Lecture03.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SciPy framework builds on top of the low-level NumPy framework for multidimensional arrays, and provides a large number of higher-level scientific algorithms. Some of the topics that SciPy covers are:\n",
    "\n",
    "* Special functions ([scipy.special](http://docs.scipy.org/doc/scipy/reference/special.html))\n",
    "* Integration ([scipy.integrate](http://docs.scipy.org/doc/scipy/reference/integrate.html))\n",
    "* Optimization ([scipy.optimize](http://docs.scipy.org/doc/scipy/reference/optimize.html))\n",
    "* Interpolation ([scipy.interpolate](http://docs.scipy.org/doc/scipy/reference/interpolate.html))\n",
    "* Fourier Transforms ([scipy.fftpack](http://docs.scipy.org/doc/scipy/reference/fftpack.html))\n",
    "* Signal Processing ([scipy.signal](http://docs.scipy.org/doc/scipy/reference/signal.html))\n",
    "* Linear Algebra ([scipy.linalg](http://docs.scipy.org/doc/scipy/reference/linalg.html))\n",
    "* Sparse Eigenvalue Problems ([scipy.sparse](http://docs.scipy.org/doc/scipy/reference/sparse.html))\n",
    "* Statistics ([scipy.stats](http://docs.scipy.org/doc/scipy/reference/stats.html))\n",
    "* Multi-dimensional image processing ([scipy.ndimage](http://docs.scipy.org/doc/scipy/reference/ndimage.html))\n",
    "* File IO ([scipy.io](http://docs.scipy.org/doc/scipy/reference/io.html))\n",
    "\n",
    "Each of these submodules provides a number of functions and classes that can be used to solve problems in their respective topics.\n",
    "\n",
    "In this lecture we will look at how to use some of these subpackages.\n",
    "\n",
    "To access the SciPy package in a Python program, we start by importing everything from the `scipy` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we only need to use part of the SciPy framework we can selectively include only those modules we are interested in. For example, to include the linear algebra package under the name `la`, we can do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ordinary differential equations (ODEs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy provides two different ways to solve ODEs: An API based on the function `odeint`, and object-oriented API based on the class `ode`. Usually `odeint` is easier to get started with, but the `ode` class offers some finer level of control.\n",
    "\n",
    "Here we will use the `odeint` functions. For more information about the class `ode`, try `help(ode)`. It does pretty much the same thing as `odeint`, but in an object-oriented fashion.\n",
    "\n",
    "To use `odeint`, first import it from the `scipy.integrate` module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint, ode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A system of ODEs are usually formulated on standard form before it is attacked numerically. The standard form is:\n",
