diff --git a/doc/pub/week40/html/._week40-bs000.html b/doc/pub/week40/html/._week40-bs000.html index a7a4a3ac7..bf08b9260 100644 --- a/doc/pub/week40/html/._week40-bs000.html +++ b/doc/pub/week40/html/._week40-bs000.html @@ -325,7 +325,7 @@ MathJax.Hub.Config({
-

Nov 2, 2021

+

Nov 3, 2021


diff --git a/doc/pub/week40/html/._week40-bs012.html b/doc/pub/week40/html/._week40-bs012.html index e7945abc7..e5d5a3168 100644 --- a/doc/pub/week40/html/._week40-bs012.html +++ b/doc/pub/week40/html/._week40-bs012.html @@ -317,28 +317,28 @@ MathJax.Hub.Config({ 
# Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-n = 1000
+n = 100
 x = 2*np.random.rand(n,1)
 y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
@@ -353,7 +353,6 @@ Xnew = np.= Xnew.dot(theta)
 ypredict2 = Xnew.dot(theta_linreg)
 
-
 n_epochs = 50
 M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
@@ -364,16 +363,20 @@ t0, t1 = 5= np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
         random_index = np.random.randint(m)
-        xi = X[random_index:random_index+m]
-        yi = y[random_index:random_index+m]
-        gradients = 2.0* xi.T @ ((xi @ theta)-yi)
+        xi = X[random_index*M:random_index*M+M]
+        yi = y[random_index*M:random_index*M+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')
diff --git a/doc/pub/week40/html/week40-bs.html b/doc/pub/week40/html/week40-bs.html
index a7a4a3ac7..bf08b9260 100644
--- a/doc/pub/week40/html/week40-bs.html
+++ b/doc/pub/week40/html/week40-bs.html
@@ -325,7 +325,7 @@ MathJax.Hub.Config({
 
 

 

-
Nov 2, 2021

+
Nov 3, 2021

 
 
 

 
diff --git a/doc/pub/week40/html/week40-reveal.html b/doc/pub/week40/html/week40-reveal.html
index ff1024f38..3aad4d3c1 100644
--- a/doc/pub/week40/html/week40-reveal.html
+++ b/doc/pub/week40/html/week40-reveal.html
@@ -184,7 +184,7 @@ MathJax.Hub.Config({
 
 

 

-
Nov 2, 2021

+
Nov 3, 2021

 
 
 

 
@@ -499,28 +499,28 @@ j = 0
       

         

   
# Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-n = 1000
+n = 100
 x = 2*np.random.rand(n,1)
 y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
@@ -535,7 +535,6 @@ Xnew = np.c_[np.ones((2,50
 M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
@@ -546,16 +545,20 @@ t0, t1 = 5, 50<
 theta = np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
         random_index = np.random.randint(m)
-        xi = X[random_index:random_index+m]
-        yi = y[random_index:random_index+m]
-        gradients = 2.0* xi.T @ ((xi @ theta)-yi)
+        xi = X[random_index*M:random_index*M+M]
+        yi = y[random_index*M:random_index*M+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')
diff --git a/doc/pub/week40/html/week40-solarized.html b/doc/pub/week40/html/week40-solarized.html
index 087358769..d3532d62a 100644
--- a/doc/pub/week40/html/week40-solarized.html
+++ b/doc/pub/week40/html/week40-solarized.html
@@ -261,7 +261,7 @@ MathJax.Hub.Config({
 
 

 

-
Nov 2, 2021

+
Nov 3, 2021

 
 
 

 
@@ -546,28 +546,28 @@ j = 0
       

         

   
# Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-n = 1000
+n = 100
 x = 2*np.random.rand(n,1)
 y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
@@ -582,7 +582,6 @@ Xnew = np.c_[np.ones((2,50
 M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
@@ -593,16 +592,20 @@ t0, t1 = 5, 50<
 theta = np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
         random_index = np.random.randint(m)
-        xi = X[random_index:random_index+m]
-        yi = y[random_index:random_index+m]
-        gradients = 2.0* xi.T @ ((xi @ theta)-yi)
+        xi = X[random_index*M:random_index*M+M]
+        yi = y[random_index*M:random_index*M+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')
diff --git a/doc/pub/week40/html/week40.html b/doc/pub/week40/html/week40.html
index 5d49816a9..da6c5d4ee 100644
--- a/doc/pub/week40/html/week40.html
+++ b/doc/pub/week40/html/week40.html
@@ -338,7 +338,7 @@ MathJax.Hub.Config({
 
