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| { | ||
| "metadata": { | ||
| "name": "" | ||
| }, | ||
| "nbformat": 3, | ||
| "nbformat_minor": 0, | ||
| "worksheets": [ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "raw", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Summary: \n", | ||
| "\n", | ||
| "I began by checking for any syntax errors. There ended up being only one syntax error; A line of the code had an extra comma in the following return statement \"return optimizer(func, a, b, full_output=True)[1].function_calls\" After fixing this, the code appeared to only be outputting the count for optimizer.breth. I first checked the variables random_a and random_b to see if they parameters met the requirements listed in the documentation for each optimizer. This appeared to be fine. Next, I checked the OPTIMIZER list by removing optimizer.brenth and running the code on the other three optimizers. This produced the same error as before-- the program was counting the first optimizer in the list but returning zero function calls for the others. \n", | ||
| "\n", | ||
| "My next line of attack was printing the results of the functions. Printing the apply_optimizer function didn't give any useful results, but printing the return value in the bench_optimizer showed again that only one of the optimizers was being counted. Since the apply_optimizer function seemed to be working, I moved on to testing the param_grid object. Upon printing, I got the following output :\n", | ||
| " <itertools.product object at 0x105ac07d0>\n", | ||
| "This didn't give any useful information. After investigating the \"product\" documentation, I realized that it would make more sense to print this object in a loop. The results of this indicated that param_grid what it was supposed to, but only for the first optimizer. After moving it inside the loop, the bench_optimizer function was printing out the correct number of function calls for all of the optimizers, however, the final output was\n", | ||
| "\n", | ||
| "Benching 1D root-finder optimizers from scipy.optimize:\n", | ||
| "599821\n", | ||
| "brenth: 0 total function calls\n", | ||
| "588991\n", | ||
| "brentq: 0 total function calls\n", | ||
| "770432\n", | ||
| "ridder: 0 total function calls\n", | ||
| "2145735\n", | ||
| "bisect: 0 total function calls.\n", | ||
| "\n", | ||
| "This ended up having something to with the print statement I put in bench_optimizers. After commenting the print statement out, the compare_ optimizers printed out the correct output.\n", | ||
| " " | ||
| ] | ||
| }, | ||
| { | ||
| "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 should 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), # Function with several local maxima\n", | ||
| " )\n", | ||
| "\n", | ||
| "OPTIMIZERS = (optimize.brenth, optimize.brentq,\n", | ||
| " optimize.ridder, optimize.bisect)\n", | ||
| "#OPTIMIZERS= (optimize.brentq,optimize.ridder, optimize.bisect) # Hrmm. It seems to work for the first element of the array.\n", | ||
| " # But it is not being recognized in the compare_optizers func\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", | ||
| " # print optimizer(func, a, b, full_output=True)[1].function_calls\n", | ||
| " return optimizer(func, a, b, full_output=True)[1].function_calls # Syntax Error: Comma at end of line. Removed.\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", | ||
| " #print sum(apply_optimizer(optimizer, func, a, b) \n", | ||
| " # for func, a, b in param_grid) #only works for first element in optimizer\n", | ||
| " #after moving param_grid into the forloop, this is working, but the call to it in compare_optimizers isn't working.\n", | ||
| " #apparently printing the sum screws with something and causes it not to print when it's calls??\n", | ||
| " return sum(apply_optimizer(optimizer, func, a, b)\n", | ||
| " for func, a, b in param_grid)\n", | ||
| "\n", | ||
| "\n", | ||
| "def compare_optimizers(optimizers): #maybe putting the function in there will work??\n", | ||
| " \"\"\" Compare all the optimizers given on a grid of a few different\n", | ||
| " functions all admitting a single 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", | ||
| " #what are these numbers?\n", | ||
| " #print random_a\n", | ||
| " #print random_b\n", | ||
| " # They appear to contain the right signs...\n", | ||
| " \n", | ||
| " # param_grid = product(FUNCTIONS, random_a, random_b) #product gives a Cartesian product of input iterables.\n", | ||
| " # print param_grid # not giving anything\n", | ||
| " #What if I put this in a forloop?\n", | ||
| " #for (x,y,z) in param_grid : print (x,y,z), param_grid #seems; to work \n", | ||
| " print(\"Benching 1D root-finder optimizers from scipy.optimize:\")\n", | ||
| " for optimizer in OPTIMIZERS:\n", | ||
| " param_grid = product(FUNCTIONS, random_a, random_b) #Moving this into the for loop seems to work, but the counts\n", | ||
| " #still aren't being recognized when I call the\n", | ||
| " #the bench_optimizer function. Hmmm.\n", | ||
| " ncalls = bench_optimizer(optimizer, param_grid)\n", | ||
| " # print ncalls # using the optimizer array that has three elements, it is not counting any elements.\n", | ||
| " #after moving param_grid inside, this is still printing the sums as 0. Hrmm.\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", | ||
| "\n" | ||
| ], | ||
| "language": "python", | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "Benching 1D root-finder optimizers from scipy.optimize:\n", | ||
| "brenth: 607945 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "brentq: 597041 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "ridder: 776904 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "bisect: 2152130 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n" | ||
| ] | ||
| } | ||
| ], | ||
| "prompt_number": 63 | ||
| }, | ||
| { | ||
| "cell_type": "raw", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "The next cell contains the corrected program." | ||
| ] | ||
| }, | ||
| { | ||
| "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", | ||
| " \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: 599291 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "brentq: 588597 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "ridder: 768560 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n", | ||
| "bisect: 2144465 total function calls" | ||
| ] | ||
| }, | ||
| { | ||
| "output_type": "stream", | ||
| "stream": "stdout", | ||
| "text": [ | ||
| "\n" | ||
| ] | ||
| } | ||
| ], | ||
| "prompt_number": 64 | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "collapsed": false, | ||
| "input": [], | ||
| "language": "python", | ||
| "metadata": {}, | ||
| "outputs": [] | ||
| } | ||
| ], | ||
| "metadata": {} | ||
| } | ||
| ] | ||
| } |