    "\n",
    "$y' = f(y, t)$\n",
    "\n",
    "where \n",
    "\n",
    "$y = [y_1(t), y_2(t), ..., y_n(t)]$ \n",
    "\n",
    "and $f$ is some function that gives the derivatives of the function $y_i(t)$. To solve an ODE we need to know the function $f$ and an initial condition, $y(0)$.\n",
    "\n",
    "Note that higher-order ODEs can always be written in this form by introducing new variables for the intermediate derivatives.\n",
    "\n",
    "Once we have defined the Python function `f` and array `y_0` (that is $f$ and $y(0)$ in the mathematical formulation), we can use the `odeint` function as:\n",
    "\n",
    "    y_t = odeint(f, y_0, t)\n",
    "\n",
    "where `t` is and array with time-coordinates for which to solve the ODE problem. `y_t` is an array with one row for each point in time in `t`, where each column corresponds to a solution `y_i(t)` at that point in time. \n",
    "\n",
    "We will see how we can implement `f` and `y_0` in Python code in the examples below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: double pendulum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider a physical example: The double compound pendulum, described in some detail here: http://en.wikipedia.org/wiki/Double_pendulum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"http://upload.wikimedia.org/wikipedia/commons/c/c9/Double-compound-pendulum-dimensioned.svg\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(url='http://upload.wikimedia.org/wikipedia/commons/c/c9/Double-compound-pendulum-dimensioned.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equations of motion of the pendulum are given on the wiki page:\n",
    "\n",
    "${\\dot \\theta_1} = \\frac{6}{m\\ell^2} \\frac{ 2 p_{\\theta_1} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_2}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}$\n",
    "\n",
    "${\\dot \\theta_2} = \\frac{6}{m\\ell^2} \\frac{ 8 p_{\\theta_2} - 3 \\cos(\\theta_1-\\theta_2) p_{\\theta_1}}{16 - 9 \\cos^2(\\theta_1-\\theta_2)}.$\n",
    "\n",
    "${\\dot p_{\\theta_1}} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) + 3 \\frac{g}{\\ell} \\sin \\theta_1 \\right ]$\n",
    "\n",
    "${\\dot p_{\\theta_2}} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot \\theta_1} {\\dot \\theta_2} \\sin (\\theta_1-\\theta_2) +  \\frac{g}{\\ell} \\sin \\theta_2 \\right]$\n",
    "\n",
    "To make the Python code simpler to follow, let's introduce new variable names and the vector notation: $x = [\\theta_1, \\theta_2, p_{\\theta_1}, p_{\\theta_2}]$\n",
    "\n",
    "${\\dot x_1} = \\frac{6}{m\\ell^2} \\frac{ 2 x_3 - 3 \\cos(x_1-x_2) x_4}{16 - 9 \\cos^2(x_1-x_2)}$\n",
    "\n",
