{
 "metadata": {
  "name": "PSEFinal2012a_Sol"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#PSE 2012 final section a solution "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fact: The second derivative test generalizes naturally to give a test for multivariable optimization. If Df represents the matrix derivative of a function f(x,y), then critical points are where Df(x,y)=0 . The second derivative, D2f(x,y), called the Hessian matrix, can be used to test if a critical point is a maximum (both eigenvalues negative), minimum (both eigenvalues positive), or a saddle point (eigenvalues have different signs). The eigenvectors tell the directions in which the second derivative is a maximum or minimum.\n",
      "\n",
      "Examples for using sympy module to compute symbolically the necessary and sufficient conditions for finding analytically critical points of a function"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Finds the critical point of a given function \"symbolically\" (analytically)\n",
      "from sympy import *\n",
      "x=Symbol('x')\n",
      "y=Symbol('y')\n",
      "f=exp(-x**2-y**2)\n",
      "print 'displays the function in latex form',latex(f)\n",
      "print 'displays the function if python form', f\n",
      "f.diff(x)# finds the partial derivative of f with respect to x\n",
      "f.diff(y) # finds the partial derivative of f with respect to y\n",
      "fgrad=[f.diff(x),f.diff(y)] # gradient of f\n",
      "print 'displays the gradient of f', fgrad\n",
      "xopt=solve(fgrad,[x,y]) # solves the necessary equations for finding the extreme points\n",
      "print 'displays the extreme point found',xopt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "displays the function in latex form e^{- x^{2} - y^{2}}\n",
        "displays the function if python form exp(-x**2 - y**2)\n",
        "displays the gradient of f [-2*x*exp(-x**2 - y**2), -2*y*exp(-x**2 - y**2)]\n",
        "displays the extreme point found"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " [(0, 0)]\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\" Identify the type of critical point (maximum, minimum, sandle) by computing the Hessian \n",
      "at the critical point and finding its  eigenvalues and eigenvectors \"\"\"\n",
      "H=hessian(f,[x,y]).evalf(subs=({x:0.0,y:0.0}))\n",
      "print 'displays the Hessian of f',H\n",
      "#Computes the eigenvalues of H\n",
      "HE=H.eigenvals()\n",
      "print 'Displays the eigenvalues and their multiplicity', HE\n",
      "#Computes the eigenvectors of H\n",
      "HEV=H.eigenvects()\n",
      "print 'Displays the eigenvalues, multiplicity, and basis',HEV"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "displays the Hessian of f [-2.0,    0]\n",
        "[   0, -2.0]\n",
        "Displays the eigenvalues and their multiplicity {-2: 2}\n",
        "Displays the eigenvalues, multiplicity, and basis [(-2.00000000000000, 2, [[1.0]\n",
        "[  0], [  0]\n",
        "[1.0]])]\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "figure()\n",
      "ax = subplot(111, projection='3d')\n",
      "\n",
      "x = linspace(-3,3,40)\n",
      "xx, yy = meshgrid(x,x)\n",
      "zz = exp(-xx**2-yy**2)\n",
      "\n",
      "ax.plot_surface(xx, yy, zz,\n",
      "                rstride=1,\n",
      "                cstride=1,\n",
      "                cmap=cm.binary,\n",
      "                linewidth=0.2)\n",
      "\n",
      "ax.set_xlabel(r'$x$')\n",
      "ax.set_ylabel('$y$')\n",
      "ax.set_zlabel('$z$')\n",
      "title(r'The function $z=\\exp(-x^2-y^2)$')\n",
      "\n",
      "\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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D8hfHsn9QCNYND3wyJt9xR0cH+vv7o7gy/4iNO2qUYDjC4aFwL5AxhnPzkpQxi8UCs9kc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\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 1: Find the critical point of the function $f(x,y)=x^2*y+y^2+y$  \n",
      "### and verify whether the point is maximum, minimum, or sandle"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Finds the critical point of a given function \"symbolically\" (analytically)\n",
