{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "COMMENTS: Mean score was 8.7/10\n", "3 points for problem 1\n", "2 points for problem 2 - deducted one if you used finite difference rather than gradient\n", "5 points fo rproblem 3 - deducted a few points if the description of results was inadequate" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Notebook Assignment 1:\n", "Determine the gradient and Hessian of $f(x) = x^4-5x^2-3x$ and use those two things to 1) identify the extreme points of the function, 2) identify which extreme points are local minima, and 3) identify which extreme point is the global minimum\n", "\n", "The derivative of f(x) is \n", "f'(x) = 4x^3-10x-3\n", "This is the characteristic polynomial of matrix $A = \\left[ \\begin{array}{ccc} 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 0.75 2.5 0 \\end{array} \\right]$ and whose eigenvalues are the roots of the characteristic polynomial" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{1.71393943618537: 1, -0.312168188344074: 1, -1.40177124784130: 1}\n" ] } ], "source": [ "import numpy as np\n", "from sympy.matrices import Matrix\n", "\n", "A = Matrix([[0,1,0],[0,0,1],[.75, 2.5, 0]])\n", "lam = A.eigenvals()\n", "print(lam)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "Part 1a solution\n", "So the extreme points are xa = -1.4018, xb = -0.3122, xc = 1.7139\n", "The Hessian of the function is \n", "f\"(x) = 12 x^2-10\n", "and evaluating f and f\" for the extreme points gives\n", "f\"(xa)=13.6>0, f\"(xb)=-8.83<0 , f\"(xc)=25.25 > 0\n", "f(xa) = 0.206, f(xb) = 0.556, f(xc)=-8.26\n", "so xa is a lcoal minimum, xb is a local maximum, and xc=1.7139 is the global minimum. \n", "\n", "PART 2: \n", "I used the Python library numdifftools to automate the computation of my function's gradient. The gradient_descent function is given below\n", "and the plot is the time history of the search. The search converges to the global minimum at 1.7139" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.7139451831013375\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'minimum = 1.71394518')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import numdifftools as nd\n", "\n", "def gradient_descent(func, start, learn_rate, n_iter=50, tolerance=1e-6 ):\n", " vector = start \n", " history= [start]\n", " for _ in range(n_iter):\n", " diff = -learn_rate * nd.Gradient(myfunc)(vector)\n", " if np.all(np.abs(diff)<=tolerance):\n", " break\n", " vector += diff\n", " history = np.vstack((history,vector))\n", " return vector,history\n", "\n", "def myfunc(v):\n", " return v**4-5*v**2-3*v\n", "\n", "ans,xhist = gradient_descent(\n", " myfunc,start=0, learn_rate=0.05, tolerance = 1.e-5\n", ")\n", "\n", "print(ans)\n", "\n", "import matplotlib.pyplot as plt \n", "yhist = myfunc(xhist)\n", "plt.plot(np.arange(len(xhist)),xhist)\n", "plt.title(\"minimum = \"+np.array2string(ans))\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "part 3) use the function to generate history plots for learning rates\n", "eta = .05 -> convergence to global minimum\n", "eta = .10 -> oscillates around global minimum\n", "eta = .15 -> converges to local minimum and then oscillates around it\n", "eta = .20 -> oscillates around local minimum\n", "eta = .25 -> diverges" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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", 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "etaTable = np.array([.05, .10, .15, .20, .25])\n", "\n", "for eta in np.nditer(etaTable):\n", " ans,xhist = gradient_descent(\n", " myfunc,start=0, learn_rate=eta, tolerance = 1.e-5\n", " )\n", " import matplotlib.pyplot as plt \n", " yhist = myfunc(xhist)\n", " plt.plot(np.arange(len(xhist)),xhist)\n", " plt.title(\"minimum = \"+np.array2string(ans)+\" eta = \" + np.array2string(eta))\n", " plt.show()\n", "\n", "\n", "\n", " " ] } ], "metadata": { "kernelspec": { "display_name": "dlenv", "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": "3.10.6" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "3df62eaf1cb282f8c42f6fbb99c9966b7664907b21a7caae10647575acce3941" } } }, "nbformat": 4, "nbformat_minor": 2 }