    "${\\dot x_2} = \\frac{6}{m\\ell^2} \\frac{ 8 x_4 - 3 \\cos(x_1-x_2) x_3}{16 - 9 \\cos^2(x_1-x_2)}$\n",
    "\n",
    "${\\dot x_3} = -\\frac{1}{2} m \\ell^2 \\left [ {\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) + 3 \\frac{g}{\\ell} \\sin x_1 \\right ]$\n",
    "\n",
    "${\\dot x_4} = -\\frac{1}{2} m \\ell^2 \\left [ -{\\dot x_1} {\\dot x_2} \\sin (x_1-x_2) +  \\frac{g}{\\ell} \\sin x_2 \\right]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = 9.82\n",
    "L = 0.5\n",
    "m = 0.1\n",
    "\n",
    "def dx(x, t):\n",
    "    \"\"\"\n",
    "    The right-hand side of the pendulum ODE\n",
    "    \"\"\"\n",
    "    x1, x2, x3, x4 = x[0], x[1], x[2], x[3]\n",
    "    \n",
    "    dx1 = 6.0/(m*L**2) * (2 * x3 - 3 * cos(x1-x2) * x4)/(16 - 9 * cos(x1-x2)**2)\n",
    "    dx2 = 6.0/(m*L**2) * (8 * x4 - 3 * cos(x1-x2) * x3)/(16 - 9 * cos(x1-x2)**2)\n",
    "    dx3 = -0.5 * m * L**2 * ( dx1 * dx2 * sin(x1-x2) + 3 * (g/L) * sin(x1))\n",
    "    dx4 = -0.5 * m * L**2 * (-dx1 * dx2 * sin(x1-x2) + (g/L) * sin(x2))\n",
    "    \n",
    "    return [dx1, dx2, dx3, dx4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose an initial state\n",
    "x0 = [pi/4, pi/2, 0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# time coodinate to solve the ODE for: from 0 to 10 seconds\n",
    "t = linspace(0, 10, 250)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve the ODE problem\n",
    "x = odeint(dx, x0, t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
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mz57tsa5Kha8wjA4SWrQDwC9+AbzzDs1u2nkGnGECsXCh2RYwNsdqon0vgFyv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P5eUkLSfvPNnjlJQQHTc957j5paQgJTbJYu5Xp94PCqq7js2JFV5yWsQ5J2sxCkvbSf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\nVGBBIOjJjtucAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5b0c690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the angles as a function of time\n",
    "\n",
    "fig, axes = plt.subplots(1,2, figsize=(12,4))\n",
    "axes[0].plot(t, x[:, 0], 'r', label=\"theta1\")\n",
    "axes[0].plot(t, x[:, 1], 'b', label=\"theta2\")\n",
    "\n",
    "\n",
    "x1 = + L * sin(x[:, 0])\n",
    "y1 = - L * cos(x[:, 0])\n",
    "\n",
    "x2 = x1 + L * sin(x[:, 1])\n",
    "y2 = y1 - L * cos(x[:, 1])\n",
    "    \n",
    "axes[1].plot(x1, y1, 'r', label=\"pendulum1\")\n",
    "axes[1].plot(x2, y2, 'b', label=\"pendulum2\")\n",
    "axes[1].set_ylim([-1, 0])\n",
    "axes[1].set_xlim([1, -1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 01 : Damped harmonic oscillator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ODE problems are important in computational physics, so we will look at one more example: the damped harmonic oscillation. This problem is well described on the wiki page: http://en.wikipedia.org/wiki/Damping\n",
