Merge pull request #136 from BethanyL/HW8

Hw8

BethanyL/HW8.ipynb

@@ -0,0 +1,170 @@
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+ "cells": [
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+ "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",
+ "\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",
+ " \n",
+ " #whatis(optimizer(func, a, b, full_output=True)[1].function_calls)\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",
+ "\n",
+ " x = 0\n",
+ " for func, a, b in param_grid:\n",
+ " x = x + apply_optimizer(optimizer, func, a, b)\n",
+ " return x\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",
+ " 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)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Benching 1D root-finder optimizers from scipy.optimize:\n",
+ "brenth: 602899 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "brentq: 591665 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "ridder: 772996 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ "bisect: 2147620 total function calls"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Step 1: This code: <br>\n",
+ "&emsp;return sum(apply_optimizer(optimizer, func, a, b)<br>\n",
+ "&emsp;&emsp;for func, a, b in param_grid)<br>\n",
+ "is not a valid for loop, so I split it up like this: <br>\n",
+ "&emsp;x = 0<br>\n",
+ "&emsp;for func, a, b in param_grid:<br>\n",
+ "&emsp;&emsp;x = x + apply_optimizer(optimizer, func, a, b)<br>\n",
+ "&emsp;return x"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Step 2: I got a TypeError because x is an integer and apply_optimizer is returning a tuple, so I checked the apply_optimizer function. This led me to check the documentation of scipy/optimize (and even the code itself). I saw that it should be returning an int, not a tuple. I used pdb to see that \"optimizer(func, a, b, full_output=True)[1].function_calls\" does indeed return a tuple. Then I realized that the comma must make a tuple. Sure enough, removing the comma fixes the problem."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Step 3: The new problem is that only brenth runs - the rest have 0 function calls. Checking the documentation did not help. However, if you comment out brenth, you see that the first optimizer will run, no matter what it is. I used pdb to step through and realized that the loop in bench_optimizer was not running. The I investigated param_grid and the documentation for product. I guessed that re-creating param_grid in the loop would fix the problem, which was correct."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}