,10 +3702,8 @@ }, { "cell_type": "markdown", - "id": "ef1a0f30", - "metadata": { - "editable": true - }, + "id": "63681987", + "metadata": {}, "source": [ "## And with loops" ] @@ -3919,12 +3711,18 @@ { "cell_type": "code", "execution_count": 21, - "id": "2bb96160", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ae061106", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f6_for at x = 0.5 is: 3.95703\n", + "The computed derivative of f6_while at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3955,12 +3753,17 @@ { "cell_type": "code", "execution_count": 22, - "id": "8434bcd7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a194eddc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The analytical derivative of f6 at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3975,10 +3778,8 @@ }, { "cell_type": "markdown", - "id": "df3fa84c", - "metadata": { - "editable": true - }, + "id": "8c21cf38", + "metadata": {}, "source": [ "## Using recursion" ] @@ -3986,12 +3787,18 @@ { "cell_type": "code", "execution_count": 23, - "id": "427c3a1f", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3eb55bad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f7 at n = 2 is: 1\n", + "The analytical derivative of f7 at n = 2 is: 1\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4024,20 +3831,16 @@ }, { "cell_type": "markdown", - "id": "6379139b", - "metadata": { - "editable": true - }, + "id": "12fbb13b", + "metadata": {}, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input." ] }, { "cell_type": "markdown", - "id": "82d727a4", - "metadata": { - "editable": true - }, + "id": "19ed9d51", + "metadata": {}, "source": [ "## Unsupported functions\n", "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", @@ -4048,11 +3851,8 @@ { "cell_type": "code", "execution_count": 24, - "id": "fce0115b", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "fb297a92", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4061,29 +3861,25 @@ " x[2] = 3\n", " return x*2\n", "\n", - "f8_grad = grad(f8)\n", + "#f8_grad = grad(f8)\n", "\n", - "x = 8.4\n", + "#x = 8.4\n", "\n", - "print(\"The derivative of f8 is:\",f8_grad(x))" + "#print(\"The derivative of f8 is:\",f8_grad(x))" ] }, { "cell_type": "markdown", - "id": "1dc97436", - "metadata": { - "editable": true - }, + "id": "06d0bc95", + "metadata": {}, "source": [ - "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." + "Here, running this code, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." ] }, { "cell_type": "markdown", - "id": "251cb0ff", - "metadata": { - "editable": true - }, + "id": "9974f300", + "metadata": {}, "source": [ "## The syntax a.dot(b) when finding the dot product" ] @@ -4091,11 +3887,8 @@ { "cell_type": "code", "execution_count": 25, - "id": "9b4aad8e", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "cbb0a202", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4104,19 +3897,17 @@ " b = np.array([1.0,2.0])\n", " return a.dot(b)\n", "\n", - "f9_grad = grad(f9)\n", + "#f9_grad = grad(f9)\n", "\n", - "x = np.array([1.0,0.0])\n", + "#x = np.array([1.0,0.0])\n", "\n", - "print(\"The derivative of f9 is:\",f9_grad(x))" + "#print(\"The derivative of f9 is:\",f9_grad(x))" ] }, { "cell_type": "markdown", - "id": "82401096", - "metadata": { - "editable": true - }, + "id": "7f08b96c", + "metadata": {}, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -4126,12 +3917,17 @@ { "cell_type": "code", "execution_count": 26, - "id": "11f68a91", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cba444cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f9 is: [1. 2.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4151,10 +3947,8 @@ }, { "cell_type": "markdown", - "id": "979bbeda", - "metadata": { - "editable": true - }, + "id": "18e2b174", + "metadata": {}, "source": [ "## Recommended to avoid\n", "The documentation recommends to avoid inplace operations such as" @@ -4163,12 +3957,21 @@ { "cell_type": "code", "execution_count": 27, - "id": "8b90b52c", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "69c6914d", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'b' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[27], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[43mb\u001b[49m\n\u001b[1;32m 2\u001b[0m a \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m b\n\u001b[1;32m 3\u001b[0m a\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m b\n", + "\u001b[0;31mNameError\u001b[0m: name 'b' is not defined" + ] + } + ], "source": [ "a += b\n", "a -= b\n", @@ -4178,10 +3981,8 @@ }, { "cell_type": "markdown", - "id": "a88d50f6", - "metadata": { - "editable": true - }, + "id": "600cc052", + "metadata": {}, "source": [ "## Using Autograd with OLS\n", "\n", @@ -4193,12 +3994,33 @@ { "cell_type": "code", "execution_count": 28, - "id": "632ffb09", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cd18340b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.94499279]\n", + " [3.03306538]]\n", + "Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]\n", + "theta from own gd\n", + "[[3.94499279]\n", + " [3.03306538]]\n" + ] + }, + { + "data": { + "image/png": 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FbGwsHnnkEZw+fdp7BSYiIiKf4vUwVFJSgvbt22PevHlV9pWWlmLXrl3429/+hl27diEzMxNHjhzBkCFDvFBSIiIi8kWSEEJ4uxBmkiRh2bJlGDZsmN1jtm/fjq5du+LEiRNo0qSJQ+ctLi5GeHg4ioqKEBYWJlNpiYiIyJ089f0d4LYzu0lRUREkSUL9+vXtHlNeXo7y8nLL7eLiYg+UjIiIiNTI681kzigrK8PUqVMxatSoahPizJkzER4ebvlJSEjwYCmJiIhITVQThioqKvCnP/0JRqMRH3zwQbXHTps2DUVFRZaf3NxcD5WSiIiI1EYVzWQVFRUYMWIEcnJysGHDhhrbDYODgxEcHOyh0hEREZGaKT4MmYPQ0aNHkZWVhcjISG8XiYiIiHyI18PQlStXcOzYMcvtnJwc7NmzBxEREYiNjcXw4cOxa9curFq1CgaDAQUFBQCAiIgIBAUFeavYRERE5CO8PrQ+Ozsbffv2rbJ9zJgxmD59OpKSkmzeLysrC3369HHoMTi0noiISH00M7S+T58+qC6PKWgaJCIiIvJBXg9DREREpGIGA7B5M5CfD8TEAKmpgL+/t0vlFIYhIiIick1mJjBpEnDq1PVt8fHA3LlAWpr3yuUk1cwzRERERAqSmQkMH24dhAAgL8+0PTPTO+VyAcMQERGRUhgMQHY2sGiR6bfB4O0S2WYwmGqEbPXrNW+bPFm55b8JwxAREZESZGYCiYlA377AqFGm34mJyqxh2by5ao3QjYQAcnNNx6kAwxAREZG3qa3JKT9f3uO8jGGIiIjIm9TY5BQTI+9xXsYwRERE5E1qbHJKTTWNGpMk2/slCUhIMB2nAgxDRERE3qTGJid/f9PweaBqIDLfnjNHNfMNMQwRERF5k1qbnNLSgCVLgLg46+3x8abtKppnyOtrk3kC1yYjIiLFMhhMo8by8mz3G5IkU8DIyVFmTYsbZ6DWzNpkREREmmZucho+3BR8bgxEamhy8vcHHFw4XanYTEZERORtPtTkpEasGSIiIlKCtDRg6FDVL3qqRgxDRERESuEDTU5qxGYyIiIi0jSGISIiItI0hiEiIiLSNIYhIiIi0jSGISIiItI0hiEiIiLSNA6tJyIi8kVuXCbD1zAMERER+ZrMTGDSJODUqevb4uNNy35wNusq2ExGRETkSzIzTeuc3RiEANNCsMOHm/aTFYYhIiIiM4MByM4GFi0y/TYYvF0i5xgMphqhGxd7NTNvmzxZfdflZgxDREREgKnGJDER6NsXGDXK9DsxUV01KZs3V60RupEQQG6u6Th3UGmYZBgiIiLylaal/Hx5j3OGisMkwxAREWmbLzUtxcTIe5yjVB4mGYaIiEjbvN20JKfUVNOoMUmyvV+SgIQE03Fy8YEwyTBERETa5s2mJbn5+5uGzwNVA5H59pw58s435ANhkmGIiIi0zVtNS+6SlgYsWQLExVlvj483bZd7niEfCJOcdJGIiLTN3LSUl2e7qUeSTPvlbFpyt6FDgfBw04guAOjTx/Qj9wzUBgNw5oxjxyo4TDIMERGRtpmbloYPNwWfGwORu5qW3MVgAGbMMF3PhQvXty9cKP/s07ZmubblxjCp0CVC2ExGRETk6aYld8jMBKKjgddesw5CgPyjuuyNHrvZjWFyxQrFDr2XhLBVJ+hbiouLER4ejqKiIoSFhXm7OEREpFQKrbmokTmcVPeVbq6hycmp3TUZDKYQU1MQAkwj1+bMMf3bVvnMYclO4PTU9zfDEBERkZo5E04AICvL1H/IVdnZplqdmsyeDUyYYPp3deWrJqR56vubzWRERKReKl3+QVY1DW2/WW1HdTl6/+hoU7hRwdB7dqAmIiJ1stWBNz5e/o7CSudsuKntqC5npyJQwdB7r9cMbdq0CTqdDrGxsZAkCcuXL7faL4TA9OnTERsbizp16qBPnz7Yv3+/dwpLRETKoPLlH2TlTLiRY/ZpZ2e5VsE8Tl4PQyUlJWjfvj3mzZtnc/+sWbPwzjvvYN68edi+fTsaN26Mfv364fLlyx4uKRERKYIPLP8gq5rCyY3kmCLA2VmuHSmfl+dx8noYGjhwIF5//XWk2ajSFEJgzpw5eOWVV5CWloaUlBR89tlnKC0tRUZGhhdKS0REXqeCPigeVV04MYuMBJYula/50JmpCBwp39WrpqH3NxFGz4zx8noYqk5OTg4KCgrQv39/y7bg4GD07t0bP/74o937lZeXo7i42OqHiIh8hAr6oHicvXASGQmkp5tmiXY1CNnrpJ6WBhw/bhqdlpFh+p2TY/txzOWLiLD9GBcuWJo3yy6V4dvXd2B8241IjvTMa6joDtQFBQUAgOjoaKvt0dHROHHihN37zZw5E+np6W4tGxEReYkK+qB4RVqaaRkOOedJqqmTur+/48P0hw41ncsWISAAnHvwGdxqPILL6PzHDs9UZii6ZshMuqlaTQhRZduNpk2bhqKiIstPbm6uu4tIRESe4mwHXi0xh5ORI2u/FpncndRraN6UADQyFqIjdiPWLx9/abUJX764w/lyu0DRYahx48YArtcQmRUWFlapLbpRcHAwwsLCrH6IiMhHONuBl5znhk7qlTmOVUx8Om4HTlU0xr8P9sK9r3Su+Q4yUHQYSkpKQuPGjbFu3TrLtmvXrmHjxo244447vFgyIiLyKl9YS0zJZOqkfv7oBXz+9BY8GL8VQx6z01/oJs0e7AzJz4GRcTLyep+hK1eu4NixY5bbOTk52LNnDyIiItCkSRNMnjwZb7zxBpo3b47mzZvjjTfeQGhoKEaNGuXFUhMRkde5o48MmbjYSV0YBQ6t+R36D3Kh/6EBfixOgRF3AgD8YMBpxKAx8m3XxNy4ur2HeT0M7dixA31vWONkypQpAIAxY8Zg4cKFePHFF3H16lWMGzcOFy9eRLdu3fDdd9+hXr163ioyEREphTMdeMlxTnRSryitwJaP9mHlF8XQ703Eb5W3ArjVcki7kMMY0jkfuscaofEt78LvoRGmHTc2wXm5eZMLtRIREWmVwWC7Zs28+Gtens1+Q0KSUFq3EZ5ssARrctuhCOGWfUEoR9/IvdDdVYLBk25F057x1ne2NULNvLr9Tc2bXLVeRgxDREREN6lp2Lx5NBlgFYiMMNXiDMcSLEMa/GDAYKzCwOhdaNMnGrf/3yjUS6hf/WPbC2E3YRiSEcMQERHRDcxB5+YIYG6uWrIElfcNweFn30Xcf/+F+hVnLYecRAImYw6OBLfF1KaL8GDhBwi+dOb6OWRcLJdhSEYMQ0REpAmO1LiYm8DsjBYTAC74R6GVYR/OoRH8YEAqNiMeuYiuV4rEe5pj0MTb0OzCjhoDVW0Dkae+v73egZqIiIhkUFOzl5kDkx9GGgqRjP3YK7XDfYkHoBsahAHPDUF4kz/6BhkMQGJP+/MQSZJpHqKhQ63DmIPNY57GMERERKR29pq9zLNF31BLY8zNc2iSwY/GbMNtH92JgJA7q+50Zh4i82g/R8OaFzAMERFpiUL/MlcUtT1HNc0WLUkwTpiIZT9EQb8CuPjbLai6PnxVrcZ2B0LsxARn5yFyIqx5A8MQEZFWKPgvc8VQ43PkQC2N3+k8vPdOJTaiD/xgQB5iEYPTrk9+6MxiuQ6ENZtNah6k6OU4iIhIJnIvuumL1PocOVhLc7v/r3iuYza+f/tXRGfMhp8kub62mzOL5cq0tIc7MQwREfk6Nyy66XNU+hyVFJZgi/6iQ8e+811bvLOzD/pOuR0BI0fUbm03ZxbLdXFpD09iGCIi8nUq+Mvc61T0HJ3ano+PRm3CoKjtiIz2R+9FTyEX8ZbJEKv4o5ZG6t3LentaGnD8OJCVBWRkmH7n5DjeHOjoYrnONKl5CfsMERH5OhX8Ze51Cn6OjJVG7Mo4BP0nhdBvj8buq60BXA8OSQEn8V3cX/DYib9DSBIkZ9b8qu3abo4slmtuUrOztIc3F2g1YxgiIvJ1KvjL3OsU9hxdvXAV6+fshf7rMqw60hynjW0AtAEASDCi+y37obvjPHRPxyF56G2Q/P4GZCbb7vxtY80vWdUUqMxNasOHm4KPghZotRSDM1ATEfm4GhbdtPxlnpOj7CHk7uTp58jG8P38veew6p3D0H8XjO/PtMVVhFoOr4srGBC7D7qBlbjvuZaISm7k8HkV85o6sUCrGZfjkBHDEBFpnp1FN+VcOkH1PPUc2QgFZ6RoPCM+wDJcP3+Cfx50rY9hyJ/qos+EtggOC679Y3ubk2GNYUhGDENERHDpL3PNcfNzdO3zxQh8ZCQAWHV3Nnd+nhb8Durd2QG6v8Sg3fAWkPzsdIrWCIYhGTEMERH9QcnNKEoh83NUuP8sVr99CKu/8cOcgocQC9vLYQhJgqT15sqbcKFWIiKSX21HD2lBLZ8jYRTYt+wo9P8+Df3WSPx0JRkCqeiNbMQjz+79JFvreZFHMAwRERHV0rUr17Bx3l7oF12B/kAzHK9sAaCFZX/HOgcxIXE9cNCBk9kavs8aPbdiGCIiInLBucPnsebtg9Cv8cfavGRcRifLvhBcxd1Re6G7pwyDn2uOuM6tgey7gb6v13zim4fvq3G9NJVhnyEiIlIuBdWICKPAoTW/Q/9BLvQ/NMCPxSkw4npZov0KoWt+CLoHgnH3pBTUjaprfQJXhu/bW+1dI6MA2YFaRgxDREQqpIAakYrSCmz+cB/0/yuGfm8ifqtsarW/fchh6DrnQ/dYI3Qe3Rp+ATWscuXM8H1zeLK3TIgG5odiGJIRwxARkcp4sUbkYs4lfPPWfuhXSfjmZDKKEG7ZF4Ry9I3ciyH3lGDwpNvQpEdcNWeyw9Hh+9nZQN++NZ8vK8tnO1xzNBkREWlTTSvIS5JpBfmhQ2WrETmyNgf6eSeg31wfW4pSYEBPy75G0lkMuvUQdPcHot/kZNSL7Vy7B3NkPS9A0eul+RqGISIiUhZnVpB3sUaksqwSP/5nP/T/vYiVvzTFkYokAEmW/cnBRzGkYx50YyPRdWwb+AfJvIioI8P3FbZemi9jGCIiImVxU41I0ckifPv2fuhXCqw50QYXRXvLvkBcQ++IvdD1uQLdpGZI6tUcQHOnzi87Faz27isYhoiISFlkrBH5Pfsk9O/mYGV2PWy62BaVuMOyryHO4rmYxbirwwW0fbQz6qbdq6yOyCpY7d1XsAM1EREpSy1WkDdcM2DbJ/uh/+wC9HvicaD8Nqv9rYJ+g659Lsa224XW386GlOfASDVvD+/X8JpyHE0mI4YhIvJZ3v6idhcnhqBfPn0Z383eh5WZBqzJaYVzoqHlcH9Uolf9vdD1LoJuQhJuu7upcyPVFDC8H4Dvvs41YBiSEcMQEfkkpXxRu0s1NSInortCP+c36LPqIvt8W1xDsOWQ+tIlDGyyHzqdhHuntEGDpPrX7+/M3D0rVmh6wkMlYBiSEcMQEfkcrcxM/EeNiPFUHg79cg0ZPzTByt0J2FvWwuqw2wKPY0i749A9XB89/5KMwNBA2+dzdO6e778Hxo7V9ISHSsB5hoiIyDYvzMPjDSWFJVg3ex/0S/2x+rd+OGOMsuzzgwE9w/ZBd+dF6MY3Qct7kyD5JdZ8UkdHoGVnu314PykHwxARkdp4YB4ebzm1PR/6d45Cv74ONpxti3J0s+yrh2IMTNgH3SCBgVNaI7J5+2rOZIfcc/JwwkOfwDBERKQ2PjQzsbHSiF0Zh7Dq43zk/XQKV64FIR8x2IyOMMIfSQEnoUvOgW5UPfQal4KgW+6o+aTVcXTunj59gNddWGGeVIlhiIhIbVQ+M3HpuVKsn7sP+iVlWHWkBbobD2EuJiEB12u7ioMb4dLk15DwxjhIfk3ke3BH5+7p04cTHmpIDcvrEhGR4phrN8xf3jeTJNOoKwV9UefvOYP/PLIJQxr/hIaNgCGvd8V/DvVCd+OPWILhiId1s1/YtXNoMmsCpOXL5C9MWpqpg3ncTYusxsdf73huDk1A1eeZEx76HI4mIyJSIyfm4fEGYRTY8+Vh6P9TAP1PUdhR2sZqfxP/UxjS+gj+7+RIBBcXwmasc/eILUfm7tHwhIdKwKH1MmIYIiKfpLAv6rJLZch6dy/0X13FqkO3ItdgXfPSte4+6Lqfg+4vMWg3vAWkTRsdG+aeleXdjuAanfBQCTi0noiIqpeWZho+78Uv6jP7zmL124egXxuIdfkpKEEXy75QlKBf433QDbiGQVNaonG7FOs7q6UjuCMrzJOqKT4MVVZWYvr06fjf//6HgoICxMTEYOzYsXj11Vfh58cuT0SkcR7+ohZGgX3LjkL/79PQb43ET1eSIZAKPxiQis1Ilg7g1oQKtBzTDXdNbo86Ed3sn0zlHcHJdyg+DL355pv46KOP8NlnnyE5ORk7duzAo48+ivDwcEyaNMnbxSMiT2OThceVF5dj4/v7oF90BasONsPxyhYArs8A/deguXhVmoHw8rOAAHASwIJ4oEMNy4KYO4JXN2cSAJw9K8dlENml+D5DgwcPRnR0ND755BPLtgceeAChoaH4/PPPHToH+wwR+Qg1r8WlshB37vB5rHn7IPRr/LE2LxmXcf3/zhBcxd1Re6G7pwzD2x9F5NQnXV8WZMkS4MEHqy9MQoJvLnuhsveEN3js+1so3MyZM0XTpk3F4cOHhRBC7NmzR0RFRYmMjAyHz1FUVCQAiKKiIncVk4jcbelSISRJCNPX7vUfSTL9LF3q7RLat3SpEPHx1uWOj1dUmY0Go9i/4qj4171Zome9X4QfKq2K29ivQDzRcqNY8fI2UXK2xHSnysqq13Xza5OQYDrOnqws+/e/8ScryxNPg+eo4D2hBJ76/lZ8M9lLL72EoqIitGrVCv7+/jAYDJgxYwZGjhxp9z7l5eUoLy+33C4uLvZEUYnIXdS8Fpe9BVXz8kzbvTgEvqK0Aps/3Af9/4qh35uI3ypvA3CbZX/7kMPQdc6H7rFG6Dy6NfwCoq1PIMeyIGrpRC0nBb8ntErxYejLL7/EF198gYyMDCQnJ2PPnj2YPHkyYmNjMWbMGJv3mTlzJtLT0z1cUiJyG7WuxaW0EGcwoHjxGvy6cCc2/NIQc86OwkXcbtkdhHLc1fBX6O4uxeBJt6FJj5YAWto/nxxBxlc7URsMpsVes7NNt/v0uf7eVNJ7gkzcWu8kg/j4eDFv3jyrbf/85z9Fy5Yt7d6nrKxMFBUVWX5yc3PZTEakZhkZjjWlONF87naVlULMnq2IJqDD3/4ulndKF2ekaKvHPYl4MRafirG3bRJLX9gqivOKnTuxHE1c5qY2W02gjja1Kc3SpUJERla9lshIIdLTFfGeUAs2k/2htLS0yhB6f39/GI1Gu/cJDg5GcHCwu4tG5PuU0sFTbbUHtjp6V0fmJqDKskr88O990H9+CfpfmyK5YjeWYDpMQ72ui0cePpUeh/Smi80yZ8+a3g8Gg+39jqzf5ehaYc6877z5vs3MBB54wPa+8+eB115z7Dy+1CyoBm6NWjIYM2aMiIuLE6tWrRI5OTkiMzNTNGzYULz44osOn4MdqIlcIEcHz8pK01+4GRmm367+da+m2gN7Hb3dXAtw6cQlsXjiD+LPiVtEA+mC5dR+qBQnESeMtenk7Op1OtOx3db7LSHB+Q7F3uyYXFkpRFycc689a4aq5anvb8WHoeLiYjFp0iTRpEkTERISIpo1ayZeeeUVUV5e7vA5GIaInCTHyC25v5TMZbq5XEoaTVbT6CqZQ9yx9cfF7GHZ4q4GO0UArlm3yEjnxOhmm0XW8Hnyf/k6cp3+/kJ8/bVzF1Tb8OztEYeONhu68T3haxiGZMQwROQEOYZLu+tLSa7aA3dx5svQheeisrxSbPngF/FStyzRJvholVO2CjomXuyaJTa//4uoLP/j9ZG7v5WC+kJVKVdt37e15ehzfWOZlBrsFYJ9hojIO2o7csudI6gUsBZXtZzp5xEf79CCqpdPX8bat/dBv9yANTmtcE60s+zzRyV61d8LXe8i6CYk4ba7bwVwq/UJ5Oxv5eW+UNVy9X0rZ/8iZ/qspacD//lP1QlEvbTIrtYxDBGpndydRWs7XNrdw+CVvGimo1+Gs2cDEybYfZ1O/HAK+jm/QZ9VF1nn26ECPSz76kuXcF+T/dANkXDv88mo3/R2m+ewMC95kZdnO6A60skZsD83TnXc1aHd1nvelfet3DOap6YCcXGm57o68fHAK6+YfpQa7LXGmWqkkydPuquGyq3YTEY+yx2dRWs7XFqNw+Dl4mJHb0OFQWz9z17x8h1Zom3I4Sp3ax74u5jSKUtkzd4trpVcc75cte1v5eG+UDVei633vLND1t3ZlFtTGdgM5jBF9hkKDQ0Vr776qrhy5Yq7yuMWDEPkk9z1n3ltR25pdXkFMweDx5UzV8SyqdvEY803iSip0OpQP1SKXuG7xf8NyhKH1vwmz6i82vS3cnNfKKeuwd57HjDN4+PI+9bd/Yuqm2eIQcgpigxDP/zwg+jatauIiYkRn376qbvKJDuGIfI5nvjP3NWaBG8Ng5drGL8cli6tOsQ6Pl6cffNj8cGfNoqBjX4WwbhqtTsMl8SIhB/E509vEeeOnLc+lyO1f45cv6vPkTMdg93Vod2R97w5DNX0vvVEYK+sFOL774V49VXTz/ffc4SYCxQZhsw+++wzER8fLzp06CCyVPDXHcMQ+RxP/Gdem5oETw+DV9qilzbKU4BocT+WWhUxKeCEmNQhW3w/a6cov2xjuhBHa//ccf03BidHR4/Nnu2+kPvqq46VIT295vetGptylRT2PUjRYUgIIUpLS8Xf/vY3ERoaKoYNGyaOHj0qZ7lkxTBEPsdT/5nX5j9gTw2D9/bcMjcpW5AhjECVSQ4NkIQBkpgW8raYOSBL7Ft+VBgNRvsncrT276uv5L9+W6+dv3/NZZH7C9pWORx5z9f0vlVbU67Swr4HKT4MlZSUiM2bN4vJkycLPz8/ERwcLKZMmSKKi51c28YDGIZIlar7D10t/5m7+69ZJcwtI4TI25kv/v3njWJIox9FLuKEwU55jM6Ux9HXuGHD2l3/za+RvXBV3WO4q7bP2Zm8HX3P+8KM5hqZk0iRYejDDz8Ujz32mGjbtq0ICAgQwcHBokuXLmLChAnik08+EXfddZeIj48X27dvd1d5XcIwRKpT01+CNf1nDgjRqJEQTszUrkpeCoVGg1Hsyjgo0vtmic6h+y0P0xsylsfZCfxceTxna4Bs7XdHbZ+zo9dcCTC+MKO5kkKbmygyDMXHx4vhw4eLt956S2zZskWUlZVVOWbGjBkiOTlZtgLKgWGIPK62zUuO9hOx9Z+5vQDlizzY9+Pqxati9fSfxdNtNop4/7wqD9Gt7l6RmeJgvxZHyiPH0g7VPZ6rNS+AqW+QO/uuOHvtrgYYX5nR3Ns1wG6kyDDkiIKCAuHn5yf3aWuFYYg8qjbt+87+JVhTn4ra/JWrhg6bznxZuHA9BXsLxSdjN4lhMVtFXVy2OmUoroihjbeJj8dsEvm/nHG+PDVxpCmnUSPXHs+Vmhdnw1xtOFsrVpsAo+T3uRo7estMtWHIaDSK7OxsuU9bKwxD5DG1bd935cu0vLz2/UZsXYcaOmw62vfj668duh6jwSh++fqweP2eLNGt7l4hwWB1lzi/0+LpNhvF6uk/i9Lzpa6XR66mHPN1Oft4ta11cndNhKPle/VV5QUYObFmSL1hSIkYhsgj5Gjfd+UvQbn/w1RSh01H/mqvKTC88EK113Pt88Vi7Rs7xLNts0VT/9wqh3UK3S+m98kSO784UP3oL0fLI3dTjiuP52p/JE/1UVFTB2d34vPAMCQnhiHyCDlCiSvnkLMqXUkdNp2pnbIXGL76qtrrMQDiJOKEHyotm0NQKgZH/ST+/eeNIm9nvnxld2dTjrOP50rNkKfDsBo6OHuCxp8HhiEZMQyRR8gRSlz5S1DOmiGlVMu7UjtlKzA4eD33S0vFEy03ihUvbxMlZ0vkuQZP90Vx5vEcGY3oiVFjNVF6B2dP0fDz4Knvb65aTyQXR1foru44f3/TitnDh5tWExfi+j5JMv2eM8d6ZWu5ViUHar9ivRwMBtNK4rauRQjT9UyeDAwdav083LSafUVpBQ7P/xEpDjzkkv9ehd/DvWpbcms3lcdltlZot7WyuTOP58j7bPFioGFD766onpZmep21vrI7nwf3c2vUUgjWDJFHyNm+7+xfgnJVpSuhZqgWZTh/7IL44pkt4qGEH0Q4Lsk77483uLsju4ZrHEgdPPX9LQlh688v31JcXIzw8HAUFRUhLCzM28UhX5aZafprG7D91/aSJaa/8hzhaI3AjY89aRJw6tT1bQkJppokZx4zMbHmWqacHPf9VbpoETBqVM3HZWQAI0fi8De/Q//+Sei31McPRSkw4HqFdzQKcCCgHRpUnoVk6xyeuB5Xmd9LN78OrryXquPs+4zIgzz1/c0wRCQ3OUKJq+T4YpMz0LkiOxvo27fGwz5sMRtzcobiSEWS1faU4KPQdcyDbmwkuo5tA/9VK7x7Pa4wh9Ib30M3UnKII5IRw5CMGIbI49T+17a3A101tVNGSDiFeCQhB0b4IxDX0CdiL3R9r0A3+VYk3hlf9ZzevB5XOBgIkZUlT78kIoViGJIRwxCRC7wZ6DIzIR4YDkBYNW8Z/7j1KBZANLsVuqH+GDAlGWHxDnyuDQZTyMjONt3u08f0o8SQ6mRTIZGv8tT3N0eTEZFtco2GcpDhmgFbP94P/WcXoN/THq2wBHMxCQm4XptTHNQQ+WOm4tN5D8M/yMkQs2KFde3Q66+bmprmzlVe7ZAcIxOJyGGsGSIiryk+VYzvZu+HfrkBq3Na47yItOwLQAV6h/+Cp1K2ILW3Hxr3a+d67ZSnOiPLRQkd2YkUgM1kMmIYIlKO41tOQT/nN+izbkH2hbaoQJBlX33pEu5rsh+6IRLufT4Z9ZuG1/4B1doZ2dsd2YkUgM1kROQTjJVG/LzwAPQLzkG/KxZ7y1oAuN7JuXlgDnTtTmDI6Pro+VQKAkJ6yluAzZvtByHAFDRyc03HKakzclqaKfDc3PE7Pl65Hb+JVIphiKg21D5qzE2uFFzButn7oF9WgdXHWqFQXJ8H2g8G3Bm+F7o7L0E3vglaDmwGIMn+yWpLCbNqu4ozDxN5BMMQuZ+vBgZbw7WV2iHXA3J/Oo1Vc45Bv74ONpxti3J0t+wLQxHuTdgP3SCBgVNaI7J5B88VTO2dkT3ckZ1Ii7TdZ8hXv6SVxFcDg9o65LqBsdKInf87BP0nhdDvaIw9V1tZ7W8WcAK6lOPQjaqH1GdSEHRLkJ0zuRk7IxOpFjtQy8jmk+mrX9JK4quBQa0dcmVQeq4U6+fug35JGVYdaYF8Y2PLPglG9Ki3D7o7LmDIuHi0HnwrJD+bi2B4HjsjE6kSw5CMqjyZvvolrSS+HBg0Njvw6V0FWPXOEejXheD7wrYoQx3LvltwGQPi9kE30ID7prRCo9YNvVjSGqhtFmoi4mgytzEYTP8h2sqAQpi+pCdPNnVaVNuXtJKodQSPI9TcIdcBwiiw58vD0P+nACt/isLO0jYArtcANfE/hSFtfoNu5C3oPT4FwWE9vFdYZ7AzMhHZob0w5Mtf0kriy4FB7R1ybSi7VIYNc/dC/9VVrDp8G04ZWgEw9QGSYETXugeg63EOuqdi0TatOSQ/G+t/qQE7IxORDdoLQ778Ja0kagsMznSmT001NfHV1CE3NdW9Za6lM/vOYvXbh6BfG4jv8tuiFF0s+0JRgv4xe6EbUIFBz7dCdEpKNWciIlI37YUhtX1Jq5WaAoOznen9/U37hg83XYetDrlz5iiu+UUYBfZmHoX+36eh39oQP5e0gcD15z/OLx+6VkehG1EHd01qi5D63as5GxGR79BeB+q6dTnM1lPUMIKnNp3pvdUh14larPLicmx8fx/0i65Af+BWnDBYN291Dj0AXbdC6J5sjA4PtVTO6C8iInA0mazsjiYDlPsl7Ss8HRicae6SY8Sbp+eqcqAW6+zBc1jzziHov/HH2rwUXEE9y6EhuIp7ovZC168Mg6e0QGzHxjc/AhGRYjAMycjheYY4zFZe5qCQlwecPQs0agTExbkvMDjb3KW2IfJ2arGEJAECWN5hOt76bRi2Xk6BgJ9lf4xfAQa3OALd8BDcPSkFoQ1DPV1yIiKXcGi9u3GYrXtVF0zcFYRsNXfl5Zm226rtU1Nn+mqmhJCEgBESOu35GNvwCgT80KHOIeg6F0D3eBQ6/bkV/ALcUAPEGdyJyEdoNwwBHGbrLq4Ek9pwde4oNXWmr2FKCD8INEEuMvvOQ8eZDyKh2/Wh8W7BGdyJyIf41XyI9+Xl5eHhhx9GZGQkQkND0aFDB+zcudPbxSJbagomgCmYGAzyPaYzc0fdyDziTbLTaViSTE2nXhzxdvib3/HW4Gz8476tDh0/9MkoJHSLdW+hzGH35ufcHHYzM937+EREMlN8GLp48SJ69uyJwMBAfPPNNzhw4ADefvtt1K9f39tFI1tcDSa14Wpzl3mIPFA1ELlriLzBYOqrtGiR6fdNobCyrBLZc/bg+c7ZaBGUg1b3NcMLq/tgw1UHZ3l2dy2WN8IuEZGbKb6Z7M0330RCQgIWLFhg2ZaYmOi9AlH1vNEPpzbNXWlppmY7W00+cnemt9O0VPLqG9DvvxX6lQLfnGyDi6IDAMAPBtyNdbir7s9o3bEOKg82RsD5M96dt4kzuBORD1J8GFq5ciUGDBiABx98EBs3bkRcXBzGjRuHJ5980u59ysvLUV5ebrldXFzsiaIS4J1+OLWd4NETnent9KMynspDnafH4CsswTKYglekdB5/j/oIT5S8i9ArhUAJgM0AIiOv94Hy1kSPaup0TkTkIMU3k/3+++/48MMP0bx5c6xduxZPP/00Jk6ciP/+97927zNz5kyEh4dbfhISEjxYYo3zRj8cOZq7zJ3pR440/Za5aUxMnARbs1j4wbTtfTyLl7qsx+b3f8WZxVmYWPg3UxC60YULpt8REdbbGzQA/v53IDzcbvObbNTU6ZyIyEGKn2coKCgInTt3xo8//mjZNnHiRGzfvh1bt9ruVGqrZighIcHt8xTQH7w1qaXC5o4qPlWMte/sx9HFO/By/sSa75CVZQqJNU0EGRcHPP448N571wPSzdw1sss8USVncCciD/DUPEOKrxmKiYlBmzZtrLa1bt0aJ0+etHuf4OBghIWFWf2QB5n74cTFWW+Pj3fv7N5pacDx46ZQkZFh+p2T49EgdHzLKbw3fCP6R+5Ew4QQjJjdA3vzGzp25/x8x/rknDoFpKfbD0KA+0Z2eaPTORGRmym+z1DPnj1x+PBhq21HjhxB06ZNvVQicoi3JrV099xRN000aOh2B37+/DD0C89DvysO+8qbA7i+/leLwBz0SjoDHHHg3DEx8vW1qW5+pdryZKdzIiIPUHwz2fbt23HHHXcgPT0dI0aMwM8//4wnn3wS8+fPx5///GeHzuGpajafwFmF7bPRDJeHWEzAe5bOz/6oRM/wfdDdeQm68U3QcmAz55qWNm92bIkQZ8yeDURHy/968r1CRG7mse9voQJ6vV6kpKSI4OBg0apVKzF//nyn7l9UVCQAiKKiIjeV0EcsXSpEfLwQpq9s0098vGm7xp2d+R9hBITxxucGEAZIwgBJvBU5Q3zxzBZx/tgF2ydYulQISTL93HgO8+3Jk4XIyhKivFyIyEjrY+T84etJRCriqe9vxdcMyYE1Qw6wt4SGuzs9K5Sx0oid/zsE/SeFWL29EZaX3Ys4nLLZyU5IEiRHOg3b6uDt72898is+Hrh0CbhyRa5LsabR15OI1Imr1suIYagG5mac6kYwaWCEUOm5Unw/ey/0S8ux6mhLFBijAQC9kY1syLS6vblpacUKU/8ab9DI60lE6sdV67XIW30wNDyr8OldBVj1zhHo14Xg+8K2KEM3y75bcBkD4vZhYotsIMuBkznS+dnf3/S6jh7tcplrzYdfTyIiVzAMKYU3VwHX0KzCwiiwe9Eh6D8+A/3PUdhZ2gZAY8v+pv6noGvzG3Qjb0Hv8SkIDusBZJcDWek1n9zRiQZrCp+e4gOvJxGRHBiGlMBefx3zXDHu7t/h47MKl10qw4a5e6H/6ir0h5ojz9gaQGsAgAQjutY9AF2PcxjydCxS7m8OyS/e+gS1Xe7jZnKGEPNIsago0+3CQuDMGeC552q+r0pfTyIiubHPkLcpob+OD84qXPBrIVa/cxj6tUFYV5CCUtS17AtFCfrH7IVuQAUGPd8K0SmNaj6hnLNqZ2fXfvh8da+JD76eRKRNnIFaK5zpr+MuPjCrsDAK/LrkCGb0y0a3W/Yhpn0UnvgsFSsKuqEUdRHvfxpPt9mENenbcf6iP5ad7o7HFqQ6FoQAeWfVdmT9tsjIqmuQ3bgfsP+a+MDrSUTkSQxD3qaU/jreWkKjFsqLy7F2xg48224jEoPy0P7BFnj1+z74uSQFANA59ADS+2ZjV8YhnLwWgw/398LAv3dBSP0Q1x5QruU+HAkr8+ebmrzS06uGIkdeExW+nkRE3sJmMneraYSYo00mjgzbloPCZxU+e/Ac1rxzCPpv/LE2LwVXUM+yLwRXcU/UXgwZUIZBk1sgtmPjas6kAI4uLFub10ThrycRUXU4z5CMvBaGHBkh5q3+HSr5khRGgQP636D/8BT0P0Zg6+UUiBsqNGP8CjC4xRHohofg7kkpCG0Y6sXSukAlrwMRkTcwDMnIK2HImRmd5eyc62jZvDWM3wHXrlzD5g/3QZ9xGSv3JSGnsonV/g51DmFIlwLoHo9Cx1Gt4BfA1l4iIl/EMCQjj4chV0aIOdpkUlsKXXbj/NEL+Oadg9CvlvBtbjKKEW7ZF4wy3NVoL3R3X8XgybchoVusx8tHRESexzAkI4+HIVf7Abm7yUQJw/hvcPib36F//yRWbm6AH4pTYMT1x4ySzmLwbYegeyAI90xKxi2Nb3F7eYiISFm4HIeauTpCzN/fvZ2kZ8xwbtkNmcNZZVkltny0D/ovLkH/a1McrWgGoJllf9uQI9B1PA3dow3RdWwb+AU4OIkhERFRLTAMuYMSZ3TOzARee82xY/PzZetXdOlEEb59ez9WrhT45mQyLokOln2BuIa+kb9C17cEgyfdisQ7WwBo4fC5iYiI5MBmMndQ2gzANTWP3WzsWGDhwqrbHexXdGz9Cejfy4F+Yzg2X0pBJQIt+yKl8xiUdBC6Yf7o/1wywuIVNiM4EREpBvsMyciro8kAz4wQq44cyz+Y2QhyhmsGbP14P/SfXcDKPQk4dO1Wq7u0CT4GXYdT0I2JQPfHk+EfxKHjRERUM/YZUjvzDMC2mprkHiFWEzlnr/6jX1FJ5rdYszUC+hUGrMlpjfOineWQAFSgV4O90PW+DN2ERNx6120AbpOvDErDuYKIiFSNYcid0tKAoUO9/0Xphr5JT4+4gC8wyHK7gXQR9zU9AN0QCQOmJKN+046yP6YiKXzOJiIiqhmbybSgpj5MLuiDLOQHNoWu3QnoRtdHz6dSEBCisWxtb84ms6++Ah580LNlIiLyIWwmI/mYFwYdPtzU56cWgUgAuBoYhvnL49HiviQASbIVU1UMBlONUHXP5ciRpufb3HeMiIgUiesYKJXBYOr4vGiR6bfBULvz2VvF3EkSgNCwQLQYoNEQZLZ5c82j8wwGU81QZqZnykRERC5hGFKizExTs1bfvsCoUabfiYm1/1JNSwOOH4fx+/U49pdZ+DT5bRQgGkZIzp3n/HlTGNAyZzqlT55c+zBLRERuw2YypbHXDyUvz7TdxSH5pedK8f3svdAvLceqo8koMN4FALgfiViC4TBCgh+caD6rzQg1Xxh95Uyn9Btn9SYiIsVhGFKS6vqhCGHqfzJ5smmEmgPhIW9HPlbNPgr99yFYX9gWZehm2VcPxRgQtx+6+6Jwpe0ChM161fFJGQHXR6j5yuir1FRTuR19zuSc3oCIiGTF0WRK4uoCr38QRoHdiw5B//EZ6H+Ows7SNlb7m/qfgq7Nb9CNvAW9x6cgOCz4+k5zbU1enilwnTtn+7FrM3u2vVovb0xEKYfMTOCBBxw79sbXzBdqxoiIPICjybTIhQVer164ig3v7oP+q6tYdbg58oytAbQGAEgwotst+6HrcR66p2KRcn9zSH7xts954yKxdepUP3v2nDnOf3nLXOulCGlppuHzI0fa7xNkDo+pfyw66ys1Y0REPoRhSEkcbHq6UBqCZWM3Q782COsKUlCKLpZ9oShB/5i90A2owKDnWyE6pa3z5XDH7Nk1jb76Y2Zr1fWtefBBU+CxNZ/QzeHRTf3BiIiodthM5ihPNG3UMDmiAHBGaow4cQpGXH/seP/T0LU6Bt2IOug7sS1C6ofIVx65rnnRItPIuJpkZJhqWtTGVo1PQsL18FjTYrmeXryXiEgF2EymJJ5q2rhhckQhSZBuCETm4e/jxPswwh+dQw9A160QQ56KQfsHW0Dyi5WvHDeWR65aGkc7XLth6RCPBNmall7x1ZoxIiIfwDBUEw82bZw9eA6r10ShsP4bGHXxPcTj9PWHQxy+CB+PgUMaYt7kAsR2bAOgjf2TKY159JW9JUFu7lsjF0/20akuPLrQH4yIiDyDzWTVcXPThjAKHND/Bv2Hp7Dyh0hsu5IM8cc8mH4wYJi0AvfG7EHK3TFo/38PIzS6ntOPoSjmYAnY7pgtd58ZJY1eq+VIQSIiLfJUMxnDUHXc8AV27co1bPpgH/QZl6Hfn4ScyiZW+2+vcxC6LmegezwKHUe1gl+Aj00SXlPfGrkorY9OTYvlss8QEVEV7DOkBDI1bZw/egHfvHMQ+tUSvs1NRjE6WvYFowx3NdqLIfdcxeDnmiO+y/Wh8T6ppr41clFaH53qFsutzZQFRERUawxD1XGx068wChz+Ngf6909Cv6UBfihOgRE9LfujpLMYfNsh6B4IQr/nUlA3qsvNZ/RtcnbMtkeJfXTcMWUBERHVmrbDUE2jjJzo9FtRWoEf5u+H/otLWPlrIo5VNAPQzHJo25AjGNLpNHSPNkSXMW3gFyBzR2Gy5s3Ra9XxVM0YERE5TFt9hlatQti9916fAM+RUUbVdPoVALbc+zo+PNAb35xMxiVR37I7ENfQN/JX6PqWQDf5VjTtaWfmZ3IP9tEhIlI9dqCWkeXJBBAWH2+a1O+ttxwfZWQjOJ2RojFevIeluD7zcEPpHAY1OwTd/f7o/1wK6sWqfPSX2nl69BoREcmKYUhGVmGopoNvqjGoLKvE1o/3Y9Vn55C/pwAVlX7IRww2IxVG+KNN8DHoOpyCbkwEuj+eDP8g1jIoiqdGrxERkewYhuyYOXMmXn75ZUyaNAlz5sxx6D5OhaE/ZA+fh092tsea421wQURYtgegAr0b7IWuz2UMfjYRt97V1OlrIA/jKvFERKrEofU2bN++HfPnz0e7du3c/lj/XhKBxbgTANBAuoj7mh6AboiEe59PRniTjjXcmxTFE6PXiIhItVQzo9+VK1fw5z//Gf/5z3/QoEEDtz9eYIDAXztnY+O7v6CwtB6+yOmJh+begfAm4W5/bCIiIvIc1dQMjR8/HoMGDcI999yD119/vdpjy8vLUV5ebrldXFzs8OMIAPDzw39LhgNBQS6WVoXYlERERBqlijC0ePFi7Nq1C9u3b3fo+JkzZyI9Pd2lx5IAwGgEfvxRO00rzi5myuBEREQ+RPHNZLm5uZg0aRK++OILhISEOHSfadOmoaioyPKTm5tr2Wd09IHlmpnYYDCtcbZokem3wSDPeWvLXK7nngMeeKDq0hV5eaZh6ZmZ1tszM03z9/TtC4waZfqdmFj1OCIiIpVQ/Giy5cuX4/7774f/DTUPBoMBkiTBz88P5eXlVvtsuXE0Wb1GjSCdPVvzA8uxerizNS6eYqtcttw8MaGSVoEnIiKfx6H1f7h8+TJOnDhhte3RRx9Fq1at8NJLLyElJaXGc1jNQN2vH3Drre6fmVipwcFeuaqTlWVqClPSKvBEROTzPBWGFN9MVq9ePaSkpFj91K1bF5GRkQ4FISupqaZO0XPnmm6bg4mZXKuHGwymmhdbgcO8bfJkzzeZVVeu6uTnO7cKPBERkYooPgy5hXn18Lg46+3x8fLU2Cg1ONRULntiYty3CrxS+1TZo7byEhFRjVQxmuxm2dnZtT+JO1cPd1dwqC1nH8/c9JWa6nhwc2YVeKX2qbJHbeUlIiKHqDIMycZdMxM7GgicCQ5ycObxbm4yTE01ffHX1NcqNdWx89vru2QexeZqDZ27hv27q7xEROR12mwmczdzcLi5T5KZJJkWC3U0OHiqXDe6ucnQ31++vlbu6lPlrmH/Su0DRkREsmAYcgc5g4OcHCnX5Mmm0WM5OVVrOuTqa+WOPlXmmhtH50tyhlL7gBERkSwYhtzF3Z203VGupUuB2bNNTYf2glpaGnD8uCkwZWTYD07VkbtPlbtrbpTaB4yIiGSh7T5D7ubOTtreLFdt+1rJ3afKmZobV8qt1D5gREQkC4Yhd3NXJ+3a8ma55O6M7e6aG7nLS0REisJmMvI8uftUubvmRql9wIiISBYMQ+Qdcvap8sToPaX2ASMiolpT/NpkcvDU2ibkArnmBTKPJgOsm7LkXgvOXfMYERFRFVyoVUYMQxpha4bohARTExZrboiIVMdT39/sQE2+Q6mj94iISNEYhsi3KHX0HhERKRY7UBMREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpik+DM2cORNdunRBvXr1EBUVhWHDhuHw4cPeLhYRERH5CMWHoY0bN2L8+PHYtm0b1q1bh8rKSvTv3x8lJSXeLhoRERH5AEkIIbxdCGecPXsWUVFR2LhxI3r16uXQfYqLixEeHo6ioiKEhYW5uYREREQkB099fwe47cxuUlRUBACIiIiwe0x5eTnKy8stt4uLi91eLiIiIlInxTeT3UgIgSlTpuDOO+9ESkqK3eNmzpyJ8PBwy09CQoIHS0lERERqoqpmsvHjx2P16tXYsmUL4uPj7R5nq2YoISGBzWREREQqwmaym0yYMAErV67Epk2bqg1CABAcHIzg4GAPlYyIiIjUTPFhSAiBCRMmYNmyZcjOzkZSUpK3i0REREQ+RPFhaPz48cjIyMCKFStQr149FBQUAADCw8NRp04dL5eOiIiI1E7xfYYkSbK5fcGCBRg7dqxD5+DQeiIiIvVhn6E/KDyrERERkcqpamg9ERERkdwYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTVBOGPvjgAyQlJSEkJASdOnXC5s2bvV0kIiIi8gGqCENffvklJk+ejFdeeQW7d+9GamoqBg4ciJMnT3q7aERERKRykhBCeLsQNenWrRs6duyIDz/80LKtdevWGDZsGGbOnFnj/YuLixEeHo6ioiKEhYW5s6hEREQkE099fyu+ZujatWvYuXMn+vfvb7W9f//++PHHH71UKiIiIvIVAd4uQE3OnTsHg8GA6Ohoq+3R0dEoKCiweZ/y8nKUl5dbbhcVFQEwJUwiIiJSB/P3trsbsRQfhswkSbK6LYSoss1s5syZSE9Pr7I9ISHBLWUjIiIi9zl//jzCw8Pddn7Fh6GGDRvC39+/Si1QYWFhldois2nTpmHKlCmW25cuXULTpk1x8uRJtz6ZSlNcXIyEhATk5uZqqq8Ur5vXrQW8bl63FhQVFaFJkyaIiIhw6+MoPgwFBQWhU6dOWLduHe6//37L9nXr1mHo0KE27xMcHIzg4OAq28PDwzX1JjILCwvjdWsIr1tbeN3aotXr9vNzbxdnxYchAJgyZQpGjx6Nzp07o0ePHpg/fz5OnjyJp59+2ttFIyIiIpVTRRh66KGHcP78efzjH/9Afn4+UlJSsGbNGjRt2tTbRSMiIiKVU0UYAoBx48Zh3LhxLt03ODgYr732ms2mM1/G6+Z1awGvm9etBbxu9163KiZdJCIiInIXxU+6SERERORODENERESkaQxDREREpGkMQ0RERKRpqgxDH3zwAZKSkhASEoJOnTph8+bN1R6/ceNGdOrUCSEhIWjWrBk++uijKscsXboUbdq0QXBwMNq0aYNly5a5q/guc+a6MzMz0a9fPzRq1AhhYWHo0aMH1q5da3XMwoULIUlSlZ+ysjJ3X4pTnLnu7Oxsm9d06NAhq+N87fUeO3aszetOTk62HKOG13vTpk3Q6XSIjY2FJElYvnx5jffxhc+3s9ftK59vZ6/bVz7fzl63r3y+Z86ciS5duqBevXqIiorCsGHDcPjw4Rrv54nPuOrC0JdffonJkyfjlVdewe7du5GamoqBAwfi5MmTNo/PycnBfffdh9TUVOzevRsvv/wyJk6ciKVLl1qO2bp1Kx566CGMHj0av/zyC0aPHo0RI0bgp59+8tRl1cjZ6960aRP69euHNWvWYOfOnejbty90Oh12795tdVxYWBjy8/OtfkJCQjxxSQ5x9rrNDh8+bHVNzZs3t+zzxdd77ty5Vtebm5uLiIgIPPjgg1bHKf31LikpQfv27TFv3jyHjveVz7ez1+0rn29nr9tM7Z9vZ6/bVz7fGzduxPjx47Ft2zasW7cOlZWV6N+/P0pKSuzex2OfcaEyXbt2FU8//bTVtlatWompU6faPP7FF18UrVq1str21FNPie7du1tujxgxQtx7771WxwwYMED86U9/kqnUtefsddvSpk0bkZ6ebrm9YMECER4eLlcR3cLZ687KyhIAxMWLF+2eUwuv97Jly4QkSeL48eOWbWp4vW8EQCxbtqzaY3zl830jR67bFjV+vm/kyHX7yuf7Rq683r7w+RZCiMLCQgFAbNy40e4xnvqMq6pm6Nq1a9i5cyf69+9vtb1///748ccfbd5n69atVY4fMGAAduzYgYqKimqPsXdOT3Plum9mNBpx+fLlKovdXblyBU2bNkV8fDwGDx5c5S9Lb6rNdd9+++2IiYnB3XffjaysLKt9Wni9P/nkE9xzzz1VZmlX8uvtCl/4fMtBjZ/v2lDz51sOvvL5LioqAoBqF2H11GdcVWHo3LlzMBgMVVarj46OrrKqvVlBQYHN4ysrK3Hu3Llqj7F3Tk9z5bpv9vbbb6OkpAQjRoywbGvVqhUWLlyIlStXYtGiRQgJCUHPnj1x9OhRWcvvKleuOyYmBvPnz8fSpUuRmZmJli1b4u6778amTZssx/j6652fn49vvvkGTzzxhNV2pb/ervCFz7cc1Pj5doUvfL5ry1c+30IITJkyBXfeeSdSUlLsHuepz7hqluO4kSRJVreFEFW21XT8zdudPac3uFrGRYsWYfr06VixYgWioqIs27t3747u3btbbvfs2RMdO3bEe++9h3fffVe+gteSM9fdsmVLtGzZ0nK7R48eyM3NxVtvvYVevXq5dE5vcbWMCxcuRP369TFs2DCr7Wp5vZ3lK59vV6n98+0MX/p8u8pXPt/PPvssfv31V2zZsqXGYz3xGVdVzVDDhg3h7+9fJe0VFhZWSYVmjRs3tnl8QEAAIiMjqz3G3jk9zZXrNvvyyy/x+OOP46uvvsI999xT7bF+fn7o0qWLYv6SqM1136h79+5W1+TLr7cQAp9++ilGjx6NoKCgao9V2uvtCl/4fNeGmj/fclHb57s2fOXzPWHCBKxcuRJZWVmIj4+v9lhPfcZVFYaCgoLQqVMnrFu3zmr7unXrcMcdd9i8T48ePaoc/91336Fz584IDAys9hh75/Q0V64bMP3FOHbsWGRkZGDQoEE1Po4QAnv27EFMTEytyywHV6/7Zrt377a6Jl99vQHTaI1jx47h8ccfr/FxlPZ6u8IXPt+uUvvnWy5q+3zXhto/30IIPPvss8jMzMSGDRuQlJRU43089hl3uKu1QixevFgEBgaKTz75RBw4cEBMnjxZ1K1b19KrfurUqWL06NGW43///XcRGhoqnnvuOXHgwAHxySefiMDAQLFkyRLLMT/88IPw9/cX//rXv8TBgwfFv/71LxEQECC2bdvm8euzx9nrzsjIEAEBAeL9998X+fn5lp9Lly5Zjpk+fbr49ttvxW+//SZ2794tHn30UREQECB++uknj1+fPc5e9+zZs8WyZcvEkSNHxL59+8TUqVMFALF06VLLMb74eps9/PDDolu3bjbPqYbX+/Lly2L37t1i9+7dAoB45513xO7du8WJEyeEEL77+Xb2un3l8+3sdfvK59vZ6zZT++f7mWeeEeHh4SI7O9vqfVtaWmo5xlufcdWFISGEeP/990XTpk1FUFCQ6Nixo9WwvDFjxojevXtbHZ+dnS1uv/12ERQUJBITE8WHH35Y5Zxff/21aNmypQgMDBStWrWy+nAphTPX3bt3bwGgys+YMWMsx0yePFk0adJEBAUFiUaNGon+/fuLH3/80YNX5BhnrvvNN98Ut956qwgJCRENGjQQd955p1i9enWVc/ra6y2EEJcuXRJ16tQR8+fPt3k+Nbze5qHT9t63vvr5dva6feXz7ex1+8rn25X3uS98vm1dMwCxYMECyzHe+oxLfxSQiIiISJNU1WeIiIiISG4MQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0SkSosWLUJISAjy8vIs25544gm0a9cORUVFXiwZEakN1yYjIlUSQqBDhw5ITU3FvHnzkJ6ejo8//hjbtm1DXFyct4tHRCoS4O0CEBG5QpIkzJgxA8OHD0dsbCzmzp2LzZs3MwgRkdNYM0REqtaxY0fs378f3333HXr37u3t4hCRCrHPEBGp1tq1a3Ho0CEYDAZER0d7uzhEpFKsGSIiVdq1axf69OmD999/H4sXL0ZoaCi+/vprbxeLiFSIfYaISHWOHz+OQYMGYerUqRg9ejTatGmDLl26YOfOnejUqZO3i0dEKsOaISJSlQsXLqBnz57o1asX/v3vf1u2Dx06FOXl5fj222+9WDoiUiOGISIiItI0dqAmIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJN+3+0i07aOseSSwAAAABJRU5ErkJggg==", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4253,10 +4075,8 @@ }, { "cell_type": "markdown", - "id": "77f1f250", - "metadata": { - "editable": true - }, + "id": "849de571", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4264,12 +4084,86 @@ { "cell_type": "code", "execution_count": 29, - "id": "ed5ad521", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ac458170", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.]