update

2023-05-03 11:48:50 -04:00
parent 356abdcde9
commit ceb79267af
3 changed files with 298 additions and 2 deletions
@@ -0,0 +1,271 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[1.         0.         0.         ... 0.         0.         0.        ]\n",
+      " [1.         0.         0.05       ... 0.         0.         0.        ]\n",
+      " [1.         0.         0.1        ... 0.         0.         0.        ]\n",
+      " ...\n",
+      " [1.         0.95       0.85       ... 0.61945344 0.55424781 0.49590594]\n",
+      " [1.         0.95       0.9        ... 0.69447375 0.6579225  0.623295  ]\n",
+      " [1.         0.95       0.95       ... 0.77378094 0.77378094 0.77378094]]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "400"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "\"\"\"\n",
+    "Importations\n",
+    "\"\"\"\n",
+    "\n",
+    "from mpl_toolkits.mplot3d import Axes3D\n",
+    "import matplotlib.pyplot as plt\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+    "\n",
+    "import pandas as pd\n",
+    "import numpy as np\n",
+    "from random import random, seed\n",
+    "\n",
+    "#plt.close()\n",
+    "#fig = plt.figure()\n",
+    "#ax = fig.gca(projection=\"3d\")\n",
+    "\n",
+    "# Make data\n",
+    "\n",
+    "x0 = np.arange(0, 1, 0.05)\n",
+    "y0 = np.arange(0, 1, 0.05)\n",
+    "\n",
+    "x, y = np.meshgrid(x0,y0)\n",
+    "\n",
+    "def FrankeFunction(x,y):\n",
+    "\tterm1 = 0.75*np.exp(-(0.25*(9*x-2)**2) - 0.25*((9*y-2)**2))\n",
+    "\tterm2 = 0.75*np.exp(-((9*x+1)**2)/49.0 - 0.1*(9*y+1))\n",
+    "\tterm3 = 0.5*np.exp(-(9*x-7)**2/4.0 - 0.25*((9*y-3)**2))\n",
+    "\tterm4 = -0.2*np.exp(-(9*x-4)**2 - (9*y-7)**2)\n",
+    "\n",
+    "\treturn term1 + term2 + term3 + term4\n",
+    "\n",
+    "z = FrankeFunction(x, y)\n",
+    "\n",
+    "matrix = np.zeros((len(y0)**2,21))\n",
+    "\n",
+    "# First column\n",
+    "\n",
+    "matrix[:,0] = 1\n",
+    "\n",
+    "# Second column\n",
+    "\n",
+    "X0 = []\n",
+    "for k in range(len(x0)):\n",
+    "\tfor i in range(len(x0)) :\n",
+    "\t\txk =  x0[k]\n",
+    "\t\tX0.append(xk)\n",
+    "\n",
+    "matrix[:,1] = X0\n",
+    "\n",
+    "# Third column\n",
+    "\n",
+    "Y0 = []\n",
+    "for k in range(len(y0)) :\n",
+    "\tfor i in range(len(y0)) :\n",
+    "\t\tyk = x0[i]\n",
+    "\t\tY0.append(yk)\n",
+    "\n",
+    "matrix[:,2] = Y0\n",
+    "\n",
+    "# Fourth column\n",
+    "\n",
+    "X02 = []\n",
+    "for k in range(len(x0)**2):\n",
+    "\tX02.append(X0[k]**2)\n",
+    "\n",
+    "matrix[:,3] = X02\n",
+    "\n",
+    "# Fifth column\n",
+    "\n",
+    "Y02 = []\n",
+    "for k in range(len(y0)**2):\n",
+    "\tY02.append(Y0[k]**2)\n",
+    "\t\n",
+    "matrix[:,4] = Y02\n",
+    "\n",
+    "# sixth column\n",
+    "\n",
+    "X0Y0 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX0Y0.append(X0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,5] = X0Y0\n",
+    "\n",
+    "#7th column\n",
+    "\n",
+    "X03 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX03.append(X0[k]*X0[k]*X0[k])\n",
+    "\n",
+    "matrix[:,6] = X03\n",
+    "\n",
+    "\n",
+    "#8th column\n",
+    "\n",
+    "Y03 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tY03.append(Y0[k]*Y0[k]*Y0[k])\n",
+    "\n",
+    "matrix[:,7] = Y03\n",
+    "\n",
+    "#9th column\n",
+    "\n",