      "from sympy import *\n",
      "x=Symbol('x')\n",
      "y=Symbol('y')\n",
      "f=x**2*y+y**2+y\n",
      "print 'displays the function in latex form',latex(f)\n",
      "print 'displays the function if python form', f\n",
      "f.diff(x)# finds the partial derivative of f with respect to x\n",
      "f.diff(y) # finds the partial derivative of f with respect to y\n",
      "fgrad=[f.diff(x),f.diff(y)] # gradient of f\n",
      "print 'displays the gradient of f', fgrad\n",
      "xopt=solve(fgrad,[x,y]) # solves the necessary equations for finding the extreme points\n",
      "print 'displays the extreme point found',xopt\n",
      "\"\"\" Identify the type of critical point (maximum, minimum, sandle) by computing the Hessian \n",
      "at the critical point and finding its  eigenvalues and eigenvectors \"\"\"\n",
      "H=hessian(f,[x,y]).evalf(subs=({x:0.0,y:0.0}))\n",
      "print 'displays the Hessian of f',H\n",
      "#Computes the eigenvalues of H\n",
      "HE=H.eigenvals()\n",
      "print 'Displays the eigenvalues and their multiplicity', HE\n",
      "#Computes the eigenvectors of H\n",
      "HEV=H.eigenvects()\n",
      "print 'Displays the eigenvalues, multiplicity, and basis',HEV"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "displays the function in latex form x^{2} y + y^{2} + y\n",
        "displays the function if python form x**2*y + y**2 + y\n",
        "displays the gradient of f [2*x*y, x**2 + 2*y + 1]\n",
        "displays the extreme point found [(0, -1/2), (-I, 0), (I, 0)]\n",
        "displays the Hessian of f [0,   0]\n",
        "[0, 2.0]\n",
        "Displays the eigenvalues and their multiplicity {2: 1, 0: 1}\n",
        "Displays the eigenvalues, multiplicity, and basis"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " [(0, 1, [[1.0]\n",
        "[  0]]), (2.00000000000000, 1, [[  0]\n",
        "[1.0]])]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 2: Find the extreme point of f numerically using the nonlinear unconstrained optimization module \n",
      "        fmin_bfgs\n",
      "Use help(fmin_bfgs) to find out how the module is defined"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fmin_bfgs\n",
      "import numpy as np\n",
      "def f(x):\n",
      "    return x[0]**2*x[1]+x[1]**2+x[1]\n",
      "x0=[0,0]\n",
      "xopt=fmin_bfgs(f,x0)\n",
      "print xopt\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: -0.250000\n",
        "         Iterations: 1\n",
        "         Function evaluations: 12\n",
        "         Gradient evaluations: 3\n",
        "[ 0.  -0.5]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.1: Generate a 3D Plot of  the function f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "\n",
      "figure()\n",
      "ax = subplot(111, projection='3d')\n",
      "\n",
      "x = linspace(-3,3,40)\n",
      "xx, yy = meshgrid(x,x)\n",
      "zz = xx**2*yy+yy**2+yy\n",
      "\n",
      "ax.plot_surface(xx, yy, zz,\n",
      "                rstride=1,\n",
      "                cstride=1,\n",
      "                cmap=cm.binary,\n",
      "                linewidth=0.2)\n",
      "\n",
      "ax.set_xlabel(r'$x$')\n",
      "ax.set_ylabel('$y$')\n",
      "ax.set_zlabel('$z$')\n",
      "title(r'The function z=x^2*y+y^2+y')\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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aVbomElQJtnnzZp4Po9GIcDgMlUqFZDLJxEdWTzAYzEhAJ13cdB9vKpWCWq2G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\n8lgvZdRxI18JT09PUaRbsGDBgL4SA1lAG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XnypMlUyIQhwcTpmmDCIFFbW8uWLVvQaDR4\neHjwy1/+0hRwTRgyTJmuCSaYYMIowsTpmmCCCSaMIkxB1wQTTDBhFGEKuiaYYIIJo4j/D8gbJBJn\nOWVLAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 3.2: Generate a countour plot of the function f"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "xlist = linspace(-3.0, 3.0, 100)\n",
      "ylist = linspace(-3.0, 3.0, 100)\n",
      "X, Y = meshgrid(xlist, ylist)\n",
      "#print X\n",
      "#print Y\n",
      "Z = X**2*Y+Y**2+Y\n",
      "figure()\n",
      "CP1 = contour(X, Y, Z)  \n",
      "clabel(CP1, inline=True, fontsize=10) \n",