\n", + " [3.]]\n", + "Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]\n", + "0 [-20.62275788] [-25.73690387]\n", + "1 [-0.03662823] [0.02925855]\n", + "2 [-0.0342458] [0.02735547]\n", + "3 [-0.03201832] [0.02557617]\n", + "4 [-0.02993573] [0.0239126]\n", + "5 [-0.0279886] [0.02235723]\n", + "6 [-0.02616812] [0.02090304]\n", + "7 [-0.02446604] [0.01954342]\n", + "8 [-0.02287468] [0.01827225]\n", + "9 [-0.02138683] [0.01708375]\n", + "10 [-0.01999575] [0.01597256]\n", + "11 [-0.01869515] [0.01493365]\n", + "12 [-0.01747915] [0.01396231]\n", + "13 [-0.01634224] [0.01305415]\n", + "14 [-0.01527928] [0.01220505]\n", + "15 [-0.01428546] [0.01141119]\n", + "16 [-0.01335628] [0.01066897]\n", + "17 [-0.01248754] [0.00997502]\n", + "18 [-0.0116753] [0.0093262]\n", + "19 [-0.01091589] [0.00871959]\n", + "20 [-0.01020588] [0.00815244]\n", + "21 [-0.00954206] [0.00762217]\n", + "22 [-0.0089214] [0.0071264]\n", + "23 [-0.00834112] [0.00666287]\n", + "24 [-0.00779859] [0.00622949]\n", + "25 [-0.00729134] [0.0058243]\n", + "26 [-0.00681708] [0.00544547]\n", + "27 [-0.00637367] [0.00509128]\n", + "28 [-0.0059591] [0.00476012]\n", + "29 [-0.0055715] [0.0044505]\n", + "theta from own gd\n", + "[[3.98281205]\n", + " [3.0137297 ]]\n", + "0 [-0.00520911] [0.00416103]\n", + "1 [-0.00487029] [0.00389038]\n", + "2 [-0.00445186] [0.00355614]\n", + "3 [-0.00403677] [0.00322456]\n", + "4 [-0.00364967] [0.00291535]\n", + "5 [-0.00329616] [0.00263296]\n", + "6 [-0.00297571] [0.00237699]\n", + "7 [-0.00268602] [0.00214559]\n", + "8 [-0.00242441] [0.00193661]\n", + "9 [-0.00218823] [0.00174795]\n", + "10 [-0.00197505] [0.00157766]\n", + "11 [-0.00178263] [0.00142396]\n", + "12 [-0.00160895] [0.00128523]\n", + "13 [-0.0014522] [0.00116001]\n", + "14 [-0.00131072] [0.001047]\n", + "15 [-0.00118302] [0.00094499]\n", + "16 [-0.00106776] [0.00085292]\n", + "17 [-0.00096373] [0.00076983]\n", + "18 [-0.00086984] [0.00069482]\n", + "19 [-0.00078509] [0.00062713]\n", + "20 [-0.0007086] [0.00056603]\n", + "21 [-0.00063957] [0.00051088]\n", + "22 [-0.00057726] [0.00046111]\n", + "23 [-0.00052102] [0.00041619]\n", + "24 [-0.00047025] [0.00037564]\n", + "25 [-0.00042444] [0.00033904]\n", + "26 [-0.00038309] [0.00030601]\n", + "27 [-0.00034576] [0.0002762]\n", + "28 [-0.00031208] [0.00024929]\n", + "29 [-0.00028167] [0.000225]\n", + "theta from own gd wth momentum\n", + "[[3.99916114]\n", + " [3.00067008]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4328,23 +4222,37 @@ }, { "cell_type": "markdown", - "id": "78643d49", - "metadata": { - "editable": true - }, + "id": "f33ed0dd", + "metadata": {}, "source": [ - "## But noen of these can compete with Newton's method" + "## But none of these can compete with Newton's method" ] }, { "cell_type": "code", "execution_count": 30, - "id": "b6031b96", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e6b06cdb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.26281735]\n", + " [2.84478178]]\n", + "Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]\n", + "0 [-14.67490857] [-18.08539155]\n", + "1 [-4.46170878e-15] [-1.45781905e-14]\n", + "2 [-1.21430643e-15] [-1.24768421e-15]\n", + "3 [4.92661467e-16] [4.50610071e-16]\n", + "4 [4.92661467e-16] [4.50610071e-16]\n", + "beta from own Newton code\n", + "[[4.26281735]\n", + " [2.84478178]]\n" + ] + } + ], "source": [ "# Using Newton's method\n", "from random import random, seed\n", @@ -4388,10 +4296,8 @@ }, { "cell_type": "markdown", - "id": "ac22e7a1", - "metadata": { - "editable": true - }, + "id": "90de8a04", + "metadata": {}, "source": [ "## Including Stochastic Gradient Descent with Autograd\n", "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." @@ -4400,12 +4306,42 @@ { "cell_type": "code", "execution_count": 31, - "id": "4852067a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a010a209", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.0586484]\n", + " [3.0718316]]\n", + "Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]\n", + "theta from own gd\n", + "[[4.0586484]\n", + " [3.0718316]]\n" + ] + }, + { + "data": { + "image/png": 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YIiIiAtSzxmx5HLkNBkNERESAevp8VBQgSfr3SxIQHa0+jjwKgyEiIiJAXUdoyRL1/9cOiDS3Fy9mvSEPxGCIiIhIIzUV+PprIDJSd3tUlHo76wx5JBZdJCIiqik1FUhJYQVqGWEwREREVJu3NzBokLNbQQ7CYTIiIiKSNQZDREREJGsMhoiIiEjWnB4Mbdu2DaNGjUJERAQkScLq1au1+yorKzF9+nR07NgRjRo1QkREBB5//HFcuHDBeQ0mIiIij+L0YKi0tBSdO3fG0qVL6+y7desW9u7di1dffRV79+5FdnY2jh8/DoVC4YSWEhERkSeShNC3PK9zSJKEVatWYfTo0QaP2b17N3r16oUzZ86gVatWJp23uLgYQUFBKCoqQmBgoI1aS0RERPbkqO9vt5taX1RUBEmS0LRpU4PHlJeXo7y8XHu7uLjYAS0jIiIid+T0YTJzlJWVYcaMGXjkkUfqjRDnzZuHoKAg7V90dLQDW0lERETuxG2CocrKSjz88MOorq7Ge++9V++xM2fORFFRkfYvPz/fQa0kIiIid+MWw2SVlZUYM2YM8vLysGXLFqPjhv7+/vD393dQ64iIiMiduXwwpAmETpw4gZycHDRv3tzZTSIiIiIP4vRg6ObNmzh58qT2dl5eHn799VcEBwcjIiICaWlp2Lt3L9atWweVSoXCwkIAQHBwMPz8/JzVbCIiIvIQTp9an5ubi+Tk5Drbx48fj9mzZyM2Nlbv/XJycjDIxEX0OLWeiIjI/chmav2gQYNQXzzmQmWQiIiIyAO5zWwyIiIiIntgMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZM3pa5MRERGRhVQqYPt2oKAACA8HkpIAb29nt8rtMBgiIiJyR9nZwHPPAefO3dkWFQUsWQKkpjqvXW6Iw2RERETuJjsbSEvTDYQA4Px59fbsbOe0y00xGCIiInInKpW6R0iIuvs029LT1ceRSRgMERERuZPt2+v2CNUkBJCfrz6OTMJgiIiIyJ0UFNj2OGIwRERE5FbCw217HDEYIiIicitJSepZY5Kkf78kAdHR6uPIJAyGiIiI3Im3t3r6PFA3INLcXryY9YbMwGCIiIjI3aSmAl9/DURG6m6PilJvZ50hs7DoIhGRO2HFYdJITQVSUvh+sAEGQ0RE7oIVh6k2b29g0CBnt8LtcZiMiMgdsOIwkd0wGCIicnWsOExkVwyGiIhcHSsOE9kVgyEiIlfHisNEdsVgiIjI1bHiMJFdMRgiInJ1rDhMZFcMhoiIXB0rDhPZFYMhIiJ3wIrDrk+lAnJzgZUr1f/l7D63waKLRETughWHXRcLYro1SQh9hSs8S3FxMYKCglBUVITAwEBnN4eIiNxZ7SVRrlwBxoypWwdKM4TJnjuLOer7mz1DREREptLXA+TtXX9BzL/+FQgKUi+bwV48l8ScISIiIlMYWhLFWG7Q1avA4MFATAyXTXFRDIaIiIiMqW9JFFNxHTmXxWCIiIjIGGNLopiC68iZrOxGGb59fTee7/WjQx6POUNERETG2Gqpk5rryA0aZJtzeogrx65i/cIjUH7jgw0XElGKngCKHfLYTu8Z2rZtG0aNGoWIiAhIkoTVq1fr7BdCYPbs2YiIiECDBg0waNAgHDp0yDmNJSIiebL1UidcRw4AcOzb3/HPEblICvoNoXFNMeGj/si+0AelaIwo7wt4Is4xPUNOD4ZKS0vRuXNnLF26VO/+BQsW4O2338bSpUuxe/duhIWFYciQISgpKXFwS4mISLaMLYkCmDdTTKbryKkqVPjhvf14uVcu2vvlIW54G7z8zSD8UNwZ1fBG1wZHMGtgLn759AjOVoTj7Z/6OaRdLlVnSJIkrFq1CqNHjwag7hWKiIhAeno6pk+fDgAoLy9HaGgo5s+fj6eeesqk87LOEBERWU0zmwzQn0g9axbQrx/w8MPAtWv6zyFJ6qAqL0820+xvFt7E928fhDK7Cut/j8MV0UK7zxcV+FPz/VAMLsXI5+5Cq766FdZZZwhAXl4eCgsLMXToUO02f39/DBw4EDt27DAYDJWXl6O8vFx7u7jYMWOORETkwTRLotSuM6QxZ4460HniCWDhQvW2mkGTjNaRO7+nAOsWnYByYwNsvtwR5eij3ddMuo4RMYegGO2NYRkdEBjVw4ktVXPpYKiwsBAAEBoaqrM9NDQUZ86cMXi/efPmYc6cOXZtGxERyZBmSZS5c9U9QbWdP68OhF58Ub1GWe3lORYvdlw16tqVsu24dIuoFtj/9XEoPyiAclcI9txKAHBnKLCtzxmkdM6DYlxT9HsqET4B/e3SDku5dDCkIdUaoxVC1NlW08yZM5GRkaG9XVxcjOjoaLu1j4iIZObf/9a/XQh1D9DnnwOnTgE7djhnHTkHrJVWcbMCW5cegDLzJpSH2+Ksqj2A9gAACdXo0/gQFP2uImVqNOKGt4Hk1domj2sPLh0MhYWFAVD3EIXXSDa7dOlSnd6imvz9/eHv72/39hERkQwZqzmkmT6/Y4dzps9rcptq5zVpij5asVba9bwb+HbhISjXSvg2vwOK0V27rwFuYWjYASjuq8CIF+IQmtjRmqtwKJcOhmJjYxEWFoaNGzeia9euAICKigps3boV8+fPd3LriIhIlkydFu+M6fP1VcrW9Fqlp6uH+kzspfo99yyUS/KgzA3EthsdocKdGV6hXpcwqt1RpIwJwL3pHdEguLf57XXQUF59nB4M3bx5EydPntTezsvLw6+//org4GC0atUK6enpePPNN9GuXTu0a9cOb775Jho2bIhHHnnEia0mIiLZMnVavDOmz5vaa1VP0cfqqmrs/u9hKP9zBcpfInGwvB2AVtr9if4noOh+Hoq/tEDP8Qnw8hlgWVsdMJRnKqcHQ3v27EFycrL2tibXZ/z48VixYgVefvll3L59G5MnT8b169fRu3dvfP/992jSpImzmkxERHKmqTl0/rz+HhjN9PmkJMe3zcJeq1tXbmHzkoNQflWGtSficLE6UbvPG1UY2Gw/FINKMOrZWLQZ1A5AO+vaacehPEu4VJ0he2GdISIisilDNYc0k3sc/GWulZsL1OhgMCgnBxdbdMC6hUeh3OCHjYUdcRsNtbsDUYT7ow9BMUrg/hc7oFlsU9u1UaUCYmIM92DVqMVUXFrqkO9vBkNERESW0DfMEx1t2+nz5ubUaAINA71WAhJKAlpguPf32FHaCaLGQhStvM8hpcMpKB5tggGTE+HX2M8211CbGQFbcbduLLpIRETksjQ1h+yVAGxJTo23t3p/Wpq6h6VGQFQNda/VhLJl+BFdAAA9Gh6Gos8lKJ4KR6e0uyF5Rdmm7fVxwQR0BkNERESW8va2z/R5K3JqinsNxsERc9H+20Vorrqs3X4OUXgJC1DeMhrLhmzDyOfbIbJHAoAE27e/Pi6YgM5hMiIiIldiRk6Nphfq7M7zWLvoJJRbGiHnaidUwg9eUCEJ23E3jqNNRDnaP9INQ17ojMZhjR13LfoYGcpzRs4Qe4aIiIhciYnT44+/9ikyf2yNNT+H4dfbcQDuLHLa3u93KDqfhWJCMPpOegLefi60Flo9Q3nOWr+NwRAREZErMTFXZtabfvgcgwAAXlDhnsCDSEm6jlFTWqH9/W0AtLFfG61laNFbR6/f9gcGQ0REnsZFqvqShUzMlbmBpkiN2AXF8CoMz4hDy/jOdm6Yjdk7Ad0MDIaIiDyJC1X1JcucKItGWEBLNCq7Ai/omx4PlAWGYtXvAxDQvJHjG2hL9kpAN5OX8UOIiMgtaGYg1c430cxAys52TruoXqoKFX58fz+m985FvP8p3H1/W4wvWwbgznR4DSFJkCQJDZa/5/6BkAthzxARkSewwwKdZD+ll0qxcdFBKLMqsO5kHC6LTtp9PqjEzeDW2NfiIXQ7+SVQfec1lby8gIwM9vLZGIMhIiJPYIMFOsm+Cn69iLULj0G5MQCbLnVCOe6s8N5UuoHhrQ5BkSLhvhc6IGjPGSDti7rBrUoFLFwI9OnDgMiGGAwREXkCF6zqK3eiWuDgqhNQLrsA5c4W+Lk0EUCodn+sz1mkdMyD4rFA9H86Eb4N+6l3qFRAPwO9fBrs5bMpBkNERJ7ABav6ylHlrUpse/cAlJ+VQHmoDU5X3Q3gbu3+3o0OIqXfFSgmRyFhVFtIXq3qnoS9fA7HYIiIyBMkJalnjRmr6puU5Pi2ebgbZ4rw3VuHsGYN8O3ZDihCN+2+ANzGkND9UAyrwMgX2iOsU6LhE2lKImRlmfbA7OWzGQZDRESewAWr+noMPXWb8n68gLVLfocypwm2Xu+IKtyjPTxEuoxR7Y5CkeaHwc93RMMWves5+R/0lUQwhr18NsNgiIjIU7hYVV+PoCdIKUQYXsC7WIU7z2eC/0koup6DYmJz9JqQAG8/M3rgDC3Kagh7+WyOC7USEXkaVqC2ifL/roTfhEcAQKfaj6b2z+yGC9BsSA+MmhaLu+5tbdmDGFuUtTZNL189q9Z7Ekd9f7NniIjI07hIVV93dOnQZax/6yjWfeuFJYUvIQJ1qxN7QUBIEl5v/g6QlWddoGksWbo29vLZBYMhIiJHYG+NSxLVAse+y4Ny6VkofwjGjpJECCRhIHIRhfMG7yfZakaXqUnQU6cCDz7I942dMBgiIrI3rhfmUqrKqrDj34eg/O91KPe3xolK3RXeuzU4gmmxm4HDJpzM0hldmuD4sCkPAnUgxN4+u2EwRERkjDW9OoaSYzXrhckk98PZSi6U4PtFB7EmW4X1eQm4Ju6s8O6HcvypxX4oBt/GqIx2iOoZD+TeCyS/YfzElszoMmfmGJOlHYIJ1ERE9bGmV8dYcqzmiy7PyrwT0uvc7gKsffsElJsaYMuVTqiAv3ZfsHQNI2IPIyXVG0OfT0STiCa6d9a8dsbqNpn72pkzc0xmydL6MIGaiMjZrO3VYSVhhxLVAr99dRxrlhVA+VMo9t6OB3Cn5+Yu39NI6XQaivHNcM+THeAT0N/wyexRt6m+xXT1YbK0wzAYIiLSxxarwMthvTAnJ4aXF5dj67sHoVx5E8rDdyFf1R5AewCAhGrc0+QgFP2vQTG1FdrfFwvJK8b0k9u6bpOpM8f+/nfg3nuZLO1ADIaIiPSxRa+Op68X5qTE8GunruObhYehXOeF7851QAm6a/c1RCmGhh+A4r5KjHghDiEdOln3YKmp6oDXFgGfqUFvQgJ7Ch2MwRARkT626NXx5PXC6htCfPDBO71m5gQO9fQyndpyBsp38qDcGoTtNzpChX7au4V5XYTi7mNQPNQAf3o2EQ2C+9joIv9gq7pNnh4cuzEGQ0RE+tjii8tT1wszNoQIqK9r8eK6PUWGAh49vUzlzULxVcvJmHfmERwuvwvAnSrPHQOOQ9H9AhRPtESPcfHw8gm12+XajCcHx26Os8mIiPSx5WwifcNJ0dHumxybmwskJ5t2bM0ZUYD+YbWxY4GFCyGE0LvsRRq+xlqMwsBmB6BILsGo59ogdkC01ZfhFJoeNUB/cCzjmWP6OOr7m8EQEZEhtvzi8qQK1CtXAo88YvrxkgQEBwNXr9bZVfMLSKqzF6gGcLtxCCp/O4KmbYLNbalr8rTg2I4YDNkQgyEishi/uOoyp2fIVnJyPCup2JTg2JMCaAuxzhARkSuw5WwiT2Es98Ue3Ln8gD7GkrK5hItDMRgiIjKGq8Drqi8x3F7kNMOKS7g4nJezG0BEZDKVSj1Es3Kl+r8qlbNbJF+agoSRkUYPrbbmcSRJPSwplxlWpszUS0/ne9/GGAwRkXvIzlbP7kpOVifvJierb2dnO7tlslWtGI09//gG/+m4CJ94j0c16gY+AoAECSK4+Z3Ec0Nq73fn8gOWMqfYJ9kMgyEicn2aYYPaXxKaYQMGRA5TdqMM376+G08nbEO0/0X0nNgRTxxIx+OqFRiDr3BF0q33I7VsCenLLyD9+8M/NugJeCQJeOmlur1MUVHyGxKSwxIuLoizyYjItXHld6e7cuwq1i88AuU3PthwIRGlaKzd1wg3cV/kASiGqzDipQQ0/20LMHkycPnynRNoEn+B+mfm1Z49dc89wI4djklcd5WZW6bO1PO02XUGcDYZERHAld+d5PiGPKx55wyUPzTDjuJEVOPOCu+RXgVQxJ+A4uGGGDQ1EQFN+6p3ZGcDY8bUn/h7+rThoKNmonp2NtC2rfWzqUwJclxp5harVDuHkIGioiIBQBQVFTm7KURkrsxMIdRfC/X/ZWY6u6Vuraq8Smx/9zfxUs8c0d7vVJ2nt2uDw2LWwBzxy6eHRbWqWs8JqoSIijL8+kiSENHR6uOMycpSH6/vHJKk3m+KrKy6bYqK0r2/rR7LljRtqt0uZ7bJSRz1/e3ywVBlZaV45ZVXRExMjAgICBCxsbFizpw5QqVSmXwOBkNEbiwnx7RgKCfH2S11OyUFJSLrpZ1ifNvtooV0Wefp9EW5GNp8t1j651xxZsc54yez1etkq6DKlCDHlgGcrekL5KKjZRUICeG472+XHyabP38+li1bhv/+97/o0KED9uzZg4kTJyIoKAjPPfecs5tHRPbGYQOburC3EGvfOg7lxgbYfLkjynFnhfdm0nWMiDkExWhvDMvogMCoHqaf2FaJv7YYFjU2PV2S1NPTg4JcdwiWxT4dyuWDoZ07dyIlJQUjRowAAMTExGDlypXYs2ePk1tGRA7z5JPArFl1t8tx6rWZRLXA/q+PQ/lBAZS7QrDnVgKAMO3+Nj5nkNIpD4pxTdHvrx3g27C/4ZPVx9SiiMaOs0VQZWpAlZtr/WPZE4t9OozLB0P9+/fHsmXLcPz4cdx999347bff8MMPP2Dx4sXObhoR2UPNhNcTJ4B//9vwF1tUlLzXCDOg4mYFtr13EMrPSqA81BZnVO0BtAcASKhGn8aHoOh3FYrJUYgf2RaSV+v6T2hKErKtevBsEVTZOniRU/VrmXL5YGj69OkoKipCXFwcvL29oVKpMHfuXIwdO9bgfcrLy1FeXq69XVxc7IimEpG19M3qMWTOHOCVV9gj9IfreTfw7cJDUK6V8G1+BxSjm3ZfA9zCkLADSLmvAiNeiENoYkfTT2zqTKv6lugwpwfPFkGVqcHLoEHAihUcgiXXn022cuVKERUVJVauXCn2798v/ve//4ng4GCxYsUKg/eZNWuWgLrwqc4fE6iJXJihhFdXS2x1IadyzohFo3NFctO9whuVOk9RqNdFMan9VqH8+0+i9HKpZQ9gyUwrWyT+WjubSpMYbej9VPP9w5lbLs1RCdQuX3QxOjoaM2bMwJQpU7Tb3njjDXz66ac4evSo3vvo6xmKjo5m0UUiV2WssKIhMik8p1FdVY3d/z0M5X+uYN2eMDSrKEQ4ClCAcGxHEuL9f4ei23mkPNECPccnwMvHikUGrCl2aYsChvp6pGoWaDTl/mlp6v/X10tVs7K1tY9FdsOii3+4desWvLx0P9De3t6orja89J+/vz/8/f3t3TQishVjCa+G2Co3xFnVh0143NvXbmPTogNQflWGtSficLE6EQ8gG+swDtG485xVtQyHz7KltvvytmZWly0Sf62dTaVZSFbfEF/tIIczt2TP5YOhUaNGYe7cuWjVqhU6dOiAffv24e2338Zf/vIXZzeNiGzF0qDGFomtzqo+XM/jXrw7CevfOgrld374vrAjbqOX9pBH8Qk+weN1TudzpfBOlWdbtNsV1siyNqgyJ8jhzC1Zc/lhspKSErz66qtYtWoVLl26hIiICIwdOxavvfYa/Pz8TDoH1yYjcnGmrsekYav1yDRDKbX/GdQ3lGJLBh5XfUtCGr5ENtK021t5n4Mi4RQUDzfA4PdSIZ0/r/+8tlyn7fXX9ZczqE1mQ5XkWI76/nb5YMgWGAwRuThNfoqhWT012SpQcdYCsH88rjh3DpKe3dWQcA5R+HOD9RjZ9yoUT4WjU9rdkLwkyxfxNHcY0NQcrqgo9VpjHE4iO3HU97cV2XVERDaimZYN3Al2DImKsk2PjTk5MTZSfK4YuQ8vAwwEQgDgBYFWyMdP31zFq5sHofOY9upACLBs6Co7Wx3YJCcDjzyi/m9MjHq7IabmcD35pPMDIZVKHSSuXKn+r0rl3PaQW2IwRESuQZPwGhmpuz0qSl1TKDNT3eORl+dWOTH5P13Aew9vxbAWe9AiOgAffB1s+eOaW5BQMxxXO7DRrCJvKCAy9ZrbtTPtOHuxJNAj0sOsBOr8/HxER0fbqy1EJHeOnNVjq+UjahHVAvtWHoXy3xeh/DkU+27HA4jQ7vfxBmBK54W+xzWnIKGp63OlpNR9fu303NiUoXwvTaBnr3wv8khm5Qw1atQIGRkZmDFjBho1amTPdtkUc4aIqA5jeUpm5AyVF5cj550DUH5+C2uP3oVzqjvBjxdUuCfwIBT9r0MxtRXaD21t3eOaWj/H0vwiwKbPjV04K9+LHM4lc4Y2btyI77//Hu3atcPy5cvt1SYiIvurL0/JhOUjrp64hk+e/gF/jtqJFkEVuP/VHnj/0ACcU0WgEW4iNWIXVkz6AYWHr2N7UWe8tH4Q2t/fxurHrXc4sWZviDXDgNa20d6ckO9FHs6SstX//e9/RVRUlOjSpYvIycmxUTFs+3FUOW8ickNmLB9x/Ps8sXBkjhgQtE94oUrnLuFeBeKp+K1i/eyfxe3rt236uHpVVQmRkyNEZqb6v7WXJsnJMW1pk/r+DbfF0hr2kJlp2rVlZjq3nWQ1l1+O4/bt25g3bx7eeustDB06FP/85z9x11132TZSsxEOkxFRvQxMPVdVqPDT8sNQLr8K5b5oHKloq3O3zgHHoOhZAMWkEHR7JM785S/sWfnaVkNdzqrOXR9rhgDJrbh8naFbt25h7969yMrKwjvvvANfX19MmTIFs2fPRpMmTWzdTqswGPJQrviPNLm90kul2LjoIJRZFVh3Mg6XRUvtPh9UYlDwfiiSb0LxfFu07hflxJaawJz1udyJq+c0kc24ZDC0bNky7N69G7t378aRI0fg7e2NTp06oU+fPujSpQs+++wzHD9+HKtWrUKPHj3s1mhzMRjyQM5aQoE8UsGvF7F24TEoNwZg06VOKEeAdl9T6QaGtzoERYqE+17ogKBWQU5sqQU8dRFSTw30SIdLBkPR0dHo06eP9q9Hjx51FkR98803kZmZiYMHD9q8sZZiMORhnLWEAtmPg3v5RLXAwVUnoFx2AcqdLfBzaaLO/lifs1Ak5iFlXCD6P50I34a+dmuLQ3hqL6qnBnqk5ZLBkCkuXryIiIgIqFyoCiiDIQ/CKbWex5JePgu+3CtvVWLbuweg/KwEykNtcLpKt2Za70YHobjnChTPRKJDyl13qj7bg6cGJ87A59KjOer72+ar1oeEhGDLli22Pi2RmjlTapk46fosKZxnRvB040wRvnvrEJRKgW/OJKII3bT7AnAbQ0L3QzGsAiOevxvhXXR7h+yGQ7y2xdXmyQa4UCu5l5Ur1WX3jcnMBMaOtX97yHKW9PKZMER6OqQXlItOQZnTBFuvd0QV7gxxtZQuY9RdR6FI88Pg9EQ0CnFw8VgO8RKZxW17hsjFuXuXsjssEyB3pr7HzO3lM7K8hABQ+OAUtMU5VOPOLK8E/5NQdD0HxcTm6DUhAd5+SVZfokWsWR6DiOyKwZCceEL3vDlrM5HjmfMeM7dCspHgSQIQjkIMRC6qg5pDMfAGRk2NQbshdwFwgRponjzE6+4/skj2GAzJhacsaqhZJiAtTR346JtS68xlAuTM3PeYmb18xXuOw5RO8jVv/44mz99r2rkdyZrlMVyFvqBnzRr3/5FFsmdmuVRyS8a65wF197wLzQCsl6lrM5HjWPIe0/Ty1V77SnM3SUJli3D8c74K/QP3I+Ul03p3mnRtZ167c3PVuWi5ufb9DLj7EG92tjrHKzlZnbeXnAyEhgIPPli3x0sTAGdnO6WpROZiArUceGrpenbNuw5L32MGCucJAAIS0vA1VkEd3HpBhQuIRAguQm/4ZG5ZBUcPG7tz1WRDvX71ceXrIbfhkqvWk5vyhO55fTRTaseOVf+X/+A6j6XvsdRU3P7wE9xq1FJncz6ikYavsQ4jMaz5Hrz38Dac3nURoVnvQZIk61dS13y5O7JHw9VXgjekvl6/+nDleHIjzBmSA3fvnnc3cuyxMvW9c/gwkJuLcwF3Ye2S36Hc1ABbrqShCg8jCdsRjgKUohGaxQbhkQf8sOL5MgRG1Vza548hUn09OqZWHXbmrK5UG7Tf0Ywlfhvjbj+ySJY4TCYH7tw97yyWBjSeMGPPEkbeYwLQGdrKRxSewxLtENhdvqeR0uk0FOOb4Z4nO8AnwMjvNGsCTlcYNnangNnU2l6GuNvwO7kU1hki2+EMLPNYGtAYyqs4d06dZKrpbXDlLz5L1fMe0/drKxLnkYU0rO4yG3H/eBRxw9tA8oox7/Es/YJ1hWFjd6qabGmPMctckBthzpBccAaWaSzNJTElr2LxYnWPREyMZTkpjpz5ZInUVJQsXYHShi3q7Kqd8OwFAUkCHrj6EeLvj7mzDpgjrtGTho0d8XwZmfWnF39kkbsRMlBUVCQAiKKiImc3xfmqqoTIyREiM1P936oqZ7fIdVRVCREVJYQ6pKn7J0lCREfrf85ycgzfT995JEmIrCzT25aVVbdtUVHmncNOTm4+Ld5OyRGDmu4V3qgUXqgSA5Ej5uDvpj0fOTnqEznqGjWvsySZ/zq7Eke+J7Ky7rxvaz9XgBDNm+tuj452ifcmuT9HfX8zGCLSMDWg0Xx515SZaXowZO4XruaLyBZBlQ2oKlVixwf7xYw+OSLB/0SdZnUMOCZe6ZcjTvx1gWnPRWam46+xvi93JzynZnPGe0Jf8KUJevgji+zEUd/fTKAm0rBmEVhTk3JrM5ZcaslipnZw68otbFp0AMqvK7D2RBwuiTtT4b1RhYHN9iMluQSjnmuD2AHR6h2mPiebNgETJjj+GvXlhkVHu+6sLg1nvifcKfGbPAITqMm9eMI/ktbkkhhbM80QY0m6TlzPqnD/Jax76xiUG/yw8WInlKG3dl8gijC81SEoFMB9GQloFtvtzh0174Xz54GWLYErV+qfxQg47hprv09PnQJ27HCv960z1zhzp8RvIjMwGCLrecp0cmsWgdXMpnrwQfMe01gAZuqMpvPnzXtcPUS1wOG1p6B87xyUO5rjp5sdIBCi3d/a+xxSEk9B8WgTJD2TCL/G99Q9ib73gj41E2wvXTKtgdbO7qrvfVq7p8+VucJsOCIPw2CIrOMpC8AC1pcgSEkBmjcHrl41/limTjs2tbfq+eeBBg3Mfq4rb1Xih2UHofy0GMoDMfi9SneF956NDkHR5zIUT0egY2o7SF5Rhk9mzpINNYsM5uaa1lhrZnd50vvUk2bDEbkI5gyR5VQq9UKNhr783bWYo6W5JObkDUmSaV/Axgpm1jwfYNI5i84WYcOiQ1izSuCbsx1wQzTV7vNHGQaH7IdiSBlGZtyNiG5hpl2PsTwWQD1ktmiRurxDzeEoexcFdZG8K5thEVWSEYd9f9s1PdtFcDaZncyZY/nsK1dnyewYU2eUBQebP63e0DRwE2eonf4hX/wrLVcMCd4jfFGuc7cW0mUx4a5tIvvlnaKkoMT0dtVkzUy8mtdoj9ld1rbNFbn7bDgiEznq+5vDZGQZlerOopPGuGPugiWJoqYOS3z5JXDvvaafV1Mw86mn1MnIhtRInBUDBuKXT49A+dElrPs5BIHllxCOAlQgHCp4I87vFBRd8qGYEIw+T3SAt5+VVYKtzWOx55pdjsyxcdREAndc44zIhTEYIuP0/QO/fTtw7Zpp95dL7oKpCdiWzMZJTQVu3wYee8zooR8/tgWvFbTHheoEPICjWINxiMadL8zKFmHw/eBd235h2iKPJTVVnXdl62DCUTk2jp5IYK/ni0iGmDNE9TP0D3xamvoXqDHNmwMXL8rnH2hNoi6gPwHbmkRdE3OSBiEHWzEIY/EZPoM6eNJZSMHatugLjgHXzWNxRI6NoQRtW7zuRDLmqO9vrk1GhtW3TpcpgRAAPPusfAIhwD5rwGnWn/qjbo+hXy/VkHAeEUiIF/h2zk/4LGI6JNRdF0z7hZ2ebv5aVtnZ6sAiOVldoFKz1tqaNXeGTWuvYeXsdao0swRrtkXDFm2rb106a55rInIY9gyRfqbMwPHyqv8feLn1CtVkq9yR7GyIZ5+DdP7O6yBQN8BRf4gl4KuvIKU9aPrMNmMVsGu1xWjvB+C8qs7GnnN7VZy2x3NNRABYgZqczZQqt5pAqHZNHo0PP5RnIARYXan3ZuFNHHpmKXqtnqk3+KlNAoCXXgTS/ij6aOukYWO9H5Kk7v3Iy7NdHos5AaUp+Tr2yrFhEUQit8dhMtLP1H+409PrDglFRwNZWcyRMNOFvYX44NFtGBGyGyHhEiJWvwuBuh9SvYGRJAGff34nQLV10rA5S0BoAsGxY9X/tbBHTO9wXHa2/mMNDeempenexxZtq41FEIncHnuGSD9T/+FOSQEWLrTs17YnrGdmTD3XKKoF9n99HMoPCqDcFYI9txIAqIscDkSuzgwwo2qvR2XN0iL6OLL3w5xq0ab2WKWk2O+9Zevnmogcz65VjGzk3Llz4tFHHxXBwcGiQYMGonPnzmLPnj0m359FFy1QVSVEVJThYn/1FPgzSVaW+vw1zxkV5XrF4iwpvqih5xqrIyPFr+P+KaZ1yhWtvfN1n1KoRJ/G+8WbQ3PE2Yy3TSsUWPsvM1P38W1VmM9RBTY17ztTC0u6SkFFFkEksgtHfX+7fDB07do10bp1azFhwgTx008/iby8PLFp0yZx8uRJk8/BYMhC9voH3lBFZVf74rAmYDNwjSpIQgVJPIAsAQjRAKVCEbZLfDR+myj47eKd+5v6JW/sS1/fNURH274CtrXBsbnXrblOU6t+1wwS7cUWzzUR6WAw9Ifp06eL/v37W3UOjw+GrOm9MMbW/8Cb+8vfWawJ2KqqRGXLcFFt4BpVkMRVnxCh/NsOUXq51OA56u2ZM+d5s+b9Yez1qvlniy99c4MbV+kZ0rDnZ5FIhhgM/SE+Pl6kp6eLtLQ00bJlS9GlSxfx4Ycf1nufsrIyUVRUpP3Lz8/33GDIEcNNtvwH3tW+vPSxIGBTVarEro8OiL/dkyMm+H5im2s01DNnSYBmKVNfrzlzHPt4mufO3sO5RORUjgqGXH422e+//473338f7dq1w4YNG/D000/j2Wefxf/+9z+D95k3bx6CgoK0f9HR0Q5ssQOZM4vGGracgeMO05BNnDlVvn4T1r76M56M24YI/yvoMykRb+4YhLJKE58fY9doqIBj7effmoKOxpj6OrRrZ5vH0yQj1y6OqCFJ6tmKmmRkexdUJCJ5sGuoZQO+vr6ib9++OtumTZsm+vTpY/A+bt0zZGovjLsMN9XmDj1DJg7VPI7lOpuaoEiMif5RfK94x7bXWPs9UV7uuKEYZ7xeluSqMV+HyCNx1fo/hIeHIyEhQWdbfHw8srKyDN7H398f/v7+9m6a7Zmz0KM5dV9cqeqtO0xDNrGsQDPcwFRpKe6KqULCpHsw8Nku8Gt8D6DqDcQssN016ivg6KjX1BmvlyUrsnPRUiKygssHQ/369cOxY8d0th0/fhytW7d2UovsxJzaKoB7DDfpoxnWSEurW7na0cMaBmoAVfXsi6qmofC/cVFvgUMBQMALi/G8+kYegPcigbh31K+RK12jtZx1LZYEN1ZW/SYiGbNrv5MN/Pzzz8LHx0fMnTtXnDhxQnz22WeiYcOG4tNPPzX5HC4/m8ySIS93GG6qj7OHNfQ8fmnjELE45A3RTLomHkCWdhp8zWMMzRDT/tVsv7Ov0ZY86VqIyG046vvbLRZqXbduHWbOnIkTJ04gNjYWGRkZePLJJ02+v8sv1GrJQo+ahVSNDV/k5Vn3q92eVaKdVYH6j144IYROz0/1H7fS8DW2SQPxWsgyTCp9Bw1vXrpzkJcXUF1t+Ny1F6f1pCrbnnQtROQWHPX97RbBkLVcPhhauVK9/pIxmZnqGV0amqE1QP/whbUzjMzJYXIDolpg32eH0HbSn9Ck4rLehfkEgPKmofA5dwY+jfx1A4ALF4AXXzT+QJs2Affea+vmExHJjqO+v11+ar0sWLrQo6Gp17aYau2oaft2Vl5cjg1z92BKx61o5VeAjMevIMhAIASoF0ENuHERPrt3qjfULCtw44ZpD5qba3W7iYjIcVw+gVoWrJmxY0qiqbnDG66w+KUVrp64hm/eOgzlOm98dz4RN9FDu+9ebDDtJK6WeE714xAeEVmBwZArsHbGTn2zaCwZ6nLDafsnNp6G8p3TUG5vih+KOqIa/bX7wr0KoWh/HIqHGmBw90hglAkn1NdbN2gQ8MYbxu/rIs+JbHjYcC4ROR6DIVdhSW0VY8ydrq/hBtP2VRUq/LT8MJTLr0K5LxpHKtoCiNHu7xRwDIoeBVBMCkH3R+Pg5RP2xx1VlvfCDRqkTpC+etVww5o3ZzDkSJa+x4mIamACtauxVXe/ZraZoR6e+mabWTK7zQFKL5Vi46KDUGZVYN3JOFwWLbX7fFCJQcH7oUi+iVHpbRHTP8rwiaxJPM/OBh580PC5s7L45eso1rzHicgtcDaZDblVMGQr1gQ0jpq2b4KCXy9i3dvHoNwQgE2XOqIMDbT7glCE4a0PIiVFwn0vdEBQqyDTT6xvaCU62rReOA7LuAYXDdqJyHYc9f3NYTJPZc1QlxMrKItqgYOrTkC57AKUO1vg59JEAKHa/TE++UhJ/B2KxwKR9EwifBv2s+yBrFm+gUs/uAY3GM4lIvfAYMhTWTpdX8MeOUwGVN6qxPb3D2LNJ8VQHmqD01V3A7hbu79Xo4NQ9L2ClMmR6JByFySvaNs8sDXLN3DpB+ez9j1eH85OI5IVDpN5KlsNddnpS+HGmSJ899YhKJUC35xJRBHuDHEF4DYGhxyAYlgZRma0R3iX0HrORLJlr+FcDoMSuQzmDNmQywZD9v71ae8K1WY6/cM5KBedgjKnCbZe74gq+Gr3tZQuY9RdR6FI88Pg9EQ0CmnksHaRG7P1e9zQ7DQnfWaI5I7BkA25ZDDkqF+f1iQKW6m6qhq/fHYUyo8uQbknHPvL2uvsj/c7BUXXfCgmNkfviQnw9uMwBFnAVu9xzk4jcjkMhmzI5YIhR//6dGD+w+1rt7HlnYNQfnEba4/fjYLqMO0+L6iQFHQAioE3MGpqDNoNiXGptjNPxI3Z4rXj7DQil8PZZJ7KGUtdWJvsa+SL5vKRK1j/1lEov/HBhoKOuIWe2n2NUYL7Ig9CMVKF4S8koHm7LqY/riNzN5gn4t5skdDO2WlEssVgyNHcbakLPUGCiIrC+cf/hsx98VD+EIwdJYkQNZa/iPK+AEX8CSgeboRB0zrCP7CvZY/rqMrCrGJMgH1npxGRS+MwmaOtXAk88ojx4zIz1SulO5OBIKEa6uG8NHyNVVAHCV0bHEFK74tQ/DUMXR5qD8lLsvxxHZm7wTwR0nChYqNEpOao728vu52Z9DP1V+Xhw+ocBpXKrs0xSKVC9dRp0Bcre0G9bZnXZLz35y04u+sC9t6Kx6ycQeg6Ns66QAgwr/fMWo58LHJtmmKjwJ38PQ07FxslIudiMORoSUnqX5e1/7Gt7Y031MmcMTHqHhoHObe7AO+P3YaXg/8Nr4ILMNRKLwiEVF/EM5O9EN07wraNcGTuhrmPpVKpg9SVK50brJJ9aIqNRkbqbo+K4nApkQdjzpCj1bfUhT52zlsR1QK/fXUcyg8KoPwpBL/cSgAQjodx3rQT2COZ1JG5G+Y8FpOs5YHLrRDJDnOGnEXfF6shNs5VqLhZgdx/HYBy5U0oD9+FfNWdX8ESqtG3yUFMiduCR3Y/b/xk9phm7MjcDVMf6623gIceYjE+IiIHYp0hG3LJYAi4M2V982b1sJgxVgQe105dx7dvHcaatV747lwHlODO89AAtzA07AAU91Vg5ItxCOnQ0vnJpI6snm3ssb78Enj+eSZZExE5GBOo5UBTGyUhwbTjzRySOrXlDBaNzkVys30IuasJHnu/H7461xclCESY10U8GbcNa1/9GVevSlhd0Bt/WZ6kDoQ0bXNmMqkjczeMPVaLFkyyJiLyYMwZcgU2ypGprqrGzysOY83HV6DcF4XD5XcBaK3dn+h/Aoru55EyqSV6jIuHl4+RBVAduHK9wcd3VO5GfY+1cqVp52AxPiIit8RhMldgxZDUrSu3sGnRASi/rsDaE3G4JFpq93mjCgOb7YdiUAlGPRuLNoNaWd4+OSeTcpkGIiKn4HIcclLfDDM9Q1IXD17G2n8ehXKDHzZe7IQy9NYeHogiDG91CAoFcF9GAprFdrNN+9z1S94WgZymHIKxYDUpyTZtJiIih2Iw5CrqGZISby/CYe9OUA7LhXJHc/x0swME7nzxtvY+B0WHU1A82gQDJifCr/E9TrgAF2SrqfCmBquAuhdJrj1oRERuisNkruaPnoyq0/k48HMZPtnZFmsOtsXvVa11DuvZ6BAUfS5D8XQEOqa2s77qs6cxtN6YNbPR9AVX0dF3AiHWICIisilOrbchvU+mC+bBFJ0twoZFh6BcLfDNmQRcF820+/xRhntbHoBiyG2MfL4dIntwsUiD7LnemL73zZo1tg+8iIiIwZAt1XkyXaiS8Jkfz2Ht4lNQbmmM3GsdUQk/7b4W0hWMbHsEilRfDHk+EY3DGju0bW7LkQnPXOiViMhumEBtL4aGT+y87IWGqBbYm3kUaz68COXucPxW1h5AlHZ/e7/foeh8FikTg9HniQ7w9mNSrtkcubaZOQu9umsSOhGRh5NXMKRSqXuE9HWGCaH+FZ+erq43Y8Nf8WU3ypDzzgEov7iNtUfb4Xx1PIB4AIAXVOgXeBCKpOsYNaUV2t/fBkAbmz22LDlybTNHBl5ERGQX8gqGduxw2K/4K8euYv3CI1B+44MNFxJRip7afY1wE8MiDiJlRBWGvxCPFu07W/VYVIsjp8I7MvAiIiK7kFcwVFho2nEW/oo/viEPyn+dgXJ7M/xYnIhq9Nfui/AqgCLuBBQPNUDysx0R0LSPRY+hwwWTwF2CmXWbrMIaREREbk9ewVBYmGnHmfgrXlWhws6PDkG54hqUv7XCsYo2AGK1+7s0OIqUHucxNukc7k7whRQZASR1s82XsAslgbskRy0l4sjAi4iI7EJes8muXUNgp05WrcR+s/AmNi46CGV2JdadiscV0UK7zxcVGBR8AIo/3cSo9LZoffFn+wQs9qih46kc1XtWXw0ivhZERBbh1Hob0nkyN21SBxKA/l/xegKJC3sLsfat41BubIDNlzuiHAHafU2lGxjR+hAUoyUMe74DgloFqXfYK2DhVG7XxWFLIiKbYjBkQybVGarxK15UCxzIPgHlsgtYszMEe24l6Jwv1ucsUjrmQfFYIPo/nQjfhr66D2jPgIWLhhIRkUywzpA9paaqp8/X+BVf0bU3tr1/EIfbLsbJPB/sF4nYjiRUwxsSqtG78SEo7rkKxeQoJAyPgfTj70DBUeDnoro9APasPcOp3ERERDYlz2AIALy9cb11F3z7lS+UayX45H+NefgbBuNOEHPFKwS/DpiGxCV/RVinjuqN2dlAm+T684DsGbBwKjcREZFNeTm7AeaaN28eJElCenq6RffP25aPJalbcW/wXoS0aYRH3+uHivxC/A/jEQnd3pwW4jIGb30NYSd/UG/Q5AHV7vXRVK/OzlbftmfAopnKrck9qk2S1EN+nMpNRERkErfKGdq9ezfGjBmDwMBAJCcnY7FmtXAjNGOO8X57caSiq86+Tr6H8aO4B42qiqA3vNDk95w8CbRta1oeEKDOGbJi1lq9NEEZYHISOBERkbtxVM6Q2/QM3bx5E48++ij+/e9/o1mzZsbvoMeRirbwRhUGNd2Ht1NycWHWB/gtaCAaGwqEgDv5Pe+9Z3oekKb2DFC3B8cWtWc0NXQiI3W3R0UxECIiIjKT2wRDU6ZMwYgRIzB48GCjx5aXl6O4uFjnDwA+fGIXLp0sQc71rnj+8WsIf/0Z4MoV0xqwYYNpx2nygOwdsKSmAqdPq2eNZWaq/5uXx0CIiIjITG6RQP35559j79692L17t0nHz5s3D3PmzKmz/aG3+6i72epbsNWQ774z7biaeUB6Zq3ZtPaMt7f10+etrY3D2jpEROTmXD4Yys/Px3PPPYfvv/8eAQEBxu8AYObMmcjIyNDeLi4uRnR09J0DjE19r0mSAC8v9Ze+seP0rUFli4DFXqxd0oNLghARkQdw+QTq1atX44EHHoB3jd4GlUoFSZLg5eWF8vJynX361EnAWrkSeOQR2zc2K8t9ggBrK2RzSRAiIrIzVqD+Q0lJCc6cOaOzbeLEiYiLi8P06dORmJho9Bx1nkxTqzibIz0dWLTItue0F2srZHNJECIicgBWoP5DkyZN6gQ8jRo1QvPmzU0KhPTS1OoxNPXdEikptjmPI1hbIdueFbaJiIgczG1mk9lUfVPfzeWORQ6trZDNJUGIiMiDuHzPkD65ubnWn0Qz9b12ArA5bFEzyBmsrZDNJUGIiMiDyLNnSKNmrZ6pU82/vy2LHKpU6lymlSvV/zU2e80a1i7pwSVBiIjIg8g7GALuTH1/8EHz7teypXqJDlsEQtnZ6oTk5GT1LLfkZPVtzVpntmZthWx7V9gmIiJyIAZDGsZ6O2q7fBnYscP6xzV18Vdbs7ZCNpcEISIiD+HyU+ttweSpeYZq5xiSmQmMHWt5w1xhijorUBMRkYvi1Hpn0PR2PP20uufHGGsThF1hirq1FbJducI2ERGRCThMVltqqjpAadHC8DG2ShDmFHUiIiKnYzCkj58f8MEH6qDHngnCnKJORETkdAyGDHFEgjCnqBMRETkdc4bqk5qqXmbDXgnCminqaWnqwKdm4janqBMRETkEgyFj7J0gbKgSdlSUOhDiFHUiIiK7YjDkCuzdA0VEREQGMRhyFZyiTkRE5BRMoCYiIiJZYzBEREREsiavYOirr+y/IjwRERG5FXkFQ5Mm2X9FeCIiInIr8gqGNOy9IjwRERG5DXkGQ5rihunpHDIjIiKSOXkGQ4DuivBEREQkW/INhjS4IjwREZGsMRjiivBERESyJt8K1JKkXv+LK8ITERHJmjx7hrgiPBEREf1BnsFQVJR6pXiuCE9ERCR78hom++gjoG1brghPREREWvIKhv78ZyAw0NmtICIiIhciz2EyIiIioj8wGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGTN5YOhefPmoWfPnmjSpAlCQkIwevRoHDt2zNnNIiIiIg/h8sHQ1q1bMWXKFOzatQsbN25EVVUVhg4ditLSUmc3jYiIiDyAJIQQzm6EOS5fvoyQkBBs3boVAwYMMOk+xcXFCAoKQlFREQIDA+3cQiIiIrIFR31/+9jtzHZSVFQEAAgODjZ4THl5OcrLy7W3i4uL7d4uIiIick8uP0xWkxACGRkZ6N+/PxITEw0eN2/ePAQFBWn/oqOjHdhKIiIiciduNUw2ZcoUrF+/Hj/88AOioqIMHqevZyg6OprDZERERG6Ew2S1TJs2DUqlEtu2bas3EAIAf39/+Pv7O6hlRERE5M5cPhgSQmDatGlYtWoVcnNzERsb6+wmERERkQdx+WBoypQpyMzMxJo1a9CkSRMUFhYCAIKCgtCgQQMnt46IiIjcncvnDEmSpHf78uXLMWHCBJPOwan1RERE7oc5Q39w8ViNiIiI3JxbTa0nIiIisjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREsuY2wdB7772H2NhYBAQEoHv37ti+fbuzm0REREQewC2CoS+++ALp6el45ZVXsG/fPiQlJeH+++/H2bNnnd00IiIicnOSEEI4uxHG9O7dG926dcP777+v3RYfH4/Ro0dj3rx5Ru9fXFyMoKAgFBUVITAw0J5NJSIiIhtx1Pe3y/cMVVRU4JdffsHQoUN1tg8dOhQ7duxwUquIiIjIU/g4uwHGXLlyBSqVCqGhoTrbQ0NDUVhYqPc+5eXlKC8v194uKioCoI4wiYiIyD1ovrftPYjl8sGQhiRJOreFEHW2acybNw9z5sypsz06OtoubSMiIiL7uXr1KoKCgux2fpcPhlq0aAFvb+86vUCXLl2q01ukMXPmTGRkZGhv37hxA61bt8bZs2ft+mS6muLiYkRHRyM/P19WuVK8bl63HPC6ed1yUFRUhFatWiE4ONiuj+PywZCfnx+6d++OjRs34oEHHtBu37hxI1JSUvTex9/fH/7+/nW2BwUFyepNpBEYGMjrlhFet7zwuuVFrtft5WXfFGeXD4YAICMjA+PGjUOPHj3Qt29ffPjhhzh79iyefvppZzeNiIiI3JxbBEMPPfQQrl69itdffx0FBQVITEzEN998g9atWzu7aUREROTm3CIYAoDJkydj8uTJFt3X398fs2bN0jt05sl43bxuOeB187rlgNdt3+t2i6KLRERERPbi8kUXiYiIiOyJwRARERHJGoMhIiIikjUGQ0RERCRrbhkMvffee4iNjUVAQAC6d++O7du313v81q1b0b17dwQEBKBNmzZYtmxZnWOysrKQkJAAf39/JCQkYNWqVfZqvsXMue7s7GwMGTIELVu2RGBgIPr27YsNGzboHLNixQpIklTnr6yszN6XYhZzrjs3N1fvNR09elTnOE97vSdMmKD3ujt06KA9xh1e723btmHUqFGIiIiAJElYvXq10ft4wufb3Ov2lM+3udftKZ9vc6/bUz7f8+bNQ8+ePdGkSROEhIRg9OjROHbsmNH7OeIz7nbB0BdffIH09HS88sor2LdvH5KSknD//ffj7Nmzeo/Py8vD8OHDkZSUhH379uFvf/sbnn32WWRlZWmP2blzJx566CGMGzcOv/32G8aNG4cxY8bgp59+ctRlGWXudW/btg1DhgzBN998g19++QXJyckYNWoU9u3bp3NcYGAgCgoKdP4CAgIccUkmMfe6NY4dO6ZzTe3atdPu88TXe8mSJTrXm5+fj+DgYPz5z3/WOc7VX+/S0lJ07twZS5cuNel4T/l8m3vdnvL5Nve6Ndz9823udXvK53vr1q2YMmUKdu3ahY0bN6KqqgpDhw5FaWmpwfs47DMu3EyvXr3E008/rbMtLi5OzJgxQ+/xL7/8soiLi9PZ9tRTT4k+ffpob48ZM0bcd999OscMGzZMPPzwwzZqtfXMvW59EhISxJw5c7S3ly9fLoKCgmzVRLsw97pzcnIEAHH9+nWD55TD671q1SohSZI4ffq0dps7vN41ARCrVq2q9xhP+XzXZMp16+OOn++aTLluT/l812TJ6+0Jn28hhLh06ZIAILZu3WrwGEd9xt2qZ6iiogK//PILhg4dqrN96NCh2LFjh9777Ny5s87xw4YNw549e1BZWVnvMYbO6WiWXHdt1dXVKCkpqbPY3c2bN9G6dWtERUVh5MiRdX5ZOpM11921a1eEh4fj3nvvRU5Ojs4+ObzeH3/8MQYPHlynSrsrv96W8ITPty244+fbGu78+bYFT/l8FxUVAUC9i7A66jPuVsHQlStXoFKp6qxWHxoaWmdVe43CwkK9x1dVVeHKlSv1HmPonI5myXXX9tZbb6G0tBRjxozRbouLi8OKFSugVCqxcuVKBAQEoF+/fjhx4oRN228pS647PDwcH374IbKyspCdnY327dvj3nvvxbZt27THePrrXVBQgG+//RaTJk3S2e7qr7clPOHzbQvu+Pm2hCd8vq3lKZ9vIQQyMjLQv39/JCYmGjzOUZ9xt1mOoyZJknRuCyHqbDN2fO3t5p7TGSxt48qVKzF79mysWbMGISEh2u19+vRBnz59tLf79euHbt264V//+hfeeecd2zXcSuZcd/v27dG+fXvt7b59+yI/Px8LFy7EgAEDLDqns1jaxhUrVqBp06YYPXq0znZ3eb3N5Smfb0u5++fbHJ70+baUp3y+p06div379+OHH34weqwjPuNu1TPUokULeHt714n2Ll26VCcq1AgLC9N7vI+PD5o3b17vMYbO6WiWXLfGF198gSeeeAJffvklBg8eXO+xXl5e6Nmzp8v8krDmumvq06ePzjV58usthMB//vMfjBs3Dn5+fvUe62qvtyU84fNtDXf+fNuKu32+reEpn+9p06ZBqVQiJycHUVFR9R7rqM+4WwVDfn5+6N69OzZu3KizfePGjbjnnnv03qdv3751jv/+++/Ro0cP+Pr61nuMoXM6miXXDah/MU6YMAGZmZkYMWKE0ccRQuDXX39FeHi41W22BUuvu7Z9+/bpXJOnvt6AerbGyZMn8cQTTxh9HFd7vS3hCZ9vS7n759tW3O3zbQ13/3wLITB16lRkZ2djy5YtiI2NNXofh33GTU61dhGff/658PX1FR9//LE4fPiwSE9PF40aNdJm1c+YMUOMGzdOe/zvv/8uGjZsKJ5//nlx+PBh8fHHHwtfX1/x9ddfa4/58ccfhbe3t/i///s/ceTIEfF///d/wsfHR+zatcvh12eIudedmZkpfHx8xLvvvisKCgq0fzdu3NAeM3v2bPHdd9+JU6dOiX379omJEycKHx8f8dNPPzn8+gwx97oXLVokVq1aJY4fPy4OHjwoZsyYIQCIrKws7TGe+HprPPbYY6J37956z+kOr3dJSYnYt2+f2LdvnwAg3n77bbFv3z5x5swZIYTnfr7NvW5P+Xybe92e8vk297o13P3z/cwzz4igoCCRm5ur8769deuW9hhnfcbdLhgSQoh3331XtG7dWvj5+Ylu3brpTMsbP368GDhwoM7xubm5omvXrsLPz0/ExMSI999/v845v/rqK9G+fXvh6+sr4uLidD5crsKc6x44cKAAUOdv/Pjx2mPS09NFq1athJ+fn2jZsqUYOnSo2LFjhwOvyDTmXPf8+fNF27ZtRUBAgGjWrJno37+/WL9+fZ1zetrrLYQQN27cEA0aNBAffvih3vO5w+utmTpt6H3rqZ9vc6/bUz7f5l63p3y+LXmfe8LnW981AxDLly/XHuOsz7j0RwOJiIiIZMmtcoaIiIiIbI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEicksrV65EQEAAzp8/r902adIkdOrUCUVFRU5sGRG5G65NRkRuSQiBLl26ICkpCUuXLsWcOXPw0UcfYdeuXYiMjHR284jIjfg4uwFERJaQJAlz585FWloaIiIisGTJEmzfvp2BEBGZjT1DROTWunXrhkOHDuH777/HwIEDnd0cInJDzBkiIre1YcMGHD16FCqVCqGhoc5uDhG5KfYMEZFb2rt3LwYNGoR3330Xn3/+ORo2bIivvvrK2c0iIjfEnCEicjunT5/GiBEjMGPGDIwbNw4JCQno2bMnfvnlF3Tv3t3ZzSMiN8OeISJyK9euXUO/fv0wYMAAfPDBB9rtKSkpKC8vx3fffefE1hGRO2IwRERERLLGBGoiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrDEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsMhoiIiEjWGAwRERGRrP0/sCxKf+B5Q7YAAAAASUVORK5CYII=", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta from own sdg\n", + "[[4.02496085]\n", + " [3.12081773]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4484,10 +4420,8 @@ }, { "cell_type": "markdown", - "id": "ba1f3157", - "metadata": { - "editable": true - }, + "id": "18298e5e", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -4495,12 +4429,26 @@ { "cell_type": "code", "execution_count": 32, - "id": "c06c4547", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3320d6c6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.96075051]\n", + " [3.02148021]]\n", + "Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]\n", + "theta from own gd\n", + "[[3.95906059]\n", + " [3.02296298]]\n", + "theta from own sdg with