testing minimization methods

farrukh.ipynb

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  "name": ""
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 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "from scipy.optimize import minimize"
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def rosen(x):\n",
      "    \"\"\"The Rosenbrock function\"\"\"\n",
      "    return sum(100.0*(x[1:]-x[:-1]**2.0)**2.0 + (1-x[:-1])**2.0)\n",
      "\n",
      "methods=['Nelder-Mead', 'Powell', 'CG', 'BFGS', 'Anneal', 'SLSQP'] "
     ],
     "language": "python",
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x0=np.array([2,3,4,5])\n",
      "\n",
      "for m in methods:\n",
      "    print m\n",
      "    opt={'disp':True}\n",
      "\n",
      "    if m=='Anneal':\n",
      "       opt['maxiter']=500\n",
      "       #opt['schedule']='fast'\n",
      "       #opt['schedule']='cauchy'\n",
      "       opt['schedule']='boltzmann'\n",
      "    res=minimize(rosen,x0,method=m,\n",
      "    \t\t\toptions=opt)\n",
      "    print res, '\\n'\n",
      "\n"
     ],
     "language": "python",
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Nelder-Mead\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 330\n",
        "         Function evaluations: 557\n",
        "  status: 0\n",
        "    nfev: 557\n",
        " success: True\n",
        "     fun: 1.3587127674836083e-09\n",
        "       x: array([ 0.99999699,  0.99999729,  0.99999459,  0.99999064])\n",
        " message: 'Optimization terminated successfully.'\n",
        "     nit: 330 \n",
        "\n",
        "Powell\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 28\n",
        "         Function evaluations: 1364\n",
        "  status: 0\n",
        " success: True\n",
        "   direc: array([[ -4.79377475e-04,  -7.63426520e-04,  -1.54154727e-03,\n",
        "         -3.08976968e-03],\n",
        "       [ -3.85266935e-03,  -9.73515947e-03,  -1.95291302e-02,\n",
        "         -3.78494124e-02],\n",
        "       [ -1.64624628e-02,  -4.25115876e-02,  -9.35815385e-02,\n",
        "         -2.22211515e-01],\n",
        "       [  1.75089522e-08,   3.58033159e-08,   2.85708782e-08,\n",
        "          7.02602663e-08]])\n",
        "    nfev: 1364\n",
        "     fun: 5.1795359650505254e-25\n",
        "       x: array([ 1.,  1.,  1.,  1.])\n",
        " message: 'Optimization terminated successfully.'\n",
        "     nit: 28 \n",
        "\n",
        "CG\n",
        "Optimization terminated successfully."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 124\n",
        "         Function evaluations: 1440\n",
        "         Gradient evaluations: 240\n",
        "  status: 0\n",
        " success: True\n",
        "    njev: 240\n",
        "    nfev: 1440\n",
        "     fun: 1.232110081155319e-10\n",
        "       x: array([ 0.99999759,  0.99999517,  0.99999031,  0.99998059])\n",
        " message: 'Optimization terminated successfully.'\n",
        "     jac: array([  5.40941797e-06,   5.19370724e-06,  -1.74661663e-07,\n",
        "        -6.75569820e-06]) \n",
        "\n",
        "BFGS\n",
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 60\n",
        "         Function evaluations: 480\n",
        "         Gradient evaluations: 80\n",
        "   status: 0\n",
        "  success: True\n",
        "     njev: 80\n",
        "     nfev: 480\n",
        " hess_inv: array([[ 0.02412562,  0.04570413,  0.09044236,  0.18041822],\n",
        "       [ 0.04570413,  0.09142452,  0.18071695,  0.36046589],\n",
        "       [ 0.09044236,  0.18071695,  0.36262278,  0.72304154],\n",
        "       [ 0.18041822,  0.36046589,  0.72304154,  1.44665636]])\n",
        "      fun: 4.69120880742064e-11\n",
        "        x: array([ 0.9999985 ,  0.99999701,  0.99999403,  0.99998804])\n",
        "  message: 'Optimization terminated successfully.'\n",
        "      jac: array([  6.94736551e-07,  -2.47249630e-06,   2.79980237e-06,\n",
        "        -8.76512818e-07]) \n",
        "\n",
        "Anneal\n",
        "Warning: Maximum number of iterations exceeded."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "  status: 3\n",
        " success: False\n",
        "  accept: 9024\n",
        "    nfev: 25101\n",
        "       T: 4676272727.9951382\n",
        "     fun: 1056134.5319457012\n",
        "       x: array([ -4.88510617e+00,  -1.06598901e-01,   3.66246724e+01,\n",
        "         1.24845183e+03])\n",
        " message: 'Maximum cooling iterations reached'\n",
        "     nit: 501 \n",
        "\n",
        "SLSQP\n",
        "Optimization terminated successfully.    (Exit mode 0)\n",
        "            Current function value: 2.88053419653e-08\n",
        "            Iterations: 38\n",
        "            Function evaluations: 249\n",
        "            Gradient evaluations: 38\n",
        "  status: 0\n",
        " success: True\n",
        "    njev: 38\n",
        "    nfev: 249\n",
        "     fun: 2.8805341965344145e-08\n",
        "       x: array([ 0.99997245,  0.99994604,  0.99989499,  0.99980146])\n",
        " message: 'Optimization terminated successfully.'\n",
        "     jac: array([ 0.00789731,  0.01259049, -0.03355575,  0.01202431,  0.        ])\n",
        "     nit: 38 \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 3
    }
   ]
  }
 ]
}