Merge pull request #142 from 7ony7he7iger/HW8_branch

Homework number eight
uw-python · Dec 2, 2014 · c45a9c2 · c45a9c2
2 parents 81936e9 + 6955fea
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diff --git a/7ony7he7iger/HW_8.ipynb b/7ony7he7iger/HW_8.ipynb
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+ "worksheets": [
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+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Homework #8"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 4,
+ "metadata": {},
+ "source": [
+ "Diagnose"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The original code that has errors/bugs. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\"\"\"\n",
+ "A script to compare different root-finding algorithms.\n",
+ "\n",
+ "This version of the script is buggy and does not execute. It is your task\n",
+ "to find an fix these bugs.\n",
+ "\n",
+ "The output of the script sould look like:\n",
+ "\n",
+ " Benching 1D root-finder optimizers from scipy.optimize:\n",
+ " brenth: 604678 total function calls\n",
+ " brentq: 594454 total function calls\n",
+ " ridder: 778394 total function calls\n",
+ " bisect: 2148380 total function calls\n",
+ "\"\"\"\n",
+ "from itertools import product\n",
+ "\n",
+ "import numpy as np\n",
+ "from scipy import optimize\n",
+ "\n",
+ "FUNCTIONS = (np.tan, # Dilating map\n",
+ " np.tanh, # Contracting map\n",
+ " lambda x: x**3 + 1e-4*x, # Almost null gradient at the root\n",
+ " lambda x: x+np.sin(2*x), # Non monotonous function\n",
+ " lambda x: 1.1*x+np.sin(4*x), # Fonction with several local maxima\n",
+ " )\n",
+ "\n",
+ "OPTIMIZERS = (optimize.brenth, optimize.brentq,\n",
+ " optimize.ridder, optimize.bisect)\n",
+ "\n",
+ "\n",
+ "def apply_optimizer(optimizer, func, a, b):\n",
+ " \"\"\" Return the number of function calls given an root-finding optimizer, \n",
+ " a function and upper and lower bounds.\n",
+ " \"\"\"\n",
+ " return optimizer(func, a, b, full_output=True)[1].function_calls,\n",
+ "\n",
+ "\n",
+ "def bench_optimizer(optimizer, param_grid):\n",
+ " \"\"\" Find roots for all the functions, and upper and lower bounds\n",
+ " given and return the total number of function calls.\n",
+ " \"\"\"\n",
+ " return sum(apply_optimizer(optimizer, func, a, b)\n",
+ " for func, a, b in param_grid)\n",
+ "\n",
+ "\n",
+ "def compare_optimizers(optimizers):\n",
+ " \"\"\" Compare all the optimizers given on a grid of a few different\n",
+ " functions all admitting a signle root in zero and a upper and\n",
+ " lower bounds.\n",
+ " \"\"\"\n",
+ " random_a = -1.3 + np.random.random(size=100)\n",
+ " random_b = .3 + np.random.random(size=100)\n",
+ " param_grid = product(FUNCTIONS, random_a, random_b)\n",
+ " print(\"Benching 1D root-finder optimizers from scipy.optimize:\")\n",
+ " for optimizer in OPTIMIZERS:\n",
+ " ncalls = bench_optimizer(optimizer, param_grid)\n",
+ " print('{name}: {ncalls} total function calls'.format(\n",
+ " name=optimizer.__name__, ncalls=ncalls))\n",
+ "\n",
+ "\n",
+ "if __name__ == '__main__':\n",
+ " compare_optimizers(OPTIMIZERS)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Benching 1D root-finder optimizers from scipy.optimize:\n"
+ ]
+ },
+ {
+ "ename": "TypeError",
+ "evalue": "unsupported operand type(s) for +: 'int' and 'tuple'",
+ "output_type": "pyerr",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-4-5c834ce551a7>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 60\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 61\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0m__name__\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'__main__'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 62\u001b[1;33m \u001b[0mcompare_optimizers\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mOPTIMIZERS\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+ "\u001b[1;32m<ipython-input-4-5c834ce551a7>\u001b[0m in \u001b[0;36mcompare_optimizers\u001b[1;34m(optimizers)\u001b[0m\n\u001b[0;32m 54\u001b[0m \u001b[1;32mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Benching 1D root-finder optimizers from scipy.optimize:\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 55\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0moptimizer\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mOPTIMIZERS\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 56\u001b[1;33m \u001b[0mncalls\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbench_optimizer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0moptimizer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparam_grid\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 57\u001b[0m print('{name}: {ncalls} total function calls'.format(\n\u001b[0;32m 58\u001b[0m name=optimizer.__name__, ncalls=ncalls))\n",
