{ "cells": [ { "cell_type": "markdown", "id": "cd348c59", "metadata": {}, "source": [ "\n", "*This notebook contains material from [CBE60499](https://ndcbe.github.io/CBE60499);\n", "content is available [on Github](git@github.com:ndcbe/CBE60499.git).*\n" ] }, { "cell_type": "markdown", "id": "df7b50fd", "metadata": {}, "source": [ "\n", "< [3.1 Linear Algebra Review and SciPy Basics](https://ndcbe.github.io/CBE60499/03.01-Math-Primer.html) | [Contents](toc.html) | [Tag Index](tag_index.html) | [3.3 Unconstrained Optimality Conditions](https://ndcbe.github.io/CBE60499/03.03-Optimality.html) >

\"Open

\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 1, "link": "[3.2 Mathematics Primer](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2-Mathematics-Primer)", "section": "3.2 Mathematics Primer" } }, "source": [ "# 3.2 Mathematics Primer\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "nbpages": { "level": 1, "link": "[3.2 Mathematics Primer](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2-Mathematics-Primer)", "section": "3.2 Mathematics Primer" } }, "outputs": [], "source": [ "# Load required Python libraries.\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy import linalg\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.1 Eigenvalues and Quadratic Programs](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1-Eigenvalues-and-Quadratic-Programs)", "section": "3.2.1 Eigenvalues and Quadratic Programs" } }, "source": [ "## 3.2.1 Eigenvalues and Quadratic Programs" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.1 Eigenvalues and Quadratic Programs](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1-Eigenvalues-and-Quadratic-Programs)", "section": "3.2.1 Eigenvalues and Quadratic Programs" } }, "source": [ "**Main Idea**: By looking at an unconstrained quadratic optimization problem, we will see how the eigenvalues tell us about the curvature (second derivatives) and help us classify the stationary points.\n", "\n", "**Reference**: Section *2.2.2 Quadratic Forms* in Biegler (2010)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.1 Eigenvalues and Quadratic Programs](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1-Eigenvalues-and-Quadratic-Programs)", "section": "3.2.1 Eigenvalues and Quadratic Programs" } }, "source": [ "![Book](figures/quad1.png)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.1 Analysis Algorithm](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.1-Analysis-Algorithm)", "section": "3.2.1.1 Analysis Algorithm" } }, "source": [ "### 3.2.1.1 Analysis Algorithm\n", "\n", "We will start by defining a functon for our classification procedure." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.1 Analysis Algorithm](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.1-Analysis-Algorithm)", "section": "3.2.1.1 Analysis Algorithm" } }, "outputs": [], "source": [ "# The main event\n", "def quad_analyze(c, a, B):\n", " '''\n", " Analyze the stationary points of a quadratic objective.\n", " \n", " Inputs:\n", " c - offset (scalar)\n", " a - linear coefficients (vector)\n", " B - quadratic coefficients (matrix)\n", " \n", " Outputs:\n", " None\n", " \n", " Displayed:\n", " 1. Inputs\n", " 2. Eigenvalues and eigenvectors\n", " 3. Stationary point (transformed coordinates)\n", " 4. Stationary point (original coordinates)\n", " 5. Function value and gradient at stationary point\n", " 6. 3D plot\n", " '''\n", " \n", " ### Display inputs\n", " print(\"***Inputs***\")\n", " print(\"c = \",c,\"\\n\")\n", " print(\"a = \",a,\"\\n\")\n", " print(\"B = \\n\",B,\"\\n\")\n", " \n", " ### Eigendecomposition\n", " print(\"***Eigendecomposition***\")\n", " l, V = linalg.eig(B)\n", " print(\"Lambda = \\n\",np.diag(l),\"\\n\")\n", " print(\"V = \\n\",V,\"\\n\")\n", " \n", " ### Calculate stationary point\n", " n = len(a)\n", " zstar = np.zeros(n)\n", " \n", " abar = (V.transpose()).dot(a)\n", " print(\"abar = \\n\",abar,\"\\n\")\n", " \n", " # Loop over dimensions\n", " for j in range(0,n):\n", " # If eigenvalue is NOT zero\n", " ##\n", " # Previous code\n", " # if(l[j] != 0):\n", " ##\n", " # More stable version\n", " if(abs(l[j]) > 1E-8):\n", " zstar[j] = -abar[j]/np.real(l[j])\n", " \n", " # Otherwise check is abar is nonzero\n", " elif(abar[j] !=0):\n", " print(\"WARNING: No stationary point exists.\")\n", " \n", " xstar = V.dot(zstar)\n", " \n", " print(\"***(Possible) Stationary Point in Transformed Coordinates:\")\n", " print(\"z* = \",zstar,\"\\n\")\n", " \n", " print(\"***(Possible) Stationary Point in Original Coordinates:\")\n", " print(\"x* = \",xstar,\"\\n\")\n", " \n", " ### Check function value and gradient\n", " fval = c + a.dot(xstar) + 0.5*xstar.dot(B.dot(xstar))\n", " grad = a + xstar.dot(B)\n", " \n", " print(\"***Checking function and gradient***\")\n", " print(\"f(x*) = \",fval)\n", " print(\"f'(x*) = \\n\",grad,\"\\n\")\n", " \n", " ### Make 3D plot\n", " # Tutorial: https://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html\n", " if(n == 2):\n", " # Create vectors in both dimensions\n", " dx = 5\n", " x1 = np.arange(xstar[0]-dx,xstar[0]+dx,0.25)\n", " x2 = np.arange(xstar[1]-dx,xstar[1]+dx,0.25)\n", " \n", " # Create a matrix of all points to sample\n", " X1, X2 = np.meshgrid(x1, x2)\n", " n1 = len(x1)\n", " n2 = len(x2)\n", " F = np.zeros([n2, n1])\n", " xtemp = np.zeros(2)\n", " for i in range(0,n1):\n", " xtemp[0] = x1[i]\n", " for j in range(0,n2):\n", " xtemp[1] = x2[j]\n", " F[j,i] = c + a.dot(xtemp) + 0.5*xtemp.dot(B.dot(xtemp))\n", " \n", " # Create 3D figure\n", " fig = plt.figure()\n", " ax = fig.gca(projection='3d')\n", " \n", " # Plot f(x)\n", " surf = ax.plot_surface(X1, X2, F, linewidth=0,cmap=cm.coolwarm,antialiased=True)\n", " \n", " # Add (possible) stationary point\n", " ax.scatter(xstar[0],xstar[1],fval,s=50,color=\"green\",depthshade=True)\n", " \n", " # Draw vertical line through stationary point to help visualization\n", " # Maximum value in array\n", " fmax = np.amax(F)\n", " fmin = np.amin(F)\n", " ax.plot([xstar[0], xstar[0]], [xstar[1], xstar[1]], [fmin,fmax],color=\"green\")\n", " \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.2 Excercise 2.8 in Biegler (2010)](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.2-Excercise-2.8-in-Biegler-(2010))", "section": "3.2.1.2 Excercise 2.8 in Biegler (2010)" } }, "source": [ "### 3.2.1.2 Excercise 2.8 in Biegler (2010)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.2 Excercise 2.8 in Biegler (2010)](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.2-Excercise-2.8-in-Biegler-(2010))", "section": "3.2.1.2 Excercise 2.8 in Biegler (2010)" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "***Inputs***\n", "c = 0 \n", "\n", "a = [1 1] \n", "\n", "B = \n", " [[2 1]\n", " [1 2]] \n", "\n", "***Eigendecomposition***\n", "Lambda = \n", " [[3.+0.j 0.+0.j]\n", " [0.+0.j 1.+0.j]] \n", "\n", "V = \n", " [[ 0.70710678 -0.70710678]\n", " [ 0.70710678 0.70710678]] \n", "\n", "abar = \n", " [1.41421356 0. ] \n", "\n", "***(Possible) Stationary Point in Transformed Coordinates:\n", "z* = [-0.47140452 -0. ] \n", "\n", "***(Possible) Stationary Point in Original Coordinates:\n", "x* = [-0.33333333 -0.33333333] \n", "\n", "***Checking function and gradient***\n", "f(x*) = -0.3333333333333333\n", "f'(x*) = \n", " [2.22044605e-16 2.22044605e-16] \n", "\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "c = 0\n", "a = np.array([1, 1])\n", "B = np.array([[2,1],[1,2]])\n", "\n", "quad_analyze(c,a,B)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.3 Activity 1](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.3-Activity-1)", "section": "3.2.1.3 Activity 1" } }, "source": [ "### 3.2.1.3 Activity 1\n", "\n", "Classify the stationary point for $f(x) = x_1 + x_2$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.3 Activity 1](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.3-Activity-1)", "section": "3.2.1.3 Activity 1" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "***Inputs***\n", "c = 0 \n", "\n", "a = [1 1] \n", "\n", "B = \n", " [[0. 