 

 

-
Nov 2, 2021

+
Nov 3, 2021

 
 
 

 
@@ -623,28 +623,28 @@ j = 0
       

         

   
# Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-n = 1000
+n = 100
 x = 2*np.random.rand(n,1)
 y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
@@ -659,7 +659,6 @@ Xnew = np.= Xnew.dot(theta)
 ypredict2 = Xnew.dot(theta_linreg)
 
-
 n_epochs = 50
 M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
@@ -670,16 +669,20 @@ t0, t1 = 5= np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
         random_index = np.random.randint(m)
-        xi = X[random_index:random_index+m]
-        yi = y[random_index:random_index+m]
-        gradients = 2.0* xi.T @ ((xi @ theta)-yi)
+        xi = X[random_index*M:random_index*M+M]
+        yi = y[random_index*M:random_index*M+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')
diff --git a/doc/pub/week40/ipynb/ipynb-week40-src.tar.gz b/doc/pub/week40/ipynb/ipynb-week40-src.tar.gz
index 44284d7bd..7878018fc 100644
Binary files a/doc/pub/week40/ipynb/ipynb-week40-src.tar.gz and b/doc/pub/week40/ipynb/ipynb-week40-src.tar.gz differ
diff --git a/doc/pub/week40/ipynb/week40.ipynb b/doc/pub/week40/ipynb/week40.ipynb
index a86a23c43..48a946bd2 100644
--- a/doc/pub/week40/ipynb/week40.ipynb
+++ b/doc/pub/week40/ipynb/week40.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "33a7f33a",
+   "id": "8c1bc594",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb6961f1",
+   "id": "532d5f80",
    "metadata": {
     "editable": true
    },
@@ -22,14 +22,14 @@
     "# Week 40: From Stochastic Gradient Descent to Neural networks\n",
     "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Ion Beams, Michigan State University, USA\n",
     "\n",
-    "Date: **Nov 2, 2021**\n",
+    "Date: **Nov 3, 2021**\n",
     "\n",
     "Copyright 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5d9b6f73",
+   "id": "642ef5f2",
    "metadata": {
     "editable": true
    },
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "896b7e7c",
+   "id": "388d28a9",
    "metadata": {
     "editable": true
    },
@@ -63,7 +63,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5285634a",
+   "id": "811c319c",
    "metadata": {
     "editable": true
    },
@@ -85,7 +85,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a063b42",
+   "id": "4e7a70d6",
    "metadata": {
     "editable": true
    },
@@ -117,7 +117,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "286abf6d",
+   "id": "1a453559",
    "metadata": {
     "editable": true
    },
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91f5da81",
+   "id": "323d7ab6",
    "metadata": {
     "editable": true
    },
@@ -147,7 +147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9a38f58",
+   "id": "61f145c0",
    "metadata": {
     "editable": true
    },
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d782cea1",
+   "id": "954c1b01",
    "metadata": {
     "editable": true
    },
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b196224",
+   "id": "942eeb65",
    "metadata": {
     "editable": true
    },
@@ -187,7 +187,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ec16fda",
+   "id": "f901816b",
    "metadata": {
     "editable": true
    },
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1f93c6a",
+   "id": "e3aba58e",
    "metadata": {
     "editable": true
    },
@@ -225,7 +225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcbae038",
+   "id": "4ca91e49",
    "metadata": {
     "editable": true
    },
@@ -237,7 +237,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c18ff285",
+   "id": "e1c5e217",
    "metadata": {
     "editable": true
    },
@@ -250,7 +250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5288661b",
+   "id": "c2ad92a4",
    "metadata": {
     "editable": true
    },
@@ -264,7 +264,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ddfb5d51",
+   "id": "f54810af",
    "metadata": {
     "editable": true
    },
@@ -275,7 +275,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "be52d134",
+   "id": "b6d7a087",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -300,7 +300,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd8c6d07",
+   "id": "aa6b9db7",
    "metadata": {
     "editable": true
    },
@@ -316,7 +316,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d3fd6f2",
+   "id": "52dba806",
    "metadata": {
     "editable": true
    },
@@ -337,7 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4809cc99",
+   "id": "256088f6",
    "metadata": {
     "editable": true
    },
@@ -360,7 +360,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "aac7dff1",
+   "id": "f3809eae",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -395,7 +395,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5396bd45",
+   "id": "f8bcda50",
    "metadata": {
     "editable": true
    },