    "\n",
    "The equation of motion for the damped oscillator is:\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega^2_0 x = 0$\n",
    "\n",
    "where $x$ is the position of the oscillator, $\\omega_0$ is the frequency, and $\\zeta$ is the damping ratio. To write this second-order ODE on standard form we introduce $p = \\frac{\\mathrm{d}x}{\\mathrm{d}t}$:\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}p}{\\mathrm{d}t} = - 2\\zeta\\omega_0 p - \\omega^2_0 x$\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}x}{\\mathrm{d}t} = p$\n",
    "\n",
    "In the implementation of this example we will add extra arguments to the RHS function for the ODE so that we can pass in the damping parameters, rather than using global variables as we did in the previous example. As a consequence of the extra arguments to the RHS, we need to pass an keyword argument `args` to the `odeint` function. Please solve above problem for undamped $\\omega_0$=0.0 , under-damped $\\omega_0$ < 1.0, critically damped $\\omega_0$ =1.0, and over damped $\\omega_0$ > 1.0 situations   using python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Example 02: SIR Epidemic models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### SIR Model\n",
    "The SIR model is the one of the simplest possible model of infection. In this model S refers to the proportion of the population that are susceptible, I is the proportion of the population that are infectious, and R is the population that is recovered from the infection and has immunity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\displaystyle \\frac{\\mathrm{d}S}{\\mathrm{d}t}= -\\beta SI $\n",
    "       \n",
    "$\\displaystyle \\frac{\\mathrm{d}I}{\\mathrm{d}t}= \\beta SI- \\gamma I$\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}R}{\\mathrm{d}t}= \\gamma I$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import necessary modules\n",
    "import scipy.integrate as spi\n",
    "import numpy as np\n",
    "import pylab as pl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set parameters and intial values\n",
    "\n",
    "beta=1.4247\n",
    "gamma=0.14286\n",
    "TS=1.0\n",
    "ND=70.0\n",
    "S0=1-1e-6\n",
    "I0=1e-6\n",
    "INPUT = (S0, I0, 0.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define the model\n",
    "\n",
    "def diff_eqs(INP,t):\n",
    "    '''The main set of equations'''\n",
    "    Y=np.zeros((3))\n",
    "    V = INP\n",
    "    Y[0] = - beta * V[0] * V[1]\n",
    "    Y[1] = beta * V[0] * V[1] - gamma * V[1]\n",
    "    Y[2] = gamma * V[1]\n",
    "    return Y   # For odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Solve the ODE\n",
    "t_start = 0.0; t_end = ND; t_inc = TS\n",
    "t_range = np.arange(t_start, t_end+t_inc, t_inc)\n",