0.]\n", " [0. 0.]] \n", "\n", "***Eigendecomposition***\n", "Lambda = \n", " [[0.+0.j 0.+0.j]\n", " [0.+0.j 0.+0.j]] \n", "\n", "V = \n", " [[1. 0.]\n", " [0. 1.]] \n", "\n", "abar = \n", " [1. 1.] \n", "\n", "WARNING: No stationary point exists.\n", "WARNING: No stationary point exists.\n", "***(Possible) Stationary Point in Transformed Coordinates:\n", "z* = [0. 0.] \n", "\n", "***(Possible) Stationary Point in Original Coordinates:\n", "x* = [0. 0.] \n", "\n", "***Checking function and gradient***\n", "f(x*) = 0.0\n", "f'(x*) = \n", " [1. 1.] \n", "\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.4 Activity 2](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.4-Activity-2)", "section": "3.2.1.4 Activity 2" } }, "source": [ "### 3.2.1.4 Activity 2" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.4 Activity 2](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.4-Activity-2)", "section": "3.2.1.4 Activity 2" } }, "source": [ "Classify the stationary point for $f(x) = x_1^2 + x_2^2 - 2x_1 x_2 + 0 x_1 - 0 x_2$ + 3.\n", "\n", "Hint: $B$ needs to be symmetric." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "nbpages": { "level": 3, "link": "[3.2.1.4 Activity 2](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.1.4-Activity-2)", "section": "3.2.1.4 Activity 2" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "***Inputs***\n", "c = 3 \n", "\n", "a = [0 0] \n", "\n", "B = \n", " [[ 2 -2]\n", " [-2 2]] \n", "\n", "***Eigendecomposition***\n", "Lambda = \n", " [[4.0000000e+00+0.j 0.0000000e+00+0.j]\n", " [0.0000000e+00+0.j 4.4408921e-16+0.j]] \n", "\n", "V = \n", " [[ 0.70710678 0.70710678]\n", " [-0.70710678 0.70710678]] \n", "\n", "abar = \n", " [0. 0.] \n", "\n", "***(Possible) Stationary Point in Transformed Coordinates:\n", "z* = [-0. 0.] \n", "\n", "***(Possible) Stationary Point in Original Coordinates:\n", "x* = [0. 0.] \n", "\n", "***Checking function and gradient***\n", "f(x*) = 3.0\n", "f'(x*) = \n", " [0. 0.] \n", "\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# YOUR SOLUTION HERE" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.2 Classifying Functions (Key Concepts from Real Analysis)](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.2-Classifying-Functions-(Key-Concepts-from-Real-Analysis))", "section": "3.2.2 Classifying Functions (Key Concepts from Real Analysis)" } }, "source": [ "## 3.2.2 Classifying Functions (Key Concepts from Real Analysis)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.3 Taylor Series Approximation](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.3-Taylor-Series-Approximation)", "section": "3.2.3 Taylor Series Approximation" } }, "source": [ "## 3.2.3 Taylor Series Approximation" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.4 Finite Difference Approximation](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4-Finite-Difference-Approximation)", "section": "3.2.4 Finite Difference Approximation" } }, "source": [ "## 3.2.4 Finite Difference Approximation" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.4 Finite Difference Approximation](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4-Finite-Difference-Approximation)", "section": "3.2.4 Finite Difference Approximation" } }, "source": [ "**Main Idea**: This example complements in class example where we use Taylor series expansions to estimate trunction error for forward, backward, and central finite difference formulas. We will revisit finite difference formulas again in a few lectures." ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[3.2.4 Finite Difference Approximation](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4-Finite-Difference-Approximation)", "section": "3.2.4 Finite Difference Approximation" } }, "source": [ "Consider the following test function:\n", "$$ f(x) = e^{x} $$\n", "\n", "with\n", "\n", "$$f'(x) = e^{x}$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "nbpages": { "level": 2, "link": "[3.2.4 Finite Difference Approximation](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4-Finite-Difference-Approximation)", "section": "3.2.4 Finite Difference Approximation" } }, "outputs": [], "source": [ "# Define the test function\n", "def my_f(x):\n", " return np.exp(x)\n", "\n", "# Specify point to examine\n", "a = 1.0\n", "\n", "# Calculate function value at x = a\n", "fa = my_f(a)\n", "\n", "# Calculate exact first derivative at x=1\n", "df1 = my_f(a) # Need to replace if you consider a different test function!\n", "\n", "# Generate values for epsilon\n", "eps = np.power(10,np.arange(-16,1,0.25))\n", "n = len(eps)" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.1 Forward Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.1-Forward-Finite-Difference)", "section": "3.2.4.1 Forward Finite Difference" } }, "source": [ "### 3.2.4.1 Forward Finite Difference\n", "\n", "$$ f'_f(a) = \\frac{f(a+\\epsilon) - f(a)}{\\epsilon} $$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.1 Forward Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.1-Forward-Finite-Difference)", "section": "3.2.4.1 Forward Finite Difference" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Preallocate error array\n", "error_forward = np.zeros(n)\n", "\n", "# Calculate finite difference approximation and error\n", "for i in range(0,n):\n", " df1_forward = (my_f(a + eps[i]) - fa)/eps[i]\n", " error_forward[i] = abs(df1_forward - df1)\n", "\n", "# Plot\n", "plt.figure()\n", "plt.loglog(eps,error_forward,label=\"Forward\",color=\"blue\")\n", "plt.xlabel(\"$\\epsilon$\")\n", "plt.ylabel(\"Absolute Error\")\n", "plt.legend()\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.2 Backward Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.2-Backward-Finite-Difference)", "section": "3.2.4.2 Backward Finite Difference" } }, "source": [ "### 3.2.4.2 Backward Finite Difference\n", "\n", "$$ f'_b(a) = \\frac{f(a) - f(a - \\epsilon)}{-\\epsilon} $$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.2 Backward Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.2-Backward-Finite-Difference)", "section": "3.2.4.2 Backward Finite Difference" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Preallocate error array\n", "error_backward = np.zeros(n)\n", "\n", "# Calculate finite difference approximation and error\n", "for i in range(0,n):\n", " df1_backward = (fa - np.exp(a - eps[i]))/eps[i]\n", " error_backward[i] = abs(df1_backward - df1)\n", "\n", "# Plot\n", "plt.figure()\n", "plt.loglog(eps,error_forward,label=\"Forward\",color=\"blue\")\n", "plt.loglog(eps,error_backward,label=\"Backward\",color=\"red\")\n", "plt.xlabel(\"$\\epsilon$\")\n", "plt.ylabel(\"Absolute Error\")\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.3 Central Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.3-Central-Finite-Difference)", "section": "3.2.4.3 Central Finite Difference" } }, "source": [ "### 3.2.4.3 Central Finite Difference\n", "\n", "$$ f'_c(a) = \\frac{f(a+\\epsilon) - f(a - \\epsilon)}{2 \\epsilon} $$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.3 Central