@@ -405,7 +405,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69a3b8e1",
+   "id": "02040fa6",
    "metadata": {
     "editable": true
    },
@@ -416,7 +416,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "596c9872",
+   "id": "e7919c6b",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -426,28 +426,28 @@
     "%matplotlib inline\n",
     "\n",
     "# Importing various packages\n",
+    "# Importing various packages\n",
     "from math import exp, sqrt\n",
     "from random import random, seed\n",
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
-    "from sklearn.linear_model import SGDRegressor\n",
     "\n",
-    "n = 1000\n",
+    "n = 100\n",
     "x = 2*np.random.rand(n,1)\n",
     "y = 4+3*x+np.random.randn(n,1)\n",
     "\n",
     "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
     "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
     "print(\"Own inversion\")\n",
     "print(theta_linreg)\n",
-    "sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n",
-    "sgdreg.fit(x,y.ravel())\n",
-    "print(\"sgdreg from scikit\")\n",
-    "print(sgdreg.intercept_, sgdreg.coef_)\n",
-    "\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
     "\n",
     "theta = np.random.randn(2,1)\n",
-    "eta = 0.1\n",
+    "eta = 1.0/np.max(EigValues)\n",
     "Niterations = 1000\n",
     "\n",
     "\n",
@@ -462,7 +462,6 @@
     "ypredict = Xnew.dot(theta)\n",
     "ypredict2 = Xnew.dot(theta_linreg)\n",
     "\n",
-    "\n",
     "n_epochs = 50\n",
     "M = 5   #size of each minibatch\n",
     "m = int(n/M) #number of minibatches\n",
@@ -473,16 +472,20 @@
     "theta = np.random.randn(2,1)\n",
     "\n",
     "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
     "    for i in range(m):\n",
     "        random_index = np.random.randint(m)\n",
-    "        xi = X[random_index:random_index+m]\n",
-    "        yi = y[random_index:random_index+m]\n",
-    "        gradients = 2.0* xi.T @ ((xi @ theta)-yi)\n",
+    "        xi = X[random_index*M:random_index*M+M]\n",
+    "        yi = y[random_index*M:random_index*M+M]\n",
+    "        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
     "        eta = learning_schedule(epoch*m+i)\n",
     "        theta = theta - eta*gradients\n",
     "print(\"theta from own sdg\")\n",
     "print(theta)\n",
     "\n",
+    "\n",
+    "\n",
+    "\n",
     "plt.plot(xnew, ypredict, \"r-\")\n",
     "plt.plot(xnew, ypredict2, \"b-\")\n",
     "plt.plot(x, y ,'ro')\n",
@@ -495,7 +498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "915d2dc5",
+   "id": "5d71ac48",
    "metadata": {
     "editable": true
    },
@@ -510,7 +513,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d79babcd",
+   "id": "867a9b01",
    "metadata": {
     "editable": true
    },
@@ -522,7 +525,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6717923",
+   "id": "0f97fa56",
    "metadata": {
     "editable": true
    },
@@ -540,7 +543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f63c31d",
+   "id": "5a094f0e",
    "metadata": {
     "editable": true
    },
@@ -559,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "428883d0",
+   "id": "16711622",
    "metadata": {
     "editable": true
    },
@@ -571,7 +574,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d558ee18",
+   "id": "e98517fe",
    "metadata": {
     "editable": true
    },
@@ -581,7 +584,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff54e584",
+   "id": "e1a15dbb",
    "metadata": {
     "editable": true
    },
@@ -597,7 +600,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7aa3431",
+   "id": "a70edb37",
    "metadata": {
     "editable": true
    },
@@ -609,7 +612,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "052fe58d",
+   "id": "6696a85a",
    "metadata": {
     "editable": true
    },
@@ -619,7 +622,7 @@
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@@ -631,7 +634,7 @@
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@@ -641,7 +644,7 @@
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@@ -653,7 +656,7 @@
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@@ -669,7 +672,7 @@
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@@ -681,7 +684,7 @@
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@@ -714,7 +717,7 @@
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@@ -726,7 +729,7 @@
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@@ -744,7 +747,7 @@
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@@ -754,7 +757,7 @@
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@@ -785,7 +788,7 @@
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@@ -800,7 +803,7 @@
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@@ -818,7 +821,7 @@
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@@ -830,7 +833,7 @@
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@@ -842,7 +845,7 @@