momentum\n", + "[[3.95611042]\n", + " [2.99475306]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4573,10 +4521,8 @@ }, { "cell_type": "markdown", - "id": "16b6b2c9", - "metadata": { - "editable": true - }, + "id": "f1411612", + "metadata": {}, "source": [ "## Similar (second order function now) problem but now with AdaGrad" ] @@ -4584,12 +4530,24 @@ { "cell_type": "code", "execution_count": 33, - "id": "d6d3a6ca", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "19414323", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own AdaGrad\n", + "[[2.00025662]\n", + " [2.99802696]\n", + " [4.00167329]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n", "# OLS example\n", @@ -4643,20 +4601,16 @@ }, { "cell_type": "markdown", - "id": "08925601", - "metadata": { - "editable": true - }, + "id": "a77cdfa4", + "metadata": {}, "source": [ "Running this code we note an almost perfect agreement with the results from matrix inversion." ] }, { "cell_type": "markdown", - "id": "cc62acf3", - "metadata": { - "editable": true - }, + "id": "9f488085", + "metadata": {}, "source": [ "## RMSprop for adaptive learning rate with Stochastic Gradient Descent" ] @@ -4664,12 +4618,24 @@ { "cell_type": "code", "execution_count": 34, - "id": "561a26b8", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "6724b3d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own RMSprop\n", + "[[1.99456598]\n", + " [2.99848815]\n", + " [3.99835783]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4729,10 +4695,8 @@ }, { "cell_type": "markdown", - "id": "f2c44a2a", - "metadata": { - "editable": true - }, + "id": "09728e4a", + "metadata": {}, "source": [ "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)" ] @@ -4740,12 +4704,24 @@ { "cell_type": "code", "execution_count": 35, - "id": "c32bd5e0", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "28aa6aad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own ADAM\n", + "[[1.99989103]\n", + " [3.00042093]\n", + " [3.99954925]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4810,10 +4786,8 @@ }, { "cell_type": "markdown", - "id": "4183d2b1", - "metadata": { - "editable": true - }, + "id": "70fc8bdd", + "metadata": {}, "source": [ "## And Logistic Regression" ] @@ -4821,12 +4795,18 @@ { "cell_type": "code", "execution_count": 36, - "id": "d1a76119", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "f3dde7c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss: 2.772588722239781\n", + "Trained loss: 1.067270675787016\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4865,10 +4845,8 @@ }, { "cell_type": "markdown", - "id": "68fef7c6", - "metadata": { - "editable": true - }, + "id": "b46c449b", + "metadata": {}, "source": [ "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n", "\n", @@ -4884,12 +4862,17 @@ { "cell_type": "code", "execution_count": 37, - "id": "d62a782e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "291c9b6d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.25 0.19661197 0.10499357]\n" + ] + } + ], "source": [ "import jax.numpy as jnp\n", "from jax import grad, jit, vmap\n", @@ -4901,9 +4884,35 @@ "derivative_fn = grad(sum_logistic)\n", "print(derivative_fn(x_small))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e201d58b", + "metadata": {}, + "outputs": [], + "source": [] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, "nbformat": 4, "nbformat_minor": 5 } diff --git a/doc/pub/week39/ipynb/week39.ipynb b/doc/pub/week39/ipynb/week39.ipynb index e19f189a4..4a48fabca 100644 --- a/doc/pub/week39/ipynb/week39.ipynb +++ b/doc/pub/week39/ipynb/week39.ipynb @@ -2,10 +2,8 @@ "cells": [ { "cell_type": "markdown", - "id": "2254a68d", - "metadata": { - "editable": true - }, + "id": "0be56d20", + "metadata": {}, "source": [ "\n", @@ -14,10 +12,8 @@ }, { "cell_type": "markdown", - "id": "31cedf5c", - "metadata": { - "editable": true - }, + "id": "41352012", + "metadata": {}, "source": [ "# Week 39: Optimization and Gradient Methods\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n", @@ -27,20 +23,16 @@ }, { "cell_type": "markdown", - "id": "923b4bde", - "metadata": { - "editable": true - }, + "id": "471d9b17", + "metadata": {}, "source": [ "## Plan for week 39, September 23-27, 2024" ] }, { "cell_type": "markdown", - "id": "73724d06", - "metadata": { - "editable": true - }, + "id": "a3f843e5", + "metadata": {}, "source": [ "## Lecture Monday September 23\n", "\n", @@ -67,10 +59,8 @@ }, { "cell_type": "markdown", - "id": "4b19d8d6", - "metadata": { - "editable": true - }, + "id": "b611ff2d", + "metadata": {}, "source": [ "## Lab sessions week 39\n", "\n", @@ -94,10 +84,8 @@ }, { "cell_type": "markdown", - "id": "c99e4edf", - "metadata": { - "editable": true - }, + "id": "126f7d60", + "metadata": {}, "source": [ "## Lecture Monday September 23, Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -115,10 +103,8 @@ }, { "cell_type": "markdown", - "id": "e31c673b", - "metadata": { - "editable": true - }, + "id": "a2682f11", + "metadata": {}, "source": [ "## Revisiting our Logistic Regression case\n", "\n", @@ -132,10 +118,8 @@ }, { "cell_type": "markdown", - "id": "ac43b608", - "metadata": { - "editable": true - }, + "id": "d51c88b5", + "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", @@ -147,20 +131,16 @@ }, { "cell_type": "markdown", - "id": "aabe79ec", - "metadata": { - "editable": true - }, + "id": "4a135362", + "metadata": {}, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$." ] }, { "cell_type": "markdown", - "id": "78804ec8", - "metadata": { - "editable": true - }, + "id": "26444396", + "metadata": {}, "source": [ "## The equations to solve\n", "\n", @@ -173,10 +153,8 @@ }, { "cell_type": "markdown", - "id": "7dbc40f0", - "metadata": { - "editable": true - }, + "id": "9bc5702f", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -185,10 +163,8 @@ }, { "cell_type": "markdown", - "id": "cfb64d4a", - "metadata": { - "editable": true - }, + "id": "a857de8b", + "metadata": {}, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -196,10 +172,8 @@ }, { "cell_type": "markdown", - "id": "18d5ecb5", - "metadata": { - "editable": true - }, + "id": "dc870dc3", + "metadata": {}, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -208,20 +182,16 @@ }, { "cell_type": "markdown", - "id": "1af7b435", - "metadata": { - "editable": true - }, + "id": "4001c458", + "metadata": {}, "source": [ "This defines what is called the Hessian matrix." ] }, { "cell_type": "markdown", - "id": "81594f4d", - "metadata": { - "editable": true - }, + "id": "4f3262b4", + "metadata": {}, "source": [ "## Solving using Newton-Raphson's method\n", "\n", @@ -232,10 +202,8 @@ }, { "cell_type": "markdown", - "id": "5d03e20f", - "metadata": { - "editable": true - }, + "id": "0d94cee2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -244,20 +212,16 @@ }, { "cell_type": "markdown", - "id": "e9ef26a5", - "metadata": { - "editable": true - }, + "id": "d92e7b5d", + "metadata": {}, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "id": "d7830188", - "metadata": { - "editable": true - }, + "id": "076acdca", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -266,10 +230,8 @@ }, { "cell_type": "markdown", - "id": "d46a0f97", - "metadata": { - "editable": true - }, + "id": "c37ab3fd", + "metadata": {}, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", @@ -278,10 +240,8 @@ }, { "cell_type": "markdown", - "id": "cf9b07d2", - "metadata": { - "editable": true - }, + "id": "4f771526", + "metadata": {}, "source": [ "## Brief reminder on Newton-Raphson's method\n", "\n", @@ -298,10 +258,8 @@ }, { "cell_type": "markdown", - "id": "4b0ccd27", - "metadata": { - "editable": true - }, + "id": "e13dad72", + "metadata": {}, "source": [ "## The equations\n", "\n", @@ -314,10 +272,8 @@ }, { "cell_type": "markdown", - "id": "38fad3c1", - "metadata": { - "editable": true - }, + "id": "aff57d4b", + "metadata": {}, "source": [ "\n", "
    \n", @@ -330,10 +286,8 @@ }, { "cell_type": "markdown", - "id": "956d8d8d", - "metadata": { - "editable": true - }, + "id": "38304c1d", + "metadata": {}, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -341,10 +295,8 @@ }, { "cell_type": "markdown", - "id": "c04d5f5b", - "metadata": { - "editable": true - }, + "id": "8da576a0", + "metadata": {}, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -353,20 +305,16 @@ }, { "cell_type": "markdown", - "id": "6381557f", - "metadata": { - "editable": true - }, + "id": "46d9c588", + "metadata": {}, "source": [ "yielding" ] }, { "cell_type": "markdown", - "id": "b794a967", - "metadata": { - "editable": true - }, + "id": "3a3ca58b", + "metadata": {}, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -375,20 +323,16 @@ }, { "cell_type": "markdown", - "id": "a585ccf0", - "metadata": { - "editable": true - }, + "id": "0c9c700f", + "metadata": {}, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "id": "fa670518", - "metadata": { - "editable": true - }, + "id": "b273b273", + "metadata": {}, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -397,10 +341,8 @@ }, { "cell_type": "markdown", - "id": "6ae1fe30", - "metadata": { - "editable": true - }, + "id": "3e0a875b", + "metadata": {}, "source": [ "## Simple geometric interpretation\n", "\n", @@ -419,10 +361,8 @@ }, { "cell_type": "markdown", - "id": "d24b1dde", - "metadata": { - "editable": true - }, + "id": "727cfd55", + "metadata": {}, "source": [ "## Extending to more than one variable\n", "\n", @@ -432,10 +372,8 @@ }, { "cell_type": "markdown", - "id": "6d83d75f", - "metadata": { - "editable": true - }, + "id": "f78349b5", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -445,20 +383,16 @@ }, { "cell_type": "markdown", - "id": "fc197a3e", - "metadata": { - "editable": true - }, + "id": "2ee16c9e", + "metadata": {}, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "id": "c9b845b1", - "metadata": { - "editable": true - }, + "id": "f95fdb8b", + "metadata": {}, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -473,20 +407,16 @@ }, { "cell_type": "markdown", - "id": "e35d282a", - "metadata": { - "editable": true - }, + "id": "3f039432", + "metadata": {}, "source": [ "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have" ] }, { "cell_type": "markdown", - "id": "fa743fe6", - "metadata": { - "editable": true - }, + "id": "dbd20795", + "metadata": {}, "source": [ "$$\n", "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n", @@ -498,20 +428,16 @@ }, { "cell_type": "markdown", - "id": "1c4a8103", - "metadata": { - "editable": true - }, + "id": "98ba6676", + "metadata": {}, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "id": "b502afca", - "metadata": { - "editable": true - }, + "id": "ad52dad5", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -522,20 +448,16 @@ }, { "cell_type": "markdown", - "id": "3ba44616", - "metadata": { - "editable": true - }, + "id": "cc09e475", + "metadata": {}, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "id": "cb9490f1", - "metadata": { - "editable": true - }, + "id": "7a1c0547", + "metadata": {}, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -546,10 +468,8 @@ }, { "cell_type": "markdown", - "id": "a0db4fd4", - "metadata": { - "editable": true - }, + "id": "9fe4208b", + "metadata": {}, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", @@ -561,10 +481,8 @@ }, { "cell_type": "markdown", - "id": "4f1f9355", - "metadata": { - "editable": true - }, + "id": "2a81e02b", + "metadata": {}, "source": [ "## Steepest descent\n", "\n", @@ -578,10 +496,8 @@ }, { "cell_type": "markdown", - "id": "13978c16", - "metadata": { - "editable": true - }, + "id": "f90232dd", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -590,10 +506,8 @@ }, { "cell_type": "markdown", - "id": "a016b4b5", - "metadata": { - "editable": true - }, + "id": "4fb8b51e", + "metadata": {}, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -604,10 +518,8 @@ }, { "cell_type": "markdown", - "id": "b3d6e411", - "metadata": { - "editable": true - }, + "id": "81da0301", + "metadata": {}, "source": [ "## More on Steepest descent\n", "\n", @@ -619,10 +531,8 @@ }, { "cell_type": "markdown", - "id": "dca89a3a", - "metadata": { - "editable": true - }, + "id": "9b1a0014", + "metadata": {}, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -631,10 +541,8 @@ }, { "cell_type": "markdown", - "id": "2bfe02b5", - "metadata": { - "editable": true - }, + "id": "52e8d174", + "metadata": {}, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning." @@ -642,10 +550,8 @@ }, { "cell_type": "markdown", - "id": "af11f055", - "metadata": { - "editable": true - }, + "id": "be802e47", + "metadata": {}, "source": [ "## The ideal\n", "\n", @@ -670,10 +576,8 @@ }, { "cell_type": "markdown", - "id": "f6227bb6", - "metadata": { - "editable": true - }, + "id": "c2404539", + "metadata": {}, "source": [ "## The sensitiveness of the gradient descent\n", "\n", @@ -692,10 +596,8 @@ }, { "cell_type": "markdown", - "id": "023a22dc", - "metadata": { - "editable": true - }, + "id": "f96c6cdf", + "metadata": {}, "source": [ "## Convex functions\n", "\n", @@ -714,10 +616,8 @@ }, { "cell_type": "markdown", - "id": "fac77758", - "metadata": { - "editable": true - }, + "id": "0deb328b", + "metadata": {}, "source": [ "## Convex function\n", "\n", @@ -735,10 +635,8 @@ }, { "cell_type": "markdown", - "id": "f6f0b048", - "metadata": { - "editable": true - }, + "id": "74dc1b02", + "metadata": {}, "source": [ "## Conditions on convex functions\n", "\n", @@ -774,10 +672,8 @@ }, { "cell_type": "markdown", - "id": "df24a7bb", - "metadata": { - "editable": true - }, + "id": "bc8bc23c", + "metadata": {}, "source": [ "## More on convex functions\n", "\n", @@ -802,10 +698,8 @@ }, { "cell_type": "markdown", - "id": "e15783d2", - "metadata": { - "editable": true - }, + "id": "b004d0d8", + "metadata": {}, "source": [ "## Some simple problems\n", "\n", @@ -832,10 +726,8 @@ }, { "cell_type": "markdown", - "id": "c66ceca3", - "metadata": { - "editable": true - }, + "id": "004c656f", + "metadata": {}, "source": [ "## Standard steepest descent\n", "\n", @@ -852,10 +744,8 @@ }, { "cell_type": "markdown", - "id": "66fc0d42", - "metadata": { - "editable": true - }, + "id": "3055088e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -864,20 +754,16 @@ }, { "cell_type": "markdown", - "id": "5101c1c7", - "metadata": { - "editable": true - }, + "id": "9d268d89", + "metadata": {}, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "id": "1fa20f33", - "metadata": { - "editable": true - }, + "id": "c8dbe560", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -886,10 +772,8 @@ }, { "cell_type": "markdown", - "id": "7d6a34ba", - "metadata": { - "editable": true - }, + "id": "fd2de293", + "metadata": {}, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", @@ -898,10 +782,8 @@ }, { "cell_type": "markdown", - "id": "3fd15bdc", - "metadata": { - "editable": true - }, + "id": "25344346", + "metadata": {}, "source": [ "## Gradient method\n", "\n", @@ -910,10 +792,8 @@ }, { "cell_type": "markdown", - "id": "8f5fda6f", - "metadata": { - "editable": true - }, + "id": "c1b8855c", + "metadata": {}, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -922,10 +802,8 @@ }, { "cell_type": "markdown", - "id": "5fe898c7", - "metadata": { - "editable": true - }, + "id": "506aceb6", + "metadata": {}, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite." @@ -933,10 +811,8 @@ }, { "cell_type": "markdown", - "id": "7da75300", - "metadata": { - "editable": true - }, + "id": "53b26051", + "metadata": {}, "source": [ "## Steepest descent method\n", "\n", @@ -946,10 +822,8 @@ }, { "cell_type": "markdown", - "id": "4e43a72e", - "metadata": { - "editable": true - }, + "id": "06b0db34", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -958,20 +832,16 @@ }, { "cell_type": "markdown", - "id": "3a3491e1", - "metadata": { - "editable": true - }, + "id": "0d9ddd86", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "816d9918", - "metadata": { - "editable": true - }, + "id": "66dff86c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -980,20 +850,16 @@ }, { "cell_type": "markdown", - "id": "ea085a25", - "metadata": { - "editable": true - }, + "id": "77c18c22", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "5c7e4027", - "metadata": { - "editable": true - }, + "id": "9dfad29a", + "metadata": {}, "source": [ "## Steepest descent method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1001,10 +867,8 @@ }, { "cell_type": "markdown", - "id": "f68b4716", - "metadata": { - "editable": true - }, + "id": "50edf2f9", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1013,10 +877,8 @@ }, { "cell_type": "markdown", - "id": "93947e25", - "metadata": { - "editable": true - }, + "id": "51d84a77", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1025,10 +887,8 @@ }, { "cell_type": "markdown", - "id": "f4bebdbd", - "metadata": { - "editable": true - }, + "id": "f3179c0a", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1037,10 +897,8 @@ }, { "cell_type": "markdown", - "id": "37bad3e3", - "metadata": { - "editable": true - }, + "id": "66bc0e76", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$." @@ -1048,10 +906,8 @@ }, { "cell_type": "markdown", - "id": "709d8e2d", - "metadata": { - "editable": true - }, + "id": "9be63d8b", + "metadata": {}, "source": [ "## Final expressions\n", "We can compute the residual iteratively as" @@ -1059,10 +915,8 @@ }, { "cell_type": "markdown", - "id": "d354f6f9", - "metadata": { - "editable": true - }, + "id": "07294b6e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1071,20 +925,16 @@ }, { "cell_type": "markdown", - "id": "ca2440ea", - "metadata": { - "editable": true - }, + "id": "5cb13e3a", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "d1c8125c", - "metadata": { - "editable": true - }, + "id": "b95b4415", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -1093,20 +943,16 @@ }, { "cell_type": "markdown", - "id": "628e5d2d", - "metadata": { - "editable": true - }, + "id": "90956a95", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "492bec97", - "metadata": { - "editable": true - }, + "id": "d4675379", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -1115,20 +961,16 @@ }, { "cell_type": "markdown", - "id": "05aef9df", - "metadata": { - "editable": true - }, + "id": "6e3a1c20", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "f5cae3d2", - "metadata": { - "editable": true - }, + "id": "e9b86a0a", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -1137,20 +979,16 @@ }, { "cell_type": "markdown", - "id": "0b421380", - "metadata": { - "editable": true - }, + "id": "a1fd88cc", + "metadata": {}, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "id": "029c5776", - "metadata": { - "editable": true - }, + "id": "39f090b1", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n", @@ -1159,10 +997,8 @@ }, { "cell_type": "markdown", - "id": "5e3cd31f", - "metadata": { - "editable": true - }, + "id": "0ad69506", + "metadata": {}, "source": [ "## Steepest descent example" ] @@ -1170,12 +1006,30 @@ { "cell_type": "code", "execution_count": 1, - "id": "c1c8c431", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "4a529fa4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%matplotlib inline\n", "\n", @@ -1203,10 +1057,8 @@ }, { "cell_type": "markdown", - "id": "247d62a6", - "metadata": { - "editable": true - }, + "id": "949a0d1c", + "metadata": {}, "source": [ "And then as countor plot" ] @@ -1214,12 +1066,20 @@ { "cell_type": "code", "execution_count": 2, - "id": "472adf77", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3b0698ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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vbmB/Vz2tA4bTnhfnH0JxVCrFkclMjUwmLyxelvIWYgQoikLrQD+He5o41NPIoZ4myvpaT1sM0E+tZWpkMjOjU5kVnc7UiGQCtBOri+CeJNvI7p497O7eO2xfnmh9NPOj57Igah7xAfFerNK7JJRMQC/Vv8yWzq3DzqvPCspkQfQ85kTOJlgX7MXqLiyXonCiv539XfXs72pgf3f9aUdlGpWKyWHxQ0dlKUyPTCEhMMxLFQshBhx2SvtaPN3Lkp7G0xaB06rUFEYkMjMqjZnRacyISp1Qy+m7FBfHjSfY0bWTfT0Hhq2EnRmUwb2ZXyIpINGLFXqHhJIJ6Lm659nYsZkYv2jmR81jfvQ84v3jvF3WBdNs7mNHRzW7OmvY01l32nwQvVpDUUQys6LdL2ZTI5MJ0srqi0KMVYqiUGPsYn+3++BiX1fdaeuoaFQqCsITmRebyfzYTKZFpkyY4R6b00ZJ3yF2du3iqOEYGpWaPxb/wSdXw5ZQMgG1DbTR7zCSE5w9ISaSGe1WdnfWsrOjhp0dNTR8ZMZ/oEbHtKgUdwiJSmNKRBJ+MhQjxLilKArNlj72d9Wzr7ue/V31NJh7hz0nUKNjZnQ682MzWRCbRVZI9IR4vTPYDdSa6pgWMdXbpXiFhBIx5iiKwvH+dra1VbG1vYpDPY3Dxp81KhVTI5KZH5vJvNhMpkQkoZsgR0xCiDNrsRjYM3Rwsquz5rRh2oSAMBbHZbMoLpu5sZnSHR2nJJSIMcFot7Kro4Yt7ZVsb68+baGm9OAoFsRmMj82i9nR6RNqbHmicrhcWOyDmAftmO2DWOx2bE4HNocTm8Px4W2n+7bd6cLhcuFUhq5diudjp+vcLzcqFWjUarQqNRq1Cq1ajUaldl+r1fhpNPhptfhpNPhrtfhptB9+rNMRpNMRqNMTrNfhp9FOiCPuiezkXLKT3dN9XXUMnrKwoU6lZkZ0GouGQkp2SIz8n44TEkqE1zSYetjUdoJNrcc50N0wrBvir9EyNyaTRXHZLI7LJjlIlmsebYqi0G+z0WMdoHdg6GIdwGCz0W+zYrTZ6LfZMNis9A/dNg0OuoOI3c6g8/TVb8cDtUpFoE5HkE5PoE5HqJ/fKRf/YbfD/fyJCAggIiCASH/3tV4jXbvRNuCws7erjm3tlWxrrzptqCcpMJyl8ZO4KGESs6LTJ8xclIlIQokYNU7FxeGeJja1nmBT23GqjV3DHs8IjhoKITnMjE6TeSEjQFEUeq0DdFosdJhNdJktdFhMdA5dd5kt9AxYPEHkXDvMflJatXroDV6Ln1b3kW6FBj+NFr1Gg16jcXc7hrobWpXK87FapULF2Y90XSg4XS6crpPdlqEui8uF3eXydGUGnY6hLo3Tc22x2xlw2LHYz7yH0fkK1us9ASU6MJDYoGDPdYznOojowED8tPI7PhLqTN1sbXMHlL0f6aIEafUsjM1macIkFsfl+NSS+OOBhBIxoqxOOzs7aljfUsHmthPDzpTRqtTMiEplaUIuS+MnkRrsmzsNXygnOxtN/QZaTUZajEbaTCZaTUbaTEZajUbazKbz7mAE6XREBgS6OwL+/sO6BWGn3A7R+xHi5+fpMgTp3UMi46Vz4HS5GHA4PJ0e8+Ag5sFBjIM2Tyfo1M6Q0Waj1zpAn9VKz4CFXqsV13m+LEYFBJIQHExCSAjxwSEkBJ+8DiYpNJT44BC0allQ67OwOAbZ3VnLptbjbG47Qdcpc1HUqCiOSmFZwmSWJU6WjuwYIKFEXHBGu5UtbZWsb6lgW3slllN20Q3V+bM4LoeLEiaxKDabUL2/Fysdf2wOB/WGPur7+mgy9tPYb6C530Bjfz9N/QZMg4Of6OtE+gcQHRRETGAgMYFBxAYFER0YRExQEFEBgUQGBBAZEECEf4AczX9CLkWh32alZ2Bg6GKhy2Kh02Kmw2ymy2Ie1pEaPMPmjh+lUalICAkhOSSM5LBQkkPCSAl1384IjyQqIEDmSpwHl6JQ2tvCpjZ3QKkwtA97PC8snksSJ7M8MY8cmYfiFRJKxAVhttvY0Hqc95uPsb2jethuugkBoSxLnMwlCZOZHpUqZ8p8DJei0Go0UtPbQ21fL7V9vZ7bzf39Z9lU/kPRgYEkhoQSHxxM4skj75CQoY9DiQkKGjfdi4lKURT6rFbaTEZaTEMdLeNQR2uou9XS3/+xwSVE70dmRAQZ4RFkDF1nRkSSER5BgG5irYY6EpotfWxqPc76lgr2d9cPG67MCI7isqQCLk8uICc01otV+hYJJeJTszkdbG2v5L2mUja1nhi2q25mcDTLh4448sMT5IjjDFyKQouxn8qebiq7u6ns6eZEdxfVvT3nnN8QovcjLTyclNAwUkJDSQodOnoODSUpJFTejCYIl6LQaTbT2G+gaagTdvJ2g6GPFuPZA6oKSAkNIzsyipyoKCZFRpMdFUV2RKT8fpxFr83CpjZ3QNnRUT0sEE4KjeWq5ClckVxIUlC494r0ARJKxHlxKi72dNaxuvEo61rLMdo/XMo+IziKK5ILuTQpX44sPsJos1HR3Ul5ZycVXZ2Ud3VS2dN91vChU6tJCwt3H/0OHfm6j4ilZS/cTg7l1fT2UtvXQ01vL3VDXbVeq/WMn3MyrEyOjmFydAx5MTHkRceQEjqxd+w9Xya7jc1tJ1jTdIxtHVXDOr/FkSlcmVzIZckFRPkFebHKiUlCifhYiqJQZmjj7YbDrGkqHTZRLD4glCuSC7kyuZC8sHiff2FTFIV2s4nSjnZKOzo8AaSx//RNAcEdPjIiIpkUGXXKUW0UqWHh6GSIRXxK3RaLp/NW1dPt6cb1WAfO+PxgnZ7c6GjyomMoiImlMDaOnKhoGebDvevxupZyVjeVsqez1tOd0qhUzI3J5JqUIpYlTiZQFmu7ICSUiLNqG+hnVeMR3m44QrWx03N/mC6Ay5LzuTJ5CjOiUlH7aBA5NYAcHQohpR3tdFpO36YdICE4xH10OnTJjY4mTcKHGEXdFgsnursoHwrLFV2dVHZ3n3Huil6tITc6msLYOIpi4ySoAB0DRtY0H+O9plKO9DZ77g/U6lmRmMe1qVOZHZ3us6+JF4KEEjGM2THI+pZy3m44wu7OGs9RgV6t4ZKEyVydUsSCuCyfXHzIPDjI0Y52StpaONzWxqH2VjrMpwcQjUpFdmQUhbFx5MfEkhcdw+ToaML9A7xQtRDnZnc6qenrdXf1Ojs41tnB0Y52+m22056rV2vIj4llWkIC0+LiKY5PJDk01Cc7pPWmHt5tPMI7jUeGLdaWEBDK1SlFXJNSRFZojBcrHJ8klAgUReFAdwNv1B/ig+Zjw07hnRmVxjWpRVyamO9Tp+8qikJNbw8HWls41NbKofY2TnR3nbYOhVqlImcogEwZOprMi46RyYRiXFMUhcZ+g6cL6O4EnjmoRAUEMC0+gWnxCRTHJzItPoFAH/r9VxSFQz1N7uHt5mP02z+czzMlIpEb0oq5IqnQp14/PwsJJT6s22bmjfoSXq8rof6UnXdTgyK5NtWd9H1lMSGHy0VZZwd7m5vY19LE/pbmM04WTAgOoXjoBXhqfDyFMXESQIRPUBSFBoOBQ+2t7qDe1kpZZwd2l2vY8zQqFfkxscxMTGJOUjKzk5J9pktoczrY3HaCdxqOsLW90rN1hp9ay4qkPG5Jn8GMqFSf7Cx9UhJKfIyiKOztquPl2gNsaCnHPvRHE6jRcVlyATemFVMcmTLh/2icLhdlXZ3sbKxnd1MTB1qaMdmHLzzmp9EyNS6e4gR3CJkWl0BccLCXKhZi7LE5HJR1dlAyFFIOtrXQYjSe9rzcqGjmJCUzLyWVuUkphPlP/K5Bt83MqsYjvF5XQtUpc/KyQqK5JX0G16ZOJUzvG2HtfEgo8RFGu5W3Gg7z35p91Jq6PfcXRSRxc/p0Lk8unNBbfSuKQm1fLzsbG9jR2MDupkYMtuGdkBC9n+foblZiEgWxcT49qU+IT6PZ2M/+lmb2Njext7mJ6t6eYY+rVSoKY+OYn5zK/JRUZiYm4q+duN1GRVE40tvMa3UHWd1UysDQ8LifWsuVKYXckTmb/PAEL1c5dkgomeAq+zt4qWYf7zQc9swVCdTquTplCremzyQvPN7LFY6cngEL2xvq2dZQz87GelpNpmGPB+v0zElOZl5yKnOSkpkcHYNG9hkR4oLqtJjZ19zMnuZGdjY2nBZS9BoNMxKSWJCSypK0dPJiYifs2StGu5VVjUf5X+0Bjvd/uMR9cWQKd2TOYnlSvk+eRHAqCSUTkMPlYmPrcV6q2cuerjrP/VkhMXwucxbXphQRpPPzXoEjxOFycbi9la31dWypr+Noe9uwFS/1ag3TExKZn5LKgpRUpsTFy2ZnQoyyNpORnY0Nnq5lu3n4wUJ0YCCLU9NZlJbOotQ0IgMm3i6+JyfHvlSzjw+aj3mG0aP9grg5fQa3ZswgLsD33rtAQsmE9Lkt/6KkpxFwTzq7OGEyd2TOYnZ0+oSbK9JpNrOproat9XVsb6w/7eyAydExLE5NY0FKGjMTk2RSqhBjyMmz3HY0NrC9oZ6dTQ3DVjlWAVPi4lmSls5FaRkUxcVPuG5mp9XEq3UHeKX2AB1W93wcjUrFcwvvYkZ0qperG30SSiagp49v5fmqPdycMYNb02eQEBjm7ZIuGEVRKOvsYENtDRvrajjS3jbs8TA/fxamprI4LYNFqWnEB4d4qVIhxPmyORwcbG1hS0MdW+vrqOjqHPZ4VEAAF6VncnFGJgtT0gjxmzgdX7vLyYbWCl6q2UedqZv1lz7gk0M5EkomIItjEK1KjV4zMbactzrs7GhsYGNtDZtqa2j7SLt3SmwcF6VnsGToSEqGZISYGNpNJrY21LGlrpatDXWYBj88Q06nVjMnKYWLMzK5JCOLlLCJc/DVNzhAuI+emSOhRIxJVoedzXV1vFd1nI21NcNaugFaLQtT07g4I4ul6RnEBslpukJMdHank30tzWysrWFDbTX1hr5hjxfGxHJ5ziSuyM4lLTzcKzWKz05CiRgzzhVEEoJDWJaZxcXpmcxNTsFPOzG6QL5MURQcThcDdjs2u4NBhxOH04XT5cLudOFwunC4XDiH7jsnlQqdWo1W8+FFM/SxTqPBT6vFX6/FT6tFrZ5Y86p8VU1vjyeg7G9pxnnKW5IElPFLQonwqkGnk631tbxzouK0IJIUEsoVOZO4InsSRXGyA/FYMuhw0Ge2YrBY6bNYMZgH6LNYMQ3YMNkGMVsHMVptmK2DmKyDmG3ui3XQgdVux2p3YB10nLZs/2jw02rw02nx1+vw12kJ1OsI8tcT7K8nyM/Pfe2vJ8TfjyB/PaEBfoQHBRAe6E9YkD/hgQEE++vl93EM6bZYWFtTxXuVx9nd1HhaQLlyUi5XT5pMYoi8H4x1EkrEqHMpCnubm3jneDlrqiqHLWImQcR7bHYHHQYTXUYzXUYLXf3u626Tme5+C11GM90mC31mKwOD9o//gudBrVKh12qGdTi0p3Q61GoV5/pNcCngcDpxuIY6LENdFofThd3p7sBcSFq1mtBAfyKC/IkOCSIqJIjo0MCh2x9ex4UFExboL7/Ho+hcAWV2YjLX5E7m8uxJRAT45pyNsU5CiRgViqJwrLODd46X8+6J48Mmq8YFBXPVpFyuysmVIDJCXC6Fjn4TzT0GWnqNtPcZaesz0W4w0j503WMaOK+vqVapCAv0JyzQn/Ag93VogL+n6xDsP9R18NN7rk92J/x1Q8MpOi0BOh1ajXpE/9+dLhc2uwOr3YHN7mBg0DH0sR2Lze7p7pisg5it7m6PacDd7ekf6gb1mQcwWKxY7Y7z+t7+Oi1xYcHEhYcQHx5MXFgIceHBJISHkBgZSlJkGAF6OVV9JJwMKKuOV7CnudGzbpFWrWZxajrX5E5mWWa2T20gONZJKBEjqtVo5K3jZbxZXkbVKSs5hvr5cXn2JK6ZNJnZSckTbu0BbxgYtNPQ1Ud9Zy9N3Qaae/pp7jl53Y/d6fzYr+Gv0xITGuQ50o/yHPm7j/4jQwKJCAogLNCfEH8/n5yfYbU7PAGlx2Sh2+i+dBnNnusuo4Vuo/kTB72okECSIsNIigwlOTKM5KgwUqLDSY8JJzokSIL6BdBi7Gd15XHeOV7Bsc4Oz/2BOh2XZeVwQ14Bc5NTJuxqsuOFhBJxwQ3Y7XxQXcUb5cfY0VjvOTrx02i5JCOTa3InsyQtQyarfgoul0Jzj4Hajh7qOvto6OqlrrOX+s4+2vpO3wjtVFq1mviIEJIiQokLdx+tx4eHEO85ig8hNMBP3gAvoEGHg3aDifY+E219RtoNQ9d9Jlp73WHRaLWd82sE+ulIi4kgPTqCtJhw9+2YCDLjIgn0m7j7VY2kqp5uVp2o4J3jFcPO4kkIDuH6yfnckJdPZkSk9wr0YRJKxAWhKAoH21r437FS3qs8jvmUCauzEpO4Ia+AK7InTajFjkaSoii095k40dbFiZZOqtq6qWnvobaj55zDB2GB/qRFh5MSHU5SZBjJkaEkRYWRHBlGbFgwWo10pMYag8Xq6Wi5O1wGmroNNHT10dzTf87JwAkRIWTFRZEVF8WkxGhy4qPJjIvETyeB/5NQFIWStlZeLz/G6srjw1aEnhaXwE35BVw9abK8bo0iCSXiMzENDvJWRRkvHD3Mie4uz/2poWFcn5fP9ZPzSQ0L916B44DLpVDf1UtZUwflTR2UN7svxoEzH0H7aTXuo+XYCM9Rc1pMBGnR4YQHyeS9icTucNLYbaChy90Nc3fFeqnt6KHLaDnj52jUKjJiI8lLiiUvOZa8pFgmJ8UQ7C9vrOdiczjYUFvN6+VlbK2v9UyQDdTpuDY3j89PmUpeTKyXq5z4JJSIT6W8q5MXjx7m7YoyT1fEX6vlypxcbs4vZFZikgwDnIGiKNR39XGkvpWypnbKmzqoaOnEYjv9bBatWk16bAQ58dHkJESTFR9FdnwUSZGhMgdHYLBYqW7rpqq9m6rWbirbuqhs7cJgsZ7x+ekxEZ6gUpgaT0FyHIF+MsHzTDrNZt4+Xs4rx44O29V4RkIid0yZyuXZk2T4eYRIKBGfmM3hYE1VJS8ePcSB1hbP/ZkREdwxZRo35uUT6ufvxQrHnj7zAEcb2jhS38rRhjaONrTRf4YOiL9OS25iDHnJseQPvXFkxkWilxc+cR4URaGj38zx5g6OndJ5O9N8I7VKRU5CNFNS4ylKjWdKWjyZsVE+OXn5bBRFYU9zEy8cOcTamiocQ4v4RfoHcFNBIZ8rLJJO8AUmoUR8rHaTiZdKD/PS0cN0D7jPJtCq1SzPzObzU6YyNzlFuiK4X8DqOnspqW3hYG0zh2pbqO/qO+15flqN+2g1JZ785Fjyk+NIj42Q7ocYMT0miyegHGts50hDGx0G02nPC/bXMyU1nuKMJKZnJDIlNUG6KUM6zCZeOXaUl0uP0Gpy/+xUwNL0TL44rZiFKWnyOngBSCgRZ3WorZV/HzrImqoTniOE+KBgbiss4taCKcQF+/aeM3ank/KmDk8IKaltodd8+img6TERTEmNdx+RpiUwKTEancb3dv8UY0u7wcTR+laO1LdypKGNsqZ2BgaHT6LWqFXkJcUyPTOJ6RlJTEtPJCok0EsVjw0Ol4tNtTW8cPQQ2xrqPffnREbxhanFXD85X9Y9+QwklIhhBp1O1lSdYOWhgxxub/PcPzMxibumFrM8M9tn31AdThflzR3srWpkX1UjB2ubT3sR99NqmJKWQHFGIsXpiRSlJRAWKENaYuxzOF1UtXVxqK6Vg7XNHKxppv0M3ZSsuEhmZacwOzuFWVnJPj25uqa3h/8cLuH18mOeuXWhfn7cVjCFO4uKSZL3n/M2JkPJo48+yhtvvEFFRQUBAQHMnz+f3/72t+Tm5n6iz5dQcv76rAO8ePQIzx8pocNsBkCv1nB17mS+MLWYKbFxXq5w9LlcCidaO9lb1cTeqgYO1DRjsg4Oe05YoD/FGYlMz0iiOCOR/ORYmQciJozW3n4O1DR7uoFVbd3DHlepYFJCDLOyk5mTncKMzGRCAnzvLJ9+m43Xykr5z+ESGvoNgHvOzvLMbO6dPoMZCUlernD8GJOh5LLLLuO2225j1qxZOBwOfvKTn3D06FHKysoICgr62M+XUPLJtZmMPHvwAP8tPcyAw33UHxMYxOeLpnJbYRExgR//855I+ges7Dxez7byOrZX1NFjGn7aZUiAHzMzk5mdnczsnFSy42RioPAdfeYB9lc3sbeqiX3VjaeFFI1axbT0RBbnZbAoL4Ps+CifmmfhdLnYXF/LykMH2dHY4Ll/RkIiX581lyVp6T718/g0xmQo+ajOzk5iY2PZsmULixcvPu1xm82G7ZRFb/r7+0lJSZFQcg4Nhj7+fmAfr5cdY9DlXn48LzqGe4tncuWkXPQ+MkSjKArV7d1sLatlW0UdJbXNOF0f/moH+umYkZnM7KxkZuekkJsYIxNShRjSZTSzv6qJvdWN7K1sPG1id0JEiCegzM5O8ak9fk50d/GvkgO8VVHueY0tiInl/plzuCw7R5azP4txEUqqqqrIycnh6NGjFBYWnvb4Qw89xMMPP3za/RJKTlfZ3c1T+/ew6kSFZ3GgmYlJfH3mHBb7SIp3OF2U1DazsbSaTceqae7pH/Z4ZlwkiyZnsDg/g+L0RHRa3whoQnxWTd0GtpW7A/7eygZsjg/3W/LTapg7KZWLC7NZkp/pMxNm200mni3Zz0tHP+xGZ0VEcv/M2VyTm4dWDnKGGfOhRFEUrr32Wnp7e9m2bdsZnyOdko93oruLv+zdzerK4569aJakpXP/zDnMTkr2am2jYWDQzs7j9WwsrWZLWc2wBab8tBpmZaewKC+DRXnppESFe69QISaIgUE7+6oa2Vpex7byWlp6Pwz/KhUUpydycWE2FxdmkRId7r1CR0nPgIXnDpfw3OESz3L2aWHhfH3WHK6bnC/hZMiYDyVf//rXWb16Ndu3byc5+ZO9ecqckg+dKYysyMrm67PmTvjJq8YBG5uPVbPuSBW7TtQP2zMmPNCfJQWZXFyYzbxJqT7VVhZitCmKQlVbN5uOVbOxtJpjje3DHs+Oj+KSKdksL8phUkL0hO7YGm02Xjx6mH+W7Pes+yTh5ENjOpR84xvf4K233mLr1q1kZGR84s+TUHLmMHJpVg7fnD13Qu/fcDKIfHD4BDuPN2B3ftg+TooMZWlhFhcXZlOcniib0wnhJW29Rk9A2V/d5FkHCdzr+qyYOokVUyd2QLHY7bxw5BDPHNhHj1XCyUljMpQoisI3vvEN3nzzTTZv3kxOTs55fb4vhxJFUfju2jW8fbzcZ8LIuYJIVlwky4tyWOYDR2BCjEcGi5Wt5bWsP1LJ9oo6Bk+Zh+ILAeVM4SQ1NIw/XnYlU+MTvFzd6BuToeRrX/saL730Em+//fawtUnCwsIICPj4hXp8OZQA/GjDWl45dnRChxG7w8nW8lpWHShna1ntaUHk5AtZdny0F6sUQpwPk9XGlrJa1h4+cVpAyYyL5Mrpk7l6Rh4JERPvdf3UcGJx2Nly170+tyQDjNFQcrY0/O9//5u77rrrYz/f10NJi7Efg9U6IcNIRXMHb+8rY/XBimFLumfGRXKpBBEhJoyzBRSVCuZkp3Ld7AIumZKNv25iLVZosds53NbKvJRUb5fiFWMylHxWvh5KJpo+8wCrD1bw1t5jVLR0eu6PCQ3iqumTuXJGHrmJMV6sUAgxkowDNtYfrWLV/jL2VTd57g/213PZtFyum11AUWr8hBze8TUSSsSYpCgK+2uaeW3XUdYdqfQMz+g0GpYWZnLtrALmT0qTyapC+JimbgPv7C/j7X1lw04zzkmI5qa5U7hqxmRCA2S/qfFKQokYU/rMA7y9v4zXdh2lrrPXc39eUizXzS7giuJcn94ATAjh5nIp7K9p4q29x1h7+IRnoTZ/nZZLp03iprlTmJqWIN2TcUZCifC6s3VFAvQ6rpiey81ziyhImdhrqkwUiqJgtgxiNFsxmqz0m6xDt22YLDYGrIMMWO1YrXYGbPYPb1sHGXQ4cdid2B0uHE4nDocLu8OJw+nCccqExzNRq1XotBq0Wg1ajRqtVoNO677WatUE+Onw99MR4K8jwF9/ym0dgQF6QoP9CQnyJyTYn5Agv6Frf3Q6Wc13PDBYrLx7oJzXdh8dth+PdE/GHwklwmsstkHePVDOf3ccHvZCkpcUy03zpnBl8WSC/PVerFCAO2j09Q/Q0W2kq8dEb5+FHoOZXoOFnj4LvQYzPX0W+vot9JusuFxj9qXhvAX46wgPDSAiLIjI8EAiwgKH3Y4KDyImKoSYqGD0E2zC5XikKAqH61p5dfdRPjh03NM9CdDruHpGHrctmEpOgkyEH8sklIhRV9/Zy8s7D/P23jKMVvdyywF6LVcUT+bmeVMoSIn3coW+xW530tppoKXdQEt7Hx1dRjq7TbR399PZbaKz28ig/dydio/S67XujsOp3YcgfwICdO6uxVDHIuCUjoVepz2tw6HVuD/WaNTnbMM7XS4cDndHxeEc6rAMfWx3OLHaHJ4uzYDVjnWoSzNgHcQ8MIjRZMVotg1dWzFbbJzvK1xEWCCx0SHERrpDSmx0CAmxYSTGhZEYF05osL8MJYyik92TV3cdobq9x3P/rKxkbl84jaUFWTInbQySUCJGhaIo7K9uYuXmA2wtr/Xcnxodzm0LpnLtrHxpr44gl0uhvauf2sYu6pt7aG7to7G1l6bWXjq6jR/7BqxSQWRYENFRwUSFBxEeFkhkWCCRw24HEhoSQEiQP3768d01cDpdnrDSa7AMdYXMw657DRa6ekx09JgYHHR87NcMDvQjKSGc5PhwkhMiSEmIID0lirSkSAKkIzhiTr72/HfHITaWVnt2AY8LC+bzi4q5ce4UQgL8vFylOElCiRhRLpfCxtIqnt24z7PfhUoFiyZncPvCacyflIZaLUePF4qiKLR39lPT2EVtYzd1jd2eIDJgtZ/18wL8dSTGhpEQF0Z8TCixUSHERIW4j/yjQoiOCJb5FWehKAr9JisdXUY6uo0fXncbae1wd6C6ekxn/XyVCuJjwshIiSIjJZr0lCj37eQo/PxkT6YLqa3XyP92H+H13UfpMbnXOQry03Pr/CLuXDKd6BDfW6xsrJFQIkaE3elkTclx/rlxHzVDrVN/nZZrZxVw5+Ji0mIivFzh+Odwuqhv6qaytoPK2g5O1HZQWdeByWw74/N1Wg2piRGkJUcNHam7j9iT4sOJCAuUoYURZLPZaW430Nzm7lA1t/VR3+wOjX39A2f8HI1aRWpSJDkZseRkxDIpI46c9BhCQ+Tss8/KZnfw3sEKnttywDO046fVcP2cQu6+aCaJkfK+4S0SSsQFZbU7eHNPKSs3H/CsIRAS4MfnFk7jjoXFRATLC+qn4XIp1Dd3U1bZSlllG8er26hp6DrjXA+tVk1aYuTQEXc0GSlRpCdHkZQQIWPoY1CvwUJtYxd1Td3UDnW2zhVW4qJDmJQZR35OAnnZ8eRlxxMUKMMPn4aiKGwtr+WZ9Xs5Ut8KgFat5orpk7nn4plkxkV5uULfI6FEXBBm6yAv7zzMf7YcpMdkASAqJJAvLJ7OLfOLCPaXF83z0d1rHgog7kt5VRuWgcHTnhcYoCcn/eSRtPs6PTlKhlrGOUVR6O41c6K2nRO1HVQNdcJa2g2nPVelgrSkKPInJZCfk0BBTgIZqdESQM/DyXkn/9iwl10nGgD3z/WSwmzuvWS2LEkwiiSUiM/EbB3kvzsOsXLzAQwWKwCJEaHcvXQm180umHD7UowERVFoau3jcHkTR8qbOFzeTHNb32nP8/fTMjkrnvycBCZnx5ObGUdCbJjMyfEhJrONqroOKqrbKa9yB9bWjv7Tnhfgr6MwN5GpeckU5SVRkJMg81M+odKGNp7duI8NR6s8912Un8lXV8yVcDIKJJSIT+VMYSQ9JoJ7L5nFFdMno9PIkfrZuFwK1fWdlBxr5EhFM0fKm+jpswx7jkoFGSnR5OckeC7pKVFy9CtO09Nnpqyy7ZSuWitmy/CumlarZnJWPEWTk5ian8zUvGSCg6R7eS5VbV08u2Efa0qO4xp6u5NwMvIklIjzYrEN8tL208PIl5fP4fJpufKmeRZtHQb2HKpj/5F6So41njZfQK/TkJedQFFeEkV5SUzJTZI3DfGpuFwKNQ1dwzpvHz37R6NWkZsVz4wpqcyels6U3ES0WjmQOJPajh6eWb+H9w4ODydfu3QeeckTbyd2b5NQIj4Rh9PFG3uO8re1u+k2uo/qJYyc3aDdwaFjTewuqWVPSS31zT3DHg/w11GUl8S0/BSK8pKYnBU/7tf2EGOToii0dhg4XO7uypWUNtL0keHBwAA9M6akMrc4g7nTM4iLltfNjzpTOLm8OJdvXr6A5KgwL1c3cUgoER9re0Udj7+zxXPqXEpUGPdfOk/CyEf0GwfYeaCG7fur2VNSO2xdEI1aRf6kRGZPTWNGURr52fFyZCq8pq2znwNH69l/pIF9h+tO69xNyohl4exsFs3KJjs9Rk4XP0VtRw9Prd3NmpLjAOi1Gj6/qJj7ls2WCf0XgIQScVZVbV08/s5WdhyvByA80J+vrpjLLfOK0MkbKgAt7X1s31fNtr1VHClv8qwWCRAdGcy86RnMmZbBjKJUQoJkxVox9rhcCidq29lTUsfuklqOnWgZtn9RXHQIC2dls3BWNsUFyRKmh5Q3dfDEu1vZU9kIQGRwAF+/bD43zC6Ug7XPQEKJOE230cLfPtjFa7uP4lIUtBo1dyx0HwmEBcoba31TN5t2nWDTrhNU13cOeywrNdpzhJmbFSdHmGLc6TVY2HWghm37qth7qA7bKUvoBwf6sWBWFkvn5TJ7WprPb0J4cp2Tx9/ZSl1nLwDZ8VE8eM0S5uemebm68UlCifAYdDh4YWsJ/9iwF5PVPXt/2ZRsvnPVIlKiw71bnJd5gsjO41Q3dHnu16hVFOUls2h2NgtmZpEUH+69IoW4wGw2O/uONLB9XxU79lfTa/jwLLGgQD0LZ2VLQMG9gvX/dh7hqbW7PScALJyczoPXLJYF2M6ThBIBwNayGn779hYauvoAyE+O5cFrljAzK9m7hXlRU2sv67dXnB5ENGpmFaWxdP4kFs3KlmW/hU9wOl2Unmhh084TbN59YtgZPUGBehbOzObiBbnMmZbus0M8BouVv6/bw3+3H8LhcqFVq7l94TTuXzFXNv37hCSU+LiGrj5++9Zmz869MaFBfOuKBVw9I98nF+XqNVjYuKOCD7aWU1bZ6rlfgogQH3K5lKGAcpxNu4YHlLCQAC5ZkMuKxfkUTErwySHM+s5eHl+1lc3HagD36tYPXLGQa2b65uvq+ZBQ4qNsdgf/2LCXf23cj93pRKtRc+fi6Xxl2RyCfGwbdYfDya6Dtby74Si7D9Z4Jquq1SpmFqVxyYJcCSJCnMXJgLJxx3E27qwYthBgUnw4Vywt5IqlBcREhXixSu/YXlHHb9/a7JlvUpSWwC9uXsakhGgvVzZ2SSjxQQdqmnjof+s9fygLJqfzg2uXkBEb6eXKRldrh4G31x5mzaZjdPeZPfdPzopjxeJ8LlkwmagI2cpciE/K4XRx8GgDH2wtY+ueSs9p8Wq1irnFGVyzfCrzpmeg8aGzU+wOJy9uK+Gpdbux2Oxo1WruvngmX1k2Bz8fnodzNhJKfIjJauP3727j1V1HAYgOCeRH1y9leVGOz7RYXS6FvYfreGNNCbsO1nDytzgiLJDLluRz5SVTSE+WiWlCfFYD1kE2767k3fVHOVze5Lk/ITaUa1dM5cqLpxARFujFCkdXu8HEb97YyMbSasC9+OTDtyxnemaSlysbWySU+IhdJ+r5xf/W0dprBODGuYV8+8pFPnOKb79xgNWbSnnrg8PDNrubNTWN61ZMZcHMLJ+dnCfESGto7uGd9UdYvbEUo8l9dopep2Hp/FxuuKyY/Jx4nzkwWn+kkkfe2EiX0YJKBXcsKuably8gQC8bJoKEkgnPZLXxxKptvLbb3R1Jigzll7euYHZ2ipcrGx2VtR28+t5B1m+vYHBovYXgQD8uX1rA9ZdOIzXJt4ashPAmm83O+h0VvPH+IY5Xt3vuz82K44bLprFsYZ5PbLfQP2Dlsbe38ta+YwCkRYfzy1tXSNcECSUT2ke7I7cvmMYDVy4g0G9iT2R1uRR2HazhlVX7OVja6Lk/Oz2GGy4rZvmiyQT42GReIcYSRVEor2rjjfdL2LjjOIN2J+AeRr3hsmlcd+k0nxja2VZey0OvrqfDYJKuyRAJJRPQmbojv7p1BbMmeHfEarOzZtMx/rf6AI0t7km8GrWKi+blctMVxRTmJvpMi1iI8aKv38K7G47yxppDdHS7D6D0Og2XLsnnlqtmkJEysc9U6R+w8vg7W3lzr3RNQELJhDPocHD9Y897FkHzhe5Id6+Z1947yNtrD9M/NF4dHOjHNcuLuPGKYtnxVIhxwOFwsnl3JS+/s4+KU4Z25hSnc9vVM5lZlDahDyo+2jX53eev4LJpud4ua9RJKJmA/vbBLt7ZXzbhuyO9BjMvvLmXNz847JkvkhgXxi1XzeCKpYUEBkzcICbERKUoCkcqmvnfqgNs3VvpOUMuPyeB+25fyMyi1AkbTk52TXadaOCN793pk6vASiiZgOwOJ3anc8J2R/qNA/z3nf289t5BzzoIhbmJ3H7tLBbOzPKpNRCEmMia2/p4dfVBVq0/4tkYcFpBMvfdtpCp+RN3CwyDxeozZ0Z+lIQSMW6YLTb+9+4BXl61H7PFvWHg5Kw47rt9IbOnpU/YoychfF13r5kX3tzDWx8cxu5wT4qdPS2d+25fQF52gperExeShBIx5g1YB3l9TQkvvbXPM2ckKy2G+25fwIKZWRJGhPAR7V39/Of1Pby74ShOpwuAhbOyuOe2BeSkx3q5OnEhSCgRY5bD6WL1hqP865WdnmXgUxMjuee2+SydlysbWwnho5rb+lj56i4+2FqGa2ivqksX53Pf7QuIjw3zcnXis5BQIsYcRVHYsb+ap57fSn1zD+BemvpLty5g+aI8tDJnRAgB1Dd1889XdrJx53EAdFoNN15RzBdumCMbaI5TEkrEmHLsRCt/+88Wz14ZocH+3HXzPK67dCp62bzK5yiKgtPhwm53nPN5arUanV6DWi2B1RdVVLXxt+e3eBZLDA7y4ws3zuXGy4t9YoXYiURCiRgT2jr7+etzm9m06wQAer2WW66czh3XzyYkyDdnoU8EVssgPV1Gujv66e0xYzRYMPUPYOq3YuofwNg/gKl/ALPRinXAjn3QweCgg0Gbw33b5uB8Xmp0Og06Py06nRa9n/ui02sJCvYnOMSf4NAAgkMDCAkLGLrtT1h4EFGxIURGhxAaESjBZpxSFIXdJbU89fxWahq6AIiLDuFrX1jCxfNzZe7ZOCGhRHiVw+ni1dUH+OfLO7DaHKhUcPnSQu69bQGxUSHeLk+cg8PupKOtj7amXlqbemhr6qWro5+ejn56ukx0d/ZjMdm8XeZ50WjVREQFExUT6gkqcYkRxCdHEJ8cSUJyBMGhMiwwljmdLj7YUsY//rudzh4TADOL0njwK8tJig/3bnHiY0koEV5TUd3G755ay4naDgCK8pL49r2XyCz6MURRFDrbDDRUd1Bf3UFTXZcngHS0GXANnQFxLv4BeqJiQ4iICiYkLJDg0FM6FkPdiqCQAAIC9ej17s7GyQ6H3k+LXq9Fq9Oc80jX6XR5uisnOyzujoudQZsDs9GKyWgd6tJ82KEx9Q9g6LXQ02mkr8f8iboywaEBJKS4A0piShSpWTGkZsaSkhGDn7/v7lky1thsdl56ex/Pv7GHQbsTP72WL906n1uvmiE7go9hEkrEqLMMDPLPV3bw6uqDuFwKIcH+fP0LS7jy4kJpsXqRoddMVXkLdZXt1Nd00FDVQUNNJxbz2bsdej8t8UnuLkJ8UgSxCeFExrg7DZExIUTGhBAY5Dcu/l8ddie93SZ6Oo2eIaeujn7am3tpbeqlramHvh7zWT9frVYRnxxJWlYsaVmxpGbFkJmbQEpGjCzo50WNLb08/sw6DhxtANwbc/7g/hWyvskYJaFEjKpdB2t44pn1tHX2A7Bs4WS+efdSIsODvFyZbzH0mqksa6HyWDOV5S1UlTXT0Wo443M1WjVJadGkZsaQmhlDYkoU8ckRJCRHEhEd7FNzMAYsNtqaemlrdg9ZNdV1ebpIRsPAGT/Hz19HVl4COXlJ5OQnkp2fKEFllCmKwvubj/HnlZvpN1lRqeCmK6Zz3+0LZTuKMUZCiRgVPX1m/vivTWzYUQFAfEwo3/3yMuZNz/RyZROf0+Gk5kQ7x0rqOVZSz/GjjWcNIElp0WTmxpOaGUNadhxpWbEkpkaikzOfzklRFHq7TZ6A0lDdSV1VOzXHWxkYWn34VH7+OrLzEikoTiV/Whr501IJDQ/0QuW+pddg4S8rN/PB1jIAYqND+O59y1gwM8vLlYmTJJSIEaUoCuu3V/CHZzfQb7KiVqu4+crp3HPrAjlCGSEDFhsVR5o8IaTiSOMZ3xiT0qLJyU8kp8B9BJ81OYGgYDnT6UJyOl0013dRWdZCVVkLlWXNVFecOaikZsVSMC2VguI0CqanEZ8UMS6GvcajvYfqeOzv62jtcIfz5YvyeOCeiwmTtU28TkKJGDE9fWYe+/s6tu2tAiAnI5Yf3L+CyVnxXq5sYnE6nJQfaaRkdzUle6qpONJ02gTUoBB/8qemUlCcSt60VLLzEiWAeMnJoFJxtImyknqOlTTQWNt52vNi4sMonptF8ZwsiudmER4V7IVqJy6rzc6/XtnJy6v243IpRIYH8uBXVrBodra3S/NpEkrEiNhTUsuv/vQeff0DaDRq7rppLnfeMEdmvV8gRoOF/dsr2bP1OPt3VGLqHz6fITYhzH3EPXRJy471qbkf401fj5nyww2UHqyn7FA9lcdacAxtPAegUqnInZLM7MWTmLN4Mpm58dJFuUCOnWjl0b+uoa7JvXr0NcuL+NbdS/HzkzOpvEFCibigHA4n//jvDl58ay/g3jjvp9+8XE7zvQB6uozsWF/GtnWllB6o8+z5ARASFuA+qp6bTfGcTOKTI71YqfisrAODHCupp2R3NQd3VVFzvG3Y49FxoSxcVsCiFYXkTU2RwPkZ2QYd/POVHfz37X0oCmSmRvPL715NenKUt0vzORJKxAXT1mHgoSdXU3q8BYDrL5vG//viRbLM82dwahA5ur9u2Doa6dlxzF6Sy5zFuUwuSpGzOSawrvZ+9m47zt6txynZXY3Navc8Fh0bysLlBSy+dAqTi5IloHwG+w7X86s/raanz4K/n5bv3LuMy5cWSFdqFEkoERfEjv3V/PrPazCarAQH+vHDr13KRfMmebusccnQa2bb2lK2rj09iOQWJrNoRSELl+VLN8RH2ax2Du6qYtu6UnZvrhi2au7JgLLksiImFyXLm+mn0N1r5ld/eo/9R+oBuHRJPg9+ZTn+MpwzKiSUiM/E6XTxz1d28p/XdwOQlxPPw9++isS4cO8WNs7Y7Q72bTvB+ndK2Lv1xLD5BJ4gsryA+KQIL1YpxppBm50DO88cUJLTo1l29TQuuXoaMbK8+nlxuRReeHMPz768A5dLISs1mke+fy3JCfL3N9IklIhPra/fwsNPrmbfYfcRxU1XFPP1L1yETieTWT8JRVGoLGth/TslbF5zhP4+i+ex7LxELrq8SIKI+MROBpSta0vZuaHMM8SjUqmYOiuDZdcUs2BZPgGBfl6udPwoOdbIL36/ip4+C8GBfvz0m5ezcJacnTOSJJSIT6WsspWfPv4OHV1G/P20fP/+S1mxKM/bZY0Lhl4z694uYe3bB2mo7vDcHxkTwsVXTmXZ1cWk58R5sUIx3lnMNravP8b6d0o4sq/Wc79/gJ6Fywu4/MaZ5E9LleGdT6Crx8TPnljF0YpmAO68YQ733LYArczhGhFjMpRs3bqVxx57jAMHDtDa2sqbb77Jdddd94k/X0LJyFq1/gi//8cG7A4nyQkR/Ob715CZGuPtssa8qvIW3nh+B9s+KMVudw/P6P20zFuax/Jriimem4VGTpkWF1hbcy8b3j3EhlWHaGno9tyfnhPHtZ+bxyVXTUUv8yXOyeFw8tf/bOHV1QcBmDEllV9992pCZbG1C25MhpI1a9awY8cOpk+fzo033iihZIxwuRSeeWkbL7zpPt138Zwcfvz1ywgOknbw2SiKwsFdVby2cjslu6s99+fkJ3LFTbNYfOkUgkJkETMx8hRFofxwI++/sZ8t7x/1DO9ERAVz7R3zuPKW2YSEypvsuazfXsFvn/qAAaud1MRIHv/pDTJ/7gIbk6Fk2DdSqSSUjAF2u5Pf/PV91m0rB+DuW+bxpVvmS/v3LJwOJ1s+OMprK7d71phQa9QsXlHI9XfOJ7cw2csVCl9m7B9g7ZsHePOFnXS1uzfH9A/Qc/mNM7n+zvnEJoR7t8AxrLq+kwcfeYOObiMRYYE89pMbZJXqC2hChBKbzYbN9uGs8/7+flJSUiSUXCAD1kF+8tg77D1Uh0aj5gdfXcEVFxd6u6wxyelwsnH1YV56ZjOtje4VIv0D9Fx2wwyu+/x8mbQqxhSH3cnm94/w2srt1FW2A6DValhx/XRuvWcxcYny+3omnd1GHvzNG1TVdRLgr+P/fng9M6akerusCWFChJKHHnqIhx9++LT7JZR8dgbjAA8+8gZlla34+2n59YPXMrc4w9tljTlnCiNhEYFcd8d8rrp1NiFhsgOsGLsUReHAzipe/ddWDg9NjJVwcm5mi40f/fYtDpY2otNq+MUDV8raTBfAhAgl0ikZGR3dRr7zy1epa+ohJNifx358A4W5id4ua0w5Wxi56a5FXH3rHPwDZSdkMb6UHqjjhac3cmhPDSDh5Fxsgw5++eRqtuypRK1W8b0vL+ea5UXeLmtcmxCh5KNkTslnV9/Uzbd/9RodXUZiIoN54mc3kZka7e2yxgyn08Wm1Yd58e+bJIyICels4eT2+y4iJj7My9WNHU6ni8efWceq9UcB+PLnFnLnDXNkvt2nJKFEnKa8qpXv/foNDMYBUhIj+MPPbiI+Vl6EwN3m3rvtBP9+ci11Ve4xeAkjYiL7aDjR+2m57o553PylxXK2zhBFUXjmpe08/8YeAG6+cjrfuGsparUEk/M1JkOJyWSiqqoKgOLiYn7/+9+zdOlSIiMjSU39+MlEEko+vdITLXz74VcZsNqZnBXHYz+5kQiZDwFAa1MPf31kFft3VAIQHBrALV9axDW3zZUwIia80gN1rPzzOkoPuldwDosI5N7vXMaya4qlKzDklVX7+fPKzQBcvWwKD35lhQST8zQmQ8nmzZtZunTpafd/8YtfZOXKlR/7+RJKPp3K2g6+8fNXMFlsTC9M4f9+eD2BAfJma7c7eH3ldl56ZjODNgc6nYZr75jHrfcukSNF4VMURWHv1uP88w8f0FDTCcCUmel882fXkpIhCygCrNl8jEf/+j4ul8LNV07nm3cvldB2HsZkKPmsJJScv+a2Pu7/yUv09FmYMjmJ3//sRgL8JZAc3V/Ln3/9jucFeNqcTP7fT64hOV3m1wjf5bA7efP5nbzw9EZsVjtarYabv7SI2+5dgp+/rA67ZlMpj/zlfQDuu30hX7xprpcrGj8klAi6e83c/5OXaGk3kJ0ew19+eZvPr9JqNll59on3WfP6fgDCI4P48oOXs/SKqXLUI8SQtuZe/vbou+zdehyAxNQovvPw9RTOSPduYWPAa+8d5Ml/bgTgwa8s59oVU71c0fggocTHmcw2/t/PX6aqrpPEuDCeeuRzREUEebssrzqws5InH3qLzjYDAFfcPIu7v7VChmqEOANFUdi5sZynHn2Xro5+VCoV19w+l7u/udzn51o989J2/vP6btRqFb/67tUsmSvrmHwcCSU+zDbo4Lu/fo1Dx5qIDA/kqUc+R1J8uLfL8hqzyco/Hl/D+28cACAhJZLvPHw9U2bKYnFCfByz0co/nhj+9/PdX97g010TRVH43dPrWLX+CDqthid+diPTC2Xl13ORUOKjHE4XP3v8HbbtrSIoUM+fH76VSZlx3i7Laz7aHbn2c/PkSE+IT+HUvyXpmrjXMfn5E6vYsqeSwAA9f/mlb7/WfhwJJT7o1PSu12l4/Ke+m96tlkH+/th7nrkj0h0R4rM7U9fkwd/cRP5U33ydsQ06+N6vX6fkWCMRYYE8/Rvf7kqfy6d9/1aPYE1ihL2+poRV64+gVqv4xQNX+mwgaWvq4YE7/+4JJNd+bh5Pvfr/JJAI8RkFhfjzwEPX88jTXyQmPozWxh4evPtZVr28x9uleYWfXsujP7iOnIxYeg0WfvTbtxiwDnq7rAlFQsk4daSi2bO4z9fuXOKzE69KD9TxrTuepq6ynYioYH77zy9x/w+v9NkWsxAjYcb8HJ5+/RssuWwKToeLv/5mFX95ZBUOu9PbpY264CA/HvvJDUSFB1HT0MXvnl7HGB5wGHcklIxDPX1mfvb4OzidLi5ZkMutV8/wdkle8cGbB/jhff/G0GshJz+RP7/8NabOyvR2WUJMSEEh/vzwt7fwpQdWoFKpePeVPfz0a89h7B/wdmmjLjoimF9+92o0GjXrtpXzxpoSb5c0YUgoGWecThe//ON7dPeaSU+O5Af3X+pz6204nS7+8fga/vCLN3E4nCxaUchj/76X6DiZdyTESFKpVNzypcX8/MnP4R+g59CeGh644+801XV5u7RRNzU/ma9/YQkAf3luCxVVbV6uaGKQUDLOPP/mHvYfqcffT8uvvneNzy0fbzZZefhbL/L6f3YAcMdXl/Kj392Cv4/9HITwpnlL8/j9f+4jNiGM5vouHrjjaQ7urvJ2WaPu5iuns3hODnaHk589sQqj2ertksY9CSXjyMHSBv71yk4AvnvfMjJSfGuJ9LamHr5z5zPs3XocvZ+WH/3uVu782iWo1fJrLMRoy8xN4I8v3U/e1BRMRis/vf8/PjcBVqVS8aOvX0pCbCitHQZ++7cPZH7JZySv5uNEr8HMw0+uxuVSuGJpAZcvLfR2SaOq9KB7Qmt9dQeRMSE89u97WXLZFG+XJYRPi4gK5rfPfolLrpqGy/nhBFinw3cmwIYE+fPL716NVqtm8+5KmV/yGUkoGQcUReGRP78/NI8kim/fe4m3SxpVB3dV8aMvr/RMaP3TS/eTW5js7bKEEIDeT8f3Hrlx2ATYR3/wP58KJnnZCXz9CxcB8OfnNlNV1+ndgsYxCSXjwIYdx9ldUotep+GX373ap3b9LTvUwMPfehH7oIM5SybLhFYhxqCTE2B/+vvb0ek0bF93jCcffguXy+Xt0kbNTVcUs3BWFg6Hi989vRaXS4ZxPg0JJWNcv8nKn/7t3qHyCzfOJTPVd+aR1Bxv5Wdf/w82q52ZC3L46e9vkwmtQoxhCy7J54e/uxW1Rs26t0t45rE1PjPHQqVS8d37lhEYoKesspW31x72dknjkoSSMe7vL26jp89CWlIkn7tulrfLGTVNdV38+CsrMRutFBSnDR2Bab1dlhDiYyy4JJ/vPHw9AG+9uIsXn97k5YpGT0xUCF/53EIAnn5xK129Ji9XNP5IKBnDjlY0e9L2g19Zjt5H3pQ7Wvv40Zf/TV+PmazJCfzyL3dKh0SIcWTZNcXc/8MrAXjhqY28+fxOL1c0eq67dBp52fGYLYP86V++E8guFAklY5TD4eSxv68D4MqLC5lWkOLlikZHX7eJH315JZ1tBpLTo3nkqS8SFOLv7bKEEOfp2s/N4wv/zz0p/++Pvcfatw54uaLRodGo+f5XV6BRq9i48zi7DtR4u6RxRULJGFVR005zWx/hoQF8bWjVwInO1D/AT+5/jub6LmITwnj0mbsIjwr2dllCiE/p9vsu4sYvLADgyYfeYvu6Y16uaHTkZMRy81Xu7T827Tru5WrGF5UyhmchfdqtjyeK5rY+WtoNzJqa5u1SRpx1YJAff3UlZSUNREQF8/jKe0lK851JvUJMVIqi8ORDb/HBmwfQajU8/JfPM2N+jrfLGnGWgUF27K9m2cLJPrcVCHz692/plIxhSfHhPhFIAJ55fA1lJQ0Eh/jzyN/vkkAixAShUqn45s+vZdGKQhwOJ49+/390thm8XdaICwzQs3xRnk8Gks9CQonwul2bynnv1X0A/PiJ28icFO/lioQQF5JGo+b7j95ETkESpv4BnvjZ6z61hon45CSUCK/q6TLy5ENvAnDDFxYwfW62lysSQowEnU7L939zE37+Og7tqfGpM3LEJyehRHiNoij84edvYui1kDEpnru+udzbJQkhRlBKRgxffvByAFb+aR01x1u9XJEYaySUCK9Z9coe9m0/gU6v5QeP3oxe7xvrsAjhy664aRZzlkzGbnfy2x++is1q93ZJYgyRUCK8or66g2efeB+Aex5YQXpOnJcrEkKMBpVKxbcfuo7wyCDqqzv415NrvV2SGEMklIhRZ7c7+N2PXmXQ5mD6/Gyu+dxcb5ckhBhF4VHBfOdXNwDw9ku72L+j0ssVibFCQokYdS8+vYnqilZCwwP57q9uRK2WX0MhfM3sRblcfdscAJ742euYjVYvVyTGAnk3EKOqq72fN/6zA4Bv/PQaomJCvFyREMJb7v3OZSSlRdPbZeL1/2z3djliDJBQIkbVi3/fyKDNQUFxGguXF3i7HCGEF/n567j7W+6z7t74z056u2VXXV8noUSMmqa6Lj548yAAd39ruax0KIRgwSX5TCpMwjowyMv/2OLtcoSXSSgRo+b5v23A5XQxe3EuhdPTvV2OEGIMUKlU3P3NFQCs/t9e2pp7vVyR8CYJJWJU1FW1s/WDUgDu+sYyL1cjhBhLiudmMW1OJg6Hk1eelW6JL5NQIkbFf5/ZjKIoLFxeQGZugrfLEUKMMZ+//2IA1r59ULolPkxCiRhxp3ZJ7vjKUi9XI4QYiwqnp1M8NwunwyXdEh8moUSMuDef3+npkmTIDsBCiLO446vug5a1bx+kv8/i5WqEN0goESPKYXeyY0MZgGehJCGEOJPC6elk5sbjdLjYubHM2+UIL5BQIkbUoT3VmPoHiIgKljNuhBAfa/GKQgC2rT3m5UqEN0goESNq6zr3XJIFywrQaOTXTQhxbouGQknJnmoZwvFB8i4hRozD7mTnhnIAFq2Q1VuFEB8vKS2azNx4XE4ZwvFFEkrEiJGhGyHEpyFDOL5LQokYMTJ0I4T4NGQIx3fJO4UYEQ67k10bZehGCHH+ZAjHd0koESOioaYDo2GAoBB/GboRQpy3uRdNBqD0YL2XKxGjSUKJGBH11R0ApGXHytCNEOK8ZU5yb0fRUNPh5UrEaJJ3CzEiPKEkK9bLlQghxqPUrBgAGqo7cblcXq5GjBYJJWJENHhCSZyXKxFCjEeJKVFotRqsA4N0tBq8XY4YJRJKxIior+4EPjzaEUKI86HVaUhOjwZkCMeXSCgRF9ygzU5rYzcgnRIhxKd38qCmvkpCia+QUCIuuKa6LlwuheAQfyKjg71djhBinDo5J+3kHDUx8UkoERdcU10XACmZMahUKi9XI4QYr1Iz3aHk5GuKmPhGJZT87W9/IyMjA39/f2bMmMG2bdtG49sKLxm0OQAIDPL3ciVCiPEsMNgPAPugw8uViNEy4qHklVde4YEHHuAnP/kJJSUlLFq0iMsvv5yGhoaR/tZCCCGEGEdGPJT8/ve/55577uHee+8lLy+PJ598kpSUFJ566qnTnmuz2ejv7x92EUIIIYRvGNFQMjg4yIEDB1ixYsWw+1esWMHOnTtPe/6jjz5KWFiY55KSkjKS5QkhhBBiDBnRUNLV1YXT6SQubvhpoXFxcbS1tZ32/B/96EcYDAbPpbGxcSTLE0IIIcQYoh2Nb/LRMzAURTnjWRl+fn74+fmNRklCCCGEGGNGtFMSHR2NRqM5rSvS0dFxWvdECCGEEL5tREOJXq9nxowZrFu3btj969atY/78+SP5rYUX6f11AJhNVi9XIoQYz8xG92uI3m9UmvpiDBjx/+nvfOc73HnnncycOZN58+bxzDPP0NDQwFe/+tWR/tbCS1JO2a/ibEN1QgjxcU6u5JqSIXto+YoRDyW33nor3d3d/PKXv6S1tZXCwkLee+890tLSRvpbCy9JSo9GrVFjMdno7jASHRfq7ZKEEONQvWe38VgvVyJGy6is6Pq1r32Nuro6bDYbBw4cYPHixaPxbYWX6PVaklKjAKivbvdyNUKI8aqhxr3buIQS3yF734gRkZrpbrc2VHd6uRIhxHhktztornfveZMqocRnSCgRIyIt++TuntIpEUKcv+b6bpwOF4FBfsTEh3m7HDFKJJSIEZGW5T7lW7YcF0J8GieHblJlt3GfIqFEjIiTwzf1VR04HU4vVyOEGG9qKloBGbrxNRJKxIhIzYwhLCIQi9nG4f213i5HCDHO7NpUDkDhjHTvFiJGlYQSMSI0Wg3zL8kHYNvaUi9XI4QYTxpqOqiv7kCr1TB/aZ63yxGjSEKJGDGLVhQCsHNDmQzhCCE+sZMHMsXzsggODfByNWI0SSgRI2bqzAzCIgIx9FpkCEcI8Ylt/cAdShYPHdgI3yGhRIwYjVbD/ItlCEcI8cmdOnQzT4ZufI6EEjGiFl0qQzhCiE9Ohm58m4QSMaJkCEcI8UkpiiJDNz5OQokYURqthgXLCgB456XdXq5GCDGWHdlXS311BzqdDN34KgklYsRd//n5qNUqdm+uoLKsxdvlCCHGqBee2gjAZTfOlKEbHyWhRIy4lIwYLrqiCIAXn97o5WqEEGPR4X01HD1Qh06n4ZYvyU7yvkpCiRgVt993kadbcuJYs7fLEUKMIYqi8PxfNwDuLolswOe7JJSIUZGSEcPSK6YCsPJPa71cjRBiLNm/vZLSg/Xo9Frpkvg4CSVi1Nz5tYvRajUc3FXNoT3V3i5HCDEGuFwuVv55HQDX3D5XuiQ+TkKJGDXxyZFccfMsAP79x3UoiuLlioQQ3rb1g1KqK1oJDPbj1nukS+LrJJSIUXX7ly/Cz1/H8dImNr132NvlCCG8aMBiY+Wf3F2Sm+5aSGh4oJcrEt4moUSMqoioYG4ZOhr662/epaO1z7sFCSG85unfvkdbcy8x8WFc//n53i5HjAESSsSou+2exUyekozZaOWxn7yG0+nydklCiFG2Y0MZH7x5AJVKxYO/uYmAQD9vlyTGAAklYtRptBq+/+jN+AfoObq/jjee2+HtkoQQo6i7o58nH3oTgJvvXkjRzAwvVyTGCgklwisSU6P46g+uAOC5v6yXlV6F8BEul4snfv4GRsMAWZMTuPPrl3i7JDGGSCgRXnPp9TOYf0k+DoeT3/3oVawDg94uSQgxwt55aTcHd1ah99Pyg/+7GZ1O6+2SxBgioUR4jUql4oFfXEdkTAiNtZ08+/sPvF2SEGIE1Z5o459PuhdPvO+7l5OaGevlisRYI6FEeFVoeCDf/dUNALz7yh72bKnwckVCiJFgs9r57Y9exT7oYNaiSVx162xvlyTGIAklwutmzM/hujvmAfB/P/gfx0ubvFyREOJCctid/ObBV6irbCcsIojv/PIGVCqVt8sSY5CEkjGstrGLnQd8Yzn2L337UqbNzmTAMshP73+Ouqp2b5ckhLgAXC4XT/zsdfZsqUDvp+WnT9xGRFSwt8sacWaLjXfWHZElD86ThJIx6mhFM3d/7z/86k9r6DWYvV3OiNPrtfz8j3cweUoyRsMAP/7KSlqberxdlhDiM1AUhb/95l02vXcEjVbNT564nSk+cvrvP/67nd89vZZf/3mNt0sZVySUjFF5OQlkpkRjNFn5y8ot3i5nVAQG+fGrv32B9Ow4ejqN/Oi+f9PV3u/tsoQQn9K//7SOd/+3171A2iM3MWdxrrdLGhXlVa28vqYEgCsvLvRyNeOLhJIxSqtR8/2vrkCtVvHB1jL2Ha73dkmjIiQskEf+fhcJKZG0Nffy46+uxNA78TtFQkw0r/xzC//751YAvvGza7jo8iIvVzQ6HE4Xv3t6HYoCly7JZ2ZRmrdLGlcklIxhk7PjueGyYgCeeGYdNpvdyxWNjqiYEB595m6iY0NpqO7gp1/7D2aT1dtlCSE+odX/28u//+jeaO+eb1/KFTfN8nJFo+e11QeprO0gNNif//fFi7xdzrgjoWSMu+/2BcREBtPU1sd/3tjj7XJGTXxSBL955i5CwwOpPNbMQ998AZvVN0KZEOPZptWH+csjqwC47d4l3Hz3Ii9XNHraOgw8+/J2AL72hSVEhMmux+dLQskYFxToxwP3updhfvGtvZyo8Z2zUlIzY3nk6S8SGOTH0f11PPTNF6RjIsQYtuHdQzz209dRFIWrbp3DF7+xzNsljRqXS+F3f1+H1eZgWn6yzCX5lCSUjAOLZ2ezeE4ODoeLnz+xCrPF5u2SRk1OfhIP//nz+PnrKNldzXfufEbOyhFijHG5XKz88zoe+/FruJwull09ja/96EqfWovkpbf3svdQHXq9lu99ZblP/dsvJAkl44BKpeKH968gLjqEprY+fvf0WhRF8XZZo2bKzAweX3kvUbEh1Fd38MAdT1N6oM7bZQkhAKtlkEe++zIv/8N9luAtX1rEd351A2q177y9HC5v4h8vuYdtvn3PxaQnR3m5ovHLd35rxrnQkAAe/s7VaDRqNuw4zttrD3u7pFGVk5/EH1+8n5yCJAy9Fn5437/54M0D3i5LCJ/W2dbHd+/6Bzs2lKHTafjer2/kSw9c6lOBpK/fwkO/fxenS2HF4jyuumSKt0sa13znN2cCKMxN5Kufd08a+9O/N/nU/BKA6LhQHvvXPSy+tBCHw8kffvEmzzy+RlZMFMILKo408s3PPU11RSthEUH89p/3sOyaYm+XNapcLoVf/2kNnT0mUhMj+d6XZdjms5JQMs7cdvVMFszMYtDu5OdPrMJk9p35JQD+AXp+9Ltb+fz9FwPwxn92yARYIUbZptWHefBL/6S3y0R6Thx/+u9XyZ+W6u2yRt2Lb+1ld0kter2WX33vagID9N4uadyTUDLOqFQqfvL/LvPML/n1n9/D5fKd+SXg/hl8/v6L+fHjt+Hnr2PfthMyAVaIUeByuXjuL+s9u/3OvWgyv//Pl4lLjPB2aaNu3+F6/vFf9zyS79xzCVlpMV6uaGKQUDIOhYYE8MiD16LTati+r5rnfWj9klMtXlHIY//+cALsN29/ij1bj3u7LCEmJEOvmYe/+SL/fWYz4J7Q+vMnP0dgkJ93C/OCtg4DD/3hXVwuhasumcJVy2QeyYUioWScmpwdz3fuc69f8o//bmft1jIvV+QdkwrcE2AnFSZhNAzwi//3PL//xRuY+ge8XZoQE8b29cf4yvV/Ys/W4+j0Wp+c0HqSwTjA9x55HYNxgNysOL49tI6UuDB87zdqArl6WRE3XzkdgEf+8j67S2q9XJF3RMeF8vjK+7j+8/NRqVSsffMgX73hz+zbdsLbpQkxrhl6zTz6/Vf49Xf+S1+PmbSsWP7w/Jd9bkLrSQPWQb7/mzeoa+ohJjKYRx68Fj+91ttlTSgqZQwveNHf309YWBgGg4HQ0FBvlzMmuVwKv/zjatZvr8DfT8uTD91C4aREb5flNaUH6/j9z9+kpaEbgBXXT+fL372c4NAAL1cmxPiyff0x/vLrd+jrMaPWqLnl7kV87qtL0fvom7DD4eQH//cme0rqCAn252+/vo2MlGhvlzVmfdr3bwklE4Dd7v5j2XuojtBgf/7q438s1oFBnvvzet56cReKohAdG8q3fnEdsxZN8nZpQox5hl4zf3v0Xba8fxSAtKxYvvvrG5lUkOTlyrzH5VL49Z/fY+3Wcvz0Wv740C0U5vruwd8nIaHExw1YB/nWQ69SVtlKbFQIT/3mduKifftn9tGuydIrivjyg1cQERXs5cqEGHsURWHDqkP844k1GHot0h0ZoigKf165mf+9ewCNRs3//fA65k3P9HZZY56EEoHBOMDXf/pf6pp6SEuK5K+/vo3wUN/epfKjXZPgEH/ufmAFl9840ycn6QlxJo21nfz51+9wZJ97Xlp6dhzf+dUNPt0dOen5N/bw9xe3AfCzb17BpUvyvVzR+CChRADQ3tXP/T/+Lx3dRnKz4vjjL24h2AdP2fuoE8ea+dMv36aqvAWAyUUpfPPn15I5Kd7LlQnhPTarnZef3cKr/9qGw+HEz1/HHV9dyg13LkCr03i7PK974/0Sfv+PDQB8466LuPXqmV6uaPyQUCI86pq6+X8/e5m+/gEKcxP53Y9vIDTY39tleZ3T6WLVy3v4z1/WYzHbUGvUXHHTLO746lIZ0hE+xeVysfWDUlb+aR1tzb0AzF6cy9d+dBXxSb63ENqZvPXBIR5/Zj0Ad94wh6/cscjLFY0vEkrEMJW1HXzjF69gMtvITI3m9z+7iehIeeMF6Grv5+nfrWb7umOAe+n6G74wn+vvXECInKUjJjBFUTiwo5Ln/rKeyjJ31zA6NpSv/vBKFlySL/u24P4ZPffabp59eQcAN185nW/evVR+NudpTIaSRx55hNWrV3Po0CH0ej19fX3n9fkSSj6b6vpOvvOr1+juNZMQG8rvf3YzKT64HPTZHNlfyz9//wHHS5sACAz24/o75nPdnfMlnIgJ5WQYeeGpjVQcHfp9D/LjprsXcsPnF+AfKHu2gPssmz/9eyOvvVcCwF03zeWe2xZIIPkUxmQo+cUvfkF4eDhNTU3885//lFDiBa0dBr798Ks0tfURERbI4z+9kdzMOG+XNWYoisKO9WW88PRG6irduy5LOBETxZnCiJ+/jitvmc0tX1pMeGSQlyscO+x2J7/56/us21YOwLe+dLFncUpx/sZkKDlp5cqVPPDAAxJKvKTXYOa7v3qdE7UdBAbo+b8fXMf0Kb63o+e5uFwudm4ol3AiJoSzhZGrbpnNTXcvkjlUHzFgHeSnj7/DnpI6NBo1P/nG5axYlOftssa1CRFKbDYbNpvN83F/fz8pKSkSSi4As8XGD//vLUqONaLTanjo21eyZK4sJvZRZwsnV90ym2vvmE9UTIiXKxTi7JxOFzs3lPHqym2cKG0GJIx8nH7jAN9/9E1Kj7fgp9fy6wevkXVILoAJEUoeeughHn744dPul1ByYdgGHTz85Gq27qlErVbxrS9dzI2X++YeFh/nTOFEp9Ow9Kqp3PTFhaRmxnq5QiE+ZLPaWff2QV7/zw5aG3sACSOfREt7Hw8+8gb1zT2EBPvz2I9vkJVaL5BRCyVnCw6n2rdvHzNnfng+t3RKxg6n08UT/1jPO+uOAHDbNTO5//OL0WhkIbEzcblc7NlynNdWbudYSb3n/jlLJnPDnfMpmpUhk+CE1/R0GVnz2j7e+e8eDL1mAELCArj6tjlcc9tcwiWMnFV5VSs/ePRNevosxEaF8PhPbyQz1Xe357jQRi2UdHV10dXVdc7npKen4+//4boYMqdkbFEUheff2MMzL20HYPbUdH7x7SsJC5F5E+dSdriB11ZuZ9fGck7+2SSnR3P5TbO4+MqpcjQqRoXT6aJkdzUfvHmAnRvLcDpcAMQlhnPDFxZw6XUz5Gyaj/Hu+qP8/tn1DNqdZKfH8NiPbyAmSoZmL6QJMXzzURJKRta6beX8398+wDboIC46hEcevJbJ2bLC6cdpquvized3snH1IQYsgwCoNWpmLchh2TXFzLlosk/vFSJGRl1VO+vfKWHj6sP0dBo99+dNTeHaz81j0fICNFpZhfVcbIMO/vDsBt7d4N5scMHMLH7xwJUEBkiIu9DGZChpaGigp6eHd955h8cee4xt29z7B2RnZxMc/PFHlRJKRl51fSc/+d3bNLX1odNq+Pa9l3D1sikyJPEJmE1WNr93hLVvHfSsdQIQHBrAkkunsOyaYiYXJcvPUnxqhl4zm9ccYf07JZ7FzsA9RHPR5UVcfuNMMnMTvFjh+NHaYeAnj73DiZp21GoV992+kDuum41aLX+fI2FMhpK77rqL55577rT7N23axEUXXfSxny+hZHSYzDYe+fMatu2rAuCKiwv57r2X4Oen83Jl40dDTQfrVx1i46pDdHX0e+5PTo/mosuLWLSikLQsmRwrPp7FbGPP5gq2ri1l37YTOBxOADRaNbMWTmLZNcXMXpwr3bjzsLukll8+uZp+k5Xw0AB+8cBVzJqa5u2yJrQxGUo+Kwklo8flUnjxrb3847/bcbkUstJi+OV3riItOcrbpY0rTqeLw/tqWP9OCTvWl2Gz2j2PpWbFsmh5AYtWFJKeLQvYiQ+dDCLb1pWyb3sl9kGH57HsvESWXVPMRZcXyWJn58nhdPHPl3fwwpt7UBTIy47nV9+7hvgYeT8ZaRJKxAWx/0g9Dz+5ml6DBX8/Ld+9bxmXLy30dlnjksVsY+eGMratLeXAzirPES9AamYMi1YUsnBZAek5cTLE44PMRit7tlawbe0x9u8YHkSS0qJZtKKAiy4rIj1HAuyn0dbZz8N/eJejx93DXtddOpVv3r0UvU46TKNBQom4YLp7zfzyj6s5cLQBgMsuyuc79y6TyWCfgal/gN2bK9i2tpSDu6qw2z8MKLGJ4cxZnMucJZMpmpmOXobNJqymui72bD3O3i0VlJbUe86cAXcQWXxpIYtWFJIhQfUz2b6vikf+8j5Gk5WgQD0/uP9SLp6f6+2yfIqEEnFBOZ0unn9zD/96ZScul0JKYgQ/+cblFE6ShYU+K7PRyq7N5Wz7oJSDu6uHHSH7B+iZMjOd6XOzKZ6bRVp2rLw5jWPG/gEO763h0O5qDu6upqWhe9jjKRkxLBwa0pMg8tlZBgZ56oWtvPn+IQAmZ8Xx8HeuJik+3Kt1+SIJJWJEHDrWyMNPrqazx4RareK2q2dyz20L8JNJdheE1TLIob017Nlawd6tx+nuMA57PDQ8kPxpqRQUp1EwPY3svESZ4DhGKYpCR2sfx0rqOXawgWOH6qmv6uDUl1itVkPRrHRmL57M7MWTSEyROVsXysHSBh796we0dhgAuPXqGXz1jsXodHKatDdIKBEjpt84wB//vYkPtpQBkJoYyQ/uX8HU/GQvVzaxKIpC7Yk2Du6qpmR3NaUH64ZNlAXQ6bXkFiZRUJxG/rRUcgqSiIyWRZ+8YXDQQe2JNo4fbXIHkZJ6utr7T3teSkYMxfOyKJ6TRdGsDIKC/c/w1cSnZTLbePrFrbz1wWEA4qJD+OHXLpOza7xMQokYcdv3VfPY02vp7nMvZ33N8iLuv3MxIUHyIjsS7HYHVWWtlB2qH3rTa/AsJX6qqNgQsvOSyMlPJCc/kez8JNk48AIbtNmprWynqqyFyrJmKstaqKtqHzYnBNyn7WZPTiS/eKi7VZwmK/2OoC17KvnDsxvo6jEBcO2KqXztzsUEBfp5uTIhoUSMin6Tlaee38qq9e69c6LCg/jWPRezdN4kGQ8fYYqi0Fzf7TkqrzjaRFNtJy7X6X/CkTEhZE6KJzUrlrShS2pWLIFB8mJ9Lk6ni/bmXuqrO6ivaqe+ptN9Xd1xWgAB9/BaTn4SBdNTKZiWRm5hsizxPgo6uo384dkNbNvrXlspOSGC739lOdOnpHq5MnGShBIxqg4da+R3T6+jocW9I+n8GZl898vLiIuW/6fRNGCxUV3ROnQE30JlectZgwpAbEIYqZnugJKQHElCcgTxyZHEJob7zFwVRVHo6zHT2tRDW1MPrU29NNV10VDdQWNtJ4M2xxk/LzQ8kOz8RCblJ5E91JWKTQiXMD6KnE4Xb609zN9f3IZlYBCNRs3nr5/NF26cK/PcxhgJJWLUDdodPP/GHp5/Yw8Oh4sAfx1f/twibrhsmuw67EUDFhs1x9uGjvY7qK9up6Gmc9h+KR+lUqmIjgslPjmChORIYuLDiIwJISomdOg6hPDIoDG/t4qiKFhMNnq6jHR39NPdaaSn0327rbmXtqZeWpt6Tpurcyq9n5aUjJhhXabM3HgJIF5WXd/J755ey7ETrQAUTErgB/evIDM1xsuViTORUCK8praxi989vY6jFc0A5GbF8e17L5HTh8cYo8FCfXUHDTWdNNZ2et6g25p6sQ4Mfuznq9UqwiKDiIwOISQ0gODQAIJD/YeuAzz3+Qfq0ek16PVa9H46dDoNej8tej8tOp0WzvbGrig4nS7sgw4GBx0M2tzX9kEHdpsDm82B2WTF1D8wdLFiNFjc1/0DGHrN9HQazxk4TlKpVMTEhxKfHEl8cgSJKVGeABKXFCGhegwxW2w899puXnn3AE6ni8AAPV+5YxHXXzpN9q0ZwySUCK9yuRTeWX+Ep5/fisliA2DpvEl85Y5FJCdEeLk6cS6KomDoMdPa1EtbUw8tTT3uLkOHkZ4uIz2d/fR2mc46JDQWBYX4Exnt7vBEDHV64hIjSEhxD1nFJPjOcNV4Zbc7eWfdYf796i76+gcAWDQ7m2/fewmxUTKRe6yTUCLGhJ4+M0+/uI01m0pRFNBo1Fy3Yip33TyXiDDZt2O8cjpdGHrNdHcY6e02ftip8HQt3B+b+gewWu3u7sbJbofN4fn41JVsz0StVqHTa4d1VvR+Ws99gUH+BIf6e7oyIWEBnk5NWHggkTEhREaHyGTTcUxRFDbtOsHfX9xGc1sfACmJEXzjrouYPyPLu8WJT0xCiRhTquo6efqFrewuqQUgMEDPHdfN5parphPgL28YvuqTvNzIvA3fdehYI399fgvllW0ARIYH8qVb5nPVJVPQjvH5TGI4CSViTDpwtIG/Pb+F49XtAERFBPHFm+Zy1SVTZGMsIQQAJ2raefblHew8UANAgL+O26+dxW1Xz5Q9t8YpCSVizHK5FDbsqOCZl7Z7loCOjwnlrpvncdlFBWhlUqEQPqmmoYt/vbKDzbsrAdCoVVy9vIi7b55PVIQM945nEkrEmDdod/DuhqP85/U9nhUYk+PD+dKt87lkwWQ540EIH9HY0su/X93Jum3lKIr7hKzli/K4++b5pCTKxPiJQEKJGDdsNjtvrT3M82/s8cyqT0+O4t7bFrBkbo7MKRBigmrrMLDytd2s2VSKc+hsrovm5vClWxeQmRrt5erEhSShZAKy2R1Y7Q7CAifm3jKWgUFeX1PCi2/txWR2n0aclRbD7dfM5JIFk2V3TyEmiJqGTl5ZdYAPtpbhGFquf/6MTO65bQG5mXFerm7kdPWbiQ71zWEoCSUT0JOrt7Nqfxm/uHkZi/MzvV3OiDGarfxv1QFeefcAlqFFvKIigrjpiulcu7yI0JAAL1cohDhfiqKw91Adr6w6wN7DdZ77Z0xJ5b7bF1KYO3EXV+wxWfjNG5s4UNPEW9//4oQ9sDwXCSUTzKDDwc2/f5GadvfeMtfMzOf71y6Z0L/c/cYB3l53hNfXlHjmnPjptVy+tIBbrppBamKklysUQnwcm83O2m3lvLLqAHVN3YB7/Zklc3K49eqZEzqMAKw9fIJH3thIj2kAjVrFY3deyfKiHG+XNeoklExAA4N2/vL+Tp7fehBFgdjQoAnfNQH3So4bdx7n5VX7qazt8Nw/f0YmN10xnZlFabK8tBBjTEe3kXfWHuattYc9c8UCA/RcfckUbrpyOgmxYV6ucGSd7I58cPgEADkJ0fz6thXkJ0/c4alzkVAygZXUNvOzl9dS39UH+EbXBNzt35Jjjbyy6gA79ld77k9OiOD6S6dy+dJCQoMn9s9AiLFMURQOljbyxpoStu+r8kxejYsO4eYrZ3DVJVMIDvLzcpUj76PdkXsuns1Xl89B58MLvkkomeDO1DX5+c3LWDLBuyYnNbT08MaaQ6zZXIrZ4p534qfXsnxRHjdcNo1JE3iynBBjjcls4/0tx3jz/UPUN/d47p+Wn8z1l01jydxJPrH+ULfRwqNvSnfkTCSU+IiPdk0un5bLD667iKiQQO8WNkosA4Os3VbOm2tKqG7o8txfMCmB6y6dxtJ5k/D303mxQiEmruM17byz7ghrt5YxMLQbc4C/jkuX5HPDZdPITI3xcoWjQ1EU3tlfxmPvbMVgsUp35AwklPiQgUE7f31/F89vPYhLUQgL9Od7Vy/m2ln5PrPGh6IoHKlo5o01h9i8+wROp/s0w6BAPcsX5nHVJVPIzYrzmZ+HECOl32Rl/fZy3l1/lBOnzPFKT47k+suKuWxJPkGBE3+I5qTG7j5++eoGdlc2AJCbGMPDtyynIEW6I6eSUOKDjjW28dD/1lPR0gnA9IxEfnT9UiYnxXq5stHV3Wvm3Q1HeXfDUc8y9gBpSZEsX5zHikV5JMaFe69AIcYZ26CDXQdq+GBrGbsO1njWFtFpNSyek821y6dSXJjiU6F/YNDOPzfu49+b9jPocOKn1XD/pfP4wpLp6DTSHfkoCSU+yu508vyWgzy9bjcDgw7UKhU3z5vCNy5fMOEnwn6Uy6VwsLSBdzccZeveKgYHHZ7HpuQmcsnCyVw0dxLRkcFerFKIscnhcHLgaAMbdx5ny+5KTBab57Hs9BiuvHgKKxbnEeZj6wYpisK6I5U8vmorrb1GAOZkp/Czmy4hLUaWxD8bCSU+rq3XyOOrtnomXIUF+vP/LpvPTXOn+MSEs48yW2xs3VPJB1vLOXC0npO/5SoVFE1OZun8SRJQhM87NYhs21tFv8nqeSw2KoTli/JYsTiPrDTfmCvyUcdbOnnsnS3sqWwEID48hAevWczyItkO4+NIKBEA7K1q5NE3N1HV5l60KDMuku9dvZiFk9N99o+oq8fExp3H2bTzOEePt3juPzWgLJmTQ0xUiBerFGJ02O1ODpaeOYhEhAWyZG4OF8/PZVp+is+uB9TVb+Yv7+/kzb3HcCkKeq2Gu5fO5J6LZxGgl4n0n4SEEuHhcLp4bfdR/vbBLnrN7kWM5k9K47vXLGZSgm9vetXe1c+W3ZVs3Hmc0lMCCsDkrDgWzs5m0axsMlOjfTbEiYnHaLay+2At2/dVsbuk1nNaPZwSROblMjU/2ad367baHTy/5SDPbtyLxeY+u+jSqZN44MqFJEdN7MXfLjQJJeI0/QNWnl2/lxe2HcLudKJWqbhhTiFfv2we0SG+uUnUqdq7+tm86wSbdp3g2IkWTv1LSIgNY+GsLBbNyqYoP9knh8DE+NbWYWD7/mq27a3iUFmT5ww1gMjwQBbPkSBykqIorCk5zpPvbffMGylMieP71y6hOCPJy9WNTxJKxFk1dvXxh9XbWXekEoAgPz33XjKLOxYVSytySHevmZ0H3C/g+482DJskGxLsz+ypacyZlsHs4nSiI2Qeihh77HYnR483s6ekjt0ltVTXdw57PD05koWzslk4O5v87ASfHZr5qJLaZh5/ZytHGtoA97yRB65cyOXTcuVn9BlIKBEf62BNM797ZwvHGtsBiA0L5ivLZnP97EJZ8OcUA9ZB9h6uZ8e+KnYeqPHs43FSdnoMs4rSmFGUxtS8JAL89V6qVPgyRVGoa+rmwNEGDhxp4EBpg2eXbXBvgjclN4mFs7NYODOblEQ5U+RUFc0d/PWDXWw+VgNAgF7HvZfM4s7F0+Vg7QKQUCI+EZdLYXVJBX9Zs5OW3n7AfWRw37LZXD+rQMLJRzidLo5VtrKnpJY9JbVUVLcPe1yrVZOfk8DUvGSK8pKYkpvkE3t9iNHncinUNHRxuLyJI+VNHCprorvXPOw54aEBzJmWwZzpGcyemkZ4qG+s9Hw+Kpo7eGrtbjaWuvfT0qhVXDe7gK9fOo+YUOmCXigSSsR5GXQ4eHXXUf61cR8d/e4XNgknH6/XYGbf4Xr2H23gwJF62ruMwx5Xq1VkpcUwNS+JorxkpuYlExUh83fE+bPbnVRUtw2FkGaOVDRjMtuGPUev1zIlN5GZRWnMKkpjUmacDDmcxUfDiEoFl0+bzFeWzyEzLtLL1U08EkrEp2KzO3h9Tyn/3LB3WDj50tKZXD+nEH+d1ssVjl2KotDc1sehY03uN46KZprb+k57XkJsKPk5CeRlJ5A/KYHcjFj8ZH8ecQpFUWhpN3CsspXyylbKKluprO1g0O4c9rwAfx2FuYkUTU5ial4yBbmJ+Onlb/RcShvaeGb9XjYd+2gYmU1mXJSXq5u4JJSIz+RM4SQyOJAvLJnOrfOLCPaXIYlPoqvH5DmyPVzeRHV9Jx/9C9No1GSlxZCfHU9eTjyTMuJIT45Cp5PulC9QFIXuXjMnats5Xt1OWWUr5VVtp81dAvdwjLvj5g4h2RmxcibYJ6AoCvuqm/jH+r2ePWokjIwuCSXigrDZHbyxp5SVmw945pyEBPhx+4JpfH5RMRHBvrXE9GdlMtuoqG6jbOjot6yylZ4+y2nP02rVZKZEk50Ry6SMWHIyYslJjyUwQCbRjmcul0JTWy+VtR2cqOlwX9e2nzGA6LQasjNiKMhJIH/okhQfLuvlnAeXS2FreQ3/2LCPI/WtgHvOyJXT87jn4lkyTDOKJJSIC8rudLKm5DjPbthHbUcPAAF6LTfOncIXl8wgPlxWP/00FEWhvcvoCSjHq9uprO0Yts/IqRJiw8hIiSI9JYqMlGgykqNIS46UM37GGJdLoa3TQF1TN7WN3dQ2dlHX2E1dUzdWm+O056vVKlITI5mUGesZ2svJiEEvw6WfisPpYu3hEzy7cR+VrV0A6LUabphTyF0XzSApUhY+G20SSsSIcLkUNpZW8Y8Neylrcm9brlWruWJ6Ll9YMoPcRN/cE+NCUhSF1g4DlXWdVNa0c6LWfUTd2WM64/NVKoiPCSM9OZLkhAj3JT6c5IQI4qJD0Mok5RGhKAoG4wDNbQaa23ppbO2lua2PhuYe6pt7GLDaz/h5fnotWWkx7u7XUCcsKzVa5hVdABbbIG/uPcbzWw/S3OPu7Ab56bl1fhF3Lp5OdKhMMvcWCSViRCmKwq4TDfxjw172Vzd57p+ZlcztC6aytDBLtu++wPr6LcOOuk/ePlPr/yS1WkVcdAiJceHERYcQGxVCTFQIsUO3Y6NDCA70kyGBM7DbnXT1mujoMtLRbaSz233d3mWktcNAS7th2DogH6XTakhNjCA9JZqMlKihSzSJ8eEyD+QCq+vs5ZUdh3lr3zFMVvf/SURQAHcsKub2hVMJDfCtHdLHIgklYtSUNrSxcvMB1h+txOly//rEhgVzy7wibpo7hagQWRthJPUaLNQ1dVPf3ENzay9NrX00tvbS0mEYthLt2QT464iJDCEyPJDwsEAiwwKJDA8adjs0xJ/QYH+Cg/zH7RuqoigMWO30m6wYTVZ6DRZ6DRZ6DGZ6+4auDRZ6+yx095rpMZhPm5R8JtGRwSQnhJMcH0FyQjgpCRESPkaB0+Vie0Ud/91+iB3H6z33p0WH84Ul07l6Zr4sejaGSCgRo66tz8iru47y2u6j9Jjckzd1Gg3LirK5ee4UZmYlyxH5KHK5FHr6zDS399HSbqCj68Oj/Y5uIx1dxmE7wn5SgQF6QoL8CAn2JyTIn5BgfwL8dAT46/D31512W6/XotVq0GnV6LQaNBr3tU6rQaNVo+LMvxMKCi6XgsPhwuFwYnc4cTg/vG13uLBa7VhtdizWwVNu27Fa7ZgHbBhNNoxmdwgxmm3D9nv5JHRaDTFRwZ7OUkxkCLFRwSTEhZEYF05CTKgMu4yyrn4zb+07xmu7j3qGaFQqWJyXwe0LpjFvUpqszTIGSSgRXjPocLD2cCX/3XHYM+MdID0mgpvmTuGamfly1s4YYbXZ6eg20tVjcncN+ixDHQQzPX0fdhH6TdZzDlWMJzqthpBgP8JDA4kY6gRFhJ28HUhkWBAR4YHERYcQHhooQXoMcLkUdlc28NruI2wqrcHhcofL0AA/bphTyC3zi0iJCvdukeKcJJSIMaGsqZ3Xdh9l9cEKz9bf0j0ZnxxOFyaz9bTug8lsZcBmZ2CoQ+G+7e5cWKx27HbnGTod7muH49ydC5Va5emqaLVqT8dFq3F/HOCvw3+oMxPgrz/lto5Af/1QN2eoqxPsHoLy02vld26cOFNXBGBqWgI3z5vCiqmTZIhmnJBQIsYUs3WQ90oqeG33Uc9ZO+Ae/71udgFXz8wnLkz2mRDC19mdTraX1/HWvmNsLav1dEVC/P24akYeN82bwqSEaC9XKc6XhBIxZh1rdHdP3iv5sHuiVqmYl5vGdbPyWVqQhZ+szyCET6ls7eLtfWWsOlDumZMG7q7ITXOncOk06YqMZxJKxJhntg6y9vAJ3tp3jIO1LZ77QwP8uLx4MldNn8zU9ARptQsxQXUbLbx/6DirDpRzrPHDHbcjgwO5asZkrp1VIF2RCUJCyQTUaDDQaTEzPSHR26VccPWdvby9v4x39pXRbvhwkbCEiBCWF+Vw6dRJTEmNl4AixDjXY7Kw/mgVaw+fYF9VE66htxytWs3i/Ayum1XAwrz0CbfOUb/NysHWVi5Kz/B2KV4hoWQC+t7aNbxRUcbi1HS+OWfehAwnTpeLPZWNvHugnA2lVZ7hHZCAIsR4dbYgAlCQEseV0ydzRfHkCbmmUb/Nyr9KDvLvQwexOR1s+eK9xAX73vy5T/v+LQP5Y5SiKPhptWjVarY21LG1oW5ChhONWs383DTm56ZhtTvYXl7L2sOVbC6robXXyH+2HOQ/Ww56AsolhdlMTU9Ao5ZFqoQYSzoMJjYfq2btkcrTgkheciyXTp3EiqIcUqLDvVfkCDo1jBgH3XtZTYqKptNi9slQ8mmNWKekrq6OX/3qV2zcuJG2tjYSExP5/Oc/z09+8hP0+k+2mZivd0oAGgx9/G3fHt6oKPPMSp+I4eSjPhpQBgY/7KBEBgdwUX4WF0/JYm5OqkySFcJLatp72FhaxabSao40tA17zBeCCJw9jHxz9jwuy85B7aMd3jE3fPP+++/zyiuvcPvtt5OdnU1paSn33Xcfd955J48//vgn+hoSSj50pnCyKDWNr8+ay+ykZC9XN7Ksdgc7KupYd6SSrWW1GK0f7qgboNexcHIaSwuzWZyXQVig7HkhxEhxulwcbWhjU2k1G0urqevsHfZ4UVoCFxdmTfggAtAzYGHloRKeO1wiYeQMxlwoOZPHHnuMp556ipqamk/0fAklpztTOJmZmMTXZs5hSVr6hJ93YXc62V/dxMahF8WOUybJqlUqpqUnsCgvg0V5GUxKiJ7wPw8hRprBYmXX8Xq2lteyvaKOXvOHG0JqNWrm5KRycWEWSwsyiQmd+MMU7SYT/zi4n/+WHmbA4d5rSsLI6cZFKPnpT3/K+++/z/79+8/4uM1mw2b78Ci4v7+flJQUCSVn0Ggw8PeD+3jtWCmDLicABTGx3D9zjs/8YSiKQllTOxtKq9lUWk1VW/ewx+PDQ1iUl87ivAxmZ6cSKHuWCPGxFEWhqq2breW1bC2v5XBdi2fjTYBgfz2LJmdwcWEWC/PSCfb382K1o6fB0MffD+zj9bJjntfcwphY7p81h0uzfOM193yM+VBSXV3N9OnTeeKJJ7j33nvP+JyHHnqIhx9++LT7JZScXbvJxD9L9vNS6REsdve8i/TwCL40bTo35BUQqPOdN+LmHgPbyuvYVl7LnsoGbA6n5zGtRk1RWgKzs5KZnZPK1LR49FqZiyKEoig0dRvYW9XI3qom9lU30tlvHvacrLhIFg91IKdlJE6403fP5XBbK8+W7GdNVaVn8u6sxCS+Pmsui1LTpBt7FqMWSs4WHE61b98+Zs6c6fm4paWFJUuWsGTJEp599tmzfp50Sj693oEBVh4+yHOHS+gf+hmG+flza0EhdxYVk+RjPz+r3cHeqka2ldeyrbx22D4aAH5aDdPSE5mVncKc7BQKUuN86oVW+LbW3v5hIaS11zjscT+thtk5qUNBJJ2kyDAvVeodg04n71edYOWhEg61f7jJ6OLUdL42a86En8d3IYxaKOnq6qKrq+ucz0lPT8ff3z3hsKWlhaVLlzJnzhxWrlyJ+jxO5ZQ5JefPPDjIq2WlrDx0kIZ+A+Cea7E8M5u7p01nVmKSzyV7RVFoPHkkWNnI3upGuo2WYc/x12kpSkugOCOR6RlJTE1LIMj/k50lJsRY5nIp1HR0c7C2hYM1zZTUttDSOzyka9VqpqTGMzsnhdnZKUxNS/DJs9q6LBZeLj3CC0cP0WF2d4v0ag1X507mS8UzyIuO8XKF48eYHL5pbm5m6dKlzJgxgxdeeAHNeR6JSij59JwuF5vravn34YPsbGzw3J8XHcNd06ZzzaTJ+Pno8IWiKNR29LC3qom9VQ3sq2qiz2Id9hy1SkVuUgwzMpIozkikKC2B+PAQL1UsxCdntTsob2qnpLbFfalrwfCR32+NWkVBchyzst0hZFp6ok/PuTrW0c7KwyWsOlHBoNM97BsTGMTni6ZyW2ERMYFB/7+9+wyO67zvPf7d3hsWZdE7SJBgpyiSlizRYmQpSiQ5Lte+iS07Za40ske6niRKnIzLTDJKMpnrGduxY0/mSk5cZDu2imUrV4wlUbJpiqREECBYQPRetmJ7O+e+2MUCy06KwAK7z2dmZxdnF+BzCGDxe/5POQVu4fqz5kLJ4pBNQ0MD//7v/54XSFwu13V9DRFKbo1+j5vvnjrJ8+fOEMvOFnfo9Xx0Uxf/c8s2Gmz2wjawwCQpE1LeHc70It8dnrxkuAeg0mpiS2M1WxpcbG2sZnNdJUadqKYIhSNJMqNuH71jM/SMTtMzNsOFKXduZd4ig1bN1oZsJbCllq0NohIYT6V4ZeAC3+/t5p3ppWtxbaty8entO7m/rQOtGNK9aWsulDz77LN85jOfuexz1/tPilBya/ljUX7cd5p/7znJVDAzhqwA3t/YxB9t2c7dTc1ip9SsGX+Q7uEp3h2e4uTwJBdm3HkrECBTTWlzOdnS4KKzrpLO2ko6airQl2DZW1h5siwz5VvgzMQcZyfm6BufpXd8hmA0fslryy1GtjZWs7Ollp3NtWysrRBzprLGAn5+cLqH/+w7jTeWWd6sViq5v62Dz2zfyXZXdYFbWBzWXCi5FUQoWRkpSeKNkSG+33uKw6MjueM1Fguf6NrKxzZvEeXKi0TiSc5OztI7OkPP2Ay9YzPM+IOXvE6lVNBS5aSztpJNdZlbe3V5ySybFG6NtCQx5vZzfnKeMxOznJnMBJGFywQQnVrFproqtjRmKnhbG1y47JaSmzt2NYvD2d/rPcWbo8Ms/tGrNpv5RNc2Pra5i0pT8e+xsppEKBFuyqjfzw9Pn+LHZ07jj2XGnTVKJQdb2vjIps3c2dCEWlRPLmsuEKJ3bIa+idls73UWbyh62ddWOyy0u8ppry6n1eWkrcpJc1WZqKqUOFmWmfYFGZz1MDjj4cKMhwszboZmPHlL2hepVUraq8vZlA29XQ0u2qvLRRXkCsYDAX52ro+fnDmdqw5DZjfsP9qynQPNLeL9bYWIUCK8J/FUil9e6Od7vd2cnFlaAldhNPHQho38QedmNoqZ51clyzJzC2HOTsxydmKOMxNznJmcy9t1djmFAmrLbDRWOGiqsNNY7sg+duCyW1AqRU+3WASjccbcPkbm/YzO+xiZ9+Xul18Zezm9Rp0JINmhwU11VbS5nGjUIoBcTTAe55WBfn529gzHpiZyx+3ZeXSf6NpKk91RwBaWBhFKhFvm7PwcPzlzmpfOn8uNuQJsKq/gDzo38+CGTsqNxXfJ8ZUSiMS4MO3mwrSbgRkPA9le8cUrIpbTqVXUl9upc9oytzIbtWVWasts1JbZSnqlxFqUliTmAiEmvAtMegJMegNMeheY9AYYdfsvWYK+nFqppKnSQUtVGW1VTtqrMxW1OqdNzPG6TmlJ4sj4GD8918ergwO5Cf0KYH99Ax/u7OK+tjb0avF7s1pEKBFuuUQ6zeGRYX56ro/Xh4dIZmf0qxQK7mho5KENnRxsacN8nVd9FpbIsownFGF4LtNjztz8jLp9jLn9pNLSVT+/zGygxmHFZbdQZTfjslmosltw2c1U2SxU2EyipH+LyLLMQjTOjD/IrD/IjD/ITCDErD/ErD/ItD/IlG/hmt+zcosxVwlrrHDkKmT15XbxvboJsizTMzfLS+fP8nL/eeYjS7vQtjrK+IPOTTy8YRPVFrGUvxBEKBFWlC8a5ef95/jZuTP0zC5dolyvVnOwuZUHN2zk/Y3NYgndLZBKS0z7Fxid9zOR63UHmPAuMOEJXHa1xcUUCnCYjJRbjJRbTDgtmcdOq4lyi4kyswG70YDdpMdmNGDQqktqYmQqLbEQjeEPxwhEonhDUTyhCJ6FMO5gBHcwc+8JhvEEI8SSqWt+TbVSSbXDkqlmOa3Z6paNhnI7jRV2Mdn5FhnyeXnx/FleOn+O0YA/d9ym0/P7HRv4cOdmtla5SurneS0SoURYNUM+Ly+dP8dL/ecY8S9dutym03N/Wzu/17GRPbV1YgLZClmIxpj0LDDlW2A2EMr24EPMBDI9+dlA6Jq99otp1SrsRj02kwG7UY/FoMOs12LW6zDptZh1Wsx6LSZ95rheo0anUWPQatBp1OiXPdaqVLd8Powsy6QkiXgyRSyRIpZMEUsmiSdTRLMfRxNJQrEEoVicUCxBOJYgFI8TimaOBSIx/JEYgXCMYOzawe5iDpMhU5mymZdVpcy47JkgUmU3i+GWFTIZXOCVC/281H+O03OzueN6tZqDLa081NHJnY1NolO0hohQIqw6WZbpnZvlpfPnePnCudy2zABOg4EPtnXwu20dIqCsMkmS8YYjeIIR3Ath3Nne/mIFwBuM4AlF8Iej+COxGw4w10OhALVShVqlRK1UZu5VSlRKJVfqwMoySLJMKi2RSqdJS/LSvXTr2whgMeiwG/U4TAacFhPlViNOs5HybEXJaTbitBiptJlLctv1QloMIq8M9OdNvlcpFNzZ2MSDHZ38TksrJjF8vCaJUCIUVFqSeHtygpfOn+XVoYHc8mIQAWUtk2WZSDyJPxLNDmXE8IejuWpDKJ4gFE0Qji+vPiSyFYpMpSKWva1EuLkchSKzMkWvWarSLFZqzAYdZp02U93RZ+4teh1GnRabUY/dqMduygxbWQ161Crxs7iWXCmIKIDbaup4oGMDv9vWgVNMtF/zRCgR1oxkOs3RiXF+ceH8JQGlTG/g7qZmPtDcwp0NTVh0Ypy9WKTSErFkkmRKIiWlSadlklI6W/mQSEvSNYOLQqFArVKiUSlRq1SolUpUy6oteo0arVol5gsUCUmW6Zuf47XhQX41PJQ3NLMYRH63vYP72trF5mbrjAglwpp0tYCiVirZU1vHB5pauKe5lUa7vXANFQRhVUSSSY6Mj/La8BCvjQzlDfuKIFI8RCgpQsFkDKVCiUldHGOmyXSad6en+NXwIK+NDDHk8+U93+oo40BTM3c2NrGnpq5kr2IsCMVElmVGAn7eHB3m8OgIvx0fJ55eWs1k0mi4o6GJDzS3cHdTc9Fc4kKWZeZiQaoMpfe3C0QoKUrfOPsG3x04yocat/GJ5ttotpQXukm31LDfl+ktDQ9xfGoibzKjXq1mb109dzU28f7GZppsdlGyF4R1IpxIcHRinMOjw7w5OsLYQiDv+TqrlXuaW/lAUwt7aourAxJLJ/nF+Gl+MHycmUiA1+/732hVxXN+10uEkiL0qbee5bh7NPfx/soW/rBlD3e52lEpimuC3kI8zq/HRjg8OsKboyPMhvO3Zm+w2rizsYn31Teyr64em15foJYKgnCxtCTRNz/HkfEx3hob5cTURG6zRchcT2t3TR3vb2zkQFML7WXOoutkTIR9/HD4BD8dOUkgmdkJW6tU8ewdj7DDWV/g1q0+EUqKkCTL/HZuiO8PHeONmf7clS1rjDY+3rybjzTuxKErvlnosixz3uPmzdFMSLn4DU4BdFVWsb++gffVN7K7pkZsHy0Iq0iWZYb9Pn4zPsaR8TGOTowTiOdfNqHeauOuxibuamxmb119US7dlWSZI3ODfH/oOIcveo/+RPNtfLhxR1G+R18PEUqK3FIKf5dAMvPLr1Wq+GDtJj7WtItdzoai63ksWiwFvzk2wpHxMQZ93rzntSoVu6pr2FfXwJ7aOrZVuYqqHCwIhSbLMuMLAY5NTvD25ARHxkeZDuVXM81aLXtr63lfQ0PRD7l64mGeH+3mJyPvMBZemhv3vspW/mfLbUVZzb5RIpSUiGgqyS8nTvP9oWOcDSxt995qqeB/NO/i9+q2FH0ynwkF+e34OL8ZH+XI+BgzFw31aFUqdriq2VNbx201dexwVRdlL00QVookywx6vbwzPcnbkxMcmxy/JIRolSp21dSwv76B/XUNbKlyFfUeRJIsc8w9wk9G3uXQ5BmScqZ6a1brinbe33shQkmJkWWZ0/4pfjT8Dr+cOE00nbn8uUap4p7qjXy4cTv7KluKPq0vlpF/PTaa68V5ovlXZFUpFHSWV7DdVc0OVw3bXC6a7Y6i7cUJwo1aiMc5NTvNqZkZTs5Mc3JmKm/5PmSW8G+trGJPbT376uvZXV2LQVP8w6aTET8vjJ3i+dFuJiP+3PEtjho+1rSL363rwlgkKyRvJRFKSlgwGePn473858i7edWTSr2F36vfwkMN2+iwVhawhatHlmWGfN5M725qgnemppgMLlzyOrtez7YqF9td1Wyvqmaby4VdbyhAiwVhdaUkiQseNydnpumenaZ7eppBn5eL/xDo1Wq2V1Wzu6aWPbV17KyuwVgCIQQgnIzz6tRZXhw7xdvukdxxs1rHA/VdfKxpF5vs1YVr4DogQokAwBn/ND8bPcnL4725uScAnTYXDzVs44G6Lsr1pbUh0VRwgXenp+iemeHU7DS9c7Mk0ulLXldntdJVUcWWqiq6KqvYUlklgoqwriXTaQa8HnrnZjk9N8vpuTnOuufz9glZVG+1ZUK6q5odrmo2VVSW1AXu0rLEb+eGeGm8h0NTZ4kt+z/aU97Ehxt38Ds1nRjEpPrrIkKJkCeRTnF49gIvjvXw5kx/bvxTpVBwR2UbDzZs5YBrQ0n+giXSac655+memaZ7ZpqTM9N5l0BfbjGobKqopLO8go0VFdSYLWLoR1hzwokE5z1uzrnnOeuep+8qAcSs1V5UKaymvASvJyPLMucXZvn5WA8/n+hlPrY0b6bJ7OThhm38Xv0Wao32wjVynRKhRLgiXzzCLydP89JYDz2+ydxxo0rDPTUbeaBuC/srW9AoS6dXdLGFeIzTc3PZ3uQsvXOzVwwqVp2Ojc4KOisq2FieubU5ysRkWmFVSLLMxEKAfo+bs+55zs5nQshYwH/JEAxkAkhXRRVdlZWZCmCVi0abHWUJB+uxkJdfTJzmFxO9DAbdueM2jYEH6rt4qH4bWxw1ovPxHohQIlyX4aCbF8d7+MV4LxPLJm3ZtQY+WLuJB+q2sMvZUNJvWIsWg0rf/GzujX/Q583beXa5WouVdqeTjjInbWVO2p3lIqwIN20xfFzweOj3uhnwerngcTPg8xJLXVr9AKgwmnIVvU3lFSKALDMXC/LKRB+/nDid1znTKlXc5ergwfqtvN/VjraEO2e3kgglwg2RZZlTvkl+Md7LK5N9eOJLF8WqNlj5YO0m7qvdzFZHregtLBNPpRj0efN6qP0e9yUrfparNptpspfR4nDQbHfQ4iij2e6g1mot6iWUwvXxx6IM+3wM+X2Ze5+XYb+PEb//skMvkPlD2lJWxkZnea5i11leWZJDMFfjjYc5NHWW/5o8w7H5EaRsLUmJgn2VLTxQ18XBmo1YNGKH6FtNhBLhpqUkibfdw/xi/DSHps4SSsVzz1UbbBys2cDB6k52OhvEH9Er8EYjDHi99HvcDHg9XPB66Pd4rhpWtEoVdTYr9VYbtVYb9VYrdRYbdTYbdRYrZQaDCIRFIJ5KMRlcYGJhgfGFABO52wJjAT++i5beLrcYPtrLnHQ4sxW4MicNNrv4XbyC6UiAX02f47+nznHcPZoLIgDby+p4oK6L+2o3l9yE/9UmQolwS8TTKd6cvcD/mzzD6zP9RFKJ3HMOrZEDrg4O1mxkX2ULelXpTZK9Ub5olGG/j2F/tgec7RGP+H2XXQG0nFGjodpswWU2U22xUG22ZD+2UG2x4DKZsep0IrgUUDyVYj4SZjoUZDoYZCYUyjwOZR8Hg8xHwtf8Oi6TmWZHGc0OBy12B83Zqlqd1SbCxzXIssxg0M1r0+c4NHWO0/6pvOc326v5YO0m7q/dTJ3JUaBWlh4RSoRbLpZOcmRuiENTZ3l9uj93kSkAvUrNvooWDlRv4C5XO5V6SwFbuv5IssxUcIGxQIDxhQCTeb3ohUsuSHglWpWKCqOJSpOJCqOJcpOJSqOJCpMJp8GAw2DAaTDi0Buw6fVibsF1iCaTeGNRvNEovmgUbzSCOxJhLhxiPhJhLhzGHQkzFw5fcr2XKzFqNNQtVsOstuwtUyVrtNnFvKMblJTSvOMZ47Xp87wx08/4sq3eFcCOsnp+p6aTe2o2Ui+CSEGIUCKsqJQkccIzyn9PneW16fNMR/M3JNviqOFuVwcfqN7ABmuV6L2/R4sl/8We90woyNSynvhMKHjJjpvXolQocOj1OPQG7AYDNp0Oq06PVafL3pYem7VaTBotRo0Gk1aLSaPBqNGu+X0rJFkmkkwSSSYIJ5NEEpn7UCJBMBFnIZ65BeMxAvHFj2MEYrFcELnSJNIr0SpVuMzmpQqW2bxU1bJYqLVYcOjFUNx7FUhEeWt2gNemz/PruQGCyaVhZo1Sxd6KZg5Wb+RA9QYqxNBMwYlQIqyaxbX9r0/388ZMf95MdoAqvYU7q9q4s6qd/ZUtmDW6ArW0uMVSSdyRCPPhMHORMPPhMPPZ+7lwGF/2j6w3GiWYiF/7C14HjVKJUaNFp1ahU6nRq9XoVCp0ajValRqdWoVWqUKlVKJSKlArlKiUStTK7L1CccU/zrIsI8kyaVkmJUmkJYmUnL2XZFJSmngqTTydIp5OE08t3SfSKaKpFJFk8pacp1apoixbaXIYDJQbjbkKVMWy+0qTCZtOLwLHCpBkmbOBGd6avcBbMwN0eyfy5oeUaY3c7erg7uoO9le2YhJbva8pIpQIBTMXC3J45gJvTPdzZH4wbydEtULJDmc9d1a18f6qdjqsleINvAAS6TT+ZUMSvlg0VzXIVQuWPQ5nKwyLFYdrzX9Za5QKRabKs1jt0WiwLKsEXa5KtDjcVWYwYtJoxM9pAQQSUX4zN8hbswP8enYAdzx/Pk67tZIDrg7udnWwtay26K/ttZ6JUCKsCfF0iuPuEd6cHeCt2QFGQp685yv1FvZXtrC/soV9FS1iBvw6kUyniaYywyCRbEhZXqlYrF7EUilSkrRU6ZAk0rK07NjV324UikwpXqVUZKorivwqy/KKjC7vXo1epc4NNenVahEq1oGklKbHO8mR+UGOzA3R453Mq4YY1Vr2VTTnKq81RlsBWyvcCBFKhDVpPOzjzWz59W33cF4VBWCDtSoXUnY6G8TVNgWhiC2ulDk6P8SRuSGOuUcIL1vhB9BqqeCuqjbudLWz09kgNjNbp0QoKUITkUm8CS+bbZtQKdb/L2Y8neIdzxhH5jK9ouVXNAbQKJR0OWrZXd7AbmcjO50NYj6KIKxjkiwzsDDHcc8oJ9xjnHCP4o7nryyzaw3sq2jJdk5ai6YaMh93MxweZk/ZbYVuSkGIUFKE/u/wsxyefwubxsY+5+3sd+6jwVhfNGVpTzzM0blMj+m388NMRwN5zytR0Gl3sdvZyO7yRnY5G3DoxI6VgrBWpSSJs4FpTrgzIeQdz2je1coBdEo1O5z17K9oYX9VK502V9EsVQ+nIhz3nuCI57ecD/ajUqj42vb/g1lTesPUIpQUof8c/xmvzx8mlFrqWdQZatlfvo99zr2UaYtn/b0sy0xE/Nk3s1FOeEYZW7b3wKJms5MdZfVsd9azs6yeZkt50byhCcJ6409EOeWd4KR3nG7POD2+SaLp/BVQRpWGHc4Gdpc3sMvZyDZHLVqVukAtvvVSUorewGl+4/kt3b5uknJmiFqBgk7rBj7Z+EfUGKoL3MrVJ0JJkUpJKXoCpzniPkK3/9RFP/Ab2eu8nd2OnZjUpgK39NabjS5wwjOWCyoDwflLXmPT6NlWVs8OZx3bHHVscdSKIR9BWAFpWWI46KHHN8FJzzgnveN5V9hdZNXo2eVsYHd5I7udjXTaXUV3BXJJlhgIDXLU8zbHvMcJLus41hpqeJ9zH/vK91KmLStgKwtLhJISkCkNHuc3nt/SH7yQO65SqNhq28Je5x522LejUxXnH2VfPMIp3wTdnnFOeifo8U1cMnFWAbRYytnqqGOLo4atjlo6bFVF96YoCCttNrpAj2+SXt8kPd5JTvunLpmUCtC0WL0sq2Ons4GWIq1eyrLMWGSMo55jvO09hifhzT1n01jZW3Y77yvfR4OxoWiG2N8LEUpKzHx8nqOeYxz1HGMiOpE7rlPq2GHfzl7nHrbYulAri6dMerGklOZ8YJaT3nHe9YzT65tkMuK/5HVapYpN9mo226vZlL21WipEUBGErPlYiD7/FGf805zxz3DaN8lsLHjJ6wwqDZvtNWwvq2OHMxNEynTFV6VdbiY2y1HP2xz1HGM6Np07rlfq2V22k71lt7PJ1lkUixFuJRFKSthEZJKj3rc56nmb+fhSOdWoMrLTsZ3bynbTZd1c1AFlkScepseb6d0t3i6eaAeZoLLBVsUmWyakdNpdtFsrxUUGhaImyzJTkQDnAjOcCUzT55vmTGCa+dil11pSoqDDVskWRy1bs7cWS0VJXCBwJjbLce8JjnmPMxYZzx3XKNRss29jr3MP2+xb0SrFFgZXIkKJgCzLDIWHc+Oc/uTSahajysh2+zZ2l+2ky7q5aId4LibLMqNhL6d9mV5gn3+aM/5pQqlLt11XoqDJ7KTDVkmbtZIOayXt1krqTQ6xc6Sw7gQSUfoX5riw7Na/MJt3zZhFShQ0W8pz1cTF+1LZN0iWZSajk5zwvcs7vnfzgogSJZttm9jrvJ1djh0YVIYCtnT9EKFEyCPJEv3BCxz3nuCE7528gKJVatli62KHfRvb7NuwakrrCr+SLDMR9uUCSp9/mnOBGXyJyGVfr1epaTaX02wpp8VSTqulnBZLBU2msqJaRSCsP7IsMx8LMRicZyjoZijkZijoZjA4f9nqB2T2A2qxVOSFjw22qpIJIIvScpqB0CAnfd286zvJbHwu95wSJZusnexx3sYu+46SXNL7XolQIlyRJEtcCA3wjjfTC3AnlrZ+V6CgzdzKDsd2dti3U613leQkLVmWmY+H6A/M5vUuBxbmiUuXv2qsEgV1JgctlnIaTWU0mstoMjtpNDtxGaxFOdlPKIxQMs5oyMNI2MtoyMNoyMtIyMNQ0H3Zqt+iGqONdkslHbZM1a/DWkWzpbxkd0mNpqOcDvRx0neKU4GevO0WNAo1m22b2eXYyU77dhFE3iMRSoTrsjiD/F1fNyf93YxGxvKer9JVscOxje32bbSb20piHsrVpGWJ8bAv1/scDnpyvdKr/THQKdXUmxw0mp00mBzUmuzUGR3UmxzUGu3oRIVFWEaSZdyxEBMRHxNhP+MRH5NhP2PZEHLxhemWU6KgPhuOM5W8ity9WB6f2Vm1x9/DSf8pzi6cIyUvdTJMKhPb7FvZ4djGFluXGJq5hUQoEW6KJ+6l29/NSf8pziycJS0vXQ3WoDKw2bqJbfYtbLVtwa61F66ha8zysvlIyMNItvc6GvYyEfaRkqWrfn6F3ky9MRNWqg02XAYr1UYbNQYbLoMNi0ZXkhWrYpWU0sxFg0xFA8xEA0xHAkxFA0xFAkyG/UxG/FesyC1y6kzZipyTRnOmMieGES+VklJcCA1wyt/DqUAvU9GpvOerdJW5ynC7pU2smlkhIpQI79ny0mZPoJdgKn9JYKOxga32LWyzbaXF3Cx+ma8gJUlMRfyMZnu5E2E/ExE/E2EfExHfZfd6uJhJrcWVDSuVeguVejMVBkv2ceZWrjeLZc0FJssygWSMuViQ+WiQudiyW/bjmegC87Eg13qjVSkUuAw26ox26kwO6kx26k1lNJnKaDCXYdHoV+Wc1iNvwktvoI8efw+nA2eISUsr7pQoabO0st22lR2OHSU7RL3aRCgRbilJlhgJj+Z6G8Ph4bznjSoDm6yddNm62GLbTLmuvEAtXV9kWcafiObK9FMRP9PRANORhcx9NIA/Eb3ur2fT6HHqzJTpTDh1Jpx6U+6xQ2vEpjVg1xqwaQzYtUb0KrV4Q76KlCSxkIwSSETxZ2+BRARvIoInFsITj+BNhPHEw3hiIbzxMMlrVMUWaZQqqg1Wqg02qo22XIWs3uSgzuTAZbCKkHmdElKC8wv99AZOc3qhj8mLqiFWtZWt9i622rbSZdtUlDter3UilAgrKpAM0Bvo45S/h75AH+F0/koVl76KLbYuuqyb2WDtEGOz70EklWAmmgkp+b3vUK737Y4Fr/uP4XJapQq71ohVo8ei0WPW6LBo9FjUutxjs1qHSa3FoNZiUGmW7pc91ipVaFRqNAplQUNOWpZIpNMkpBTxdIpoOkk0nSCaSmYepxJE00kiqQShVJxgMkYoGc8+jhNKxghmj/sTkcsul70eNo2ByrxKVqayVaGzUG3MBJEynUlMfr5JkiwxEZ2kL3CG3sBp+oP9uUtuQGbCfrOpKVfJbTI1ohTL+AtKhBJh1UiyxHB4JNNLCfQxGBpCYukPpAIFTaYmOi0b2GjdQIelXYSUW0ySZQKJKJ54GG8823OPh/I+Xt7TDySiNxVirkVBpgKgU6nRKtVolSrUShUqhRKVQpG9V6Jc9vhKf5bl7HlJSKRlmbQkkZYXb3ImgEgpEuk0SSlFXEqRXqG3L4tGh11rzFaYDDh0Jpw6I06dGaduqRq1+FhMXL61FkPIuYXznAue59zCecLp/Mm+ZVoHXdmO0GZrp1gts8aIUCIUTCQV4czCOU4v9NEXOMPcsvX+kB9SNlg7aDe3Y1IbC9Ta0iTLMpFUAn8yE1QWEtFMpSAVW6oYJOMEU5lKQmRZhSGWXqw6ZKoQCSl97X+wAJQoMKjzKzp6lQZj9rFZo8Os1l2mQqTHqtFnhrm0BqwaQ0nsWrqWSLLEeGSC88H+K4YQnVJHh6WdLdkh42p9tRiKXMNEKBHWDE/cm3ljyb65XC6k1Bpq2WBpp93SToe5HaeudK+mud6kZYmklCaRThOXUnnVi4SUJimlkbKVjZQsIeXuZVLS1as1SxUVBSqlMlddUWerLYvVGK0qe69U5x6rCzyUJFy/hJRgKDRMf+gC/cELDIQGiabz51IthpCN2Yprk7Gx5LcoWE9EKClCSSmMSqFFqVjf12PJhZSFc5wPXmA2PnvJa8q1Ttot7bSb22gzt1JnrBWrewShSASSAQZCgwyEBukPDjAcHs7bfgBAr9TRZm6j07qxaEJIIh1Aq7IVuhkFIUJJETrr/Q4Dge9RbTpAnekglca96z6gAPgTAS6ELtAfHKA/2M9oZAz5ogWTOqWOFlMzbeZW2syttJpbsJTYdviCsB6lpBTj0QkGQoMMZoPI8guFLrJpbHRkK6UbLO3UGeuKoiMSSowyEf5vJkOHiKXmuL/pVZSK9R2ubsaaDCUPPvgg3d3dzM3N4XA4OHjwIP/4j/9ITU3NdX1+qYeSt6b+F/PRY7mPNUpL0QUUyOyPMhQa5nywn4HQIEPh4UtKuZDZ9KjF3EyzqZkWUzONpgZxlU5BKCBZlpmLzzMcHmY4PMJQaJiRyCgJKX8vnsyQbQ2t5lY6zG20W9qp1FUUzXDb8iASSJzPHVeg4kDd97DrNhawdYWxJkPJV7/6Vfbt20d1dTWTk5P8+Z//OQBHjhy5rs8v9VAiy2k8sW4mQoeYDP+KeHqpt5EJKHdTYzpAlWEfKmXxbKwkyRJT0alcuXcgNMR0bPqS1ylRUmespdnURIupmWZTE7WG2nVf8hWEtUiWZXxJPyPh0bwQcvGEVMhclbzV3JKrdLaYmjEW0eR2WZYJJoeYCr/GZOhXlwSRCsMeas0HqTEdQKdyFLClhbMmQ8nFXnrpJR5++GHi8TgazaW9/Hg8Tjy+tE9AIBCgoaGB8fHxkgwly8lyGm+sh8nw68yEDxNLL11UT6XQ876ab2HXtRewhSsrnAozEhplJJK5jYZHCSQXLnmdSqFiv3Mff9T0iQK0UhCK01BomG8O/CvB1KVXHlYr1NQZa2kyNtJkbqLJ2ECVvqqo9wl5e+YvmY0sda4VqCg37KLadDfVpjtLNogst7CwQH19PX6/H5vt+ufVrFoo8Xq9PPbYY0xOTvLrX//6sq/58pe/zFe+8pXVaI4gCIIgCCtsfHycurq66379ioeSp556im984xtEIhH27t3Lyy+/jNPpvOxrL66USJKE1+tFo9GUXMVkMWWW0jmDOO9SOu9SPGcozfMuxXMGcd5nzpxhw4YNKG9g358bDiXXU804fvw4u3fvBsDtduP1ehkdHeUrX/kKNpuNl19++YYmOJXi3JJSPGcQ511K512K5wyled6leM4gzvtmzvuGZwR+9rOf5eMf//hVX9PU1JR7XF5eTnl5OR0dHXR2dlJfX8/Ro0fZt2/fjf7TgiAIgiAUsRsOJYsh42YsFmWWD9EIgiAIgiDATYSS63Xs2DGOHTvGHXfcgcPhYGhoiC9+8Yu0trbecJVEp9PxpS99CZ1Ot0KtXXtK8ZxBnHcpnXcpnjOU5nmX4jmDOO+bOe8Vm+ja29vLE088walTpwiHw1RXV3Pffffxt3/7t9TW1q7EPykIgiAIwjq2preZFwRBEAShdBTv7jaCIAiCIKwrIpQIgiAIgrAmiFAiCIIgCMKaIEKJIAiCIAhrwroNJfF4nO3bt6NQKOju7i50c1bcgw8+SENDA3q9nurqaj75yU8yNTVV6GatmJGREf7kT/6E5uZmDAYDra2tfOlLXyKRSFz7k9e5v//7v2f//v0YjUbsdnuhm7NivvnNb9Lc3Ixer2fXrl289dZbhW7SinrzzTf5/d//fWpqalAoFLzwwguFbtKKe/rpp7ntttuwWCxUVlby8MMPc/78+Wt/4jr3rW99i61bt2K1WrFarezbt49XXnml0M1aVU8//TQKhYInn3zyhj5v3YaSv/zLv6SmpqbQzVg1Bw4c4Mc//jHnz5/npz/9KYODg3zkIx8pdLNWzLlz55AkiW9/+9v09fXx1a9+lX/913/lC1/4QqGbtuISiQQf/ehHeeyxxwrdlBXzox/9iCeffJK/+Zu/4eTJk9x5553cf//9jI2NFbppKyYcDrNt2za+8Y1vFLopq+bw4cM8/vjjHD16lEOHDpFKpbj33nsJh8OFbtqKqqur4x/+4R84ceIEJ06c4AMf+AAPPfQQfX19hW7aqjh+/Djf+c532Lp1641/srwO/fKXv5Q3btwo9/X1yYB88uTJQjdp1b344ouyQqGQE4lEoZuyav7pn/5Jbm5uLnQzVs0zzzwj22y2QjdjRezZs0d+9NFH845t3LhR/qu/+qsCtWh1AfLzzz9f6Gasurm5ORmQDx8+XOimrDqHwyH/27/9W6GbseKCwaDc3t4uHzp0SL7rrrvkJ5544oY+f91VSmZnZ/mzP/sz/uM//gOj0Vjo5hSE1+vl+9//Pvv370ej0RS6OasmEAhQVlZW6GYI71EikeCdd97h3nvvzTt+7733cuTIkQK1SlgNgUAAoKR+j9PpNM899xzhcLgkrvn2+OOP88ADD3Dw4MGb+vx1FUpkWebTn/40jz76aO4qxKXkqaeewmQy4XQ6GRsb48UXXyx0k1bN4OAgX//613n00UcL3RThPXK73aTTaaqqqvKOV1VVMTMzU6BWCStNlmU+//nPc8cdd9DV1VXo5qy43t5ezGYzOp2ORx99lOeff55NmzYVulkr6rnnnuPdd9/l6aefvumvsSZCyZe//GUUCsVVbydOnODrX/86CwsL/PVf/3Whm3xLXO95L/qLv/gLTp48yauvvopKpeJTn/pU7iKH68WNnjPA1NQU9913Hx/96Ef50z/90wK1/L25mfMudgqFIu9jWZYvOSYUj89+9rP09PTwwx/+sNBNWRUbNmygu7ubo0eP8thjj/HII49w5syZQjdrxYyPj/PEE0/wve99D71ef9NfZ01sM+92u3G73Vd9TVNTEx//+Mf5+c9/nvfGlU6nUalU/OEf/iHf/e53V7qpt9T1nvflvsETExPU19dz5MiRdVUSvNFznpqa4sCBA9x+++08++yzKJVrIkffsJv5Xj/77LM8+eST+P3+FW7d6kokEhiNRn7yk5/woQ99KHf8iSeeoLu7m8OHDxewdatDoVDw/PPP8/DDDxe6Kavic5/7HC+88AJvvvkmzc3NhW5OQRw8eJDW1la+/e1vF7opK+KFF17gQx/6ECqVKncsnU6jUChQKpXE4/G8565kxa4SfCPKy8spLy+/5uu+9rWv8Xd/93e5j6empvjgBz/Ij370I26//faVbOKKuN7zvpzFLBmPx29lk1bcjZzz5OQkBw4cYNeuXTzzzDPrNpDAe/teFxutVsuuXbs4dOhQXig5dOgQDz30UAFbJtxqsizzuc99jueff5433nijZAMJZP4v1tv79Y2455576O3tzTv2mc98ho0bN/LUU09dVyCBNRJKrldDQ0Pex2azGYDW1lbq6uoK0aRVcezYMY4dO8Ydd9yBw+FgaGiIL37xi7S2tq6rKsmNmJqa4u6776ahoYF//ud/Zn5+Pvecy+UqYMtW3tjYGF6vl7GxMdLpdG4fnra2ttzP/Hr3+c9/nk9+8pPs3r2bffv28Z3vfIexsbGinjMUCoUYGBjIfTw8PEx3dzdlZWWXvLcVi8cff5wf/OAHvPjii1gsltycIZvNhsFgKHDrVs4XvvAF7r//furr6wkGgzz33HO88cYb/Nd//Vehm7ZiLBbLJXOFFudA3tAcolu6FmiVDQ8Pl8SS4J6eHvnAgQNyWVmZrNPp5KamJvnRRx+VJyYmCt20FfPMM8/IwGVvxe6RRx657Hm//vrrhW7aLfUv//IvcmNjo6zVauWdO3cW/TLR119//bLf10ceeaTQTVsxV/odfuaZZwrdtBX1x3/8x7mf7YqKCvmee+6RX3311UI3a9XdzJLgNTGnRBAEQRAEYf0O0guCIAiCUFREKBEEQRAEYU0QoUQQBEEQhDVBhBJBEARBENYEEUoEQRAEQVgTRCgRBEEQBGFNEKFEEARBEIQ1QYQSQRAEQRDWBBFKBEEQBEFYE0QoEQRBEARhTRChRBAEQRCENeH/A32m0EKAuoNVAAAAAElFTkSuQmCC", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh)\n", @@ -1228,10 +1088,8 @@ }, { "cell_type": "markdown", - "id": "1d2adcea", - "metadata": { - "editable": true - }, + "id": "b3d4208f", + "metadata": {}, "source": [ "Find guesses" ] @@ -1239,11 +1097,8 @@ { "cell_type": "code", "execution_count": 3, - "id": "74ddc5e4", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "d7e4a182", + "metadata": {}, "outputs": [], "source": [ "x = guesses[-1]\n", @@ -1252,10 +1107,8 @@ }, { "cell_type": "markdown", - "id": "214c9dba", - "metadata": { - "editable": true - }, + "id": "fbc59d26", + "metadata": {}, "source": [ "Run it!" ] @@ -1263,12 +1116,17 @@ { "cell_type": "code", "execution_count": 4, - "id": "95c42263", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "18be8fa1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.69230769 -0.38461539]\n" + ] + } + ], "source": [ "def f1d(alpha):\n", " return f(x + alpha*s)\n", @@ -1281,10 +1139,8 @@ }, { "cell_type": "markdown", - "id": "92f9ab9e", - "metadata": { - "editable": true - }, + "id": "7f40f5f6", + "metadata": {}, "source": [ "What happened?" ] @@ -1292,12 +1148,30 @@ { "cell_type": "code", "execution_count": 5, - "id": "effee474", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "dbdb7d4e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "pt.axis(\"equal\")\n", "pt.contour(xmesh, ymesh, fmesh, 50)\n", @@ -1307,20 +1181,16 @@ }, { "cell_type": "markdown", - "id": "1c38b8fc", - "metadata": { - "editable": true - }, + "id": "851db164", + "metadata": {}, "source": [ "Note that we did only one iteration here. We can easily add more using our previous guesses." ] }, { "cell_type": "markdown", - "id": "6d5a203d", - "metadata": { - "editable": true - }, + "id": "f1300342", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -1331,10 +1201,8 @@ }, { "cell_type": "markdown", - "id": "786af0d8", - "metadata": { - "editable": true - }, + "id": "15530c95", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -1343,10 +1211,8 @@ }, { "cell_type": "markdown", - "id": "54ccbdaa", - "metadata": { - "editable": true - }, + "id": "35222dc4", + "metadata": {}, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -1354,10 +1220,8 @@ }, { "cell_type": "markdown", - "id": "5cbbbf34", - "metadata": { - "editable": true - }, + "id": "a5ab4e81", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -1366,10 +1230,8 @@ }, { "cell_type": "markdown", - "id": "14aad7a0", - "metadata": { - "editable": true - }, + "id": "922a54c4", + "metadata": {}, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$." @@ -1377,10 +1239,8 @@ }, { "cell_type": "markdown", - "id": "f4f89438", - "metadata": { - "editable": true - }, + "id": "606d1a71", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "An example is given by the eigenvectors of the matrix" @@ -1388,10 +1248,8 @@ }, { "cell_type": "markdown", - "id": "6d7ac1c8", - "metadata": { - "editable": true - }, + "id": "e46ac6fc", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -1400,20 +1258,16 @@ }, { "cell_type": "markdown", - "id": "eb177cc8", - "metadata": { - "editable": true - }, + "id": "aec2962a", + "metadata": {}, "source": [ "which is zero unless $i=j$." ] }, { "cell_type": "markdown", - "id": "ef75dbc7", - "metadata": { - "editable": true - }, + "id": "f62eeb16", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n", @@ -1422,10 +1276,8 @@ }, { "cell_type": "markdown", - "id": "07b865d4", - "metadata": { - "editable": true - }, + "id": "bde9cf46", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -1434,10 +1286,8 @@ }, { "cell_type": "markdown", - "id": "6112ebc5", - "metadata": { - "editable": true - }, + "id": "1b354afe", + "metadata": {}, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -1446,10 +1296,8 @@ }, { "cell_type": "markdown", - "id": "6bacd6db", - "metadata": { - "editable": true - }, + "id": "a3e7fc78", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -1458,10 +1306,8 @@ }, { "cell_type": "markdown", - "id": "b0193cce", - "metadata": { - "editable": true - }, + "id": "9608b5e1", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "The coefficients are given by" @@ -1469,10 +1315,8 @@ }, { "cell_type": "markdown", - "id": "b3fd5bdb", - "metadata": { - "editable": true - }, + "id": "d667abb4", + "metadata": {}, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -1481,20 +1325,16 @@ }, { "cell_type": "markdown", - "id": "232b00b2", - "metadata": { - "editable": true - }, + "id": "2b909963", + "metadata": {}, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "id": "9ed202e9", - "metadata": { - "editable": true - }, + "id": "0e9960df", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -1503,20 +1343,16 @@ }, { "cell_type": "markdown", - "id": "403b4e33", - "metadata": { - "editable": true - }, + "id": "4d334201", + "metadata": {}, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "id": "748fb2e9", - "metadata": { - "editable": true - }, + "id": "f06c6496", + "metadata": {}, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1525,10 +1361,8 @@ }, { "cell_type": "markdown", - "id": "730efe01", - "metadata": { - "editable": true - }, + "id": "69adaefe", + "metadata": {}, "source": [ "## Conjugate gradient method and iterations\n", "\n", @@ -1545,10 +1379,8 @@ }, { "cell_type": "markdown", - "id": "2c79b8e8", - "metadata": { - "editable": true - }, + "id": "35cf8e92", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1557,20 +1389,16 @@ }, { "cell_type": "markdown", - "id": "3d3935aa", - "metadata": { - "editable": true - }, + "id": "686fe37b", + "metadata": {}, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "id": "54cfaf35", - "metadata": { - "editable": true - }, + "id": "b6cdf1da", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1579,20 +1407,16 @@ }, { "cell_type": "markdown", - "id": "0043d35a", - "metadata": { - "editable": true - }, + "id": "f03df570", + "metadata": {}, "source": [ "instead." ] }, { "cell_type": "markdown", - "id": "8929fedc", - "metadata": { - "editable": true - }, + "id": "d2619eaa", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" @@ -1600,10 +1424,8 @@ }, { "cell_type": "markdown", - "id": "9311b95e", - "metadata": { - "editable": true - }, + "id": "7c99b348", + "metadata": {}, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1612,10 +1434,8 @@ }, { "cell_type": "markdown", - "id": "3f33016f", - "metadata": { - "editable": true - }, + "id": "06107635", + "metadata": {}, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1624,10 +1444,8 @@ }, { "cell_type": "markdown", - "id": "73cdd288", - "metadata": { - "editable": true - }, + "id": "7d57e70c", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1636,10 +1454,8 @@ }, { "cell_type": "markdown", - "id": "abd1a6ae", - "metadata": { - "editable": true - }, + "id": "d07728a4", + "metadata": {}, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1649,10 +1465,8 @@ }, { "cell_type": "markdown", - "id": "f2e4782d", - "metadata": { - "editable": true - }, + "id": "64a6011d", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "Let $\\boldsymbol{r}_k$ be the residual at the $k$-th step:" @@ -1660,10 +1474,8 @@ }, { "cell_type": "markdown", - "id": "9dfbf9d8", - "metadata": { - "editable": true - }, + "id": "395293fb", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1672,10 +1484,8 @@ }, { "cell_type": "markdown", - "id": "e36dedbd", - "metadata": { - "editable": true - }, + "id": "2742cfb7", + "metadata": {}, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1688,10 +1498,8 @@ }, { "cell_type": "markdown", - "id": "05ef1b6f", - "metadata": { - "editable": true - }, + "id": "6bca98e3", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1700,10 +1508,8 @@ }, { "cell_type": "markdown", - "id": "678cd3ca", - "metadata": { - "editable": true - }, + "id": "0b38ac3f", + "metadata": {}, "source": [ "## Conjugate gradient method\n", "We can also compute the residual iteratively as" @@ -1711,10 +1517,8 @@ }, { "cell_type": "markdown", - "id": "477780d2", - "metadata": { - "editable": true - }, + "id": "0588ed16", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1723,20 +1527,16 @@ }, { "cell_type": "markdown", - "id": "759aa071", - "metadata": { - "editable": true - }, + "id": "2f7bd339", + "metadata": {}, "source": [ "which equals" ] }, { "cell_type": "markdown", - "id": "6a8b8882", - "metadata": { - "editable": true - }, + "id": "5d46e7c8", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1745,20 +1545,16 @@ }, { "cell_type": "markdown", - "id": "9c18a422", - "metadata": { - "editable": true - }, + "id": "a6dfda96", + "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", - "id": "158fd52e", - "metadata": { - "editable": true - }, + "id": "bea30687", + "metadata": {}, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1767,20 +1563,16 @@ }, { "cell_type": "markdown", - "id": "09b0ced5", - "metadata": { - "editable": true - }, + "id": "ec002ff0", + "metadata": {}, "source": [ "which gives" ] }, { "cell_type": "markdown", - "id": "6cb853e2", - "metadata": { - "editable": true - }, + "id": "a45514a5", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1789,10 +1581,8 @@ }, { "cell_type": "markdown", - "id": "e62d7d23", - "metadata": { - "editable": true - }, + "id": "60756713", + "metadata": {}, "source": [ "## Revisiting our first homework\n", "\n", @@ -1813,11 +1603,8 @@ { "cell_type": "code", "execution_count": 6, - "id": "78275bb8", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "9e6108fd", + "metadata": {}, "outputs": [], "source": [ "m = 100\n", @@ -1827,10 +1614,8 @@ }, { "cell_type": "markdown", - "id": "090981ec", - "metadata": { - "editable": true - }, + "id": "146e4fe9", + "metadata": {}, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1838,10 +1623,8 @@ }, { "cell_type": "markdown", - "id": "42f3c46e", - "metadata": { - "editable": true - }, + "id": "c5c0a7f1", + "metadata": {}, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1850,20 +1633,16 @@ }, { "cell_type": "markdown", - "id": "d0636bc8", - "metadata": { - "editable": true - }, + "id": "f5f1aea6", + "metadata": {}, "source": [ "such that" ] }, { "cell_type": "markdown", - "id": "0cc4c910", - "metadata": { - "editable": true - }, + "id": "76b1993f", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1872,10 +1651,8 @@ }, { "cell_type": "markdown", - "id": "50b1a26d", - "metadata": { - "editable": true - }, + "id": "b5a211bb", + "metadata": {}, "source": [ "## Gradient descent example\n", "\n", @@ -1886,10 +1663,8 @@ }, { "cell_type": "markdown", - "id": "e565508f", - "metadata": { - "editable": true - }, + "id": "4b0b1b01", + "metadata": {}, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1902,20 +1677,16 @@ }, { "cell_type": "markdown", - "id": "70b56dd4", - "metadata": { - "editable": true - }, + "id": "c5751686", + "metadata": {}, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "id": "b38ad286", - "metadata": { - "editable": true - }, + "id": "a2d6f6a6", + "metadata": {}, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1924,20 +1695,16 @@ }, { "cell_type": "markdown", - "id": "00bf9bc8", - "metadata": { - "editable": true - }, + "id": "af74580d", + "metadata": {}, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized." ] }, { "cell_type": "markdown", - "id": "98291f1c", - "metadata": { - "editable": true - }, + "id": "949f8aab", + "metadata": {}, "source": [ "## The derivative of the cost/loss function\n", "\n", @@ -1946,10 +1713,8 @@ }, { "cell_type": "markdown", - "id": "9c310532", - "metadata": { - "editable": true - }, + "id": "5e3860a4", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1960,20 +1725,16 @@ }, { "cell_type": "markdown", - "id": "87fd4a33", - "metadata": { - "editable": true - }, + "id": "765febad", + "metadata": {}, "source": [ "where $X$ is the design matrix defined above." ] }, { "cell_type": "markdown", - "id": "c284f092", - "metadata": { - "editable": true - }, + "id": "65781e41", + "metadata": {}, "source": [ "## The Hessian matrix\n", "The Hessian matrix of $C(\\beta)$ is given by" @@ -1981,10 +1742,8 @@ }, { "cell_type": "markdown", - "id": "908fa0f6", - "metadata": { - "editable": true - }, + "id": "7e1e9714", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -1996,20 +1755,16 @@ }, { "cell_type": "markdown", - "id": "776049f2", - "metadata": { - "editable": true - }, + "id": "9d48eebb", + "metadata": {}, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite." ] }, { "cell_type": "markdown", - "id": "45876eb7", - "metadata": { - "editable": true - }, + "id": "fd88e7fd", + "metadata": {}, "source": [ "## Simple program\n", "\n", @@ -2018,10 +1773,8 @@ }, { "cell_type": "markdown", - "id": "e8e4d474", - "metadata": { - "editable": true - }, + "id": "e12fb5d1", + "metadata": {}, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -2030,10 +1783,8 @@ }, { "cell_type": "markdown", - "id": "2592690e", - "metadata": { - "editable": true - }, + "id": "eeb13498", + "metadata": {}, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -2045,10 +1796,8 @@ }, { "cell_type": "markdown", - "id": "46ea28e7", - "metadata": { - "editable": true - }, + "id": "7ffca923", + "metadata": {}, "source": [ "## Gradient Descent Example\n", "\n", @@ -2058,12 +1807,31 @@ { "cell_type": "code", "execution_count": 7, - "id": "ad7843c3", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9321710e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.30768763 4.39313488]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n", + "[[3.95814165]\n", + " [3.0184648 ]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "# Importing various packages\n", @@ -2115,10 +1883,8 @@ }, { "cell_type": "markdown", - "id": "383aacfa", - "metadata": { - "editable": true - }, + "id": "e65d5b5b", + "metadata": {}, "source": [ "## And a corresponding example using **scikit-learn**" ] @@ -2126,12 +1892,19 @@ { "cell_type": "code", "execution_count": 8, - "id": "db09e070", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "e73c4b82", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.94758046]\n", + " [2.92347862]]\n", + "[3.94453204] [2.94467121]\n" + ] + } + ], "source": [ "# Importing various packages\n", "from random import random, seed\n", @@ -2153,10 +1926,8 @@ }, { "cell_type": "markdown", - "id": "2b79dd09", - "metadata": { - "editable": true - }, + "id": "0cffa723", + "metadata": {}, "source": [ "## Gradient descent and Ridge\n", "\n", @@ -2165,10 +1936,8 @@ }, { "cell_type": "markdown", - "id": "1e62170f", - "metadata": { - "editable": true - }, + "id": "e70974bf", + "metadata": {}, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -2177,20 +1946,16 @@ }, { "cell_type": "markdown", - "id": "ea483c73", - "metadata": { - "editable": true - }, + "id": "8e2c0506", + "metadata": {}, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows" ] }, { "cell_type": "markdown", - "id": "dfca16fa", - "metadata": { - "editable": true - }, + "id": "673104d6", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -2201,20 +1966,16 @@ }, { "cell_type": "markdown", - "id": "eaa15bcc", - "metadata": { - "editable": true - }, + "id": "f5d61a03", + "metadata": {}, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "id": "5772c714", - "metadata": { - "editable": true - }, + "id": "7e9aec7d", + "metadata": {}, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -2223,10 +1984,8 @@ }, { "cell_type": "markdown", - "id": "b321aa3b", - "metadata": { - "editable": true - }, + "id": "54248fbe", + "metadata": {}, "source": [ "## The Hessian matrix for Ridge Regression\n", "The Hessian matrix of Ridge Regression for our simple example is given by" @@ -2234,10 +1993,8 @@ }, { "cell_type": "markdown", - "id": "ed4d25e3", - "metadata": { - "editable": true - }, + "id": "0b57c03b", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -2249,10 +2006,8 @@ }, { "cell_type": "markdown", - "id": "1ab1d1e5", - "metadata": { - "editable": true - }, + "id": "562d6a77", + "metadata": {}, "source": [ "This implies that the Hessian matrix is positive definite, hence the stationary point is a\n", "minimum.\n", @@ -2263,10 +2018,8 @@ }, { "cell_type": "markdown", - "id": "3f38965b", - "metadata": { - "editable": true - }, + "id": "018079a6", + "metadata": {}, "source": [ "## Program example for gradient descent with Ridge Regression" ] @@ -2274,12 +2027,31 @@ { "cell_type": "code", "execution_count": 9, - "id": "7342e5ed", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "12f965e7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eigenvalues of Hessian Matrix:[0.32374405 4.06221646]\n", + "[[4.0585026]\n", + " [2.9999519]]\n", + "[[4.05843037]\n", + " [3.00001709]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from random import random, seed\n", "import numpy as np\n", @@ -2335,10 +2107,8 @@ }, { "cell_type": "markdown", - "id": "f189af87", - "metadata": { - "editable": true - }, + "id": "06107436", + "metadata": {}, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -2357,10 +2127,8 @@ }, { "cell_type": "markdown", - "id": "f49c05f9", - "metadata": { - "editable": true - }, + "id": "bd3205c7", + "metadata": {}, "source": [ "## Improving gradient descent with momentum\n", "\n", @@ -2370,12 +2138,56 @@ { "cell_type": "code", "execution_count": 10, - "id": "9fef300b", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "98ec014e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.59779819]) = 0.35736\n", + ">2 f([0.47823856]) = 0.22871\n", + ">3 f([0.38259084]) = 0.14638\n", + ">4 f([0.30607268]) = 0.09368\n", + ">5 f([0.24485814]) = 0.05996\n", + ">6 f([0.19588651]) = 0.03837\n", + ">7 f([0.15670921]) = 0.02456\n", + ">8 f([0.12536737]) = 0.01572\n", + ">9 f([0.10029389]) = 0.01006\n", + ">10 f([0.08023512]) = 0.00644\n", + ">11 f([0.06418809]) = 0.00412\n", + ">12 f([0.05135047]) = 0.00264\n", + ">13 f([0.04108038]) = 0.00169\n", + ">14 f([0.0328643]) = 0.00108\n", + ">15 f([0.02629144]) = 0.00069\n", + ">16 f([0.02103315]) = 0.00044\n", + ">17 f([0.01682652]) = 0.00028\n", + ">18 f([0.01346122]) = 0.00018\n", + ">19 f([0.01076897]) = 0.00012\n", + ">20 f([0.00861518]) = 0.00007\n", + ">21 f([0.00689214]) = 0.00005\n", + ">22 f([0.00551372]) = 0.00003\n", + ">23 f([0.00441097]) = 0.00002\n", + ">24 f([0.00352878]) = 0.00001\n", + ">25 f([0.00282302]) = 0.00001\n", + ">26 f([0.00225842]) = 0.00001\n", + ">27 f([0.00180673]) = 0.00000\n", + ">28 f([0.00144539]) = 0.00000\n", + ">29 f([0.00115631]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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/P78Kr7Gzs4OdnZ050SxSsKcTejR3x57zl/HDvgRMH9xadiQiIrISQgis/tc4sv7ArU1tbm2Rq5k1MqLT6RAaGorIyMhy2yMjI9GrV69KX5OXlweVqvy3UauNjzwWQpjz7a3Sg6XDamv2J0BvsP3jJSKi2nH0QiZOJGdBp1Hhnq6284Teyph9mWbGjBlYunQpli9fjujoaEyfPh3x8fGmyy6zZs3CuHHjTPsPHz4c69atw+LFi3H+/Hns3LkTzzzzDLp16wZ/f9ucFXy1Ie194eaoRVJmAf45fUl2HCIishJlE1eHhfjCzVEnOU3dMusyDQCMGTMG6enpmD9/PpKTkxESEoKNGzciKCgIAJCcnFxuzZEJEyYgOzsbn376KZ577jm4ublh4MCBeOedd2rvKCyYvVaNu7s0wVc7Y7F6bzwGtPWWHYmIiCxcbmEJNpSu4l02/9CWKcIKrpVkZWXB1dUVmZmZcHFxkR3HbKcvZiP8w3+gVinYPXMgvF3sZUciIiILFrEvHi+tPYpgTyf8/Vw/q50vUt33bz6bph609nFG16Zu0BsE1kQlyo5DREQWruwSzZhbA622iJiDZaSelN0fHrEvAQZOZCUioiqcTMnCoYQMaFQK7u0aIDtOvWAZqSd3dfSDs50G8ZfzsPu87T4kkIiIbs73paMig2/xgZez9S9zUR0sI/XEUafBiNJnCqzmiqxERFSJgmI91h0wXs635RVXr8UyUo/K1hz54/hFXM4tkpyGiIgsze/HkpFVUIImbg7o29JTdpx6wzJSj0KauCKkiQuK9AZT8yUiIipz9cRVlcr2J66WYRmpZ2X3i6/eG98gVqAlIqLqOXcpB3tjLkOlAPeHNYyJq2VYRurZyM7+cNCqce5SLvbHXZEdh4iILETEPuOoyIA23vBzdZCcpn6xjNQzZ3st7upofDggJ7ISEREAFJUYsDaq4U1cLcMyIkHZD9rGo8nIzC+WnIaIiGSLPHER6blF8HGxw4A2XrLj1DuWEQm6NnVDGx9nFBQbsL702QNERNRwfb/POFJ+f2ggNOqG99bc8I7YAiiKgge6BQIwzpzmRFYiooYr4XIetp9JA2C8i6YhYhmR5O4uTaDTqBCdnIUjiZmy4xARkSRlE1f7tvJEoLuj5DRysIxI4uaowx0hvgD+G54jIqKGpURvwJooYxkpW/qhIWIZkahsIuuGQ0nILSyRnIaIiOrbllOXcDGrEB5OOgy+xUd2HGlYRiTqHuyO5p5OyC3S45fDSbLjEBFRPfu+dImHe0MDoNM03LfkhnvkFkBRFNNkJa45QkTUsCRn5mPLqVQADXfiahmWEcnuDQ2AVq3gcGImTiRlyY5DRET15Id9iTAIoFuwO1p4NZIdRyqWEck8G9mZrhNyIisRUcOgNwj8sN84cfXBbg17VARgGbEIZTOofzp4AflFeslpiIiorm0/cwkXMvLhYq/BsBA/2XGkYxmxAH1aeiKgsQOyC0qw8Wiy7DhERFTHvt9rHBW5p2sA7LVqyWnkYxmxACqVgjFhxmE6XqohIrJtl7IL8Wf0RQAwrcbd0LGMWIj7wwKhUoB9sVdwNjVbdhwiIqojP0YlosQg0KWpG9r6usiOYxFYRiyEr6s9Brb1BvDf8B0REdkWIQQiSkfAH2zAK65ei2XEgpRNZF17IBGFJZzISkRka3afT0dseh4a2WlwVydOXC3DMmJB+rfxgo+LHa7kFeOP4xdlxyEiolpWNvI9orM/HHUayWksB8uIBdGoVRjNiaxERDbpSm4RNh1LAcBLNNdiGbEwo8MCoSjAzrPpiEvPlR2HiIhqybqDF1CkN6C9vws6BLjKjmNRWEYsTKC7I/q09AQAROzjRFYiIlsghDA9FK/sie30H5YRC/Rg6Q/qmqhEFOsNktMQEdHNOhB/BWdSc+CgVWNkZ3/ZcSwOy4gFGtTOBx5OOlzKLsTfJ1NlxyEiopu0unTi6p0d/eBir5WcxvKwjFggnUaF+8ICAMA0rEdERNYpq6AYvx5JAsCH4lWFZcRCla05su30JSRl5EtOQ0RENbX+UBIKig1o5d0IXZs2lh3HIrGMWKhgTyf0aO4Og4DpMdNERGR9rp64qiiK5DSWiWXEgpVNZP1hXwL0BiE5DRERmetoYiaOJ2VBp1bhni5NZMexWCwjFmxIe1+4OWqRlFmAf85ckh2HiIjMtLp0AcuhIb5o7KSTnMZysYxYMHutGneXNmlOZCUisi65hSXYcMg4cfUBTly9LpYRC1d2qebP6FSkZhVITkNERNX165Ek5BSWoJmHI3o295Adx6KxjFi41j7O6NrUDXqDwJqoRNlxiIiomsrWFhlzKyeu3gjLiBUoWzo4Yl8CDJzISkRk8U6mZOFQQgY0KgX3hQbIjmPxWEaswF0d/eBsp0H85TzsPp8uOw4REd3A96WjIoPa+cDL2U5yGsvHMmIFHHUajCh9lsFqTmQlIrJoBcV6rDtgvKzOiavVwzJiJcomsv5x/CIu5xZJTkNERFX5/VgysgpK0MTNAX1becmOYxVYRqxESBNXhDRxQZHeYGrcRERkecomro4OC4RaxYmr1cEyYkXKnlezem88hOBEViIiS3PuUg72xlyGSgFG38qJq9XFMmJFRnb2h4NWjXOXcrE/7orsOEREdI2IfcZRkf5tvOHn6iA5jfVgGbEizvZaDO/kBwD4Znec5DRERHS1/CI91pQ+2PSBWzlx1RwsI1ZmfK9mAICNR5NxISNfbhgiIjL58UAiruQVI9DdAbe385Edx6qwjFiZ9v6u6NXCA3qDwIqdMbLjEBERAINBYPkO47/Jj/UO5sRVM7GMWKFJfYMBGBfVyS4olpyGiIj+OpmKmLRcONtrcH8YL9GYi2XECvVv7Y0WXk7ILiwxTZYiIiJ5lm4/DwB4qHtTNLLTSE5jfVhGrJBKpWBin+YAgK92xqJEb5CciIio4TqamIl/Yy5Do1IwoXReH5mHZcRK3dO1CTycdLiQkY9Nx1NkxyEiarCW7jCOitzV0Y+389YQy4iVsteq8UiPIADAl9tjuAgaEZEESRn5+PVIMgBgUt/mktNYL5YRKza2ZxB0GhUOJ2QgiougERHVu693xUJvEOjR3B0hTVxlx7FaLCNWzLORHe7p0gQA8GXp5CkiIqofOYUlWFX6JPXJHBW5KTUqI4sWLUJwcDDs7e0RGhqK7du3X3f/wsJCzJ49G0FBQbCzs0OLFi2wfPnyGgWm8ib2Md7m+8eJi4hLz5Wchoio4fhhXwKyC0rQ3MsJA9p4y45j1cwuIxEREXj22Wcxe/ZsHDx4EH379sWwYcMQHx9f5WtGjx6Nv/76C8uWLcOpU6ewevVqtG3b9qaCk1ErH2f0b+MFIWBacIeIiOpWid6A5aULT07sEwwVFzm7KYowc+Zj9+7d0bVrVyxevNi0rV27dhg1ahQWLFhQYf9NmzbhgQcewPnz5+Hu7l6jkFlZWXB1dUVmZiZcXFxq9DVs2Y4zaXhk2b9w0KqxZ9btcHXUyo5ERGTTNh5Nxv9WHkBjRy12zbwdDjq17EgWqbrv32aNjBQVFSEqKgrh4eHltoeHh2PXrl2VvmbDhg0ICwvD//3f/6FJkyZo3bo1nn/+eeTnV/1clcLCQmRlZZX7oKr1bumBtr7OyC/WY+VePkCPiKiulc3TG9sjiEWkFphVRtLS0qDX6+HjU/4BQD4+PkhJqXyti/Pnz2PHjh04duwYfvrpJyxcuBA//vgjnnzyySq/z4IFC+Dq6mr6CAzk0rrXoyiK6Zayr3fFoqiEi6AREdWVqLgrOBifAZ1ahUd6BsmOYxNqNIFVUcpfGxNCVNhWxmAwQFEUrFy5Et26dcMdd9yBDz74ACtWrKhydGTWrFnIzMw0fSQkcMnzGxnRyR/ezna4mFWIX48kyY5DRGSzypZ+H9XFH97O9pLT2AazyoinpyfUanWFUZDU1NQKoyVl/Pz80KRJE7i6/nf/dbt27SCEQGJiYqWvsbOzg4uLS7kPuj6dRoXxpcsQL+UiaEREdSI+PQ+bS1e9LnssB908s8qITqdDaGgoIiMjy22PjIxEr169Kn1N7969kZSUhJycHNO206dPQ6VSISAgoAaRqSoPd28KB60aJ5KzsPtcuuw4REQ2Z/nOGBgEcFtrL7TxdZYdx2aYfZlmxowZWLp0KZYvX47o6GhMnz4d8fHxmDp1KgDjJZZx48aZ9n/ooYfg4eGBRx99FCdOnMA///yDF154AY899hgcHLiGf21yc9ThvlBjwVvK23yJiGpVZn4xfthvnDYwqXSNJ6odZj/neMyYMUhPT8f8+fORnJyMkJAQbNy4EUFBxkk8ycnJ5dYcadSoESIjI/H0008jLCwMHh4eGD16NN54443aOwoyeaxPML77Nw5/n0zF2dRstPRmcyciqg2r98Yjr0iPNj7O6NvKU3Ycm2L2OiMycJ0R80z+Zj8iT1zEg92aYsE9HWTHISKyesV6A/q+swUpWQX4v/s6YnQY7/KsjjpZZ4SsQ9kzEtYdSER6TqHkNERE1u+3I8lIySqAZyM7jOzsLzuOzWEZsUG3NmuMjgGuKCwx4Ls9VS/TT0RENyaEwNIdxtt5x/cMgp2Gi5zVNpYRG3T1Imjf7olFQbFeciIiIuu15/xlHLuQBXutCg/34CJndYFlxEYNC/GFv6s90nKKsP7QBdlxiIis1rLSUZF7uwbA3UknOY1tYhmxUVq1Co/2Nt56xkXQiIhqJvbwKeRu+hO+WWmYyNt56wzLiA0b0y0Qjew0OJOag22nL8mOQ0RkXZYtQ9Mu7bD6+5ex6/PH0HxDhOxENotlxIa52Gsx5lbj7WdLt3MRNCKiaktMhHj8cahKR5VVwgBMmQJU8RgTujksIzZuQq9mUCnAjrNpiE7Okh2HiMg6nDkDxXDNE9D1euDsWTl5bBzLiI0LdHfEsA5+ADg6QkRUXQXNmqPCTDu1GmjZUkYcm8cy0gCUPUNhw+ELSM0qkJyGiMjybf33DJSrN6jVwJIlAB/wWidYRhqALk0bIyyoMYr1Al/vjpUdh4jIogkh4Pj2mwCA2B79gS1bgNhYYOJEqblsGctIA1G2CNrKf+ORV1QiOQ0RkeWK+m07+hzeBgDw+Ph9oH9/jojUMZaRBmLwLT4I8nBERl4x1kZxNjgRUVVK5s2HCgLHe4XD+dausuM0CCwjDYRapeCx0kXQlu2IgcHARdCIiK4Vs/VfdNv/NwDA453XJadpOFhGGpD7QgPgYq9BbHoe/oy+KDsOEZHFyXx5DlQQONDtdvj26SY7ToPBMtKAONlpTA954m2+RETlpe89gI67IwEA9q/Pk5ymYWEZaWDG92wGjUrB3tjLOJyQITsOEZHFuPTiq1BBYHfn/rglvLfsOA0Ky0gD4+tqjxGd/AEAS3dwdISICAAKDh9F639+BwDoX3lFcpqGh2WkAZrY1ziRdePRZFzIyJechohIvpQXZkMlBLaG9EXPuwfKjtPgsIw0QO39XdGrhQf0BoEVOzk6QkQNm+HYcTT981cAQMZzM6FWKTd4BdU2lpEGalLp6Mj3exOQXVAsOQ0RkTypL74ClRCIbNcbgx4Mlx2nQWIZaaD6t/ZGCy8nZBeWIGJfguw4RERyREfDe9N6AED8k8+hkZ1GcqCGiWWkgVKpFEzsY1wi/qudsSjRG27wCiIi25Mxaw5UQmBz656445GhsuM0WCwjDdg9XZvA3UmHCxn52HQ8RXYcIqL6FR0Nlw1rAQBHHn0Gfq4OkgM1XCwjDZi9Vo1HShdB+3J7DITgEvFE1HDkvToXKiGwqXVPDBs7THacBo1lpIEb2yMIOo0KhxMyEBV3RXYcIqL6cfIkHNatAQBsGT0FIU1cJQdq2FhGGjgvZzvc3bkJAC4RT0QNR/HceVCEwOZWPTD4Qc4VkY1lhEyLoG0+kYK49FzJaYiI6tjJk9D8EAEAWHvnYxjY1ltyIGIZIbT2cUa/1l4QwnhnDRGRLTO8/oZpVOS2MeFQcZEz6VhGCAAwua/xNt8f9icgPadQchoiojpy8iSU71cDAL66fSzu7RogORABLCNUqndLD4Q0cUFekR5L/jkvOw4RUZ0wvP46FIMBf7TqgR73DoKDTi07EoFlhEopioLnBrcBAHy9KxapWQWSExER1bJTp6B8/z0AYNntYzGxT7DkQFSGZYRM+rfxQmhQYxSWGPDZlrOy4xAR1aqyUZHIlt0x4IEhcLbXyo5EpVhGyERRFDwX3hoAsGpvPBKv5ElORERUS06dAlYb54qsGDwe43oGSQ5EV2MZoXJ6tfBErxYeKNYLfPo3R0eIyDbo578OVemoyKCHh8JRxwfiWRKWEaqgbHRkTVQiYtO47ggRWbnTp0130Hw3ZAIe7NZUciC6FssIVRAa5I4BbbygNwgs/PO07DhERDelZP780lGRbhgy9g7Ya3kHjaVhGaFKzSi9s2b94SScvpgtOQ0RUQ2dPg1V6VyRiGGP4f4writiiVhGqFIdAlwxtL0vhAA+jOToCBFZpyLTXJFuGDb+TmjVfNuzRDwrVKUZ4a2hKMDvx1Jw7EKm7DhEROY5cwaa1asAAGvvegyjujSRHIiqwjJCVWrt44yRnfwBAB9wdISIrEzhXONckT9b3Irhj46Ams+gsVgsI3Rd0wa1hlql4O+TqYiKuyI7DhFR9Zw5A+33xlGRDSMnY1iIr+RAdD0sI3RdwZ5OuK/0QVIfRJ6SnIaIqHoKrhoVGTFxBJ/Ma+FYRuiGnr69JbRqBTvPpmPXuTTZcYiIru/sWehK1xX5/Z4puL2dt+RAdCMsI3RDAY0dTYsEvf/HaQghJCciIqpa3px5UBn0+KvFrRg1eQQUhaMilo5lhKrlyQEtYadRISruCraeviQ7DhFR5c6ehV2EcVTkr/unoE9LT8mBqDpYRqhafFzsTQ+Wev+PUxwdISKLlDNnHtQGPf5uHoZRj9/NURErwTJC1Ta1Xws46dQ4diELm49flB2HiKi8s2fhUDoq8s+D/0O3YHfJgai6WEao2jwa2eGxPsEAjHfW6A0cHSEiy5H16lzTqMjdU+6WHYfMwDJCZpnUtzlc7DU4fTEHvx5Jkh2HiMjo3Dk4/fA9AGD3I0+hU6Cb3DxkFpYRMourgxaP39YcALDwzzMo0RskJyIiAjJmG0dFtjQPxT1TOSpibVhGyGwTegfD3UmHmLRcrDtwQXYcImrozp2D8xrjXJH9459GOz8XyYHIXCwjZLZGdho80a8FAOCjv86gsEQvORERNWTppaMiW5uH4p4n7pUdh2qAZYRq5JEeQfB2tsOFjHz8sC9BdhwiaqjOn4db6ajIkYnPooVXI8mBqCZYRqhGHHRqPDWwJQDgk7/PoqCYoyNEVP9SZ86B2qDHtuahuHvqPbLjUA2xjFCNjbk1EE3cHJCaXYjv9sTJjkNEDYw4dw4ea4130ERPfhaB7o6SE1FN1aiMLFq0CMHBwbC3t0doaCi2b99erdft3LkTGo0GnTt3rsm3JQtjp1Fj2u2tAACLtp5DbmGJ5ERE1JBcnPka1AY9/mkeipGcK2LVzC4jERERePbZZzF79mwcPHgQffv2xbBhwxAfH3/d12VmZmLcuHG4/fbbaxyWLM89XZugmYcjLucWYcWuWNlxiKiBEOfOwXOdcVTkzNTn4OfqIDkR3Qyzy8gHH3yAiRMnYtKkSWjXrh0WLlyIwMBALF68+LqvmzJlCh566CH07NmzxmHJ8mjUKkwf3BoAsGTbOWTmF0tOREQNQdJLc6Ax6LG9eShGcK6I1TOrjBQVFSEqKgrh4eHltoeHh2PXrl1Vvu6rr77CuXPn8Nprr1Xr+xQWFiIrK6vcB1muuzr6o7VPI2QVlGDp9vOy4xCRjTOcOw+fnyIAAHFPPQcvZzvJiehmmVVG0tLSoNfr4ePjU267j48PUlJSKn3NmTNnMHPmTKxcuRIajaZa32fBggVwdXU1fQQGBpoTk+qZWqVgRunoyPIdMUjPKZSciIhsWeKLr0Jj0GNn8664awrnitiCGk1gvfaRzEKISh/TrNfr8dBDD2HevHlo3bp1tb/+rFmzkJmZafpISOA6FpZuSHtftPd3QW6RHkv+4egIEdWNknPn4f+zcVTkwjMvws1RJzkR1QazyoinpyfUanWFUZDU1NQKoyUAkJ2djf379+Opp56CRqOBRqPB/PnzcfjwYWg0Gvz999+Vfh87Ozu4uLiU+yDLpigKng9vAwD4elcsUrMKJCciIluU8IJxVGRXi1AMm8K5IrbCrDKi0+kQGhqKyMjIctsjIyPRq1evCvu7uLjg6NGjOHTokOlj6tSpaNOmDQ4dOoTu3bvfXHqyKP3beKFrUzcUlhjw2ZazsuMQkY0pPncegeuNoyIXp78EZ3ut5ERUW6o3ieMqM2bMwNixYxEWFoaePXviiy++QHx8PKZOnQrAeInlwoUL+Oabb6BSqRASElLu9d7e3rC3t6+wnayfoih4fkgbPPTlv1i1Nx6Tb2uOgMZchIiIakfcc6+gpUGPPS26YshkPpnXlphdRsaMGYP09HTMnz8fycnJCAkJwcaNGxEUFAQASE5OvuGaI2S7erXwRK8WHth1Lh2f/HUW79zXUXYkIrIBhWfOodkvPwAALj83E446s9++yIIpQgghO8SNZGVlwdXVFZmZmZw/YgWi4i7j3sW7oVYp+HNGPwR7OsmORERW7uTIh9B2w2rsbRmKTtH/wk6jlh2JqqG67998Ng3VutAgdwxo4wW9QeCjP0/LjkNEVi7/zDm0/NU4KpL54iwWERvEMkJ1YsZg45016w8n4fTFbMlpiMianZ/xCjQGPfa1DEX/xzhXxBaxjFCd6BDgiqHtfSEE8GEkR0eIqGayT51F640/AgDyZr4MrZpvW7aIZ5XqzIzw1lAU4PdjKTh2IVN2HCKyQjHPvQKtoQRRrULR51GOitgqlhGqM619nDGykz8A4AOOjhCRmbK2bMctG9cAAApffgVqVcWVvsk2sIxQnZo2qDXUKgV/n0xFVNwV2XGIyFosWwbngbdBIwwQAHoUp8lORHWIZYTqVLCnE+7rGgAAeP3XEzAYLP5OciKSLTER4vHHUTYOogBQPTEVSEyUmYrqEMsI1bnpg1vDSafGoYQMROznQw+J6PrE6dNQDIbyG/V64CwfM2GrWEaozvm62mP6YONTm9/+/STScwolJyIiS3Z097GKG9VqoGXL+g9D9YJlhOrFhF7N0NbXGZn5xXhn00nZcYjIQuVdyYTXe28BAIRSeqFGrQaWLAECAiQmo7rEMkL1QqNW4c27jQ9H/GF/IvbHXpaciIgs0ZHHn4NfxkWkuHmj4MhxYMsWIDYWmDhRdjSqQywjVG9Cg9wxJiwQAPDKz8dQojfc4BVE1JDEbdmNsLVfAQBS3noPDiHtgP79OSLSALCMUL16aVhbuDlqcTIlGyt2xcqOQ0QWQuj1KJw4GRphQFTYQHR+YqzsSFSPWEaoXrk76TBzaFsAxmXikzPzJSciIktw6NX/Q+uY48jROcBvxRLZcaiesYxQvRsdFoiuTd2QW6THG79Gy45DRJJlnYtHyw/fBAAcnPI8/NvzrpmGhmWE6p1KpeCNUR2gUoDfjiZj2+lLsiMRkURxE6bAuSAXpwLboPu7r8qOQxKwjJAUt/i7YEKvYADAa+uPoaBYLzkREclw/tsf0WHHJugVFQo/WQSdnVZ2JJKAZYSkmT64Fbyd7RCbnocl287LjkNE9UyfkwvH6c8AALYPexAdRw6UnIhkYRkhaZzttXj1rlsAAJ9tPYu49FzJiYioPkX/7wX4picjxcUT7ZculB2HJGIZIanu6uiHPi09UVRiwJz1xyEEH6RH1BBc/vcA2qz8AgAQ/fKb8PLzlJyIZGIZIakURcH8ke2hU6uw7fQlbDqWIjsSEdU1gwGZ4x6D1qDH7o59cdsLk2UnIslYRki65l6NMLVfcwDAvF9OIKewRHIiIqpL5xcsRPDpw8jROcDli0VQqxTZkUgylhGyCP8b0BKB7g5IySrAx3+dkR2HiOpI0YVkeL35GgBg28NPoX33EMmJyBKwjJBFsNeqMX+E8R+lZTticColW3IiIqoLcROmwjk/B9F+LdFn4TzZcchCsIyQxRjQ1htD2vtAbxB45eejnMxKZGPSfvoVrf7cAL2iQtI7C+Hq4iA7ElkIlhGyKHOGt4eDVo19sVew9sAF2XGIqLbk58Mw9QkAwOb+92LgI3dIDkSWhGWELEoTNwdMG9QKAPDWxmhk5BVJTkREtSF2+svwTk1EirMHWi35EIrCSav0H5YRsjgT+wSjlXcjXM4twv9tPiU7DhHdpILDR9Fk6acAgJ1Pz0GrVk0kJyJLwzJCFkerVuGNUcbJrKv3xuNg/BXJiYioxgwGpD38KLT6Emxv2xNDX31CdiKyQCwjZJG6N/fAPV2bQAjglZ+PQW/gZFYia5T68WIEHI9CrtYe+o8/gpM9H4RHFbGMkMWaNawdXOw1OJ6Uhe/2xMmOQ0RmEhcvwnH2ywCAX+5+HP0GhUlORJaKZYQslpezHV4Y2hYA8N7mU0jNLpCciIjMkTjpSTTKy0K0d3P0+vh1TlqlKrGMkEV7qFtTdAxwRXZhCd76LVp2HCKqprzfNyPw17UwQMGROe+gqY+L7EhkwVhGyKKpVQreHNUBigL8fCgJu86myY5ERDdSUID8SVMAAOt7jcTIx++WHIgsHcsIWbwOAa4Y2yMIAPDK+mMoKjFITkRE15P68mvwSIrDxUbu8P74Pdhr1bIjkYVjGSGr8Fx4G3g20uH8pVx8uf287DhEVAXDiWg0/vgDAMAvj72I3qEtJCcia8AyQlbB1UGL2Xe2AwB88vcZJFzOk5yIiCoQAmljH4NWX4JtLW/FXfOekZ2IrATLCFmNUZ2boHuwOwqKDZj3ywnZcYjoGjlfLIP3gT3I19gh+c334OvGB+FR9bCMkNVQFAVvjAqBRqXgz+iLiDxxUXYkIiqTlgblhRcAACuHTsB99/aRHIisCcsIWZVWPs6YfFtzAMDcDceRV1QiORERAUDaE8/AKTsD0V7N0OXDedCo+fZC1cefFrI6Tw9siSZuDriQkY9P/z4rOw5Rg6f/6294/rgaBij4e9p8hLb0kR2JrAzLCFkdR50Grw2/BQDw5fbzOJuaLTkRUQNWWIjsRycBAH4MuwMPPjtGciCyRiwjZJUG3+KD29t6o1gv8OrPxyEEH6RHJEP2vDfhlhCDS05uUL+9AO5OOtmRyAqxjJBVUhQFc0e0h51Ghd3n0/HVzljZkYgaHP3JU7B/920AwNdjpuPuASGSE5G1YhkhqxXo7oiX7zCuPbLg92gcTsiQG4ioIRECSQ9NgLakGNubh2LUW89CpeKD8KhmWEbIqo3rGYSh7X1RrBd4avUBZOYXy45E1CCc/eBzBB7cgwKNDrkffISWfBAe3QSWEbJqiqLgnfs6ItDdAQmX8zFz7RHOHyGqY+lxSfCYMwsA8NfoqRg6srfkRGTtWEbI6rk6aPHpg12hVSv4/VgKvt0TJzsSkc0yGASOPTIVjfMyEePbDAO+eFt2JLIBLCNkEzoFumHmMOP8kTd+jcaxC5mSExHZps3zP0W/Hb8AANRffAFHJy75TjePZYRsxmO9m2FQOx8U6Q14ctUBZBdw/ghRbYp9830MLX34nQDQNDVebiCyGSwjZDMURcF793dEEzcHxKXnYda6o5w/QlRLrpw+j6BXnkfZ/TIKAEyZAiQmSkxFtoJlhGyKm6MOHz/YBRqVgl+PJGP13gTZkYisnsEg8M8Lb6HCjbt6PXCWj2Sgm8cyQjYnNKgxXhjSBgAw75fjiE7OkpyIyLr9+N1mDN74XcVPqNVAy5b1H4hsDssI2aTJfZtjQBsvFJYY54/kFvLpvkQ1ceh4HEKnT4ZjSSEyg1oYCwhg/HPJEiAgQG5AsgksI2STVCoF74/uDF8Xe5y/lItXfj7G+SNEZsrILcSVB8aixeVEXHH3gcu/O4HYWGDLFuOfEyfKjkg2gmWEbJa7kw6fPNQFapWCnw5ewJr9nGhHVF1CCPwx8UUMOLYdxWoNdD+theLjYxwJ6d+fIyJUq2pURhYtWoTg4GDY29sjNDQU27dvr3LfdevWYfDgwfDy8oKLiwt69uyJzZs31zgwkTlubeaOGYNbAwDmbDiG0xezJScisg4bP/0e9/7wKQDg0uvvwOk2rrJKdcfsMhIREYFnn30Ws2fPxsGDB9G3b18MGzYM8fGV32/+zz//YPDgwdi4cSOioqIwYMAADB8+HAcPHrzp8ETV8US/FujbyhMFxQY8ufIA8oo4f4Toeo7vO4HuM/8HtTDg3NC74T9zuuxIZOMUYeaF9O7du6Nr165YvHixaVu7du0watQoLFiwoFpfo3379hgzZgzmzJlTrf2zsrLg6uqKzMxMuLjwYUxkvrScQtzx0XakZhfi/tAAvHt/J9mRiCxSZmYu4jt2Q4f4E0gMbIUm0QehODnJjkVWqrrv32aNjBQVFSEqKgrh4eHltoeHh2PXrl3V+hoGgwHZ2dlwd3evcp/CwkJkZWWV+yC6GZ6N7PDRA12gUoA1UYlYd4DzR4iuJYTAgfsnokP8CWTbO8H19w0sIlQvzCojaWlp0Ov18PHxKbfdx8cHKSkp1foa77//PnJzczF69Ogq91mwYAFcXV1NH4GBgebEJKpUzxYemHa7cf7IKz8fw9nUHMmJiCzLjnkfYUBkBAAg7bMv4dy+reRE1FDUaAKropRfh08IUWFbZVavXo25c+ciIiIC3t7eVe43a9YsZGZmmj4SEriKJtWOpwa2RK8WHsgr0uOpVQdQUKyXHYnIIpz5cxdC35oJADg07kkEP/ag5ETUkJhVRjw9PaFWqyuMgqSmplYYLblWREQEJk6ciB9++AGDBg267r52dnZwcXEp90FUG9QqBQsf6AzPRnY4mZKNeb8clx2JSLrsi2lweGA0HIsLcbx9d3RatlB2JGpgzCojOp0OoaGhiIyMLLc9MjISvXr1qvJ1q1evxoQJE7Bq1SrceeedNUtKVEu8ne3x0QOdoSjA6r0JWH/oguxIRNIIvR7n77wPAekXkOLmjYCN66BoNLJjUQNj9mWaGTNmYOnSpVi+fDmio6Mxffp0xMfHY+rUqQCMl1jGjRtn2n/16tUYN24c3n//ffTo0QMpKSlISUlBZmZm7R0FkZl6t/TE0wOMz9R4ed1RxKTlSk5EJMfhZ2ajU9Q2FKk1yPhmFVyb+suORA2Q2WVkzJgxWLhwIebPn4/OnTvjn3/+wcaNGxEUFAQASE5OLrfmyJIlS1BSUoInn3wSfn5+po9p06bV3lEQ1cC0Qa3RPdgduUV6PLmS80eo4Yn7YQM6LH4XALDn2bloO/x2yYmooTJ7nREZuM4I1ZWLWQUY9tF2XM4twtgeQXh9VIjsSET1Iu9sDIo6d4Fbbia29xmO3lt/hkrNJ4RQ7aqTdUaIbI2Piz0+GG1cAO3bPXHYeDRZciKiuicKCpA6bCTccjNxyq8l2v/0LYsIScWfPmrw+rfxxhP9WwAAXvrxCOLSOX+EbNu5Rx5Hs7NHkWHfCIXfR8Dd01V2JGrgWEaIADw3uDXCghoju7AET606iMISzh8h25T8yRK0XPstDFCwY86H6HhbV9mRiFhGiABAo1bh4we7wM1Ri6MXMrFg40nZkYhqXf6+/XCf8QwAYP2IibjjpYmSExEZsYwQlfJ3czDNH1mxKxabj1fvEQdEVuHKFeQNvxt2JUXY1epW9P32Y6hUN145m6g+sIwQXWVgWx88fltzAMALaw4j4XKe5EREtcBgQPLI0fC4mIgEVx9ov18FTxcH2amITFhGiK7xwpA26NLUDVkFJZj49T5cyS2SHYnopiQ8/wr8tv+JQrUWO97+HLd2bSk7ElE5LCNE19CqVfj0oa7wcbHD6Ys5GLv8X2TmF8uORVQjZ75biyYfvg0AWDX+JYx+fKTkREQVsYwQVaKJmwNWTuoBDycdjl3IwqNf7UVuYYnsWETVl5iI+EXL4D15PFQQ2NJ3BB78fC7UnCdCFohlhKgKLb0b4duJ3eHqoMWB+AxM+no/l4wn67BsGURQEJo+OQmuBblIdfdB919Xwl6rlp2MqFIsI0TXcYu/C75+rBsa2Wmw+3w6pn4XxTVIyLIlJkI8/jgUg8G0ySvjEhyzMuRlIroBlhGiG+gc6IblE26FvVaFracuYdrqQyjRG278QiIJLkUdKVdEABj/fvaspEREN8YyQlQN3YLd8eW4MOjUKmw6noLn1hyG3mDxz5ikBuZiZj62v72k4ifUaqAl76Ahy8UyQlRNfVt5YdHDXaFRKVh/KAmzfzoKK3joNTUQ6TmF2Hz/E7hnzwYAgFBKJ6qq1cCSJUBAgMR0RNfHMkJkhkG3+OCjB7pApQDf70vAvF9OsJCQdJl5xfjlgacxLvJrAMCVN9+BEh8PbNkCxMYCE7nsO1k2jewARNbmzo5+yC/uhOfXHMaKXbFw0Knx4pA2UBTeMkn1L7ugGOsefhaP/vYlACD91fnwePlF4yc5GkJWgiMjRDVwX2gA3hgVAgBYvPUcPv2bkwOp/uUX6fHjuBfx6M+LAABpL8yGx/xXJaciMh/LCFENPdIjCK/c2Q4A8H7kaSzdfl5yImpICor1WD1pNh5dsxAAkDrteXj+3xtyQxHVEMsI0U2Y1Lc5nhvcGgDwxm/R+G5PnORE1BAU6w1YPXUuHvv2HQBAypSn4f3h/0lORVRzLCNEN+mpgS3xRP8WAIBXfj6GH6MSJSciW6Y3CKx8+i2MX/4mACBpwuPwXfwRwDlLZMVYRohukqIoeHFIG0zo1QwA8OKPh/HrkSS5ocgmGQwCK597F2M/fw0qCFx4cAL8l3/OIkJWj2WEqBYoioI5d92CB24NhEEAz35/CH+euCg7FtkQIQRWv/wRHvpoFtTCgIR7HkKT75axiJBNYBkhqiUqlYI37+6AkZ39UWIQ+N/KA9h+5pLsWGQDhBD4Ye5i3P/uC9AIAxLuvBeBa74FVPwnnGwDf5KJapFapeD9+zthSHsfFOkNmPzNfuyNuSw7Flm5dW8vx6g3p0FnKEFc+AgEro9gESGbwp9molqmUavw8YNd0L+NFwqKDXhsxT4cSsiQHYus1IYPvsOdc/4HO30JYvsNQdCvPxqXeCeyISwjRHXATqPG54+EomdzD+QUlmDcsn9xIilLdiyyMhsXRWDQzEmwLylCbK+BaPbHBkCrlR2LqNaxjBDVEXutGkvHh6FrUzdkFZRg7LJ/cTY1W3YssgaJiTjwwuvo9+wEOBYXIiasL5r9vRHQ6WQnI6oTLCNEdcjJToMVj3VDSBMXpOcW4eGl/yIuPVd2LLJky5ZBNG2Kru/NgVNxAS4FNEezbZsAOzvZyYjqDMsIUR1zsdfim8e6o7VPI1zMKsRDX/6LCxn5smORJUpMhJg8GcpVT4L2TI6DcpmToMm2sYwQ1QN3Jx2+m9QdwZ5OuJCRj4e/3INzl3JkxyJLIgTOvTS3XBEBAEWvB87yQYxk21hGiOqJt7M9Vk7qjoDGDohNz8PwT3bgp4NcOp6Agtx87B06Bi1WLav4SbUaaNmy/kMR1SOWEaJ65O/mgHVP9ELP5h7IK9JjesRhvPjjYeQX6WVHI0lio2NwplNPdPtjDQxQcLLPEIiyW3fVamDJEiAgQG5IojrGMkJUz7xd7PHdpO6YdnsrKArww/5EjPxsB85c5J02Dc3fEZHQ9uyBDucOI8fOEce/WIm22zdBiY0FtmwBYmOBiRNlxySqc4oQ11ygtEBZWVlwdXVFZmYmXFxcZMchqjW7zqZhWsQhXMouhL1WhddHhuD+sEDZsaiO5RfpsWb2R7j3o9lwKi5AsncAtL/+As9bO8uORlSrqvv+zZERIol6tfTExmf6ok9LTxQUG/DCj0cw44dDyC0skR2N6sjZlEysGTEZ4957Dk7FBYjt2hveJw6ziFCDxjJCJJmXsx2+eawbng9vDZUCrDtwASM+3YHoZK7Yamt+2nEaZwfehXGbvwIAJE2Ygmb/boXaw11yMiK5WEaILIBKpeCpga2wenIP+LjY4dylXIz6bCdW/RsPK7iSSjeQW1iC+Yt+R+t7h2Fo9A6UqDXI+uxz+H/1OaDRyI5HJB3njBBZmPScQsz44TC2nb4EABjeyR9v3R0CZ3s+k8TqJCYi/t9DWPrLATyz5gN45mUiz80Ddht+hrpvH9npiOpcdd+/WUaILJDBIPDF9vN4d/Mp6A0CzTwc8elDXRHSxFV2NKomsXQpMGUKFIMBAoACIPeWDnD6/VegaVPZ8YjqBcsIkQ2IiruMp1cdRFJmAXRqFV69qx0e6REERVFkR6PryD0XC4dWLaASBtM2oShQTp4EWreWmIyofvFuGiIbEBrkjt+e6YtB7bxRpDfg1fXH8eSqA8gqKJYdjapwPCkTX01/t1wRAWBc5j0pSVIqIsvGMkJk4Ro76fDluDC8cmc7aFQKNh5NwZ0fb8fhhAzZ0egqQgis/vMYDg1/GE/9sqjiDlzWnahKLCNEVkBRFEzq2xw/PtELAY0dkHA5H/d9vgvLd8TwbhsLkFVQjE9nLULfewfi4QO/AQCK+/Q1FhCAy7oT3QDnjBBZmcz8Yrz442FsPn4RADD4Fh+8e19HuDnqJCdrmI4dj0PchCdw5/7fAQBZfoFw/mY5lEGDgMRE4xN3W7ZkEaEGiRNYiWyYEALf7I7Dm79Fo0hvQBM3B3zyUBd0bdpYdrQGQwiBP/9vGTq8MRO+OekwKArSJkyG98fvA40ayY5HZBFYRogagKOJmXhq9QHEpedBo1Lw4tA2mNSnOVQq3m1TZxITkbtjD06/+ym6HNgGAEjxbYpG336NRoP6y81GZGFYRogaiKyCYsxadxS/HUkGAHQOdMPjtzXHkPa+ULOU1Kq8RUvg8NQTxjtjABig4PhDkxHy5YdQHB0lpyOyPCwjRA2IEAKr9sZj/i8nUFhivKU00N0Bj/YKxuhbA9HIjkuO34y4tBzsf+sz3PPhTFxd74RKBSUujvNBiKrAMkLUAKVmF+Db3XH4bk8cruQZ1yJxttfgoW5NMaF3M/i5OkhOaD2EEIiKu4K/l/+M21Z8iB4JxyrfccsWoH//es1GZC1YRogasPwiPdYeSMTyHTE4n5YLANCoFNzZ0Q+T+zbnsvJVSUyE/uQpbBGu+GXLcQz/4TMMOrcPAFCk1kJrKDFdogFgvGU3NpYjI0RVYBkhIhgMAn+fTMXSHeex5/xl0/buwe6Y3Lc5Brb15mTXUgWffwHdk09AVfosGQHjQkx6lRrZD42F21vzgT/+AKZMAfT6/9YOmThRcnIiy8UyQkTlHE3MxLId5/HrkWSUGIy/9s09nfBYn2Dc2zUADjq15IRyXMjIx9r1u/HUo4Oguuafw4Jhd8J+4QflnyfDtUOIqo1lhIgqlZyZjxW7YrHq33hkF5QAABo7avFIjyCM7RkEb2d7yQnrWGIicOYMTjh548uTOVB+XIMndv6AVpcTKu7L+SBEN4VlhIiuK6ewBGv2J2D5zhgkXM4HAOjUKozs7I+JfYPR1tf2ftcMXy6FMnUKFIMBBgC5Ogc4FxmPXQDl7pThfBCim8cyQkTVojcI/HE8BV9uP48D8Rmm7X1beWJS3+a4rZUnFMUK55WUjoCgVSvkefsi8sctGP7wEKhQ/p+8Ym9faJ95CnB0BF54gfNBiGoRywgRmS0q7gqW7TiPTcdSUDqtBK19GmFSn+YY0dkf9loLnldyVfnA5s3A448DBgOEouCUTzCap8ZCZzBUfN2ffwK33/7f1+B8EKJaU6dlZNGiRXj33XeRnJyM9u3bY+HChejbt2+V+2/btg0zZszA8ePH4e/vjxdffBFTp06t9vdjGSGqXwmX87B8Zwx+2JeA3CI9AMDFXoO2vi4I9nRCsJcTgj2d0MLLCYHujrDTSCgpV5WP/F83wv7JJ6CUlg8IgcrGcngphqh+1VkZiYiIwNixY7Fo0SL07t0bS5YswdKlS3HixAk0bdq0wv4xMTEICQnB5MmTMWXKFOzcuRP/+9//sHr1atx77721ejBEVLsy84vx/d54rNgVi+TMgkr3USlAQGNHY0nxdEJzr7I/G8HPxf7Gtw5/8AGwaJHx8kiHDkCPHkDjqx745+EBBAejKDMTKSUaXExOR8nefei+5F2ohAEGKAAEVDc4Fv3SZVALAzB1Ki/FENWTOisj3bt3R9euXbF48WLTtnbt2mHUqFFYsGBBhf1feuklbNiwAdHR0aZtU6dOxeHDh7F79+5qfU+WESK5ivUGnEzOxvm0HMSk5SImLRfnLxn/zCksqfJ1dhqVqaT8V1YaobmnExo76QBvb+DSpRt+/7IRjWv/rLarR0B4KYao3lT3/dusB1YUFRUhKioKM2fOLLc9PDwcu3btqvQ1u3fvRnh4eLltQ4YMwbJly1BcXAytVlvhNYWFhSgsLCx3MEQkj1atQocAV3QIKL9yqxACl3IKEVNaTGLScnE+LRfnL+Ug/nIeCksMOJmSjZMp2RW+5v8OrscLly5Vq1QoVfxZJVXpOInB8N8ISFnxCAhgCSGyMGaVkbS0NOj1evj4+JTb7uPjg5SUlEpfk5KSUun+JSUlSEtLg5+fX4XXLFiwAPPmzTMnGhFJoCgKvJ3t4e1sj+7NPcp9rkRvwIWMfJxPyy1fVi7lICmzAAOObTdvdON6KisfQ4ZwBITIStToUZ7X3uYnhLjurX+V7V/Z9jKzZs3CjBkzTH/PyspCYGBgTaISkSQatQpBHk4I8nDCgDblP5dfpEeG/WGIebNvvpBcr3ywhBBZBbPKiKenJ9RqdYVRkNTU1AqjH2V8fX0r3V+j0cDDw6PS19jZ2cHOzs6caERkRRx0ajjMfRlYtLBac0YqUKuBt98GwsJYPohsgFllRKfTITQ0FJGRkbj77rtN2yMjIzFy5MhKX9OzZ0/88ssv5bb98ccfCAsLq3S+CBE1IKmpxrtpFi8GSkqATp2A7t0r3k3TrBmQmws4ORn/5KUXIptS41t7P//8c/Ts2RNffPEFvvzySxw/fhxBQUGYNWsWLly4gG+++QbAf7f2TpkyBZMnT8bu3bsxdepU3tpLRERk4+rkbhoAGDNmDNLT0zF//nwkJycjJCQEGzduRFBQEAAgOTkZ8fHxpv2Dg4OxceNGTJ8+HZ999hn8/f3x8ccfV7uIEBERkW3jcvBERERUJ6r7/n2jRQuJiIiI6hTLCBEREUnFMkJERERSsYwQERGRVCwjREREJBXLCBEREUnFMkJERERSsYwQERGRVCwjREREJJXZy8HLULZIbFZWluQkREREVF1l79s3WuzdKspIdnY2ACAwMFByEiIiIjJXdnY2XF1dq/y8VTybxmAwICkpCc7OzlAUpda+blZWFgIDA5GQkGCzz7yx9WPk8Vk/Wz9GWz8+wPaPkcdXc0IIZGdnw9/fHypV1TNDrGJkRKVSISAgoM6+vouLi03+gF3N1o+Rx2f9bP0Ybf34ANs/Rh5fzVxvRKQMJ7ASERGRVCwjREREJFWDLiN2dnZ47bXXYGdnJztKnbH1Y+TxWT9bP0ZbPz7A9o+Rx1f3rGICKxEREdmuBj0yQkRERPKxjBAREZFULCNEREQkFcsIERERSWXzZeTNN99Er1694OjoCDc3t2q9RgiBuXPnwt/fHw4ODujfvz+OHz9ebp/CwkI8/fTT8PT0hJOTE0aMGIHExMQ6OILru3LlCsaOHQtXV1e4urpi7NixyMjIuO5rFEWp9OPdd9817dO/f/8Kn3/ggQfq+GgqqsnxTZgwoUL2Hj16lNvHUs4fYP4xFhcX46WXXkKHDh3g5OQEf39/jBs3DklJSeX2k3UOFy1ahODgYNjb2yM0NBTbt2+/7v7btm1DaGgo7O3t0bx5c3z++ecV9lm7di1uueUW2NnZ4ZZbbsFPP/1UV/GrxZxjXLduHQYPHgwvLy+4uLigZ8+e2Lx5c7l9VqxYUenvZEFBQV0fSqXMOb6tW7dWmv3kyZPl9rOkc2jO8VX274miKGjfvr1pH0s6f//88w+GDx8Of39/KIqCn3/++YavsYjfQWHj5syZIz744AMxY8YM4erqWq3XvP3228LZ2VmsXbtWHD16VIwZM0b4+fmJrKws0z5Tp04VTZo0EZGRkeLAgQNiwIABolOnTqKkpKSOjqRyQ4cOFSEhIWLXrl1i165dIiQkRNx1113XfU1ycnK5j+XLlwtFUcS5c+dM+/Tr109Mnjy53H4ZGRl1fTgV1OT4xo8fL4YOHVoue3p6erl9LOX8CWH+MWZkZIhBgwaJiIgIcfLkSbF7927RvXt3ERoaWm4/Gefw+++/F1qtVnz55ZfixIkTYtq0acLJyUnExcVVuv/58+eFo6OjmDZtmjhx4oT48ssvhVarFT/++KNpn127dgm1Wi3eeustER0dLd566y2h0WjEnj176vRYqmLuMU6bNk288847Yu/eveL06dNi1qxZQqvVigMHDpj2+eqrr4SLi0uF300ZzD2+LVu2CADi1KlT5bJf/btkSefQ3OPLyMgod1wJCQnC3d1dvPbaa6Z9LOn8bdy4UcyePVusXbtWABA//fTTdfe3lN9Bmy8jZb766qtqlRGDwSB8fX3F22+/bdpWUFAgXF1dxeeffy6EMP5warVa8f3335v2uXDhglCpVGLTpk21nr0qJ06cEADK/UDs3r1bABAnT56s9tcZOXKkGDhwYLlt/fr1E9OmTautqDVS0+MbP368GDlyZJWft5TzJ0TtncO9e/cKAOX+QZVxDrt16yamTp1ablvbtm3FzJkzK93/xRdfFG3bti23bcqUKaJHjx6mv48ePVoMHTq03D5DhgwRDzzwQC2lNo+5x1iZW265RcybN8/09+r++1QfzD2+sjJy5cqVKr+mJZ3Dmz1/P/30k1AURcTGxpq2WdL5u1p1yoil/A7a/GUac8XExCAlJQXh4eGmbXZ2dujXrx927doFAIiKikJxcXG5ffz9/RESEmLapz7s3r0brq6u6N69u2lbjx494OrqWu0cFy9exG+//YaJEydW+NzKlSvh6emJ9u3b4/nnnzc9Pbm+3Mzxbd26Fd7e3mjdujUmT56M1NRU0+cs5fwBtXMOASAzMxOKolS4FFmf57CoqAhRUVHl/n8FgPDw8CqPZffu3RX2HzJkCPbv34/i4uLr7lPf5wqo2TFey2AwIDs7G+7u7uW25+TkICgoCAEBAbjrrrtw8ODBWstdXTdzfF26dIGfnx9uv/12bNmypdznLOUc1sb5W7ZsGQYNGoSgoKBy2y3h/NWEpfwOWsWD8upTSkoKAMDHx6fcdh8fH8TFxZn20el0aNy4cYV9yl5fH1JSUuDt7V1hu7e3d7VzfP3113B2dsY999xTbvvDDz+M4OBg+Pr64tixY5g1axYOHz6MyMjIWsleHTU9vmHDhuH+++9HUFAQYmJi8Oqrr2LgwIGIioqCnZ2dxZw/oHbOYUFBAWbOnImHHnqo3EOu6vscpqWlQa/XV/q7U9WxpKSkVLp/SUkJ0tLS4OfnV+U+9X2ugJod47Xef/995ObmYvTo0aZtbdu2xYoVK9ChQwdkZWXho48+Qu/evXH48GG0atWqVo/hempyfH5+fvjiiy8QGhqKwsJCfPvtt7j99tuxdetW3HbbbQCqPs/1fQ5v9vwlJyfj999/x6pVq8ptt5TzVxOW8jtolWVk7ty5mDdv3nX32bdvH8LCwmr8PRRFKfd3IUSFbdeqzj7VUd3jAyrmNDfH8uXL8fDDD8Pe3r7c9smTJ5v+d0hICFq1aoWwsDAcOHAAXbt2rdbXrkpdH9+YMWNM/zskJARhYWEICgrCb7/9VqF0mfN1zVFf57C4uBgPPPAADAYDFi1aVO5zdXkOr8fc353K9r92e01+H+tSTfOsXr0ac+fOxfr168uV0B49epSbZN27d2907doVn3zyCT7++OPaC15N5hxfmzZt0KZNG9Pfe/bsiYSEBLz33numMmLu16xrNc2yYsUKuLm5YdSoUeW2W9r5M5cl/A5aZRl56qmnbnhXQLNmzWr0tX19fQEY26Kfn59pe2pqqqkZ+vr6oqioCFeuXCn3X9epqano1atXjb7v1ap7fEeOHMHFixcrfO7SpUsVWmxltm/fjlOnTiEiIuKG+3bt2hVarRZnzpy56Tey+jq+Mn5+fggKCsKZM2cA1P35A+rnGIuLizF69GjExMTg77//vuGjv2vzHFbG09MTarW6wn8tXf27cy1fX99K99doNPDw8LjuPub8DNSWmhxjmYiICEycOBFr1qzBoEGDrruvSqXCrbfeavqZrS83c3xX69GjB7777jvT3y3lHN7M8QkhsHz5cowdOxY6ne66+8o6fzVhMb+DtTb7xMKZO4H1nXfeMW0rLCysdAJrRESEaZ+kpCRpE1j//fdf07Y9e/ZUe/Lj+PHjK9yBUZWjR48KAGLbtm01zmuumz2+MmlpacLOzk58/fXXQgjLOX9C1PwYi4qKxKhRo0T79u1Fampqtb5XfZzDbt26iSeeeKLctnbt2l13Amu7du3KbZs6dWqFyXPDhg0rt8/QoUOlTmA15xiFEGLVqlXC3t7+hpMJyxgMBhEWFiYeffTRm4laIzU5vmvde++9YsCAAaa/W9I5rOnxlU3UPXr06A2/h8zzdzVUcwKrJfwO2nwZiYuLEwcPHhTz5s0TjRo1EgcPHhQHDx4U2dnZpn3atGkj1q1bZ/r722+/LVxdXcW6devE0aNHxYMPPljprb0BAQHizz//FAcOHBADBw6Udmtvx44dxe7du8Xu3btFhw4dKtwWeu3xCSFEZmamcHR0FIsXL67wNc+ePSvmzZsn9u3bJ2JiYsRvv/0m2rZtK7p06WLxx5ednS2ee+45sWvXLhETEyO2bNkievbsKZo0aWKR508I84+xuLhYjBgxQgQEBIhDhw6Vu5WwsLBQCCHvHJbdNrls2TJx4sQJ8eyzzwonJyfTnQczZ84UY8eONe1fdlvh9OnTxYkTJ8SyZcsq3Fa4c+dOoVarxdtvvy2io6PF22+/bRG39lb3GFetWiU0Go347LPPqrzNeu7cuWLTpk3i3Llz4uDBg+LRRx8VGo2mXEm11OP78MMPxU8//SROnz4tjh07JmbOnCkAiLVr15r2saRzaO7xlXnkkUdE9+7dK/2alnT+srOzTe9zAMQHH3wgDh48aLrTzlJ/B22+jIwfP14AqPCxZcsW0z4AxFdffWX6u8FgEK+99prw9fUVdnZ24rbbbqvQhvPz88VTTz0l3N3dhYODg7jrrrtEfHx8PR3Vf9LT08XDDz8snJ2dhbOzs3j44Ycr3GJ37fEJIcSSJUuEg4NDpetOxMfHi9tuu024u7sLnU4nWrRoIZ555pkKa3XUB3OPLy8vT4SHhwsvLy+h1WpF06ZNxfjx4yucG0s5f0KYf4wxMTGV/kxf/XMt8xx+9tlnIigoSOh0OtG1a9dyIzHjx48X/fr1K7f/1q1bRZcuXYROpxPNmjWrtCCvWbNGtGnTRmi1WtG2bdtyb3QymHOM/fr1q/RcjR8/3rTPs88+K5o2bSp0Op3w8vIS4eHhYteuXfV4ROWZc3zvvPOOaNGihbC3txeNGzcWffr0Eb/99luFr2lJ59Dcn9GMjAzh4OAgvvjii0q/niWdv7IRnKp+3iz1d1ARonSmChEREZEEXGeEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKSimWEiIiIpGIZISIiIqlYRoiIiEgqlhEiIiKS6v8B0CYa08e5UzUAAAAASUVORK5CYII=", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2436,10 +2248,8 @@ }, { "cell_type": "markdown", - "id": "921364c2", - "metadata": { - "editable": true - }, + "id": "35d2b3d9", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] @@ -2447,12 +2257,56 @@ { "cell_type": "code", "execution_count": 11, - "id": "f8a5ce22", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ca391f17", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + ">0 f([0.74724774]) = 0.55838\n", + ">1 f([0.54175461]) = 0.29350\n", + ">2 f([0.37175575]) = 0.13820\n", + ">3 f([0.24640494]) = 0.06072\n", + ">4 f([0.15951871]) = 0.02545\n", + ">5 f([0.1015491]) = 0.01031\n", + ">6 f([0.0638484]) = 0.00408\n", + ">7 f([0.03976851]) = 0.00158\n", + ">8 f([0.02459084]) = 0.00060\n", + ">9 f([0.01511937]) = 0.00023\n", + ">10 f([0.00925406]) = 0.00009\n", + ">11 f([0.00564365]) = 0.00003\n", + ">12 f([0.0034318]) = 0.00001\n", + ">13 f([0.00208188]) = 0.00000\n", + ">14 f([0.00126053]) = 0.00000\n", + ">15 f([0.00076202]) = 0.00000\n", + ">16 f([0.00046006]) = 0.00000\n", + ">17 f([0.00027746]) = 0.00000\n", + ">18 f([0.00016719]) = 0.00000\n", + ">19 f([0.00010067]) = 0.00000\n", + ">20 f([6.05804744e-05]) = 0.00000\n", + ">21 f([3.64373635e-05]) = 0.00000\n", + ">22 f([2.19069576e-05]) = 0.00000\n", + ">23 f([1.31664443e-05]) = 0.00000\n", + ">24 f([7.91100141e-06]) = 0.00000\n", + ">25 f([4.75216828e-06]) = 0.00000\n", + ">26 f([2.85408468e-06]) = 0.00000\n", + ">27 f([1.71384267e-06]) = 0.00000\n", + ">28 f([1.02900153e-06]) = 0.00000\n", + ">29 f([6.17748881e-07]) = 0.00000\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "from numpy import asarray\n", "from numpy import arange\n", @@ -2521,10 +2375,8 @@ }, { "cell_type": "markdown", - "id": "65e56e6a", - "metadata": { - "editable": true - }, + "id": "181b30b4", + "metadata": {}, "source": [ "## Overview video on Stochastic Gradient Descent\n", "\n", @@ -2533,10 +2385,8 @@ }, { "cell_type": "markdown", - "id": "2d2037ee", - "metadata": { - "editable": true - }, + "id": "b51d1452", + "metadata": {}, "source": [ "## Batches and mini-batches\n", "\n", @@ -2554,10 +2404,8 @@ }, { "cell_type": "markdown", - "id": "5f913a46", - "metadata": { - "editable": true - }, + "id": "85bbbc0c", + "metadata": {}, "source": [ "## Stochastic Gradient Descent (SGD)\n", "\n", @@ -2586,10 +2434,8 @@ }, { "cell_type": "markdown", - "id": "fde89a95", - "metadata": { - "editable": true - }, + "id": "56b2b867", + "metadata": {}, "source": [ "## Stochastic Gradient Descent\n", "\n", @@ -2603,10 +2449,8 @@ }, { "cell_type": "markdown", - "id": "f1febade", - "metadata": { - "editable": true - }, + "id": "386e0c45", + "metadata": {}, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -2616,10 +2460,8 @@ }, { "cell_type": "markdown", - "id": "113ad334", - "metadata": { - "editable": true - }, + "id": "0f6d09dd", + "metadata": {}, "source": [ "## Computation of gradients\n", "\n", @@ -2629,10 +2471,8 @@ }, { "cell_type": "markdown", - "id": "fcfad3c2", - "metadata": { - "editable": true - }, + "id": "99541bf1", + "metadata": {}, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2642,10 +2482,8 @@ }, { "cell_type": "markdown", - "id": "3960683f", - "metadata": { - "editable": true - }, + "id": "a24ce1cc", + "metadata": {}, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -2656,10 +2494,8 @@ }, { "cell_type": "markdown", - "id": "cd094911", - "metadata": { - "editable": true - }, + "id": "d6c2eea5", + "metadata": {}, "source": [ "## SGD example\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", @@ -2678,10 +2514,8 @@ }, { "cell_type": "markdown", - "id": "b08c3f72", - "metadata": { - "editable": true - }, + "id": "b2561a99", + "metadata": {}, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -2693,10 +2527,8 @@ }, { "cell_type": "markdown", - "id": "9db9ffdd", - "metadata": { - "editable": true - }, + "id": "a0fb8d89", + "metadata": {}, "source": [ "## The gradient step\n", "\n", @@ -2705,10 +2537,8 @@ }, { "cell_type": "markdown", - "id": "a1123570", - "metadata": { - "editable": true - }, + "id": "71856a7b", + "metadata": {}, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -2718,10 +2548,8 @@ }, { "cell_type": "markdown", - "id": "4aa14e3d", - "metadata": { - "editable": true - }, + "id": "9859ff14", + "metadata": {}, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -2732,10 +2560,8 @@ }, { "cell_type": "markdown", - "id": "faf90618", - "metadata": { - "editable": true - }, + "id": "6558ed12", + "metadata": {}, "source": [ "## Simple example code" ] @@ -2743,11 +2569,8 @@ { "cell_type": "code", "execution_count": 12, - "id": "142d8977", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "f8cee4e8", + "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", @@ -2768,10 +2591,8 @@ }, { "cell_type": "markdown", - "id": "59cce93f", - "metadata": { - "editable": true - }, + "id": "aac3d48e", + "metadata": {}, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -2784,10 +2605,8 @@ }, { "cell_type": "markdown", - "id": "9235ce3a", - "metadata": { - "editable": true - }, + "id": "657c6870", + "metadata": {}, "source": [ "## When do we stop?\n", "\n", @@ -2805,10 +2624,8 @@ }, { "cell_type": "markdown", - "id": "462fb963", - "metadata": { - "editable": true - }, + "id": "5a8d8a8d", + "metadata": {}, "source": [ "## Slightly different approach\n", "\n", @@ -2825,10 +2642,8 @@ }, { "cell_type": "markdown", - "id": "03a44915", - "metadata": { - "editable": true - }, + "id": "e0c75855", + "metadata": {}, "source": [ "## Time decay rate\n", "\n", @@ -2844,12 +2659,17 @@ { "cell_type": "code", "execution_count": 13, - "id": "d3c88238", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8368a998", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "gamma_j after 500 epochs: 9.97108e-05\n" + ] + } + ], "source": [ "import numpy as np \n", "\n", @@ -2879,10 +2699,8 @@ }, { "cell_type": "markdown", - "id": "0cca9644", - "metadata": { - "editable": true - }, + "id": "a99e7227", + "metadata": {}, "source": [ "## Code with a Number of Minibatches which varies\n", "\n", @@ -2892,12 +2710,36 @@ { "cell_type": "code", "execution_count": 14, - "id": "70ae46ab", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "b567ba9d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "Eigenvalues of Hessian Matrix:[0.29653038 4.0474753 ]\n", + "theta from own gd\n", + "[[4.08687303]\n", + " [3.00141727]]\n", + "theta from own sdg\n", + "[[4.014934 ]\n", + " [3.0042992]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Importing various packages\n", "from math import exp, sqrt\n", @@ -2969,10 +2811,8 @@ }, { "cell_type": "markdown", - "id": "9f81139d", - "metadata": { - "editable": true - }, + "id": "8ea309ee", + "metadata": {}, "source": [ "## Replace or not\n", "\n", @@ -2984,10 +2824,8 @@ }, { "cell_type": "markdown", - "id": "3774b1c5", - "metadata": { - "editable": true - }, + "id": "5573b607", + "metadata": {}, "source": [ "## Momentum based GD\n", "\n", @@ -2999,10 +2837,8 @@ }, { "cell_type": "markdown", - "id": "892c72ae", - "metadata": { - "editable": true - }, + "id": "5c393430", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -3011,10 +2847,8 @@ }, { "cell_type": "markdown", - "id": "5c8241e2", - "metadata": { - "editable": true - }, + "id": "03d76b90", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3029,10 +2863,8 @@ }, { "cell_type": "markdown", - "id": "d7ee1aaa", - "metadata": { - "editable": true - }, + "id": "c9de2175", + "metadata": {}, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -3048,10 +2880,8 @@ }, { "cell_type": "markdown", - "id": "f790d762", - "metadata": { - "editable": true - }, + "id": "a493002b", + "metadata": {}, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -3060,20 +2890,16 @@ }, { "cell_type": "markdown", - "id": "b12e5973", - "metadata": { - "editable": true - }, + "id": "cb1d7212", + "metadata": {}, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$." ] }, { "cell_type": "markdown", - "id": "8838a68e", - "metadata": { - "editable": true - }, + "id": "91135b7f", + "metadata": {}, "source": [ "## More on momentum based approaches\n", "\n", @@ -3086,10 +2912,8 @@ }, { "cell_type": "markdown", - "id": "3e556267", - "metadata": { - "editable": true - }, + "id": "57c90f73", + "metadata": {}, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -3098,20 +2922,16 @@ }, { "cell_type": "markdown", - "id": "6d16c301", - "metadata": { - "editable": true - }, + "id": "28fc8c64", + "metadata": {}, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "id": "f98707a7", - "metadata": { - "editable": true - }, + "id": "9ea86afa", + "metadata": {}, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -3120,20 +2940,16 @@ }, { "cell_type": "markdown", - "id": "66db7bc3", - "metadata": { - "editable": true - }, + "id": "259f8bd9", + "metadata": {}, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "id": "76740b12", - "metadata": { - "editable": true - }, + "id": "1b3b21b9", + "metadata": {}, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -3142,10 +2958,8 @@ }, { "cell_type": "markdown", - "id": "d62ee1e2", - "metadata": { - "editable": true - }, + "id": "931ce41d", + "metadata": {}, "source": [ "## Momentum parameter\n", "\n", @@ -3158,10 +2972,8 @@ }, { "cell_type": "markdown", - "id": "1467cb4a", - "metadata": { - "editable": true - }, + "id": "d1d161a1", + "metadata": {}, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -3170,10 +2982,8 @@ }, { "cell_type": "markdown", - "id": "f0653e5e", - "metadata": { - "editable": true - }, + "id": "4f3657ba", + "metadata": {}, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -3203,10 +3013,8 @@ }, { "cell_type": "markdown", - "id": "974d2676", - "metadata": { - "editable": true - }, + "id": "81824da9", + "metadata": {}, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -3215,10 +3023,8 @@ }, { "cell_type": "markdown", - "id": "5deb5229", - "metadata": { - "editable": true - }, + "id": "6295bc9d", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3233,20 +3039,16 @@ }, { "cell_type": "markdown", - "id": "b0aa3cd9", - "metadata": { - "editable": true - }, + "id": "7a094665", + "metadata": {}, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$." ] }, { "cell_type": "markdown", - "id": "977e1000", - "metadata": { - "editable": true - }, + "id": "f0c6bb20", + "metadata": {}, "source": [ "## Second moment of the gradient\n", "\n", @@ -3274,10 +3076,8 @@ }, { "cell_type": "markdown", - "id": "85444c1a", - "metadata": { - "editable": true - }, + "id": "ce3b45b6", + "metadata": {}, "source": [ "## RMS prop\n", "\n", @@ -3289,10 +3089,8 @@ }, { "cell_type": "markdown", - "id": "fcef9dca", - "metadata": { - "editable": true - }, + "id": "ee7e2069", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3307,10 +3105,8 @@ }, { "cell_type": "markdown", - "id": "e04785f0", - "metadata": { - "editable": true - }, + "id": "ec4f73bb", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -3319,10 +3115,8 @@ }, { "cell_type": "markdown", - "id": "2b946f7f", - "metadata": { - "editable": true - }, + "id": "fa5cb9a2", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -3331,10 +3125,8 @@ }, { "cell_type": "markdown", - "id": "0d50342d", - "metadata": { - "editable": true - }, + "id": "eb93379a", + "metadata": {}, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -3349,10 +3141,8 @@ }, { "cell_type": "markdown", - "id": "dbaf9004", - "metadata": { - "editable": true - }, + "id": "b46162a4", + "metadata": {}, "source": [ "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n", "\n", @@ -3378,10 +3168,8 @@ }, { "cell_type": "markdown", - "id": "450a8247", - "metadata": { - "editable": true - }, + "id": "d103bc6a", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3396,10 +3184,8 @@ }, { "cell_type": "markdown", - "id": "6219f30d", - "metadata": { - "editable": true - }, + "id": "a0f031f6", + "metadata": {}, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -3408,10 +3194,8 @@ }, { "cell_type": "markdown", - "id": "f42274c5", - "metadata": { - "editable": true - }, + "id": "2b384f75", + "metadata": {}, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -3420,10 +3204,8 @@ }, { "cell_type": "markdown", - "id": "bcc4b1cc", - "metadata": { - "editable": true - }, + "id": "216435a6", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -3432,10 +3214,8 @@ }, { "cell_type": "markdown", - "id": "5c72c26b", - "metadata": { - "editable": true - }, + "id": "8b79e19e", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -3444,10 +3224,8 @@ }, { "cell_type": "markdown", - "id": "f8fff908", - "metadata": { - "editable": true - }, + "id": "ba777281", + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -3456,10 +3234,8 @@ }, { "cell_type": "markdown", - "id": "c69a2902", - "metadata": { - "editable": true - }, + "id": "f34eb136", + "metadata": {}, "source": [ "\n", "
    \n", @@ -3473,10 +3249,8 @@ }, { "cell_type": "markdown", - "id": "6dd75fb7", - "metadata": { - "editable": true - }, + "id": "695da6fd", + "metadata": {}, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -3492,10 +3266,8 @@ }, { "cell_type": "markdown", - "id": "5fbbd545", - "metadata": { - "editable": true - }, + "id": "8771f487", + "metadata": {}, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -3504,10 +3276,8 @@ }, { "cell_type": "markdown", - "id": "8e70ad9d", - "metadata": { - "editable": true - }, + "id": "6b816830", + "metadata": {}, "source": [ "## Algorithms and codes for Adagrad, RMSprop and Adam\n", "\n", @@ -3518,10 +3288,8 @@ }, { "cell_type": "markdown", - "id": "e3cefb0c", - "metadata": { - "editable": true - }, + "id": "4efb5cb8", + "metadata": {}, "source": [ "## Practical tips\n", "\n", @@ -3538,10 +3306,8 @@ }, { "cell_type": "markdown", - "id": "2ff5b285", - "metadata": { - "editable": true - }, + "id": "de7affbf", + "metadata": {}, "source": [ "## Automatic differentiation\n", "\n", @@ -3576,10 +3342,8 @@ }, { "cell_type": "markdown", - "id": "5f22e864", - "metadata": { - "editable": true - }, + "id": "3383da7c", + "metadata": {}, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -3588,20 +3352,16 @@ }, { "cell_type": "markdown", - "id": "e90f5286", - "metadata": { - "editable": true - }, + "id": "a8a03664", + "metadata": {}, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "id": "6eaa4220", - "metadata": { - "editable": true - }, + "id": "da4e8c9e", + "metadata": {}, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -3610,10 +3370,8 @@ }, { "cell_type": "markdown", - "id": "f5b7003f", - "metadata": { - "editable": true - }, + "id": "b35c008d", + "metadata": {}, "source": [ "Using **autograd** we have" ] @@ -3621,12 +3379,27 @@ { "cell_type": "code", "execution_count": 15, - "id": "ef5394f1", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9bb36858", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max absolute difference is: 1.77636e-15\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "\n", @@ -3666,10 +3439,8 @@ }, { "cell_type": "markdown", - "id": "6504c892", - "metadata": { - "editable": true - }, + "id": "9f8c7b5e", + "metadata": {}, "source": [ "## Using autograd\n", "\n", @@ -3683,12 +3454,18 @@ { "cell_type": "code", "execution_count": 16, - "id": "a678aaaf", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "65176228", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f1 evaluated at a = 1 using autograd is: 3\n", + "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3711,10 +3488,8 @@ }, { "cell_type": "markdown", - "id": "f1246511", - "metadata": { - "editable": true - }, + "id": "44375951", + "metadata": {}, "source": [ "## Autograd with more complicated functions\n", "\n", @@ -3726,12 +3501,23 @@ { "cell_type": "code", "execution_count": 17, - "id": "d9e84c1e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "63ebdbaf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Evaluating at x1 = 1, x2 = 3\n", + "------------------------------\n", + "The derivative of f2 w.r.t x1: 12\n", + "The analytical derivative of f2 w.r.t x1: 12\n", + "\n", + "The derivative of f2 w.r.t x2: -4\n", + "The analytical derivative of f2 w.r.t x2: -4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3770,20 +3556,16 @@ }, { "cell_type": "markdown", - "id": "0580051a", - "metadata": { - "editable": true - }, + "id": "ddef1f9a", + "metadata": {}, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] }, { "cell_type": "markdown", - "id": "90286d6e", - "metadata": { - "editable": true - }, + "id": "c6ff810b", + "metadata": {}, "source": [ "## More complicated functions using the elements of their arguments directly" ] @@ -3791,12 +3573,18 @@ { "cell_type": "code", "execution_count": 18, - "id": "46516c99", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "8c1ef66a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed gradient of f3 is: [ 2. 3. 5. 7. 88.]\n", + "The analytical gradient of f3 is: [ 2. 3. 5. 7. 88.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3819,10 +3607,8 @@ }, { "cell_type": "markdown", - "id": "61a6f532", - "metadata": { - "editable": true - }, + "id": "7ac0e490", + "metadata": {}, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -3834,10 +3620,8 @@ }, { "cell_type": "markdown", - "id": "8627d731", - "metadata": { - "editable": true - }, + "id": "f817a4b1", + "metadata": {}, "source": [ "## Functions using mathematical functions from Numpy" ] @@ -3845,12 +3629,18 @@ { "cell_type": "code", "execution_count": 19, - "id": "dd7cf53a", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "9950eceb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f4 at x = 2.7 is: 13.8759\n", + "The analytical gradient of f4 at x = 2.7 is: 13.8759\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3873,10 +3663,8 @@ }, { "cell_type": "markdown", - "id": "dbc2f6c3", - "metadata": { - "editable": true - }, + "id": "2d3597e1", + "metadata": {}, "source": [ "## More autograd" ] @@ -3884,12 +3672,17 @@ { "cell_type": "code", "execution_count": 20, - "id": "5c842a06", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a694b773", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f5 at x = 2.7 is: 5.4\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3909,10 +3702,8 @@ }, { "cell_type": "markdown", - "id": "844e01b1", - "metadata": { - "editable": true - }, + "id": "63681987", + "metadata": {}, "source": [ "## And with loops" ] @@ -3920,12 +3711,18 @@ { "cell_type": "code", "execution_count": 21, - "id": "85d188e2", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "ae061106", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f6_for at x = 0.5 is: 3.95703\n", + "The computed derivative of f6_while at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3956,12 +3753,17 @@ { "cell_type": "code", "execution_count": 22, - "id": "b0afa960", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "a194eddc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The analytical derivative of f6 at x = 0.5 is: 3.95703\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3976,10 +3778,8 @@ }, { "cell_type": "markdown", - "id": "581e341f", - "metadata": { - "editable": true - }, + "id": "8c21cf38", + "metadata": {}, "source": [ "## Using recursion" ] @@ -3987,12 +3787,18 @@ { "cell_type": "code", "execution_count": 23, - "id": "d4c349a5", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "3eb55bad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The computed derivative of f7 at n = 2 is: 1\n", + "The analytical derivative of f7 at n = 2 is: 1\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4025,20 +3831,16 @@ }, { "cell_type": "markdown", - "id": "d4ae05a6", - "metadata": { - "editable": true - }, + "id": "12fbb13b", + "metadata": {}, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input." ] }, { "cell_type": "markdown", - "id": "13ef97cc", - "metadata": { - "editable": true - }, + "id": "19ed9d51", + "metadata": {}, "source": [ "## Unsupported functions\n", "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", @@ -4049,11 +3851,8 @@ { "cell_type": "code", "execution_count": 24, - "id": "5e7a3e34", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "fb297a92", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4071,20 +3870,16 @@ }, { "cell_type": "markdown", - "id": "a70af861", - "metadata": { - "editable": true - }, + "id": "06d0bc95", + "metadata": {}, "source": [ "Here, running this code, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." ] }, { "cell_type": "markdown", - "id": "846d050e", - "metadata": { - "editable": true - }, + "id": "9974f300", + "metadata": {}, "source": [ "## The syntax a.dot(b) when finding the dot product" ] @@ -4092,11 +3887,8 @@ { "cell_type": "code", "execution_count": 25, - "id": "a69564a2", - "metadata": { - "collapsed": false, - "editable": true - }, + "id": "cbb0a202", + "metadata": {}, "outputs": [], "source": [ "import autograd.numpy as np\n", @@ -4114,10 +3906,8 @@ }, { "cell_type": "markdown", - "id": "453994b2", - "metadata": { - "editable": true - }, + "id": "7f08b96c", + "metadata": {}, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -4127,12 +3917,17 @@ { "cell_type": "code", "execution_count": 26, - "id": "a6462c1e", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "id": "cba444cd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The gradient of f9 is: [1. 2.]\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4152,10 +3947,42 @@ }, { "cell_type": "markdown", - "id": "b2b3574e", - "metadata": { - "editable": true - }, + "id": "18e2b174", + "metadata": {}, + "source": [ + "## Recommended to avoid\n", + "The documentation recommends to avoid inplace operations such as" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "69c6914d", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'b' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[27], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[43mb\u001b[49m\n\u001b[1;32m 2\u001b[0m a \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m b\n\u001b[1;32m 3\u001b[0m a\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m=\u001b[39m b\n", + "\u001b[0;31mNameError\u001b[0m: name 'b' is not defined" + ] + } + ], + "source": [ + "a += b\n", + "a -= b\n", + "a*= b\n", + "a /=b" + ] + }, + { + "cell_type": "markdown", + "id": "600cc052", + "metadata": {}, "source": [ "## Using Autograd with OLS\n", "\n", @@ -4166,13 +3993,34 @@ }, { "cell_type": "code", - "execution_count": 27, - "id": "f5ac02a2", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 28, + "id": "cd18340b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.94499279]\n", + " [3.03306538]]\n", + "Eigenvalues of Hessian Matrix:[0.31248425 4.44418124]\n", + "theta from own gd\n", + "[[3.94499279]\n", + " [3.03306538]]\n" + ] + }, + { + "data": { + "image/png": 