Merge pull request #144 from jtzhanguw/HW8_branch

HW8
uw-python · Dec 2, 2014 · 68a842c · 68a842c
2 parents fc9216a + 00228e7
commit 68a842c
Showing 1 changed file with 258 additions and 0 deletions.
diff --git a/jtzhanguw/HW8.ipynb b/jtzhanguw/HW8.ipynb
@@ -0,0 +1,258 @@
+{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:5bd0ba64ceca92c6049b68f2e268ea323e093d066f5c6e1dbd4233398295a611"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Homework\n",
+ "Below is a script taken from [scipy lectures](http:https://scipy-lectures.github.io/advanced/debugging/)\n",
+ "\n",
+ "It is meant to compare the performance of several root-finding algorithms within the ``scipy.optimize``\n",
+ "package, but it breaks. Use one or more of the above tools to figure out what's going on and to fix\n",
+ "the script.\n",
+ "\n",
+ "When you turn in this homework (via github pull request, of course), please **write a one to two paragraph summary**\n",
+ "of the process you used to debug this, including any dead ends (it may help to take notes as you go)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "``` python\n",
+ "\"\"\"\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)\n",
+ "```"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from itertools import product\n",
+ "\n",
+ "import numpy as np\n",
+ "from scipy import optimize"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "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",
+ " )"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "OPTIMIZERS = (optimize.brenth, optimize.brentq,\n",
+ " optimize.ridder, optimize.bisect)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 21
+ },
+ {
+ "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\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [],
+ "prompt_number": 23
+ },
+ {
+ "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",
+ " print(\"Benching 1D root-finder optimizers from scipy.optimize:\")\n",
+ " for optimizer in OPTIMIZERS:\n",
+ " param_grid = product(FUNCTIONS, random_a, random_b)\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",
+ "brenth: 605758 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "brentq: 594716 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "ridder: 775608 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "bisect: 2150110 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When I ran the script, firstly it failed and showed that \"unsupported operand type(s) for +: 'int' and 'tuple'\", because the sum function in bench_optimizer cannot operate on tuples. It means that the type apply_optimizer function returns has a problem. I removed the comma at the end of \"optimizer(func, a, b, full_output=True)[1].function_calls\" in apply_optimizer function, then it worked, but only for brenth, not for the other brentq, ridder and bisect. \n",
+ "\n",
+ "Secondly, I moved the \"param_grid = product(FUNCTIONS, random_a, random_b)\n",
+ "\" into for loop and then it is working now."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}