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@@ -860,7 +863,7 @@
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@@ -883,7 +886,7 @@
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@@ -901,7 +904,7 @@
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@@ -913,7 +916,7 @@
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@@ -925,7 +928,7 @@
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@@ -937,7 +940,7 @@
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@@ -949,7 +952,7 @@
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@@ -961,7 +964,7 @@
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@@ -978,7 +981,7 @@
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@@ -997,7 +1000,7 @@
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@@ -1009,7 +1012,7 @@
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@@ -1029,7 +1032,7 @@
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@@ -1067,7 +1070,7 @@
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@@ -1079,7 +1082,7 @@
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@@ -1089,7 +1092,7 @@
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@@ -1101,7 +1104,7 @@
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@@ -1112,7 +1115,7 @@
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-   "id": "77001fff",
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@@ -1157,7 +1160,7 @@
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@@ -1174,7 +1177,7 @@
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@@ -1202,7 +1205,7 @@
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@@ -1217,7 +1220,7 @@
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@@ -1261,7 +1264,7 @@
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@@ -1271,7 +1274,7 @@
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@@ -1282,7 +1285,7 @@
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@@ -1310,7 +1313,7 @@
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@@ -1325,7 +1328,7 @@
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@@ -1336,7 +1339,7 @@
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@@ -1364,7 +1367,7 @@
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@@ -1375,7 +1378,7 @@
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@@ -1400,7 +1403,7 @@
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@@ -1411,7 +1414,7 @@
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@@ -1447,7 +1450,7 @@
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@@ -1467,7 +1470,7 @@
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@@ -1478,7 +1481,7 @@
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@@ -1516,7 +1519,7 @@
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@@ -1526,7 +1529,7 @@
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@@ -1540,7 +1543,7 @@
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-   "id": "94b90bdb",
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@@ -1562,7 +1565,7 @@
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@@ -1572,7 +1575,7 @@
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@@ -1583,7 +1586,7 @@
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-   "id": "0c11abcc",
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@@ -1605,7 +1608,7 @@
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@@ -1618,7 +1621,7 @@
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-   "id": "80798223",
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@@ -1643,7 +1646,7 @@
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@@ -1655,7 +1658,7 @@
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-   "id": "65e2eb3b",
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@@ -1670,7 +1673,7 @@
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@@ -1684,7 +1687,7 @@
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@@ -1702,7 +1705,7 @@
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@@ -1726,7 +1729,7 @@
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@@ -1744,7 +1747,7 @@
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@@ -1784,7 +1787,7 @@
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@@ -1813,7 +1816,7 @@
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@@ -1834,7 +1837,7 @@
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@@ -1863,7 +1866,7 @@
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@@ -1884,7 +1887,7 @@
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@@ -1905,7 +1908,7 @@
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@@ -1922,7 +1925,7 @@
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@@ -1943,7 +1946,7 @@
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@@ -1959,7 +1962,7 @@
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@@ -1976,7 +1979,7 @@
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-   "id": "609e4e46",