      "title('Contour Plot') \n",
      "xlabel('x (cm)')\n",
      "ylabel('y (cm)')\n",
      "show() \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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lqEzMxk0sCPM7ItYIXG8O2fNAMZ/3bb0tf0Mm5HxYdGYeWTSYa32zVhJJYCtb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\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider the function f(x) and its derivative\n",
      "\n",
      "            def f(x):\n",
      "                return (x[0]**2+x[1]**2)**2-x[0]**2-x[1]+x[2]**2\n",
      "            def fprime(x):\n",
      "                grad = numpy.zeros((len(x),), float)\n",
      "                grad[0] = 4*x[0]*(x[0]**2+x[1]**2)-2*x[0]\n",
      "                grad[1] = 4*x[1]*(x[0]**2+x[1]**2)-1\n",
      "                grad[2] = 2*x[2]\n",
      "            return grad\n",
      "\n",
      "### Problem 4: Use the fmin_bfgs module to compute the local minimum of the function a) without using the gradient of f and b) by using the specified gradient by the function fprime. *Compute the executions times for each case*.\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fmin_bfgs\n",
      "import numpy as np\n",
      "import time\n",
      "def f(x):\n",
      "    return (x[0]**2+x[1]**2)**2-x[0]**2-x[1]+x[2]**2\n",
      "def fprime(x):\n",
      "    grad = numpy.zeros((len(x),), float)\n",
      "    grad[0] = 4*x[0]*(x[0]**2+x[1]**2)-2*x[0]\n",
      "    grad[1] = 4*x[1]*(x[0]**2+x[1]**2)-1\n",
      "    grad[2] = 2*x[2]\n",
      "    return grad\n",
      "tic=time.time()\n",
      "c0=[0,0,0]\n",
      "xopt=fmin_bfgs(f,c0)\n",
      "toc=time.time()-tic\n",
      "print 'a) Min:', xopt\n",
      "print 'Time elapsed for a)',toc\n",
      "\n",
      "tic=time.time()\n",
      "c0=[0,0,0]\n",
      "xopt=fmin_bfgs(f, c0, fprime=fprime, epsilon=5)\n",
      "toc=time.time()-tic\n",
      "print 'b) Min:', xopt\n",
      "print 'Time elapsed for b)',toc "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: -0.472470\n",
        "         Iterations: 5\n",
        "         Function evaluations: 40\n",
        "         Gradient evaluations: 8\n",
        "a) Min: [  5.09166246e-08   6.29960510e-01  -7.33826933e-09]\n",
        "Time elapsed for a) 0.00300002098083\n",
        "Optimization terminated successfully.\n",
        "         Current function value: -0.472470\n",
        "         Iterations: 5\n",
        "         Function evaluations: 8\n",
        "         Gradient evaluations: 8\n",
        "b) Min: [ 0.          0.62996052  0.        ]\n",
        "Time elapsed for b) 0.0019998550415\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Given a set of points (x,y) and a parametrized function $f(c,x)$, the method of least squares  identifies the parameters $c$  so that the Euclidian distance of the function from the data is minimum i.e.\n",
      "\n",
      "$\\sum_{i=1}^m \\(f(c,x_i) - y_i)^2$ with respect to $c=[c_1,c_2,...,c_n]$\n",
      "\n",
      "The following code presents the setup and the solution of the least squares problem  for the nonlinear function $f(c,x)=c_0+c_1 exp(c_2 x)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.optimize import fmin_bfgs\n",
      "import numpy as np\n",
      "xdata = np.reshape(np.arange(0,1,0.1),(-1,1))\n",
      "ydata = 1+2*np.exp(0.75*xdata)\n",
      "fun = lambda c: sum((c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2)\n",
      "c0=[0,0,0]\n",
      "xopt=fmin_bfgs(fun,c0)\n",
      "print xopt\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 0.000000\n",
        "         Iterations: 23\n",
        "         Function evaluations: 155\n",
        "         Gradient evaluations: 31\n",
        "[ 1.00000485  1.9999951   0.75000141]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 5: Compute the linear least squares fit to the data generated by the following program with the nonlinear function\n",
      "\n",
      "        fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *\n",
      "from numpy import *\n",
      "from scipy.optimize import fmin\n",
      "\n",
      "## Parametric function: 'v' is the parameter vector, 'x' the independent variable\n",