+    "X02Y0 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX02Y0.append(X0[k]*X0[k]*Y0[k]) \n",
+    "\t\n",
+    "matrix[:,8] = X02Y0\n",
+    "\t\n",
+    "#10th column \t\n",
+    " \n",
+    "X0Y02 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX0Y02.append(X0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,9] = X0Y02\n",
+    "\n",
+    "#11th column\n",
+    "\n",
+    "X04 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX04.append(X0[k]*X0[k]*X0[k]*X0[k])\n",
+    "\t\n",
+    "matrix[:,10] = X04\n",
+    "\n",
+    "#12th column\n",
+    "\n",
+    "Y04 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tY04.append(Y0[k]*Y0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,11] = Y04\n",
+    "\n",
+    "#13th column\n",
+    "\n",
+    "X03Y0 =[]\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX03Y0.append(X0[k]*X0[k]*X0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,12] = X03Y0\n",
+    "\n",
+    "#14th column\n",
+    "\n",
+    "X02Y02 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX02Y02.append(X0[k]*X0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,13] = X02Y02\n",
+    "\n",
+    "#15th column\n",
+    "\n",
+    "X0Y03 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX0Y03.append(X0[k]*Y0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,14] = X0Y03\n",
+    "\n",
+    "#16th column\n",
+    "\n",
+    "X05 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX05.append(X0[k]*X0[k]*X0[k]*X0[k]*X0[k])\n",
+    "\t\n",
+    "matrix[:,15] = X05\n",
+    "\n",
+    "#17th column\n",
+    "\n",
+    "Y05 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tY05.append(Y0[k]*Y0[k]*Y0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,16] = Y05\n",
+    "\n",
+    "#18th column\n",
+    "\n",
+    "X04Y0 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX04Y0.append(X0[k]*X0[k]*X0[k]*X0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,17] = X04Y0\n",
+    "\n",
+    "#19th column\n",
+    "\n",
+    "X03Y02 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX03Y02.append(X0[k]*X0[k]*X0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,18] = X03Y02\n",
+    "\n",
+    "#20th column\n",
+    "\n",
+    "X02Y03 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX02Y03.append(X0[k]*X0[k]*Y0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,19] = X02Y03\n",
+    "\n",
+    "#21th column\n",
+    "\n",
+    "X0Y04 = []\n",
+    "for k in range(len(x0)*len(y0)):\n",
+    "\tX0Y04.append(X0[k]*Y0[k]*Y0[k]*Y0[k]*Y0[k])\n",
+    "\t\n",
+    "matrix[:,20] = X0Y04\n",
+    "\n",
+    "print(matrix)\n",
+    "len(matrix)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.9.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
@@ -4235,10 +4235,18 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 1,
   "id": "e8fdc7be",
   "metadata": {},
-   "outputs": [],
+   "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",
@@ -4250,6 +4258,14 @@
    "derivative_fn = grad(sum_logistic)\n",
    "print(derivative_fn(x_small))"
   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1a930655",
+   "metadata": {},
+   "outputs": [],
+   "source": []
  }
 ],
 "metadata": {
@@ -0,0 +1,9 @@
+import jax.numpy as jnp
+from jax import grad, jit, vmap
+
+def sum_logistic(x):
+  return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))
+
+x_small = jnp.arange(3.)
+derivative_fn = grad(sum_logistic)
+print(derivative_fn(x_small))