    "RES = spi.odeint(diff_eqs,INPUT,t_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  9.99999000e-01   1.00000000e-06   0.00000000e+00]\n",
      " [  9.99996055e-01   3.64966741e-06   2.95304063e-07]\n",
      " [  9.99985485e-01   1.31593559e-05   1.35516202e-06]\n",
      " [  9.99947369e-01   4.74532092e-05   5.17732698e-06]\n",
      " [  9.99809987e-01   1.71058575e-04   1.89549056e-05]\n",
      " [  9.99315303e-01   6.16116637e-04   6.85803972e-05]\n",
      " [  9.97537151e-01   2.21568587e-03   2.47163570e-04]\n",
      " [  9.91184992e-01   7.92727469e-03   8.87733548e-04]\n",
      " [  9.68987928e-01   2.78532303e-02   3.15884192e-03]\n",
      " [  8.97021359e-01   9.20814169e-02   1.08972243e-02]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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fLWgquuUWqF0bXnih2DL8aeZRx7LFJBhG5acoM4V/ArOA35ewLEYQDRqEWH0E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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa1a800410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#print results\n",
    "print RES[:10]\n",
    "\n",
    "#Ploting\n",
    "pl.plot(RES[:,0], '-bs', label='Susceptibles')  # I change -g to g--  # RES[:,0], '-g',\n",
    "pl.plot(RES[:,2], '-g^', label='Recovereds')  # RES[:,2], '-k',\n",
    "pl.plot(RES[:,1], '-ro', label='Infectious')\n",
    "pl.legend(loc=0)\n",
    "pl.title('SIR epidemic without births or deaths')\n",
    "pl.xlabel('Time')\n",
    "pl.ylabel('Susceptibles, Recovereds, and Infectious')\n",
    "pl.savefig('2.1-SIR-high.png', dpi=900) # This does, too\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Exercise 02: SIR Epidemic models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can include Birth and Death in to SIR model. If we assume life expectancy to be 1/$\\mu$ Then the governing equations become:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\displaystyle \\frac{\\mathrm{d}S}{\\mathrm{d}t}= \\mu -\\beta SI -\\mu S$\n",
    "       \n",
    "$\\displaystyle \\frac{\\mathrm{d}I}{\\mathrm{d}t}= \\beta SI- \\gamma I - \\mu I$\n",
    "\n",
    "$\\displaystyle \\frac{\\mathrm{d}R}{\\mathrm{d}t}= \\gamma I -\\mu R$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please solve the above SIR model and generate plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourier transform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fourier transforms are one of the universal tools in computational physics, which appear over and over again in different contexts. SciPy provides functions for accessing the classic [FFTPACK](http://www.netlib.org/fftpack/) library from NetLib, which is an efficient and well tested FFT library written in FORTRAN. The SciPy API has a few additional convenience functions, but overall the API is closely related to the original FORTRAN library.\n",