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@@ -2017,7 +2020,7 @@
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@@ -2027,7 +2030,7 @@
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@@ -2038,7 +2041,7 @@
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@@ -2098,7 +2101,7 @@
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@@ -2108,7 +2111,7 @@
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@@ -2119,7 +2122,7 @@
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@@ -2139,7 +2142,7 @@
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@@ -2151,7 +2154,7 @@
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@@ -2163,7 +2166,7 @@
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@@ -2178,7 +2181,7 @@
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@@ -2190,7 +2193,7 @@
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@@ -2207,7 +2210,7 @@
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@@ -2222,7 +2225,7 @@
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@@ -2240,7 +2243,7 @@
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@@ -2252,7 +2255,7 @@
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@@ -2270,7 +2273,7 @@
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@@ -2283,7 +2286,7 @@
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@@ -2295,7 +2298,7 @@
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@@ -2313,7 +2316,7 @@
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@@ -2331,7 +2334,7 @@
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@@ -2341,7 +2344,7 @@
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@@ -2359,7 +2362,7 @@
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@@ -2378,7 +2381,7 @@
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@@ -2391,7 +2394,7 @@
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@@ -2409,7 +2412,7 @@
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@@ -2420,7 +2423,7 @@
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@@ -2439,7 +2442,7 @@
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   {
    "cell_type": "markdown",
-   "id": "f765f92b",
+   "id": "e41c38bf",
    "metadata": {
     "editable": true
    },
@@ -2457,7 +2460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9fc9109",
+   "id": "fa1ca397",
    "metadata": {
     "editable": true
    },
@@ -2470,7 +2473,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fb6b2b5",
+   "id": "320791d1",
    "metadata": {
     "editable": true
    },
@@ -2490,7 +2493,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00b0cdd3",
+   "id": "480ff354",
    "metadata": {
     "editable": true
    },
@@ -2523,7 +2526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bbe5eb6",
+   "id": "94619368",
    "metadata": {
     "editable": true
    },
@@ -2535,7 +2538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "955277a1",
+   "id": "388ff7f4",
    "metadata": {
     "editable": true
    },
@@ -2554,7 +2557,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85dbde51",
+   "id": "d9d7c987",
    "metadata": {
     "editable": true
    },
@@ -2568,7 +2571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15a3f221",
+   "id": "8a3e33b4",
    "metadata": {
     "editable": true
    },
@@ -2591,7 +2594,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5da193b4",
+   "id": "30971d96",
    "metadata": {
     "editable": true
    },
@@ -2610,7 +2613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1698ade8",
+   "id": "1471a891",
    "metadata": {
     "editable": true
    },
@@ -2622,7 +2625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "897ae188",
+   "id": "c0d00750",
    "metadata": {
     "editable": true
    },
@@ -2632,7 +2635,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ece1ed87",
+   "id": "05c9d4ee",
    "metadata": {
     "editable": true
    },
@@ -2644,7 +2647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "417a7ba7",
+   "id": "1406fbbe",
    "metadata": {
     "editable": true
    },
@@ -2661,7 +2664,7 @@
   {
    "cell_type": "code",
    "execution_count": 20,
-   "id": "5ec3241b",
+   "id": "65d6a383",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -2743,7 +2746,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97f15041",
+   "id": "9f0fe103",
    "metadata": {
     "editable": true
    },
@@ -2781,7 +2784,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3fa1b4e",
+   "id": "d8ec7ed4",
    "metadata": {
     "editable": true
    },
@@ -2811,7 +2814,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21e86c9d",
+   "id": "9a8b3d4b",
    "metadata": {
     "editable": true
    },
@@ -2832,7 +2835,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e772cdce",
+   "id": "21e1e7a1",
    "metadata": {
     "editable": true
    },
@@ -2844,7 +2847,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "698958e9",
+   "id": "100a1461",