      "fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)\n",
      "\n",
      "## Noisy function (used to generate data to fit)\n",
      "v_real = [1.5, 0.1, 2.]\n",
      "fn = lambda x: fp(v_real, x)\n",
      "## Generating noisy data to fit\n",
      "n = 30\n",
      "xmin = 0.1\n",
      "xmax = 5\n",
      "x = linspace(xmin,xmax,n)\n",
      "y = fn(x) + rand(len(x))*0.2*(fn(x).max()-fn(x).min())\n",
      "plot (x,y,marker='o', linestyle='--', color='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "[<matplotlib.lines.Line2D at 0x6c91170>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Specify the code for finding the  least squares fit to the above data with the function\n",
      "\n",
      "        fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fun = lambda v: sum((v[0]/(x**v[1])*sin(v[2]*x) - y)**2)\n",
      "v0=[1,0.1,2]\n",
      "v_opt=fmin_bfgs(fun,v0)\n",
      "print v_opt "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 3.479917\n",
        "         Iterations: 8\n",
        "         Function evaluations: 65\n",
        "         Gradient evaluations: 13\n",
        "[ 1.70606399  0.23590853  1.98891436]\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###and plot both the nonlinear fit and the data in the same plot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pylab as pl\n",
      "# Make x, y arrays for each graph\n",
      "fp = lambda v, x: v[0]/(x**v[1])*sin(v[2]*x)\n",
      "x1 = x\n",
      "y1 = y\n",
      "x2 = x\n",
      "y2 = fp(v_opt,x)\n",
      "# use pylab to plot x and y\n",
      "plot1=pl.plot(x1, y1, 'r',label='given data')\n",
      "plot2=pl.plot(x2, y2, 'g',label='least squares approximation')\n",
      "# give plot a title\n",
      "pl.title('Plot given data and their least squares appr')\n",
      "# make axis labels\n",
      "pl.xlabel('x axis')\n",
      "pl.ylabel('y axis')\n",
      "# set axis limits\n",
      "pl.xlim(0.0, 5.0)\n",
      "pl.ylim(-1.5, 2.0)\n",
      "# make legend\n",
      "pl.legend(loc='upper left')\n",
      "# show the plot on the screen\n",
      "pl.show()\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "                                                    \n",
      "        \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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xI9m/fz9RUFBgMxFOnjyZKCgokBMnTpDk5GQyZMgQsnz5coHnWeL31R9/EDJj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\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Problem 6: Compute the value of $\u03c0$ in parallel using the fact that $\u03c0=\\int_0^1 \\ 4/(1+x^2) \\ \\mathrm{d} x$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Symbolic computation of the integral*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "x=Symbol('x')\n",
      "exact=integrate(4/(1+x**2), (x, 0, 1))\n",
      "print exact"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "pi\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*Numerical computation of the integral  using a general purpose toutine quad*"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.integrate import quad\n",
      "def f(x):\n",
      "    return 4/(1+x**2)\n",
      "result = quad(f, 0, 1)\n",
      "print result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(3.1415926535897936, 3.4878684980086326e-14)\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "error =N(pi)-result[0]\n",
      "print error"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-4.44089209850063e-16\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compute the integral in parallel by dividing the interval of integration in n  subintervals where n is the number of engines used and summing the n results\n",
      "\n",
      "$\u03c0=\\sum_{i=0}^{n-1}\\int_{x_i}^{x_{i+1}} \\frac{4}{(1+x^2)} \\ \\mathrm{d} x$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os,sys,time\n",
      "import numpy\n",
      "import numpy as np\n",
      "\n",
      "from IPython.core.display import display, Math\n",
      "\n",
      "from IPython import parallel\n",
      "rc = parallel.Client()\n",