    "\n",
    "To use the `fftpack` module in a python program, include it using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.fft import fftfreq\n",
    "from scipy.fftpack import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To demonstrate how to do a fast Fourier transform with SciPy, let's look at the FFT of the solution to the damped oscillator from the previous exercise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "from scipy import *\n",
    "from scipy.integrate import odeint, ode\n",
    "def dy(y, t, zeta, w0):\n",
    "    \"\"\"\n",
    "    The right-hand side of the damped oscillator ODE\n",
    "    \"\"\"\n",
    "    x, p = y[0], y[1]\n",
    "    \n",
    "    dx = p\n",
    "    dp = -2 * zeta * w0 * p - w0**2 * x\n",
    "\n",
    "    return [dx, dp]\n",
    "y0 = [1.0, 0.0]\n",
    "t = linspace(0, 10, 1000)\n",
    "w0 = 2*pi*1.0\n",
    "y1 = odeint(dy, y0, t, args=(0.0, w0)) \n",
    "y2 = odeint(dy, y0, t, args=(0.2, w0))\n",
    "y3 = odeint(dy, y0, t, args=(1.0, w0)) \n",
    "y4 = odeint(dy, y0, t, args=(5.0, w0))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets calculte the fourier transform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(t)\n",
    "dt = t[1]-t[0]\n",
    "\n",
    "# calculate the fast fourier transform\n",
    "# y2 is the solution to the under-damped oscillator from the previous section\n",
    "F = fft(y1[:,0]) \n",
    "\n",
    "# calculate the frequencies for the components in F\n",
    "w = fftfreq(N, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JkeGc0RowI5AVOTFa6A30O8IynIUqgm7H0MssZUFUQeyXACxqmvYAgK8B+KOd\nXqRp2qc1TTujadqZqakpQUe7HbGQG0kZkRMz5ERiGDmRrxmK9gD6Q11vtpER3B2VMnHXgG4wZUQg\n1rJVTPhdQ28/7YesWhlN0wyn0ADdK85XmygKTkfRQXtmzi1jWN+agTUBFLK8eToHx3jkxINUQfx+\nMTORTEII4iEPEnnxqfi1rD5PS3WwICdrAPojIXOdr3WhaVpG0zT6r/CHAN7G4HO5QFaIMJWvIuRx\njNy2CAATfhecdiLt3FGDRp6GzEUbzGSBkhNjEZ+ZiJzW7TUToe9Y0C0lHZWvNlGqt0Ya792PbjpK\n8LnpPY0yrbkfsrz5dQNtxBTxsJzUH52DYySFBujnbmsQ3vlC78noCHhdRuQU1scN3rVIsCAnLwE4\nTAjZTwhxAfg4gC/2v4AQMt331ycBXGTwuVwQD3uQzItPNSTzNcOevK0TxhVdXFVrtpAp1REzEEIG\n5KWjaIeRcVLl6XTOiE5HGU+POLrpKDlG3qjB7KWjxJ57o9M9Yjy65pHiLGzkqpgxaCyDbjmdL1Rv\nGSWCsiI+yXwNPpcdQffohd6APEc4ma8ibtAxEwnT5ETTtCaATwF4Gjrp+LymaecJIb9KCHmy87Jf\nIIScJ4S8DuAXAPyU2c/lhemwB822hs2SWBaeyFdNLWGaDnuEezzpzibkeNiYoMc6PyeaVCXzVQTc\nDgQMKpVYyINas41cRezIbN3jMS4jsZAHKcFhZDPpSqBHYEXLyHquiqiJ3SPxkFd454umaUjla4gZ\nlBFZnS+9cQRGZUROrUwir8+lGnVWEoUMR7jZamOzaDwVLxLGtPMd0DTtKwC+csfX/lXfn/8FgH/B\n4rN4o6sMczVDRWVGkcpXcXBq0vDPx8MenFvLMTzRYJiNQEz63XDYiHClksobm8RLQdNBiXwVEZ+L\n1bH2RLGm112YIydu3EiXGJ5qMHr1Pcbum/47JQWTqo2cubz8dF+rqKi19NvlBuqttuFIJkDrqeRE\nToySE2mRk1zV8JkB/dyNloZMqY6pEcffG0W6WENbg2ECKxLWhNg7ICPv2m5rSBVqhiMQAI2ciE