{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Solutions to Exercises\n",
      "\n",
      "All the code below must be run in context. None will work here."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 01-0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Econcat = np.concatenate([np.linalg.eig(vec)[0].reshape((1, M)) for vec in A])\n",
      "# Econcat = np.concatenate([np.linalg.eig(vec)[0][None] for vec in A])\n",
      "print np.allclose(Econcat, Evec)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%capture out\n",
      "from IPython.parallel import Client\n",
      "\n",
      "N = 1000\n",
      "M = 4\n",
      "np.random.seed(201)\n",
      "A = np.random.random((N, M, M))\n",
      "%timeit Evec = np.array(zip(*map(np.linalg.eig, A))[0])\n",
      "for Neng in range(1, 9):\n",
      "    ##%pxconfig --targets :2\n",
      "    dview = engines[:Neng]\n",
      "    dview.block = True\n",
      "    dview.activate()\n",
      "    dview.scatter('A', A.copy())\n",
      "    %px import numpy as np\n",
      "    %timeit %px Evec = np.array(zip(*map(np.linalg.eig, A))[0])\n",
      "    Evec_parallel = dview.gather('Evec')\n",
      "    #print np.allclose(Evec, Evec_parallel)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print out.stdout.split('\\n')[0].split()\n",
      "values = [l.split()[5] for l in out.stdout.split('\\n')[1:9]]\n",
      "plt.plot(np.arange(1, 9), values)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 02-0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymks\n",
      "??pymks.bin"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 02-1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the following, we will just check that one test response is reasonably close to a response calculated with the influence coefficients. We construct a `test_microstructre` and use the `fipy_response` function to calculate `test_response`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.seed(103)\n",
      "test_microstructure = np.random.random(N**2)\n",
      "test_response = fipy_response(test_microstructure, dt=dt, N=N)\n",
      "\n",
      "binned_test_microstructure = bin(test_microstructure, Nbin).reshape((N, N, Nbin))\n",
      "Fm = np.fft.fft2(binned_test_microstructure, axes=(0, 1))\n",
      "Fr = np.sum(Fm * Fcoeff, axis=-1)\n",
      "            \n",
      "calc_response = np.fft.ifft2(Fr, axes=(0, 1)).real.flatten()\n",
      "\n",
      "\n",
      "print test_response[:20]\n",
      "print calc_response[:20]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 03-0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.signal\n",
      "import scipy.ndimage\n",
      "?scipy.signal.fftconvolve\n",
      "\n",
      "y_alt = scipy.ndimage.convolve(X[0], filter(np.linspace(0, 20, Nspace)), mode='wrap')\n",
      "print np.allclose(np.roll(y_alt, 40), y[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 03-1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X0 = np.random.random((1, Nspace))\n",
      "y0 = model.predict(X0)\n",
      "import scipy.ndimage\n",
      "y_alt = scipy.ndimage.convolve(X0[0], filter(np.linspace(0, 20, Nspace)), mode='wrap')\n",
      "print np.allclose(np.roll(y_alt, 40), y0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 04-0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "mse = metrics.mean_squared_error\n",
      "\n",
      "Nbins = np.arange(2, 100, 10)\n",
      "\n",
      "errors = []\n",
      "\n",
      "for Nbin in Nbins:\n",
      "    print Nbin\n",
      "    model = MKSRegressionModel(Nbin=Nbin)\n",
      "    model.fit(X, y)\n",
      "    errors.append(mse(model.predict(X), y))\n",
      "    \n",
      "plt.plot(Nbins, errors)\n",
      "plt.xlabel('Nbin')\n",
      "plt.ylabel('MSE')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 04-1\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "errors = []\n",
      "\n",
      "Nbins = np.arange(2, 20)\n",
      "for Nbin in Nbins:\n",
      "    model = MKSRegressionModel(Nbin=Nbin)\n",
      "    model.fit(X_train, y_train)\n",
      "    errors.append(mse(model.predict(X_test), y_test))\n",
      "    \n",
      "plt.plot(Nbins, errors)\n",
      "plt.xlabel('Nbin')\n",
      "plt.ylabel('MSE')\n",
      "\n",
      "argmin = np.argmin(errors)\n",
      "print \"optimal Nbin: {0}, mse: {1:1.3e}\".format(Nbins[argmin], errors[argmin])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 05-0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "??model.resize_coeff"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 06-0"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 06-1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "??FastMKSRegressionModel"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}