      "rc.block = True # let's start synchronous"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# index-access of a client gives us a DirectView\n",
      "e0 = rc[0]\n",
      "eall = rc[:]\n",
      "even = rc[::2]\n",
      "odd = rc[1::2]\n",
      "\n",
      "# this is the one we are going to use the most:\n",
      "dview = eall\n",
      "map(display, [e0, eall, even, odd]);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": [
        "<DirectView 0>"
       ]
      },
      {
       "output_type": "display_data",
       "text": [
        "<DirectView [0, 1, 2, 3]>"
       ]
      },
      {
       "output_type": "display_data",
       "text": [
        "<DirectView [0, 2]>"
       ]
      },
      {
       "output_type": "display_data",
       "text": [
        "<DirectView [1, 3]>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rc.ids"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "[0, 1, 2, 3]"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%px from  scipy.integrate import quad\n",
      "%px import time\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*** Estimate pi sequentially using map function*** "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "step=0.25\n",
      "a=[i*step for i in range(0,4)]\n",
      "b=[i*step for i in range(1,5)]\n",
      "\n",
      "def quadf(aa,bb):\n",
      "    time.sleep(1)\n",
      "    return quad(lambda x: 4/(1+x**2), aa,bb)\n",
      "tic = time.time()\n",
      "s_result=map(quadf,a,b)\n",
      "toc=time.time()-tic\n",
      "print 'Execution time',toc\n",
      "print 'Estimate of the subintegrals',s_result\n",
      "print 'Estimate of pi',sum(s_result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Execution time 4.02300000191\n",
        "Estimate of the subintegrals [(0.9799146525074566, 1.0879238093813377e-14), (0.8746757834957677, 9.710851939190498e-15), (0.7194139991699131, 7.987099861161008e-15), (0.5675882184166557, 6.301495085921435e-15)]\n",
        "Estimate of pi 3.14159265359\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 6.1 Estimate the pi using parallel map function "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tic=time.time()\n",
      "p_result=eall.map(quadf,a,b)\n",
      "toc= time.time()-tic\n",
      "print toc\n",
      "print p_result\n",
      "print sum(p_result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.01999998093\n",
        "[(0.9799146525074566, 1.0879238093813377e-14), (0.8746757834957677, 9.710851939190498e-15), (0.7194139991699131, 7.987099861161008e-15), (0.5675882184166557, 6.301495085921435e-15)]\n",
        "3.14159265359\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 6.2 Estimate pi using parallel map_sync function and time the computation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tic=time.time()\n",
      "sp_result=eall.map_sync(quadf,a,b)\n",
      "toc= time.time()-tic\n",
      "print toc\n",
      "print sp_result\n",
      "print sum(sp_result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.01999998093\n",
        "[(0.9799146525074566, 1.0879238093813377e-14), (0.8746757834957677, 9.710851939190498e-15), (0.7194139991699131, 7.987099861161008e-15), (0.5675882184166557, 6.301495085921435e-15)]\n",
        "3.14159265359\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 6.3 Estimate pi using parallel map_async function and time the computation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tic=time.time()\n",
      "ap_result=eall.map_async(quadf,a,b)\n",
      "toc= time.time()-tic\n",
      "print toc\n",
      "print ap_result.get()\n",
      "print sum(ap_result.get())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.0179998874664\n",
        "[(0.9799146525074566, 1.0879238093813377e-14), (0.8746757834957677, 9.710851939190498e-15), (0.7194139991699131, 7.987099861161008e-15), (0.5675882184166557, 6.301495085921435e-15)]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "3.14159265359\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 6.4 Estimate pi using parallel decorator and time the computation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lview = rc.load_balanced_view() # default load-balanced view\n",