01\ndKfDmkpHuYUbnmS+akqB97x5cefuzsExocT0Ajw5XrFR5et22DHudwk/93q2ajiFBvQVqQs8t1kj\nD3RkRAI5cdgIJvzGiH7E54TbYRMfgS0Y71QE+tLaAu+bfta9EDmxyMkdkKFU6PI8M0pFRqqBhTKM\nhcXXypiY/StBAAAgAElEQVRVKrFudE3cuVMFc6FvQI9wFapNoXuBUoUqxv0uuB2jF3pTRIPuLjkT\nAU3T9MiJyTQrINab762SMOfkiO58SeSriAbdI23a7oc+AkJsjY+maXqdoAkZkeEIs9DZomCRkztA\nUw0ylIqZNNK0hEFsiXwVLrsNYyMuz+uHaG++q1RMGXnxtTJJk+kRQE7EJ5mvmYr2AJ2uBoF3na82\nUW20TaXQeu394g2PGT0SD3uFd77oaVZzxlJ058t2uYF6s20qAiEnumbeyREFi5zcAZuNICY4tGl0\neV4/ZMw6obUbRgvCAP0hERmByFV0pWJGGcpINaRM1vcAckZmm2k1p4gFPVJSaGbqAIIeJwJuh2An\nh8qIucgJID7iYzbNILrzhepZM0ZeRs1dIl+F0248hSYSFjnZAdOCK9aNLs/rx7QEFp4wWRAG6A93\nodYUtvOFxV3rPy82HZXMV+F1Gm9bBHq/s9hz1xAzGTmJdXa+iEo1sPIu42GP0KWFibz5FJoMJydh\nYso0hejOl96sJOMyIsUR7nShGU2hiYRFTnZATHAYOdFZnjdlYHkexVTQDUIEezwF8x4PzY+Lum9W\nOddYSGwhb7LAJkoFiCMnrbaGdNFcCg3Q71oTmGpIMTA8QKdIXXSUyiQRFB05KdebKFSbprtH+jtf\nRIBGe81EuwEIr5VJ5KumImsiYZGTHTAd0meGiOp8SXWW5zkMzlQA9J0vUwG30Lyr2ZZcQHxxaZec\nmGwTF10rkzLZYQQAAbcDPpe9u2SSNzIlffKnaa9YcK1MNz1itlYmJLYOIpmvmTaWone+dKNUDJ5H\nQFzEhz77ZhxKQLwjzCKFJgoWOdkB8bAH1Ya4zhczy/P6MR0Wt6uhO3fDbORE8JRY2vVillRFQ3qq\noSEo1ZAqmCeCdJ+HqMgJizoZoEdgRRkeOqTPbyKFBujnTndGs4tAggGBpTIiyptnFcmkpGxdIKma\nDLjgcpgzoaIdYbPNACJhkZMdEBcc2jSzPK8fsZBH2A4S1kpFZFpH9w6N5+UBnVRpGrApINWgdxiZ\nr+8BdFImjJwwSo/Qn6fvxxtpBkQQ0NNRbU2PIPEGnfzJwsmJBj1dEs8bLNqfgX4ZEXduFs8jdYTz\nVf41dywGOYqERU52gOiR2Sw6GoBeUZgI0DSMWSXuczkQ9DiEpnVYKPBurYyAcxdrTZTrLTbnFpiO\nYpUemfC7hHY1mB3SRzHVeQ8RKwM2i3VojCZ/RkPu7moK3ui2P5vUfxN+F2wESAuSbRbNAECvI0zE\nHJ97aQAbYJGTHdFl4QKUSr3ZRqZUZxY5yVebqNRbDE62N2i1OotzizaYLNYS0PcQQQZ7Rp6NjKTy\nNSFhZHo3Zkdzi54knCywKRqkZFJExCfBqJYKgNAlomaX51E47DZMBATKCKPIiciIT3fKtFUQe+9C\n5JCtXuibhTIUbzBZhTZFKZUUo2r13swQAUqlwE6pxEIe1FttbJf511PRvLzR5Xn9iAqqlekuz2OS\nQhMnIyxmJVHEQm6U6y0UBbT3JzpG3kwXGkUs5BZCBFk6lDSqKEK2KYG1Iif3MNwOO8Z8TiHevNnl\nef0QmY5K5Kr6inWTHg8gzlOjO4xYGJ5xnwtOOxEiIymGRFAkgdVbW9koQlGFvPlKE7Vm23QqCuh1\ncoiIwLL0ioU6Z4zSrIC4WhmWDmVUYOQkwZDAioBFTnaBPmRLoMfDxPCImxmSYhT6BvT6jZSAroat\ncmeHEQPDo6caxBhMlvswRM6VMbvDqB+xkFvYmQE2zoLLYcO439V9T55I5Kuw2wgm/AyiawJrZRKM\n0iMAhKX+us8jAyMfcDvgd9nF6JFcFUGPAz6XeYdSBCxysgtETQBlaXiiAmtlWBWEAToxa7U17l0N\nrJdexQR1viTzNfhddgQYRKl69VRiIj6sIiexsJilhd0oFaMV9vrSQhEGU99hZGcw+TMqqFaG7rli\nlWaIhjzIlPhPEqYEiOW5RUROWN61CFjkZBeINDxml+dRhDwOeJ2CWDhjpQLwJ1Ws5m5QiBo9rRdo\nsvIu6cwQvnfNsrUV6HnzvD1j1gRWNzxinBxmMiLoecyWze+56kc06O609/OdEstir04/okE30vdY\nlEoELHKyC+IhMfs8kp0CTRYFYYQQIeFvvXaDnTIUVQfBMlesv49HiFecZrDZl8LlsGFCQKohU6qj\nrbEjgqKWFiYZFh8DegRGTOSkijijMwfdDnicNmF3zfJ5BPhHfJL5KlwONg4l0Cn2FkRgLXLyPYBo\nyIO2ABbOWmBEGMztch2NlsZMGfYW0vH2ivX3N9vaSiFqaaFeu8FORqICNkHzSKH1vy8vpPI1BN3s\n8vLRkBvpIv96KpaTP3Unh3+qgXl6JChKj+i1VCwcSqBHYHm297fbGtIFdpFMEbDIyS4Q1fmSYLzr\nICZgZgjLNmIAmAzoSwu5e2oMtrb2Q0RxaW86LDulEg+5uXtqrLY/U4iMrrGcAxHr1FNtcVxIV220\nkKs02BLYIP+0dpJxekRc5IRdLRWgE9hKo4UCRycnU+o0A1iRk3sfwpQhg+V5/aC1