    "metadata": {
     "editable": true
    },
@@ -2859,7 +2862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a28d2d91",
+   "id": "fcc4eef2",
    "metadata": {
     "editable": true
    },
@@ -2876,7 +2879,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d166896b",
+   "id": "a25f726d",
    "metadata": {
     "editable": true
    },
@@ -2888,7 +2891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83d8a52c",
+   "id": "0d98d20e",
    "metadata": {
     "editable": true
    },
@@ -2901,7 +2904,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9043e67e",
+   "id": "2f4c366c",
    "metadata": {
     "editable": true
    },
@@ -2913,7 +2916,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38ef410a",
+   "id": "6dd7c96e",
    "metadata": {
     "editable": true
    },
@@ -2927,7 +2930,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05b1fa07",
+   "id": "a513b6e5",
    "metadata": {
     "editable": true
    },
@@ -2939,7 +2942,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9038c068",
+   "id": "2af99fb5",
    "metadata": {
     "editable": true
    },
@@ -2951,7 +2954,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a87dd367",
+   "id": "988f1325",
    "metadata": {
     "editable": true
    },
@@ -2963,7 +2966,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0e44d26",
+   "id": "ccd7f26c",
    "metadata": {
     "editable": true
    },
@@ -2973,7 +2976,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fe053b3",
+   "id": "12e11580",
    "metadata": {
     "editable": true
    },
@@ -2985,7 +2988,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab2ee7cb",
+   "id": "1e70b838",
    "metadata": {
     "editable": true
    },
@@ -2995,7 +2998,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8eb8e72c",
+   "id": "1edf7ab2",
    "metadata": {
     "editable": true
    },
@@ -3007,7 +3010,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eaa9d407",
+   "id": "d36fd2da",
    "metadata": {
     "editable": true
    },
@@ -3021,7 +3024,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "020c12af",
+   "id": "4ee56ad9",
    "metadata": {
     "editable": true
    },
@@ -3033,7 +3036,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14cfc5fa",
+   "id": "160efabd",
    "metadata": {
     "editable": true
    },
@@ -3043,7 +3046,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c665c2",
+   "id": "cab136bb",
    "metadata": {
     "editable": true
    },
@@ -3055,7 +3058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "553452a0",
+   "id": "217ca399",
    "metadata": {
     "editable": true
    },
@@ -3065,7 +3068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c23c4b45",
+   "id": "63747f21",
    "metadata": {
     "editable": true
    },
@@ -3077,7 +3080,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3e24109",
+   "id": "54d3e3e3",
    "metadata": {
     "editable": true
    },
@@ -3089,7 +3092,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99e69f17",
+   "id": "f6ec4ea3",
    "metadata": {
     "editable": true
    },
@@ -3101,7 +3104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0413cbf",
+   "id": "1f48793d",
    "metadata": {
     "editable": true
    },
@@ -3111,7 +3114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "243c6e25",
+   "id": "e340e6d7",
    "metadata": {
     "editable": true
    },
@@ -3123,7 +3126,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cdf0babe",
+   "id": "ba026ba1",
    "metadata": {
     "editable": true
    },
@@ -3133,7 +3136,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d332ef89",
+   "id": "836235e1",
    "metadata": {
     "editable": true
    },
@@ -3145,7 +3148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dee62e2",
+   "id": "4c7e35e8",
    "metadata": {
     "editable": true
    },
@@ -3169,7 +3172,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6b1b7c2",
+   "id": "5e17d297",
    "metadata": {
     "editable": true
    },
@@ -3181,7 +3184,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25fa99aa",
+   "id": "90a264a8",
    "metadata": {
     "editable": true
    },
@@ -3191,7 +3194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f20e502",
+   "id": "9c45cadd",
    "metadata": {
     "editable": true
    },
@@ -3203,7 +3206,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40c1ebc1",
+   "id": "a02fe84e",
    "metadata": {
     "editable": true
    },
@@ -3215,7 +3218,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "932d51af",
+   "id": "1123e58e",
    "metadata": {
     "editable": true
    },
@@ -3227,7 +3230,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ac07ae0",
+   "id": "b93e2324",
    "metadata": {
     "editable": true
    },
@@ -3237,7 +3240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8f9b3b42",
+   "id": "c8c7b816",
    "metadata": {
     "editable": true
    },