Finite Difference](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.3-Central-Finite-Difference)", "section": "3.2.4.3 Central Finite Difference" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Preallocate error array\n", "error_central = np.zeros(n)\n", "\n", "# Calculate finite difference approximation and error\n", "for i in range(0,n):\n", " df1_central = (np.exp(a + eps[i]) - np.exp(a - eps[i]))/(2*eps[i])\n", " error_central[i] = abs(df1_central - df1)\n", "\n", "# Plot\n", "plt.figure()\n", "plt.loglog(eps,error_forward,label=\"Forward\",color=\"blue\")\n", "plt.loglog(eps,error_backward,label=\"Backward\",color=\"red\")\n", "plt.loglog(eps,error_central,label=\"Central\",color=\"green\")\n", "plt.xlabel(\"$\\epsilon$\")\n", "plt.ylabel(\"Absolute Error\")\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 3, "link": "[3.2.4.4 Activity](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4-Activity)", "section": "3.2.4.4 Activity" } }, "source": [ "### 3.2.4.4 Activity\n", "1. Record the results for the test function $f(x) = e^x$ at $x=1$.\n", "2. Try the point $x=10$ and record the results.\n", "3. Try a different test function." ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[3.2.4.4.1 Original: $f(x) = e^{x}$ at $x=1$](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4.1-Original:-$f(x)-=-e^{x}$-at-$x=1$)", "section": "3.2.4.4.1 Original: $f(x) = e^{x}$ at $x=1$" } }, "source": [ "#### 3.2.4.4.1 Original: $f(x) = e^{x}$ at $x=1$\n", "\n", "**Forward**: Lowest absolute error of $10^{-8}$ at $\\epsilon$ = $10^{-8}$\n", "\n", "**Backward**: Lowest absolute error of $10^{-8}$ at $\\epsilon$ = $10^{-8}$\n", "\n", "**Central**: Lowest absolute error of $10^{-10}$ at $\\epsilon$ = $10^{-6}$\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[3.2.4.4.2 Variant: $f(x) = e^{x}$ at $x=10$](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4.2-Variant:-$f(x)-=-e^{x}$-at-$x=10$)", "section": "3.2.4.4.2 Variant: $f(x) = e^{x}$ at $x=10$" } }, "source": [ "#### 3.2.4.4.2 Variant: $f(x) = e^{x}$ at $x=10$\n", "\n", "**Forward**: Lowest absolute error of $10^{-8}$ at $\\epsilon$ = $10^{-8}$\n", "\n", "**Backward**: Lowest absolute error of $10^{-8}$ at $\\epsilon$ = $10^{-8}$\n", "\n", "**Central**: Lowest absolute error of $10^{-10}$ at $\\epsilon$ = $10^{-6}$" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[3.2.4.4.3 Your own test function](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4.3-Your-own-test-function)", "section": "3.2.4.4.3 Your own test function" } }, "source": [ "#### 3.2.4.4.3 Your own test function\n", "\n", "**Forward**: Lowest absolute error of ... at $\\epsilon$ = ...\n", "\n", "**Backward**: \n", "\n", "**Central**:" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 4, "link": "[3.2.4.4.4 Discussion](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4.4-Discussion)", "section": "3.2.4.4.4 Discussion" } }, "source": [ "#### 3.2.4.4.4 Discussion\n", "\n", "Are there any general trends from these (limited) computational experiments?\n", "\n", "What is the best $\\epsilon$ for an arbitrary function?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "nbpages": { "level": 4, "link": "[3.2.4.4.4 Discussion](https://ndcbe.github.io/CBE60499/03.02-Math-Primer-2.html#3.2.4.4.4-Discussion)", "section": "3.2.4.4.4 Discussion" } }, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "679f594e", "metadata": {}, "source": [ "\n", "< [3.1 Linear Algebra Review and SciPy Basics](https://ndcbe.github.io/CBE60499/03.01-Math-Primer.html) | [Contents](toc.html) | [Tag Index](tag_index.html) | [3.3 Unconstrained Optimality Conditions](https://ndcbe.github.io/CBE60499/03.03-Optimality.html) >

\"Open

\"Download\"" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 2 }