      "@lview.parallel()\n",
      "def quadf(aa,bb):\n",
      "    time.sleep(1)\n",
      "    return quad(lambda x: 4/(1+x**2), aa,bb)\n",
      "tic = time.time()\n",
      "p_result=quadf.map(a,b)\n",
      "toc=time.time()-tic\n",
      "print toc\n",
      "print p_result\n",
      "print sum(p_result)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.03099989891\n",
        "[(0.9799146525074566, 1.0879238093813377e-14), (0.8746757834957677, 9.710851939190498e-15), (0.7194139991699131, 7.987099861161008e-15), (0.5675882184166557, 6.301495085921435e-15)]\n",
        "3.14159265359\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Examples of countour plots"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt # The code below assumes this convenient renaming\n",
      "plt.figure() # Create a new figure window\n",
      "xlist = np.linspace(-2.0, 2.0, 100) # Create 1-D arrays for x,y dimensions\n",
      "ylist = np.linspace(-2.0, 2.0, 100)\n",
      "X,Y = np.meshgrid(xlist, ylist) # Create 2-D grid xlist,ylist values\n",
      "Z = np.sqrt(X**2 + Y**2) # Compute function values on the grid\n",
      "plt.contour(X, Y, Z, [0.5, 1.0, 1.2, 1.5], colors = 'k', linestyles = 'solid')\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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jx4/ToEGD3h5EaPwf5a+//iJtbW36/vvvqbKyku84b0hKSqJFixaRrq4uOTs709atW+nZ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\nLAwVPyGEWBgqfkIIsTD/A8IjrL2GedeiAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *\n",
      "xlist = linspace(-3.0, 3.0, 100)\n",
      "ylist = linspace(-3.0, 3.0, 100)\n",
      "X, Y = meshgrid(xlist, ylist)\n",
      "#print X\n",
      "#print Y\n",
      "Z = (X**2 + Y**2)\n",
      "#print Z \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure()\n",
      "CP1 = contour(X, Y, Z)  \n",
      "clabel(CP1, inline=True, fontsize=10) \n",
      "title('Contour Plot') \n",
      "xlabel('x (cm)')\n",
      "ylabel('y (cm)')\n",
      "show() \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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mKmmsZhWhNKcX4YCs/SmgwHjV/eptkDNSVgY7Db3jaVYt/qmpqaSmptK2bVsy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\nRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure()\n",
      "CP2 = contourf(X, Y, Z)\n",
      "colorbar(CP2) \n",
      "title('Contour Plot') \n",
      "xlabel('x (cm)')\n",
      "ylabel('y (cm)')\n",
      "show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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1aCuMt0/Guw9PMX+DyxRgbLPLyz5ufd/duxEWFoYePXq0uq35j62npqZiyZIl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\n"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure()\n",
      "levels = [0.0, 0.5, 1, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0]\n",
      "CP3 = contour(X, Y, Z, levels, colors='k')\n",
      "clabel(CP3, colors = 'k', fmt = '%2.1f', fontsize=14) \n",
      "CP4 = contourf(X, Y, Z, levels) \n",
      "colorbar(CP4)\n",
      "title('Contour Plot') \n",
      "xlabel('x (cm)')\n",
      "ylabel('y (cm)')\n",
      "show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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0+QUk7zyD1c8/cmZXCh0G16DfhNo07uhYJss/LjybrS8c4PJ1WPyucTfSuXAY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      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import pylab as pl\n",
      "# Make x, y arrays for each graph\n",
      "x1 = [1, 2, 3, 4, 5]\n",
      "y1 = [1, 4, 9, 16, 25]\n",
      "x2 = [1, 2, 4, 6, 8]\n",
      "y2 = [2, 4, 8, 12, 16]\n",
      "# use pylab to plot x and y\n",
      "plot1=pl.plot(x1, y1, 'r',label='red line')\n",
      "plot2=pl.plot(x2, y2, 'g',label='green line')\n",
      "# give plot a title\n",
      "pl.title('Plot of y vs. x')\n",
      "# make axis labels\n",
      "pl.xlabel('x axis')\n",
      "pl.ylabel('y axis')\n",
      "# set axis limits\n",
      "pl.xlim(0.0, 9.0)\n",
      "pl.ylim(0.0, 30.)\n",
      "# make legend\n",
      "pl.legend(loc='upper left')\n",
      "# show the plot on the screen\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    }
   ],
   "metadata": {}
  }
 ]
}