@@ -3249,7 +3252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba4701b4",
+   "id": "e185ca0a",
    "metadata": {
     "editable": true
    },
@@ -3259,7 +3262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f3dd13f",
+   "id": "6087b111",
    "metadata": {
     "editable": true
    },
@@ -3273,7 +3276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f46643d3",
+   "id": "20fc7314",
    "metadata": {
     "editable": true
    },
@@ -3291,7 +3294,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72c17c61",
+   "id": "cc682107",
    "metadata": {
     "editable": true
    },
@@ -3301,7 +3304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a4b9cd6",
+   "id": "e048bf4d",
    "metadata": {
     "editable": true
    },
@@ -3319,7 +3322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "660de22f",
+   "id": "6f55d291",
    "metadata": {
     "editable": true
    },
@@ -3329,7 +3332,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d91e1536",
+   "id": "edd966f8",
    "metadata": {
     "editable": true
    },
@@ -3347,7 +3350,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28b057da",
+   "id": "d6fe086b",
    "metadata": {
     "editable": true
    },
@@ -3374,7 +3377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cbee200c",
+   "id": "9541d79b",
    "metadata": {
     "editable": true
    },
@@ -3386,7 +3389,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cfd8e707",
+   "id": "cba8762c",
    "metadata": {
     "editable": true
    },
@@ -3398,7 +3401,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c059e74",
+   "id": "4b26de68",
    "metadata": {
     "editable": true
    },
@@ -3408,7 +3411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87b9c575",
+   "id": "20c4375e",
    "metadata": {
     "editable": true
    },
@@ -3420,7 +3423,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9417f6ec",
+   "id": "be1ed1e5",
    "metadata": {
     "editable": true
    },
@@ -3430,7 +3433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07278244",
+   "id": "261bb8b0",
    "metadata": {
     "editable": true
    },
@@ -3442,7 +3445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d2ebc91",
+   "id": "f4f6f49c",
    "metadata": {
     "editable": true
    },
@@ -3452,7 +3455,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68aee93b",
+   "id": "cc0d0da1",
    "metadata": {
     "editable": true
    },
@@ -3464,7 +3467,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a65994f4",
+   "id": "b9b6d15f",
    "metadata": {
     "editable": true
    },
@@ -3476,7 +3479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d86a2149",
+   "id": "844d96b5",
    "metadata": {
     "editable": true
    },
@@ -3499,7 +3502,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f18e1be4",
+   "id": "8ace79d2",
    "metadata": {
     "editable": true
    },
@@ -3511,7 +3514,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61435fe1",
+   "id": "6b086fb0",
    "metadata": {
     "editable": true
    },
@@ -3521,7 +3524,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bbf8110f",
+   "id": "8c88ee52",
    "metadata": {
     "editable": true
    },
@@ -3533,7 +3536,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a518090",
+   "id": "bbe2623b",
    "metadata": {
     "editable": true
    },
@@ -3543,7 +3546,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85824270",
+   "id": "dce58ee6",
    "metadata": {
     "editable": true
    },
@@ -3555,7 +3558,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "815818ed",
+   "id": "6b18fdf9",
    "metadata": {
     "editable": true
    },
@@ -3567,7 +3570,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fda6b470",
+   "id": "8714fbd1",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week40/week40.do.txt b/doc/src/week40/week40.do.txt
index ba7cf4a32..1829183b4 100644
--- a/doc/src/week40/week40.do.txt
+++ b/doc/src/week40/week40.do.txt
@@ -231,28 +231,28 @@ We note that we have defined several hyperparameters. These are now the number o
 
 !bc pycod
 # Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-n = 1000
+n = 100
 x = 2*np.random.rand(n,1)
 y = 4+3*x+np.random.randn(n,1)
 
 X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
@@ -267,7 +267,6 @@ Xnew = np.c_[np.ones((2,1)), xnew]
 ypredict = Xnew.dot(theta)
 ypredict2 = Xnew.dot(theta_linreg)
 
-
 n_epochs = 50
 M = 5   #size of each minibatch
 m = int(n/M) #number of minibatches
@@ -278,16 +277,20 @@ def learning_schedule(t):
 theta = np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
         random_index = np.random.randint(m)
-        xi = X[random_index:random_index+m]
-        yi = y[random_index:random_index+m]
-        gradients = 2.0* xi.T @ ((xi @ theta)-yi)
+        xi = X[random_index*M:random_index*M+M]
+        yi = y[random_index*M:random_index*M+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')