+ "\u001b[1;32m<ipython-input-4-5c834ce551a7>\u001b[0m in \u001b[0;36mbench_optimizer\u001b[1;34m(optimizer, param_grid)\u001b[0m\n\u001b[0;32m 41\u001b[0m \"\"\"\n\u001b[0;32m 42\u001b[0m return sum(apply_optimizer(optimizer, func, a, b)\n\u001b[1;32m---> 43\u001b[1;33m for func, a, b in param_grid)\n\u001b[0m\u001b[0;32m 44\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 45\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'int' and 'tuple'"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 4,
+ "metadata": {},
+ "source": [
+ "Debug 1. Fix a runtime error"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, encountered a TypeError in line 43 as above. It says there comes an integer and a tuple in the operand + in the sum() function which are not able to add these two different types of input. To find out where a tuple is generated and further to fix this, I tried debug magic function."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%debug"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "> \u001b[1;32m<ipython-input-4-5c834ce551a7>\u001b[0m(43)\u001b[0;36mbench_optimizer\u001b[1;34m()\u001b[0m\n",
+ "\u001b[1;32m 42 \u001b[1;33m return sum(apply_optimizer(optimizer, func, a, b)\n",
+ "\u001b[0m\u001b[1;32m---> 43 \u001b[1;33m for func, a, b in param_grid)\n",
+ "\u001b[0m\u001b[1;32m 44 \u001b[1;33m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[0m\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ipdb> print apply_optimizer(optimizer, *param_grid.next())\n"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(9,)\n"
+ ]
+ },
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "ipdb> q\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Here I found ',' was generated by the function apply_optimizer and that is from the typo '.function_calls,', which made a tuple '(9,)' instead of an integer expected as a return of the function. I fixed this typo for the corrected running the code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def apply_optimizer(optimizer, func, a, b):\n",
+ " \"\"\" Return the number of function calls given an root-finding optimizer,\n",
+ " a function and upper and lower bounds.\n",
+ " \"\"\"\n",
+ " return optimizer(func, a, b, full_output=True)[1].function_calls"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "compare_optimizers(OPTIMIZERS)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Benching 1D root-finder optimizers from scipy.optimize:\n",
+ "brenth: 605054 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "brentq: 0 total function calls\n",
+ "ridder: 0 total function calls\n",
+ "bisect: 0 total function calls\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Fixed the runtime error still got different results from the expected ones; brentq, ridder, and bisect produced nothing. "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 4,
+ "metadata": {},
+ "source": [
+ "Debug 2. Fix a semantic error"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It appears that the same iterable generated by the random number function was not input in to 'brentq', 'ridder', and 'bisect' optimizers; the entire loop for each optimizer suddenly broke after 'brenth' ran. So I fixed this adding list() in front of the ouput of 'param_grid' liner to create the same iterable for each optimizer and applied this to the original code."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "def compare_optimizers(optimizers):\n",
+ " \"\"\" Compare all the optimizers given on a grid of a few different\n",
+ " functions all admitting a signle root in zero and a upper and\n",
+ " lower bounds.\n",
+ " \"\"\"\n",
+ " random_a = -1.3 + np.random.random(size=100)\n",
+ " random_b = .3 + np.random.random(size=100)\n",
+ " param_grid = list(product(FUNCTIONS, random_a, random_b))\n",
+ " print(\"Benching 1D root-finder optimizers from scipy.optimize:\")\n",
+ " for optimizer in OPTIMIZERS:\n",
+ " ncalls = bench_optimizer(optimizer, param_grid)\n",
+ " print('{name}: {ncalls} total function calls'.format(\n",
+ " name=optimizer.__name__, ncalls=ncalls))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Test the fixed code again."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "compare_optimizers(OPTIMIZERS)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Benching 1D root-finder optimizers from scipy.optimize:\n",
+ "brenth: 601987 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "brentq: 592551 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "ridder: 771204 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "bisect: 2147060 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 4,
+ "metadata": {},
+ "source": [
+ "Summary"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Finally, it worked pretty well as we expected. \n",
+ "\n",
+ "To summarize, there were a runtime error (TypeError) and a semantic error (Failure to the for looping) in the given code. I debugged these first with 'debug magic' function to point out the typo and fix the runtime error. Then with an investigation of the iterating process, I found a dead end of the code's inputting the iterable to the loop and eventually fixed 'param_grid' to generate the same iterable to be input for each optimizer."
+ ]
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}