{ "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) >
"
]
},
{
"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": [
""
]
},
{
"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": {
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\n",
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}
],
"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
}