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FbGwsHnnkEZw+fdp7BSYiIiKf4vUwVFJSgvbt22PevHlV9pWWlmLXrl3429/+hl27diEzMxNHjhzBkCFDvFBSIiIi8kWSEEJ4uxBmkiRh2bJlGDZsmN1jtm/fjq5du+LEiRNo0qSJQ+ctLi5GeHg4ioqKEBYWJlNpiYiIyJ089f0d4LYzu0lRUREkSUL9+vXtHlNeXo7y8nLL7eLiYg+UjIiIiNTI681kzigrK8PUqVMxatSoahPizJkzER4ebvlJSEjwYCmJiIhITVQThioqKvCnP/0JRqMRH3zwQbXHTps2DUVFRZaf3NxcD5WSiIiI1EYVzWQVFRUYMWIEcnJysGHDhhrbDYODgxEcHOyh0hEREZGaKT4MmYPQ0aNHkZWVhcjISG8XiYiIiHyI18PQlStXcOzYMcvtnJwc7NmzBxEREYiNjcXw4cOxa9curFq1CgaDAQUFBQCAiIgIBAUFeavYRERE5CO8PrQ+Ozsbffv2rbJ9zJgxmD59OpKSkmzeLysrC3369HHoMTi0noiISH00M7S+T58+qC6PKWgaJCIiIvJBXg9DREREpGIGA7B5M5CfD8TEAKmpgL+/t0vlFIYhIiIick1mJjBpEnDq1PVt8fHA3LlAWpr3yuUk1cwzRERERAqSmQkMH24dhAAgL8+0PTPTO+VyAcMQERGRUhgMQHY2sGiR6bfB4O0S2WYwmGqEbPXrNW+bPFm55b8JwxAREZESZGYCiYlA377AqFGm34mJyqxh2by5ao3QjYQAcnNNx6kAwxAREZG3qa3JKT9f3uO8jGGIiIjIm9TY5BQTI+9xXsYwRERE5E1qbHJKTTWNGpMk2/slCUhIMB2nAgxDRERE3qTGJid/f9PweaBqIDLfnjNHNfMNMQwRERF5k1qbnNLSgCVLgLg46+3x8abtKppnyOtrk3kC1yYjIiLFMhhMo8by8mz3G5IkU8DIyVFmTYsbZ6DWzNpkREREmmZucho+3BR8bgxEamhy8vcHHFw4XanYTEZERORtPtTkpEasGSIiIlKCtDRg6FDVL3qqRgxDRERESuEDTU5qxGYyIiIi0jSGISIiItI0hiEiIiLSNIYhIiIi0jSGISIiItI0hiEiIiLSNA6tJyIi8kVuXCbD1zAMERER+ZrMTGDSJODUqevb4uNNy35wNusq2ExGRETkSzIzTeuc3RiEANNCsMOHm/aTFYYhIiIiM4MByM4GFi0y/TYYvF0i5xgMphqhGxd7NTNvmzxZfdflZgxDREREgKnGJDER6NsXGDXK9DsxUV01KZs3V60RupEQQG6u6Th3UGmYZBgiIiLylaal/Hx5j3OGisMkwxAREWmbLzUtxcTIe5yjVB4mGYaIiEjbvN20JKfUVNOoMUmyvV+SgIQE03Fy8YEwyTBERETa5s2mJbn5+5uGzwNVA5H59pw58s435ANhkmGIiIi0zVtNS+6SlgYsWQLExVlvj483bZd7niEfCJOcdJGIiLTN3LSUl2e7qUeSTPvlbFpyt6FDgfBw04guAOjTx/Qj9wzUBgNw5oxjxyo4TDIMERGRtpmbloYPNwWfGwORu5qW3MVgAGbMMF3PhQvXty9cKP/s07ZmubblxjCp0CVC2ExGRETk6aYld8jMBKKjgddesw5CgPyjuuyNHrvZjWFyxQrFDr2XhLBVJ+hbiouLER4ejqKiIoSFhXm7OEREpFQKrbmokTmcVPeVbq6hycmp3TUZDKYQU1MQAkwj1+bMMf3bVvnMYclO4PTU9zfDEBERkZo5E04AICvL1H/IVdnZplqdmsyeDUyYYPp3deWrJqR56vubzWRERKReKl3+QVY1DW2/WW1HdTl6/+hoU7hRwdB7dqAmIiJ1stWBNz5e/o7CSudsuKntqC5npyJQwdB7r9cMbdq0CTqdDrGxsZAkCcuXL7faL4TA9OnTERsbizp16qBPnz7Yv3+/dwpLRETKoPLlH2TlTLiRY/ZpZ2e5VsE8Tl4PQyUlJWjfvj3mzZtnc/+sWbPwzjvvYN68edi+fTsaN26Mfv364fLlyx4uKRERKYIPLP8gq5rCyY3kmCLA2VmuHSmfl+dx8noYGjhwIF5//XWk2ajSFEJgzpw5eOWVV5CWloaUlBR89tlnKC0tRUZGhhdKS0REXqeCPigeVV04MYuMBJYula/50JmpCBwp39WrpqH3NxFGz4zx8noYqk5OTg4KCgrQv39/y7bg4GD07t0bP/74o937lZeXo7i42OqHiIh8hAr6oHicvXASGQmkp5tmiXY1CNnrpJ6WBhw/bhqdlpFh+p2TY/txzOWLiLD9GBcuWJo3yy6V4dvXd2B8241IjvTMa6joDtQFBQUAgOjoaKvt0dHROHHihN37zZw5E+np6W4tGxEReYkK+qB4RVqaaRkOOedJqqmTur+/48P0hw41ncsWISAAnHvwGdxqPILL6PzHDs9UZii6ZshMuqlaTQhRZduNpk2bhqKiIstPbm6uu4tIRESe4mwHXi0xh5ORI2u/FpncndRraN6UADQyFqIjdiPWLx9/abUJX764w/lyu0DRYahx48YArtcQmRUWFlapLbpRcHAwwsLCrH6IiMhHONuBl5znhk7qlTmOVUx8Om4HTlU0xr8P9sK9r3Su+Q4yUHQYSkpKQuPGjbFu3TrLtmvXrmHjxo244447vFgyIiLyKl9YS0zJZOqkfv7oBXz+9BY8GL8VQx6z01/oJs0e7AzJz4GRcTLyep+hK1eu4NixY5bbOTk52LNnDyIiItCkSRNMnjwZb7zxBpo3b47mzZvjjTfeQGhoKEaNGuXFUhMRkde5o48MmbjYSV0YBQ6t+R36D3Kh/6EBfixOgRF3AgD8YMBpxKAx8m3XxNy4ur2HeT0M7dixA31vWONkypQpAIAxY8Zg4cKFePHFF3H16lWMGzcOFy9eRLdu3fDdd9+hXr163ioyEREphTMdeMlxTnRSryitwJaP9mHlF8XQ703Eb5W3ArjVcki7kMMY0jkfuscaofEt78LvoRGmHTc2wXm5eZMLtRIREWmVwWC7Zs28+Gtens1+Q0KSUFq3EZ5ssARrctuhCOGWfUEoR9/IvdDdVYLBk25F057x1ne2NULNvLr9Tc2bXLVeRgxDREREN6lp2Lx5NBlgFYiMMNXiDMcSLEMa/GDAYKzCwOhdaNMnGrf/3yjUS6hf/WPbC2E3YRiSEcMQERHRDcxB5+YIYG6uWrIElfcNweFn30Xcf/+F+hVnLYecRAImYw6OBLfF1KaL8GDhBwi+dOb6OWRcLJdhSEYMQ0REpAmO1LiYm8DsjBYTAC74R6GVYR/OoRH8YEAqNiMeuYiuV4rEe5pj0MTb0OzCjhoDVW0Dkae+v73egZqIiIhkUFOzl5kDkx9GGgqRjP3YK7XDfYkHoBsahAHPDUF4kz/6BhkMQGJP+/MQSZJpHqKhQ63DmIPNY57GMERERKR29pq9zLNF31BLY8zNc2iSwY/GbMNtH92JgJA7q+50Zh4i82g/R8OaFzAMERFpiUL/MlcUtT1HNc0WLUkwTpiIZT9EQb8CuPjbLai6PnxVrcZ2B0LsxARn5yFyIqx5A8MQEZFWKPgvc8VQ43PkQC2N3+k8vPdOJTaiD/xgQB5iEYPTrk9+6MxiuQ6ENZtNah6k6OU4iIhIJnIvuumL1PocOVhLc7v/r3iuYza+f/tXRGfMhp8kub62mzOL5cq0tIc7MQwREfk6Nyy66XNU+hyVFJZgi/6iQ8e+811bvLOzD/pOuR0BI0fUbm03ZxbLdXFpD09iGCIi8nUq+Mvc61T0HJ3ano+PRm3CoKjtiIz2R+9FTyEX8ZbJEKv4o5ZG6t3LentaGnD8OJCVBWRkmH7n5DjeHOjoYrnONKl5CfsMERH5OhX8Ze51Cn6OjJVG7Mo4BP0nhdBvj8buq60BXA8OSQEn8V3cX/DYib9DSBIkZ9b8qu3abo4slmtuUrOztIc3F2g1YxgiIvJ1KvjL3OsU9hxdvXAV6+fshf7rMqw60hynjW0AtAEASDCi+y37obvjPHRPxyF56G2Q/P4GZCbb7vxtY80vWdUUqMxNasOHm4KPghZotRSDM1ATEfm4GhbdtPxlnpOj7CHk7uTp58jG8P38veew6p3D0H8XjO/PtMVVhFoOr4srGBC7D7qBlbjvuZaISm7k8HkV85o6sUCrGZfjkBHDEBFpnp1FN+VcOkH1PPUc2QgFZ6RoPCM+wDJcP3+Cfx50rY9hyJ/qos+EtggOC679Y3ubk2GNYUhGDENERHDpL3PNcfNzdO3zxQh8ZCQAWHV3Nnd+nhb8Durd2QG6v8Sg3fAWkPzsdIrWCIYhGTEMERH9QcnNKEoh83NUuP8sVr99CKu/8cOcgocQC9vLYQhJgqT15sqbcKFWIiKSX21HD2lBLZ8jYRTYt+wo9P8+Df3WSPx0JRkCqeiNbMQjz+79JFvreZFHMAwRERHV0rUr17Bx3l7oF12B/kAzHK9sAaCFZX/HOgcxIXE9cNCBk9kavs8aPbdiGCIiInLBucPnsebtg9Cv8cfavGRcRifLvhBcxd1Re6G7pwyDn2uOuM6tgey7gb6v13zim4fvq3G9NJVhnyEiIlIuBdWICKPAoTW/Q/9BLvQ/NMCPxSkw4npZov0KoWt+CLoHgnH3pBTUjaprfQJXhu/bW+1dI6MA2YFaRgxDREQqpIAakYrSCmz+cB/0/yuGfm8ifqtsarW/fchh6DrnQ/dYI3Qe3Rp+ATWscuXM8H1zeLK3TIgG5odiGJIRwxARkcp4sUbkYs4lfPPWfuhXSfjmZDKKEG7ZF4Ry9I3ciyH3lGDwpNvQpEdcNWeyw9Hh+9nZQN++NZ8vK8tnO1xzNBkREWlTTSvIS5JpBfmhQ2WrETmyNgf6eSeg31wfW4pSYEBPy75G0lkMuvUQdPcHot/kZNSL7Vy7B3NkPS9A0eul+RqGISIiUhZnVpB3sUaksqwSP/5nP/T/vYiVvzTFkYokAEmW/cnBRzGkYx50YyPRdWwb+AfJvIioI8P3FbZemi9jGCIiImVxU41I0ckifPv2fuhXCqw50QYXRXvLvkBcQ++IvdD1uQLdpGZI6tUcQHOnzi87Faz27isYhoiISFlkrBH5Pfsk9O/mYGV2PWy62BaVuMOyryHO4rmYxbirwwW0fbQz6qbdq6yOyCpY7d1XsAM1EREpSy1WkDdcM2DbJ/uh/+wC9HvicaD8Nqv9rYJ+g659Lsa224XW386GlOfASDVvD+/X8JpyHE0mI4YhIvJZ3v6idhcnhqBfPn0Z383eh5WZBqzJaYVzoqHlcH9Uolf9vdD1LoJuQhJuu7upcyPVFDC8H4Dvvs41YBiSEcMQEfkkpXxRu0s1NSInortCP+c36LPqIvt8W1xDsOWQ+tIlDGyyHzqdhHuntEGDpPrX7+/M3D0rVmh6wkMlYBiSEcMQEfkcrcxM/EeNiPFUHg79cg0ZPzTByt0J2FvWwuqw2wKPY0i749A9XB89/5KMwNBA2+dzdO6e778Hxo7V9ISHSsB5hoiIyDYvzMPjDSWFJVg3ex/0S/2x+rd+OGOMsuzzgwE9w/ZBd+dF6MY3Qct7kyD5JdZ8UkdHoGVnu314PykHwxARkdp4YB4ebzm1PR/6d45Cv74ONpxti3J0s+yrh2IMTNgH3SCBgVNaI7J5+2rOZIfcc/JwwkOfwDBERKQ2PjQzsbHSiF0Zh7Dq43zk/XQKV64FIR8x2IyOMMIfSQEnoUvOgW5UPfQal4KgW+6o+aTVcXTunj59gNddWGGeVIlhiIhIbVQ+M3HpuVKsn7sP+iVlWHWkBbobD2EuJiEB12u7ioMb4dLk15DwxjhIfk3ke3BH5+7p04cTHmpIDcvrEhGR4phrN8xf3jeTJNOoKwV9UefvOYP/PLIJQxr/hIaNgCGvd8V/DvVCd+OPWILhiId1s1/YtXNoMmsCpOXL5C9MWpqpg3ncTYusxsdf73huDk1A1eeZEx76HI4mIyJSIyfm4fEGYRTY8+Vh6P9TAP1PUdhR2sZqfxP/UxjS+gj+7+RIBBcXwmasc/eILUfm7tHwhIdKwKH1MmIYIiKfpLAv6rJLZch6dy/0X13FqkO3ItdgXfPSte4+6Lqfg+4vMWg3vAWkTRsdG+aeleXdjuAanfBQCTi0noiIqpeWZho+78Uv6jP7zmL124egXxuIdfkpKEEXy75QlKBf433QDbiGQVNaonG7FOs7q6UjuCMrzJOqKT4MVVZWYvr06fjf//6HgoICxMTEYOzYsXj11Vfh58cuT0SkcR7+ohZGgX3LjkL/79PQb43ET1eSIZAKPxiQis1Ilg7g1oQKtBzTDXdNbo86Ed3sn0zlHcHJdyg+DL355pv46KOP8NlnnyE5ORk7duzAo48+ivDwcEyaNMnbxSMiT2OThceVF5dj4/v7oF90BasONsPxyhYArs8A/deguXhVmoHw8rOAAHASwIJ4oEMNy4KYO4JXN2cSAJw9K8dlENml+D5DgwcPRnR0ND755BPLtgceeAChoaH4/PPPHToH+wwR+Qg1r8WlshB37vB5rHn7IPRr/LE2LxmXcf3/zhBcxd1Re6G7pwzD2x9F5NQnXV8WZMkS4MEHqy9MQoJvLnuhsveEN3js+1so3MyZM0XTpk3F4cOHhRBC7NmzR0RFRYmMjAyHz1FUVCQAiKKiIncVk4jcbelSISRJCNPX7vUfSTL9LF3q7RLat3SpEPHx1uWOj1dUmY0Go9i/4qj4171Zome9X4QfKq2K29ivQDzRcqNY8fI2UXK2xHSnysqq13Xza5OQYDrOnqws+/e/8ScryxNPg+eo4D2hBJ76/lZ8M9lLL72EoqIitGrVCv7+/jAYDJgxYwZGjhxp9z7l5eUoLy+33C4uLvZEUYnIXdS8Fpe9BVXz8kzbvTgEvqK0Aps/3Af9/4qh35uI3ypvA3CbZX/7kMPQdc6H7rFG6Dy6NfwCoq1PIMeyIGrpRC0nBb8ntErxYejLL7/EF198gYyMDCQnJ2PPnj2YPHkyYmNjMWbMGJv3mTlzJtLT0z1cUiJyG7WuxaW0EGcwoHjxGvy6cCc2/NIQc86OwkXcbtkdhHLc1fBX6O4uxeBJt6FJj5YAWto/nxxBxlc7URsMpsVes7NNt/v0uf7eVNJ7gkzcWu8kg/j4eDFv3jyrbf/85z9Fy5Yt7d6nrKxMFBUVWX5yc3PZTEakZhkZjjWlONF87naVlULMnq2IJqDD3/4ulndKF2ekaKvHPYl4MRafirG3bRJLX9gqivOKnTuxHE1c5qY2W02gjja1Kc3SpUJERla9lshIIdLTFfGeUAs2k/2htLS0yhB6f39/GI1Gu/cJDg5GcHCwu4tG5PuU0sFTbbUHtjp6V0fmJqDKskr88O990H9+CfpfmyK5YjeWYDpMQ72ui0cePpUeh/Smi80yZ8+a3g8Gg+39jqzf5ehaYc6877z5vs3MBB54wPa+8+eB115z7Dy+1CyoBm6NWjIYM2aMiIuLE6tWrRI5OTkiMzNTNGzYULz44osOn4MdqIlcIEcHz8pK01+4GRmm367+da+m2gN7Hb3dXAtw6cQlsXjiD+LPiVtEA+mC5dR+qBQnESeMtenk7Op1OtOx3db7LSHB+Q7F3uyYXFkpRFycc689a4aq5anvb8WHoeLiYjFp0iTRpEkTERISIpo1ayZeeeUVUV5e7vA5GIaInCTHyC25v5TMZbq5XEoaTVbT6CqZQ9yx9cfF7GHZ4q4GO0UArlm3yEjnxOhmm0XW8Hnyf/k6cp3+/kJ8/bVzF1Tb8OztEYeONhu68T3haxiGZMQwROQEOYZLu+tLSa7aA3dx5svQheeisrxSbPngF/FStyzRJvholVO2CjomXuyaJTa//4uoLP/j9ZG7v5WC+kJVKVdt37e15ehzfWOZlBrsFYJ9hojIO2o7csudI6gUsBZXtZzp5xEf79CCqpdPX8bat/dBv9yANTmtcE60s+zzRyV61d8LXe8i6CYk4ba7bwVwq/UJ5Oxv5eW+UNVy9X0rZ/8iZ/qspacD//lP1QlEvbTIrtYxDBGpndydRWs7XNrdw+CVvGimo1+Gs2cDEybYfZ1O/HAK+jm/QZ9VF1nn26ECPSz76kuXcF+T/dANkXDv88mo3/R2m+ewMC95kZdnO6A60skZsD83TnXc1aHd1nvelfet3DOap6YCcXGm57o68fHAK6+YfpQa7LXGmWqkkydPuquGyq3YTEY+yx2dRWs7XFqNw+Dl4mJHb0OFQWz9z17x8h1Zom3I4Sp3ax74u5jSKUtkzd4trpVcc75cte1v5eG+UDVei633vLND1t3ZlFtTGdgM5jBF9hkKDQ0Vr776qrhy5Yq7yuMWDEPkk9z1n3ltR25pdXkFMweDx5UzV8SyqdvEY803iSip0OpQP1SKXuG7xf8NyhKH1vwmz6i82vS3cnNfKKeuwd57HjDN4+PI+9bd/Yuqm2eIQcgpigxDP/zwg+jatauIiYkRn376qbvKJDuGIfI5nvjP3NWaBG8Ng5drGL8cli6tOsQ6Pl6cffNj8cGfNoqBjX4WwbhqtTsMl8SIhB/E509vEeeOnLc+lyO1f45cv6vPkTMdg93Vod2R97w5DNX0vvVEYK+sFOL774V49VXTz/ffc4SYCxQZhsw+++wzER8fLzp06CCyVPDXHcMQ+RxP/Gdem5oETw+DV9qilzbKU4BocT+WWhUxKeCEmNQhW3w/a6cov2xjuhBHa//ccf03BidHR4/Nnu2+kPvqq46VIT295vetGptylRT2PUjRYUgIIUpLS8Xf/vY3ERoaKoYNGyaOHj0qZ7lkxTBEPsdT/5nX5j9gTw2D9/bcMjcpW5AhjECVSQ4NkIQBkpgW8raYOSBL7Ft+VBgNRvsncrT276uv5L9+W6+dv3/NZZH7C9pWORx5z9f0vlVbU67Swr4HKT4MlZSUiM2bN4vJkycLPz8/ERwcLKZMmSKKi51c28YDGIZIlar7D10t/5m7+69ZJcwtI4TI25kv/v3njWJIox9FLuKEwU55jM6Ux9HXuGHD2l3/za+RvXBV3WO4q7bP2Zm8HX3P+8KM5hqZk0iRYejDDz8Ujz32mGjbtq0ICAgQwcHBokuXLmLChAnik08+EXfddZeIj48X27dvd1d5XcIwRKpT01+CNf1nDgjRqJEQTszUrkpeCoVGg1Hsyjgo0vtmic6h+y0P0xsylsfZCfxceTxna4Bs7XdHbZ+zo9dcCTC+MKO5kkKbmygyDMXHx4vhw4eLt956S2zZskWUlZVVOWbGjBkiOTlZtgLKgWGIPK62zUuO9hOx9Z+5vQDlizzY9+Pqxati9fSfxdNtNop4/7wqD9Gt7l6RmeJgvxZHyiPH0g7VPZ6rNS+AqW+QO/uuOHvtrgYYX5nR3Ns1wG6kyDDkiIKCAuHn5yf3aWuFYYg8qjbt+87+JVhTn4ra/JWrhg6bznxZuHA9BXsLxSdjN4lhMVtFXVy2OmUoroihjbeJj8dsEvm/nHG+PDVxpCmnUSPXHs+Vmhdnw1xtOFsrVpsAo+T3uRo7estMtWHIaDSK7OxsuU9bKwxD5DG1bd935cu0vLz2/UZsXYcaOmw62vfj668duh6jwSh++fqweP2eLNGt7l4hwWB1lzi/0+LpNhvF6uk/i9Lzpa6XR66mHPN1Oft4ta11cndNhKPle/VV5QUYObFmSL1hSIkYhsgj5Gjfd+UvQbn/w1RSh01H/mqvKTC88EK113Pt88Vi7Rs7xLNts0VT/9wqh3UK3S+m98kSO784UP3oL0fLI3dTjiuP52p/JE/1UVFTB2d34vPAMCQnhiHyCDlCiSvnkLMqXUkdNp2pnbIXGL76qtrrMQDiJOKEHyotm0NQKgZH/ST+/eeNIm9nvnxld2dTjrOP50rNkKfDsBo6OHuCxp8HhiEZMQyRR8gRSlz5S1DOmiGlVMu7UjtlKzA4eD33S0vFEy03ihUvbxMlZ0vkuQZP90Vx5vEcGY3oiVFjNVF6B2dP0fDz4Knvb65aTyQXR1foru44f3/TitnDh5tWExfi+j5JMv2eM8d6ZWu5ViUHar9ivRwMBtNK4rauRQjT9UyeDAwdav083LSafUVpBQ7P/xEpDjzkkv9ehd/DvWpbcms3lcdltlZot7WyuTOP58j7bPFioGFD766onpZmep21vrI7nwf3c2vUUgjWDJFHyNm+7+xfgnJVpSuhZqgWZTh/7IL44pkt4qGEH0Q4Lsk77483uLsju4ZrHEgdPPX9LQlh688v31JcXIzw8HAUFRUhLCzM28UhX5aZafprG7D91/aSJaa/8hzhaI3AjY89aRJw6tT1bQkJppokZx4zMbHmWqacHPf9VbpoETBqVM3HZWQAI0fi8De/Q//+Sei31McPRSkw4HqFdzQKcCCgHRpUnoVk6xyeuB5Xmd9LN78OrryXquPs+4zIgzz1/c0wRCQ3OUKJq+T4YpMz0LkiOxvo27fGwz5sMRtzcobiSEWS1faU4KPQdcyDbmwkuo5tA/9VK7x7Pa4wh9Ib30M3UnKII5IRw5CMGIbI49T+17a3A101tVNGSDiFeCQhB0b4IxDX0CdiL3R9r0A3+VYk3hlf9ZzevB5XOBgIkZUlT78kIoViGJIRwxCRC7wZ6DIzIR4YDkBYNW8Z/7j1KBZANLsVuqH+GDAlGWHxDnyuDQZTyMjONt3u08f0o8SQ6mRTIZGv8tT3N0eTEZFtco2GcpDhmgFbP94P/WcXoN/THq2wBHMxCQm4XptTHNQQ+WOm4tN5D8M/yMkQs2KFde3Q66+bmprmzlVe7ZAcIxOJyGGsGSIiryk+VYzvZu+HfrkBq3Na47yItOwLQAV6h/+Cp1K2ILW3Hxr3a+d67ZSnOiPLRQkd2YkUgM1kMmIYIlKO41tOQT/nN+izbkH2hbaoQJBlX33pEu5rsh+6IRLufT4Z9ZuG1/4B1doZ2dsd2YkUgM1kROQTjJVG/LzwAPQLzkG/KxZ7y1oAuN7JuXlgDnTtTmDI6Pro+VQKAkJ6yluAzZvtByHAFDRyc03HKakzclqaKfDc3PE7Pl65Hb+JVIphiKg21D5qzE2uFFzButn7oF9WgdXHWqFQXJ8H2g8G3Bm+F7o7L0E3vglaDmwGIMn+yWpLCbNqu4ozDxN5BMMQuZ+vBgZbw7WV2iHXA3J/Oo1Vc45Bv74ONpxti3J0t+wLQxHuTdgP3SCBgVNaI7J5B88VTO2dkT3ckZ1Ii7TdZ8hXv6SVxFcDg9o65LqBsdKInf87BP0nhdDvaIw9V1tZ7W8WcAK6lOPQjaqH1GdSEHRLkJ0zuRk7IxOpFjtQy8jmk+mrX9JK4quBQa0dcmVQeq4U6+fug35JGVYdaYF8Y2PLPglG9Ki3D7o7LmDIuHi0HnwrJD+bi2B4HjsjE6kSw5CMqjyZvvolrSS+HBg0Njvw6V0FWPXOEejXheD7wrYoQx3LvltwGQPi9kE30ID7prRCo9YNvVjSGqhtFmoi4mgytzEYTP8h2sqAQpi+pCdPNnVaVNuXtJKodQSPI9TcIdcBwiiw58vD0P+nACt/isLO0jYArtcANfE/hSFtfoNu5C3oPT4FwWE9vFdYZ7AzMhHZob0w5Mtf0kriy4FB7R1ybSi7VIYNc/dC/9VVrDp8G04ZWgEw9QGSYETXugeg63EOuqdi0TatOSQ/G+t/qQE7IxORDdoLQ778Ja0kagsMznSmT001NfHV1CE3NdW9Za6lM/vOYvXbh6BfG4jv8tuiFF0s+0JRgv4xe6EbUIFBz7dCdEpKNWciIlI37YUhtX1Jq5WaAoOznen9/U37hg83XYetDrlz5iiu+UUYBfZmHoX+36eh39oQP5e0gcD15z/OLx+6VkehG1EHd01qi5D63as5GxGR79BeB+q6dTnM1lPUMIKnNp3pvdUh14larPLicmx8fx/0i65Af+BWnDBYN291Dj0AXbdC6J5sjA4PtVTO6C8iInA0mazsjiYDlPsl7Ss8HRicae6SY8Sbp+eqcqAW6+zBc1jzziHov/HH2rwUXEE9y6EhuIp7ovZC168Mg6e0QGzHxjc/AhGRYjAMycjheYY4zFZe5qCQlwecPQs0agTExbkvMDjb3KW2IfJ2arGEJAECWN5hOt76bRi2Xk6BgJ9lf4xfAQa3OALd8BDcPSkFoQ1DPV1yIiKXcGi9u3GYrXtVF0zcFYRsNXfl5Zm226rtU1Nn+mqmhJCEgBESOu35GNvwCgT80KHOIeg6F0D3eBQ6/bkV/ALcUAPEGdyJyEdoNwwBHGbrLq4Ek9pwde4oNXWmr2FKCD8INEEuMvvOQ8eZDyKh2/Wh8W7BGdyJyIf41XyI9+Xl5eHhhx9GZGQkQkND0aFDB+zcudPbxSJbagomgCmYGAzyPaYzc0fdyDziTbLTaViSTE2nXhzxdvib3/HW4Gz8476tDh0/9MkoJHSLdW+hzGH35ufcHHYzM937+EREMlN8GLp48SJ69uyJwMBAfPPNNzhw4ADefvtt1K9f39tFI1tcDSa14Wpzl3mIPFA1ELlriLzBYOqrtGiR6fdNobCyrBLZc/bg+c7ZaBGUg1b3NcMLq/tgw1UHZ3l2dy2WN8IuEZGbKb6Z7M0330RCQgIWLFhg2ZaYmOi9AlH1vNEPpzbNXWlppmY7W00+cnemt9O0VPLqG9DvvxX6lQLfnGyDi6IDAMAPBtyNdbir7s9o3bEOKg82RsD5M96dt4kzuBORD1J8GFq5ciUGDBiABx98EBs3bkRcXBzGjRuHJ5980u59ysvLUV5ebrldXFzsiaIS4J1+OLWd4NETnent9KMynspDnafH4CsswTKYglekdB5/j/oIT5S8i9ArhUAJgM0AIiOv94Hy1kSPaup0TkTkIMU3k/3+++/48MMP0bx5c6xduxZPP/00Jk6ciP/+97927zNz5kyEh4dbfhISEjxYYo3zRj8cOZq7zJ3pR440/Za5aUxMnARbs1j4wbTtfTyLl7qsx+b3f8WZxVmYWPg3UxC60YULpt8REdbbGzQA/v53IDzcbvObbNTU6ZyIyEGKn2coKCgInTt3xo8//mjZNnHiRGzfvh1bt9ruVGqrZighIcHt8xTQH7w1qaXC5o4qPlWMte/sx9HFO/By/sSa75CVZQqJNU0EGRcHPP448N571wPSzdw1sss8USVncCciD/DUPEOKrxmKiYlBmzZtrLa1bt0aJ0+etHuf4OBghIWFWf2QB5n74cTFWW+Pj3fv7N5pacDx46ZQkZFh+p2T49EgdHzLKbw3fCP6R+5Ew4QQjJjdA3vzGzp25/x8x/rknDoFpKfbD0KA+0Z2eaPTORGRmym+z1DPnj1x+PBhq21HjhxB06ZNvVQicoi3JrV099xRN000aOh2B37+/DD0C89DvysO+8qbA7i+/leLwBz0SjoDHHHg3DEx8vW1qW5+pdryZKdzIiIPUHwz2fbt23HHHXcgPT0dI0aMwM8//4wnn3wS8+fPx5///GeHzuGpajafwFmF7bPRDJeHWEzAe5bOz/6oRM/wfdDdeQm68U3QcmAz55qWNm92bIkQZ8yeDURHy/968r1CRG7mse9voQJ6vV6kpKSI4OBg0apVKzF//nyn7l9UVCQAiKKiIjeV0EcsXSpEfLwQpq9s0098vGm7xp2d+R9hBITxxucGEAZIwgBJvBU5Q3zxzBZx/tgF2ydYulQISTL93HgO8+3Jk4XIyhKivFyIyEjrY+T84etJRCriqe9vxdcMyYE1Qw6wt4SGuzs9K5Sx0oid/zsE/SeFWL29EZaX3Ys4nLLZyU5IEiRHOg3b6uDt72898is+Hrh0CbhyRa5LsabR15OI1Imr1suIYagG5mac6kYwaWCEUOm5Unw/ey/0S8ux6mhLFBijAQC9kY1syLS6vblpacUKU/8ab9DI60lE6sdV67XIW30wNDyr8OldBVj1zhHo14Xg+8K2KEM3y75bcBkD4vZhYotsIMuBkznS+dnf3/S6jh7tcplrzYdfTyIiVzAMKYU3VwHX0KzCwiiwe9Eh6D8+A/3PUdhZ2gZAY8v+pv6noGvzG3Qjb0Hv8SkIDusBZJcDWek1n9zRiQZrCp+e4gOvJxGRHBiGlMBefx3zXDHu7t/h47MKl10qw4a5e6H/6ir0h5ojz9gaQGsAgAQjutY9AF2PcxjydCxS7m8OyS/e+gS1Xe7jZnKGEPNIsago0+3CQuDMGeC552q+r0pfTyIiubHPkLcpob+OD84qXPBrIVa/cxj6tUFYV5CCUtS17AtFCfrH7IVuQAUGPd8K0SmNaj6hnLNqZ2fXfvh8da+JD76eRKRNnIFaK5zpr+MuPjCrsDAK/LrkCGb0y0a3W/Yhpn0UnvgsFSsKuqEUdRHvfxpPt9mENenbcf6iP5ad7o7HFqQ6FoQAeWfVdmT9tsjIqmuQ3bgfsP+a+MDrSUTkSQxD3qaU/jreWkKjFsqLy7F2xg48224jEoPy0P7BFnj1+z74uSQFANA59ADS+2ZjV8YhnLwWgw/398LAv3dBSP0Q1x5QruU+HAkr8+ebmrzS06uGIkdeExW+nkRE3sJmMneraYSYo00mjgzbloPCZxU+e/Ac1rxzCPpv/LE2LwVXUM+yLwRXcU/UXgwZUIZBk1sgtmPjas6kAI4uLFub10ThrycRUXU4z5CMvBaGHBkh5q3+HSr5khRGgQP636D/8BT0P0Zg6+UUiBsqNGP8CjC4xRHohofg7kkpCG0Y6sXSukAlrwMRkTcwDMnIK2HImRmd5eyc62jZvDWM3wHXrlzD5g/3QZ9xGSv3JSGnsonV/g51DmFIlwLoHo9Cx1Gt4BfA1l4iIl/EMCQjj4chV0aIOdpkUlsKXXbj/NEL+Oadg9CvlvBtbjKKEW7ZF4wy3NVoL3R3X8XgybchoVusx8tHRESexzAkI4+HIVf7Abm7yUQJw/hvcPib36F//yRWbm6AH4pTYMT1x4ySzmLwbYegeyAI90xKxi2Nb3F7eYiISFm4HIeauTpCzN/fvZ2kZ8xwbtkNmcNZZVkltny0D/ovLkH/a1McrWgGoJllf9uQI9B1PA3dow3RdWwb+AU4OIkhERFRLTAMuYMSZ3TOzARee82xY/PzZetXdOlEEb59ez9WrhT45mQyLokOln2BuIa+kb9C17cEgyfdisQ7WwBo4fC5iYiI5MBmMndQ2gzANTWP3WzsWGDhwqrbHexXdGz9Cejfy4F+Yzg2X0pBJQIt+yKl8xiUdBC6Yf7o/1wywuIVNiM4EREpBvsMyciro8kAz4wQq44cyz+Y2QhyhmsGbP14P/SfXcDKPQk4dO1Wq7u0CT4GXYdT0I2JQPfHk+EfxKHjRERUM/YZUjvzDMC2mprkHiFWEzlnr/6jX1FJ5rdYszUC+hUGrMlpjfOineWQAFSgV4O90PW+DN2ERNx6120AbpOvDErDuYKIiFSNYcid0tKAoUO9/0Xphr5JT4+4gC8wyHK7gXQR9zU9AN0QCQOmJKN+046yP6YiKXzOJiIiqhmbybSgpj5MLuiDLOQHNoWu3QnoRtdHz6dSEBCisWxtb84ms6++Ah580LNlIiLyIWwmI/mYFwYdPtzU56cWgUgAuBoYhvnL49HiviQASbIVU1UMBlONUHXP5ciRpufb3HeMiIgUiesYKJXBYOr4vGiR6bfBULvz2VvF3EkSgNCwQLQYoNEQZLZ5c82j8wwGU81QZqZnykRERC5hGFKizExTs1bfvsCoUabfiYm1/1JNSwOOH4fx+/U49pdZ+DT5bRQgGkZIzp3n/HlTGNAyZzqlT55c+zBLRERuw2YypbHXDyUvz7TdxSH5pedK8f3svdAvLceqo8koMN4FALgfiViC4TBCgh+caD6rzQg1Xxh95Uyn9Btn9SYiIsVhGFKS6vqhCGHqfzJ5smmEmgPhIW9HPlbNPgr99yFYX9gWZehm2VcPxRgQtx+6+6Jwpe0ChM161fFJGQHXR6j5yuir1FRTuR19zuSc3oCIiGTF0WRK4uoCr38QRoHdiw5B//EZ6H+Ows7SNlb7m/qfgq7Nb9CNvAW9x6cgOCz4+k5zbU1enilwnTtn+7FrM3u2vVovb0xEKYfMTOCBBxw79sbXzBdqxoiIPICjybTIhQVer164ig3v7oP+q6tYdbg58oytAbQGAEgwotst+6HrcR66p2KRcn9zSH7xts954yKxdepUP3v2nDnOf3nLXOulCGlppuHzI0fa7xNkDo+pfyw66ys1Y0REPoRhSEkcbHq6UBqCZWM3Q782COsKUlCKLpZ9oShB/5i90A2owKDnWyE6pa3z5XDH7Nk1jb76Y2Zr1fWtefBBU+CxNZ/QzeHRTf3BiIiodthM5ihPNG3UMDmiAHBGaow4cQpGXH/seP/T0LU6Bt2IOug7sS1C6ofIVx65rnnRItPIuJpkZJhqWtTGVo1PQsL18FjTYrmeXryXiEgF2EymJJ5q2rhhckQhSZBuCETm4e/jxPswwh+dQw9A160QQ56KQfsHW0Dyi5WvHDeWR65aGkc7XLth6RCPBNmall7x1ZoxIiIfwDBUEw82bZw9eA6r10ShsP4bGHXxPcTj9PWHQxy+CB+PgUMaYt7kAsR2bAOgjf2TKY159JW9JUFu7lsjF0/20akuPLrQH4yIiDyDzWTVcXPThjAKHND/Bv2Hp7Dyh0hsu5IM8cc8mH4wYJi0AvfG7EHK3TFo/38PIzS6ntOPoSjmYAnY7pgtd58ZJY1eq+VIQSIiLfJUMxnDUHXc8AV27co1bPpgH/QZl6Hfn4ScyiZW+2+vcxC6LmegezwKHUe1gl+Aj00SXlPfGrkorY9OTYvlss8QEVEV7DOkBDI1bZw/egHfvHMQ+tUSvs1NRjE6WvYFowx3NdqLIfdcxeDnmiO+y/Wh8T6ppr41clFaH53qFsutzZQFRERUawxD1XGx068wChz+Ngf6909Cv6UBfihOgRE9LfujpLMYfNsh6B4IQr/nUlA3qsvNZ/RtcnbMtkeJfXTcMWUBERHVmrbDUE2jjJzo9FtRWoEf5u+H/otLWPlrIo5VNAPQzHJo25AjGNLpNHSPNkSXMW3gFyBzR2Gy5s3Ra9XxVM0YERE5TFt9hlatQti9916fAM+RUUbVdPoVALbc+zo+PNAb35xMxiVR37I7ENfQN/JX6PqWQDf5VjTtaWfmZ3IP9tEhIlI9dqCWkeXJBBAWH2+a1O+ttxwfZWQjOJ2RojFevIeluD7zcEPpHAY1OwTd/f7o/1wK6sWqfPSX2nl69BoREcmKYUhGVmGopoNvqjGoLKvE1o/3Y9Vn55C/pwAVlX7IRww2IxVG+KNN8DHoOpyCbkwEuj+eDP8g1jIoiqdGrxERkewYhuyYOXMmXn75ZUyaNAlz5sxx6D5OhaE/ZA+fh092tsea421wQURYtgegAr0b7IWuz2UMfjYRt97V1OlrIA/jKvFERKrEofU2bN++HfPnz0e7du3c/lj/XhKBxbgTANBAuoj7mh6AboiEe59PRniTjjXcmxTFE6PXiIhItVQzo9+VK1fw5z//Gf/5z3/QoEEDtz9eYIDAXztnY+O7v6CwtB6+yOmJh+begfAm4W5/bCIiIvIc1dQMjR8/HoMGDcI999yD119/vdpjy8vLUV5ebrldXFzs8OMIAPDzw39LhgNBQS6WVoXYlERERBqlijC0ePFi7Nq1C9u3b3fo+JkzZyI9Pd2lx5IAwGgEfvxRO00rzi5myuBEREQ+RPHNZLm5uZg0aRK++OILhISEOHSfadOmoaioyPKTm5tr2Wd09IHlmpnYYDCtcbZokem3wSDPeWvLXK7nngMeeKDq0hV5eaZh6ZmZ1tszM03z9/TtC4waZfqdmFj1OCIiIpVQ/Giy5cuX4/7774f/DTUPBoMBkiTBz88P5eXlVvtsuXE0Wb1GjSCdPVvzA8uxerizNS6eYqtcttw8MaGSVoEnIiKfx6H1f7h8+TJOnDhhte3RRx9Fq1at8NJLLyElJaXGc1jNQN2vH3Drre6fmVipwcFeuaqTlWVqClPSKvBEROTzPBWGFN9MVq9ePaSkpFj91K1bF5GRkQ4FISupqaZO0XPnmm6bg4mZXKuHGwymmhdbgcO8bfJkzzeZVVeu6uTnO7cKPBERkYooPgy5hXn18Lg46+3x8fLU2Cg1ONRULntiYty3CrxS+1TZo7byEhFRjVQxmuxm2dnZtT+JO1cPd1dwqC1nH8/c9JWa6nhwc2YVeKX2qbJHbeUlIiKHqDIMycZdMxM7GgicCQ5ycObxbm4yTE01ffHX1NcqNdWx89vru2QexeZqDZ27hv27q7xEROR12mwmczdzcLi5T5KZJJkWC3U0OHiqXDe6ucnQ31++vlbu6lPlrmH/Su0DRkREsmAYcgc5g4OcHCnX5Mmm0WM5OVVrOuTqa+WOPlXmmhtH50tyhlL7gBERkSwYhtzF3Z203VGupUuB2bNNTYf2glpaGnD8uCkwZWTYD07VkbtPlbtrbpTaB4yIiGSh7T5D7ubOTtreLFdt+1rJ3afKmZobV8qt1D5gREQkC4Yhd3NXJ+3a8ma55O6M7e6aG7nLS0REisJmMvI8uftUubvmRql9wIiISBYMQ+Qdcvap8sToPaX2ASMiolpT/NpkcvDU2ibkArnmBTKPJgOsm7LkXgvOXfMYERFRFVyoVUYMQxpha4bohARTExZrboiIVMdT39/sQE2+Q6mj94iISNEYhsi3KHX0HhERKRY7UBMREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpjEMERERkaYxDBEREZGmMQwRERGRpik+DM2cORNdunRBvXr1EBUVhWHDhuHw4cPeLhYRERH5CMWHoY0bN2L8+PHYtm0b1q1bh8rKSvTv3x8lJSXeLhoRERH5AEkIIbxdCGecPXsWUVFR2LhxI3r16uXQfYqLixEeHo6ioiKEhYW5uYREREQkB099fwe47cxuUlRUBACIiIiwe0x5eTnKy8stt4uLi91eLiIiIlInxTeT3UgIgSlTpuDOO+9ESkqK3eNmzpyJ8PBwy09CQoIHS0lERERqoqpmsvHjx2P16tXYsmUL4uPj7R5nq2YoISGBzWREREQqwmaym0yYMAErV67Epk2bqg1CABAcHIzg4GAPlYyIiIjUTPFhSAiBCRMmYNmyZcjOzkZSUpK3i0REREQ+RPFhaPz48cjIyMCKFStQr149FBQUAADCw8NRp04dL5eOiIiI1E7xfYYkSbK5fcGCBRg7dqxD5+DQeiIiIvVhn6E/KDyrERERkcqpamg9ERERkdwYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTGIaIiIhI0xiGiIiISNMYhoiIiEjTVBOGPvjgAyQlJSEkJASdOnXC5s2bvV0kIiIi8gGqCENffvklJk+ejFdeeQW7d+9GamoqBg4ciJMnT3q7aERERKRykhBCeLsQNenWrRs6duyIDz/80LKtdevWGDZsGGbOnFnj/YuLixEeHo6ioiKEhYW5s6hEREQkE099fyu+ZujatWvYuXMn+vfvb7W9f//++PHHH71UKiIiIvIVAd4uQE3OnTsHg8GA6Ohoq+3R0dEoKCiweZ/y8nKUl5dbbhcVFQEwJUwiIiJSB/P3trsbsRQfhswkSbK6LYSoss1s5syZSE9Pr7I9ISHBLWUjIiIi9zl//jzCw8Pddn7Fh6GGDRvC39+/Si1QYWFhldois2nTpmHKlCmW25cuXULTpk1x8uRJtz6ZSlNcXIyEhATk5uZqqq8Ur5vXrQW8bl63FhQVFaFJkyaIiIhw6+MoPgwFBQWhU6dOWLduHe6//37L9nXr1mHo0KE27xMcHIzg4OAq28PDwzX1JjILCwvjdWsIr1tbeN3aotXr9vNzbxdnxYchAJgyZQpGjx6Nzp07o0ePHpg/fz5OnjyJp59+2ttFIyIiIpVTRRh66KGHcP78efzjH/9Afn4+UlJSsGbNGjRt2tTbRSMiIiKVU0UYAoBx48Zh3LhxLt03ODgYr732ms2mM1/G6+Z1awGvm9etBbxu9163KiZdJCIiInIXxU+6SERERORODENERESkaQxDREREpGkMQ0RERKRpqgxDH3zwAZKSkhASEoJOnTph8+bN1R6/ceNGdOrUCSEhIWjWrBk++uijKscsXboUbdq0QXBwMNq0aYNly5a5q/guc+a6MzMz0a9fPzRq1AhhYWHo0aMH1q5da3XMwoULIUlSlZ+ysjJ3X4pTnLnu7Oxsm9d06NAhq+N87fUeO3aszetOTk62HKOG13vTpk3Q6XSIjY2FJElYvnx5jffxhc+3s9ftK59vZ6/bVz7fzl63r3y+Z86ciS5duqBevXqIiorCsGHDcPjw4Rrv54nPuOrC0JdffonJkyfjlVdewe7du5GamoqBAwfi5MmTNo/PycnBfffdh9TUVOzevRsvv/wyJk6ciKVLl1qO2bp1Kx566CGMHj0av/zyC0aPHo0RI0bgp59+8tRl1cjZ6960aRP69euHNWvWYOfOnejbty90Oh12795tdVxYWBjy8/OtfkJCQjxxSQ5x9rrNDh8+bHVNzZs3t+zzxdd77ty5Vtebm5uLiIgIPPjgg1bHKf31LikpQfv27TFv3jyHjveVz7ez1+0rn29nr9tM7Z9vZ6/bVz7fGzduxPjx47Ft2zasW7cOlZWV6N+/P0pKSuzex2OfcaEyXbt2FU8//bTVtlatWompU6faPP7FF18UrVq1str21FNPie7du1tujxgxQtx7771WxwwYMED86U9/kqnUtefsddvSpk0bkZ6ebrm9YMECER4eLlcR3cLZ687KyhIAxMWLF+2eUwuv97Jly4QkSeL48eOWbWp4vW8EQCxbtqzaY3zl830jR67bFjV+vm/kyHX7yuf7Rq683r7w+RZCiMLCQgFAbNy40e4xnvqMq6pm6Nq1a9i5cyf69+9vtb1///748ccfbd5n69atVY4fMGAAduzYgYqKimqPsXdOT3Plum9mNBpx+fLlKovdXblyBU2bNkV8fDwGDx5c5S9Lb6rNdd9+++2IiYnB3XffjaysLKt9Wni9P/nkE9xzzz1VZmlX8uvtCl/4fMtBjZ/v2lDz51sOvvL5LioqAoBqF2H11GdcVWHo3LlzMBgMVVarj46OrrKqvVlBQYHN4ysrK3Hu3Llqj7F3Tk9z5bpv9vbbb6OkpAQjRoywbGvVqhUWLlyIlStXYtGiRQgJCUHPnj1x9OhRWcvvKleuOyYmBvPnz8fSpUuRmZmJli1b4u6778amTZssx/j6652fn49vvvkGTzzxhNV2pb/ervCFz7cc1Pj5doUvfL5ry1c+30IITJkyBXfeeSdSUlLsHuepz7hqluO4kSRJVreFEFW21XT8zdudPac3uFrGRYsWYfr06VixYgWioqIs27t3747u3btbbvfs2RMdO3bEe++9h3fffVe+gteSM9fdsmVLtGzZ0nK7R48eyM3NxVtvvYVevXq5dE5vcbWMCxcuRP369TFs2DCr7Wp5vZ3lK59vV6n98+0MX/p8u8pXPt/PPvssfv31V2zZsqXGYz3xGVdVzVDDhg3h7+9fJe0VFhZWSYVmjRs3tnl8QEAAIiMjqz3G3jk9zZXrNvvyyy/x+OOP46uvvsI999xT7bF+fn7o0qWLYv6SqM1136h79+5W1+TLr7cQAp9++ilGjx6NoKCgao9V2uvtCl/4fNeGmj/fclHb57s2fOXzPWHCBKxcuRJZWVmIj4+v9lhPfcZVFYaCgoLQqVMnrFu3zmr7unXrcMcdd9i8T48ePaoc/91336Fz584IDAys9hh75/Q0V64bMP3FOHbsWGRkZGDQoEE1Po4QAnv27EFMTEytyywHV6/7Zrt377a6Jl99vQHTaI1jx47h8ccfr/FxlPZ6u8IXPt+uUvvnWy5q+3zXhto/30IIPPvss8jMzMSGDRuQlJRU43089hl3uKu1QixevFgEBgaKTz75RBw4cEBMnjxZ1K1b19KrfurUqWL06NGW43///XcRGhoqnnvuOXHgwAHxySefiMDAQLFkyRLLMT/88IPw9/cX//rXv8TBgwfFv/71LxEQECC2bdvm8euzx9nrzsjIEAEBAeL9998X+fn5lp9Lly5Zjpk+fbr49ttvxW+//SZ2794tHn30UREQECB++uknj1+fPc5e9+zZs8WyZcvEkSNHxL59+8TUqVMFALF06VLLMb74eps9/PDDolu3bjbPqYbX+/Lly2L37t1i9+7dAoB45513xO7du8WJEyeEEL77+Xb2un3l8+3sdfvK59vZ6zZT++f7mWeeEeHh4SI7O9vqfVtaWmo5xlufcdWFISGEeP/990XTpk1FUFCQ6Nixo9WwvDFjxojevXtbHZ+dnS1uv/12ERQUJBITE8WHH35Y5Zxff/21aNmypQgMDBStWrWy+nAphTPX3bt3bwGgys+YMWMsx0yePFk0adJEBAUFiUaNGon+/fuLH3/80YNX5BhnrvvNN98Ut956qwgJCRENGjQQd955p1i9enWVc/ra6y2EEJcuXRJ16tQR8+fPt3k+Nbze5qHT9t63vvr5dva6feXz7ex1+8rn25X3uS98vm1dMwCxYMECyzHe+oxLfxSQiIiISJNU1WeIiIiISG4MQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0RERKRpDENERESkaQxDREREpGkMQ0SkSosWLUJISAjy8vIs25544gm0a9cORUVFXiwZEakN1yYjIlUSQqBDhw5ITU3FvHnzkJ6ejo8//hjbtm1DXFyct4tHRCoS4O0CEBG5QpIkzJgxA8OHD0dsbCzmzp2LzZs3MwgRkdNYM0REqtaxY0fs378f3333HXr37u3t4hCRCrHPEBGp1tq1a3Ho0CEYDAZER0d7uzhEpFKsGSIiVdq1axf69OmD999/H4sXL0ZoaCi+/vprbxeLiFSIfYaISHWOHz+OQYMGYerUqRg9ejTatGmDLl26YOfOnejUqZO3i0dEKsOaISJSlQsXLqBnz57o1asX/v3vf1u2Dx06FOXl5fj222+9WDoiUiOGISIiItI0dqAmIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJNYxgiIiIiTWMYIiIiIk1jGCIiIiJN+3+0i07aOseSSwAAAABJRU5ErkJggg==", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4227,23 +4075,95 @@ }, { "cell_type": "markdown", - "id": "31c54ed4", - "metadata": { - "editable": true - }, + "id": "849de571", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] }, { "cell_type": "code", - "execution_count": 28, - "id": "e24d96d9", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 29, + "id": "ac458170", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.]\n", + " [3.]]\n", + "Eigenvalues of Hessian Matrix:[0.30306759 4.65944342]\n", + "0 [-20.62275788] [-25.73690387]\n", + "1 [-0.03662823] [0.02925855]\n", + "2 [-0.0342458] [0.02735547]\n", + "3 [-0.03201832] [0.02557617]\n", + "4 [-0.02993573] [0.0239126]\n", + "5 [-0.0279886] [0.02235723]\n", + "6 [-0.02616812] [0.02090304]\n", + "7 [-0.02446604] [0.01954342]\n", + "8 [-0.02287468] [0.01827225]\n", + "9 [-0.02138683] [0.01708375]\n", + "10 [-0.01999575] [0.01597256]\n", + "11 [-0.01869515] [0.01493365]\n", + "12 [-0.01747915] [0.01396231]\n", + "13 [-0.01634224] [0.01305415]\n", + "14 [-0.01527928] [0.01220505]\n", + "15 [-0.01428546] [0.01141119]\n", + "16 [-0.01335628] [0.01066897]\n", + "17 [-0.01248754] [0.00997502]\n", + "18 [-0.0116753] [0.0093262]\n", + "19 [-0.01091589] [0.00871959]\n", + "20 [-0.01020588] [0.00815244]\n", + "21 [-0.00954206] [0.00762217]\n", + "22 [-0.0089214] [0.0071264]\n", + "23 [-0.00834112] [0.00666287]\n", + "24 [-0.00779859] [0.00622949]\n", + "25 [-0.00729134] [0.0058243]\n", + "26 [-0.00681708] [0.00544547]\n", + "27 [-0.00637367] [0.00509128]\n", + "28 [-0.0059591] [0.00476012]\n", + "29 [-0.0055715] [0.0044505]\n", + "theta from own gd\n", + "[[3.98281205]\n", + " [3.0137297 ]]\n", + "0 [-0.00520911] [0.00416103]\n", + "1 [-0.00487029] [0.00389038]\n", + "2 [-0.00445186] [0.00355614]\n", + "3 [-0.00403677] [0.00322456]\n", + "4 [-0.00364967] [0.00291535]\n", + "5 [-0.00329616] [0.00263296]\n", + "6 [-0.00297571] [0.00237699]\n", + "7 [-0.00268602] [0.00214559]\n", + "8 [-0.00242441] [0.00193661]\n", + "9 [-0.00218823] [0.00174795]\n", + "10 [-0.00197505] [0.00157766]\n", + "11 [-0.00178263] [0.00142396]\n", + "12 [-0.00160895] [0.00128523]\n", + "13 [-0.0014522] [0.00116001]\n", + "14 [-0.00131072] [0.001047]\n", + "15 [-0.00118302] [0.00094499]\n", + "16 [-0.00106776] [0.00085292]\n", + "17 [-0.00096373] [0.00076983]\n", + "18 [-0.00086984] [0.00069482]\n", + "19 [-0.00078509] [0.00062713]\n", + "20 [-0.0007086] [0.00056603]\n", + "21 [-0.00063957] [0.00051088]\n", + "22 [-0.00057726] [0.00046111]\n", + "23 [-0.00052102] [0.00041619]\n", + "24 [-0.00047025] [0.00037564]\n", + "25 [-0.00042444] [0.00033904]\n", + "26 [-0.00038309] [0.00030601]\n", + "27 [-0.00034576] [0.0002762]\n", + "28 [-0.00031208] [0.00024929]\n", + "29 [-0.00028167] [0.000225]\n", + "theta from own gd wth momentum\n", + "[[3.99916114]\n", + " [3.00067008]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients for OLS\n", "from random import random, seed\n", @@ -4302,23 +4222,37 @@ }, { "cell_type": "markdown", - "id": "416d20eb", - "metadata": { - "editable": true - }, + "id": "f33ed0dd", + "metadata": {}, "source": [ "## But none of these can compete with Newton's method" ] }, { "cell_type": "code", - "execution_count": 29, - "id": "9d60ac01", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 30, + "id": "e6b06cdb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.26281735]\n", + " [2.84478178]]\n", + "Eigenvalues of Hessian Matrix:[0.33978889 4.51659846]\n", + "0 [-14.67490857] [-18.08539155]\n", + "1 [-4.46170878e-15] [-1.45781905e-14]\n", + "2 [-1.21430643e-15] [-1.24768421e-15]\n", + "3 [4.92661467e-16] [4.50610071e-16]\n", + "4 [4.92661467e-16] [4.50610071e-16]\n", + "beta from own Newton code\n", + "[[4.26281735]\n", + " [2.84478178]]\n" + ] + } + ], "source": [ "# Using Newton's method\n", "from random import random, seed\n", @@ -4362,10 +4296,8 @@ }, { "cell_type": "markdown", - "id": "de82bfbc", - "metadata": { - "editable": true - }, + "id": "90de8a04", + "metadata": {}, "source": [ "## Including Stochastic Gradient Descent with Autograd\n", "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." @@ -4373,13 +4305,43 @@ }, { "cell_type": "code", - "execution_count": 30, - "id": "877c2b05", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 31, + "id": "a010a209", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[4.0586484]\n", + " [3.0718316]]\n", + "Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]\n", + "theta from own gd\n", + "[[4.0586484]\n", + " [3.0718316]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta from own sdg\n", + "[[4.02496085]\n", + " [3.12081773]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4458,23 +4420,35 @@ }, { "cell_type": "markdown", - "id": "b73c6697", - "metadata": { - "editable": true - }, + "id": "18298e5e", + "metadata": {}, "source": [ "## Same code but now with momentum gradient descent" ] }, { "cell_type": "code", - "execution_count": 31, - "id": "7f00a2d7", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 32, + "id": "3320d6c6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[3.96075051]\n", + " [3.02148021]]\n", + "Eigenvalues of Hessian Matrix:[0.27470622 4.24106503]\n", + "theta from own gd\n", + "[[3.95906059]\n", + " [3.02296298]]\n", + "theta from own sdg with momentum\n", + "[[3.95611042]\n", + " [2.99475306]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using SGD\n", "# OLS example\n", @@ -4547,23 +4521,33 @@ }, { "cell_type": "markdown", - "id": "2102c235", - "metadata": { - "editable": true - }, + "id": "f1411612", + "metadata": {}, "source": [ "## Similar (second order function now) problem but now with AdaGrad" ] }, { "cell_type": "code", - "execution_count": 32, - "id": "5f75ec0f", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 33, + "id": "19414323", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own AdaGrad\n", + "[[2.00025662]\n", + " [2.99802696]\n", + " [4.00167329]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n", "# OLS example\n", @@ -4617,33 +4601,41 @@ }, { "cell_type": "markdown", - "id": "5c66075e", - "metadata": { - "editable": true - }, + "id": "a77cdfa4", + "metadata": {}, "source": [ "Running this code we note an almost perfect agreement with the results from matrix inversion." ] }, { "cell_type": "markdown", - "id": "a95c1509", - "metadata": { - "editable": true - }, + "id": "9f488085", + "metadata": {}, "source": [ "## RMSprop for adaptive learning rate with Stochastic Gradient Descent" ] }, { "cell_type": "code", - "execution_count": 33, - "id": "527efcff", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 34, + "id": "6724b3d2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own RMSprop\n", + "[[1.99456598]\n", + " [2.99848815]\n", + " [3.99835783]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4703,23 +4695,33 @@ }, { "cell_type": "markdown", - "id": "d771fa2d", - "metadata": { - "editable": true - }, + "id": "09728e4a", + "metadata": {}, "source": [ "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)" ] }, { "cell_type": "code", - "execution_count": 34, - "id": "e778dd2b", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 35, + "id": "28aa6aad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Own inversion\n", + "[[2.]\n", + " [3.]\n", + " [4.]]\n", + "theta from own ADAM\n", + "[[1.99989103]\n", + " [3.00042093]\n", + " [3.99954925]]\n" + ] + } + ], "source": [ "# Using Autograd to calculate gradients using RMSprop and Stochastic Gradient descent\n", "# OLS example\n", @@ -4784,23 +4786,27 @@ }, { "cell_type": "markdown", - "id": "79899022", - "metadata": { - "editable": true - }, + "id": "70fc8bdd", + "metadata": {}, "source": [ "## And Logistic Regression" ] }, { "cell_type": "code", - "execution_count": 35, - "id": "6285f635", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 36, + "id": "f3dde7c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial loss: 2.772588722239781\n", + "Trained loss: 1.067270675787016\n" + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -4839,10 +4845,8 @@ }, { "cell_type": "markdown", - "id": "23027ae4", - "metadata": { - "editable": true - }, + "id": "b46c449b", + "metadata": {}, "source": [ "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n", "\n", @@ -4857,13 +4861,18 @@ }, { "cell_type": "code", - "execution_count": 36, - "id": "a2f5be06", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "execution_count": 37, + "id": "291c9b6d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.25 0.19661197 0.10499357]\n" + ] + } + ], "source": [ "import jax.numpy as jnp\n", "from jax import grad, jit, vmap\n", @@ -4875,9 +4884,35 @@ "derivative_fn = grad(sum_logistic)\n", "print(derivative_fn(x_small))" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e201d58b", + "metadata": {}, + "outputs": [], + "source": [] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, "nbformat": 4, "nbformat_minor": 5 }