MjxZOMtqdUBf\nWjjh5z+jIMkwPQKI6WrIV5uoNtrMo2u8a066kz8ZKXFRSwtZ7x6h8sZTtllHqQA9usZ7SmxvOiyb\nZ3Iy4Oo4OZzPzbALDRAz9JN1SlsELHKyC0SEkVktz+tHLORBrcl3aSEPZaiTKs4FsRzSI/R9eYF2\n1bBKRQFiuhpShRoI0Q0GC/RSDfyjaywJrIgR9qyjVECny4gzOUnkqxjzOZlFMh0dJyfNWUbSjCMn\nIkbYp7opbStycs9jIqC35fE0mHyMPP+uBlbrwvshonWbdXpEBIGlBoI1EeTd1ZDKVzEZcMPBYDos\nBe+2XE1jN6SPQsQIex6TP6NBD4qc66l4bMjlLSPlehOFWpNptJsSHZ5k0IqcfA/BbiOYCvDNu7IO\nawJiuhpYrQvvB+/ISatbEMZOGdJUwz1HYAXsBWJNBIEOgeVo5HMVtq2tQM8r5ikjvemwPEgVX4PJ\nnJxwrqfqzcG5twgs62YAEbDIyR7g3ZbLcjosBX1oeJ+bZVgT0L2HTKmGBqdUQ6ZYY9raCuipBt6F\ng6w2+/ZDRD1VMl9jqsAB/vVUPO6arsLgXXPicdoQ8rCb/ClisSXrFBqg6z++tRt0VhK7cwfcdD4V\nXyIYYZhCEwGLnOwB3m25rLtegL7pjpyVCuv9DLGQp5Nq4HPf3btmrAx5T3dM5tntMKLo7k7h7BWz\n3n4aC3lQbbSRr/JJNfRC3+yJN9/oWo3Z8jwK3pETHpFMQJftTY6t26wLvYHefCquUSoOzgJvWORk\nD/Buy+VheDxOOyKclxbqypCxkecc/uaRHqHvx7WQrVDFFOO7nvC7YCNAmtO5G602Not19tE1zqP3\neRSWArrB5J0eYR2B6NZBcLrrTEmPZLK/a30+VYaTk9OrAWN/31yjVAW2XaEiYJGTPRAPe5CrNFBt\ntLi8P50Oyxoxjp5ao9VGpsS2Wh3gv/MlyckrjnWWjfFKNfDweBx2GyYD/Gp80hyKeAFxBJZHypJ3\nJwbLdCUAhLwOuB02bqSKV/cIbxlJdabDhr1spsNSRENurq3baQ6peN6wyMke6M4o4KYM2Yc1AX3+\nCC9lmC7UoGns127HOKcaknm2ra0UsZCH6wAl1jMVKHgWl/LyLnkP2UoXagh6HPC62OblYx3D0+aU\nakgV2M7vATr1VBz3i/HqHuEtI/SuWabQAL4EVl838haNnBBCPkgIuUwIuUYI+eUdvu8mhPxZ5/sv\nEEIWWXwub1BB55UiSeTYToeliAX5FfIm8nyUykTADRvhFznh0doK9Nf4sCdVdGsrFwLLsTuKVwpN\nROSEx11Hg2402xq2yuxbt0udWUlcZIRjcWm3+JiTjPCK+PAo4gV0PVKqt1Dk4ORslzvTYe+hTh2A\nATkhhNgB/B6ADwE4AeAThJATd7zspwFsa5p2CMBvA/hNs58rAjzbcvWZCuyW5/UjHtanO/IoCktx\nMjx2G8EUx84XHq2tAN/cPI/WVooox1qZbmsrY2XodzsQdDvuORnhOQG02z3CyWByi67RtA7DWUlA\nf+s2z8gJH2cB4KNHeh1Gb720ziMArmmadkPTtDqAPwXw1B2veQrAH3X+/OcA3kdYx8U4gOc8iO1y\ng+nyvH70lhayV4Y8Oowo9EFsHFNoHJUKDyXOo7WVIhp0I1Oqo95k37qdzNdgI3o0jDX04lJ+BbE8\nDE+Uq4zwqZOh75nm9TwW9D1XLGclAXQVhotjrQxfJ4eH/ktychZ4g4VkzAJY6fv7audrO75G07Qm\ngByAiTvfiBDySULIWULI2XQ6zeBo5hDy8lsdnmC89KofMY7eQyJfhdNOMO5jW7sB8K1Y5xWlou/J\nQ6nwam3tf08+BLaKqaA+YZk1eBFYTdNbW3nk5anh4WHoedX3ADqpKtSaKNfZpxpSjPdc9WMq6OYS\ngag2WshXm1z0CM9BbDymTIuAUgWxmqZ9WtO0M5qmnZmampJ9nO4+Dy5stsB+qiNFLx3Fx/BEgx7Y\nuBgePi2XtLWVhwIPuB0IuB1cQva8Wlv735MHGUxymF9BwWvoXbbcQL3V5hJd45lqSHGOnOifwV62\n05ycBaDT3s9Bj6Q4RjJ57mDisZ9LBFiQkzUA831/n+t8bcfXEEIcAMIAMgw+mztiQT6zTui6cNZd\nLwDfQl5e7c+Afu6tUh21JtvWbV6trRTRIJ/cPO+Qvf4ZfJQhr7ZFanhYt273nAX2sk1nD3ExmIUa\n3A4bQl52s5IoeA5iY70hvB+8CCxPhzLk0aP0vCInYa8THue9Mx0WYENOXgJwmBCynxDiAvBxAF+8\n4zVfBPCTnT//QwDf0HgNhmAMXm25SU4FYQAwybHzJZmvcekwAnrKkHW/f697hJMyDPEJI6fyVYQ4\ntLYCfFsu9eV5vO7agzqHrdspjrVUAEeD2XEWeJTw8Rph325rSBf5yUgs5MFmsc68ISDFMZKpr8Lg\nE/Hh1WHEG6bJSaeG5FMAngZwEcDnNU07Twj5VULIk52XfQbABCHkGoBfAnBXu7Gq4DVkK1moMl+e\nR0E7X2hdC0skc3zaLQF+9Ru9wlJ+3jyfFBr74VoUE35XZ+s2WxmpNVvYKrGfDkvRS0dxIrCcIz6s\nwXMsOa/ISaakEwdeMhINudFqa8iU+MgIt3NzIrD34owTAGASC9Q07SsAvnLH1/5V35+rAD7K4rNE\ngw7ZylebTKcCJnN8J/bpQ7bYPpylmr4unBc5iXFqy+VZWErfly6kY+nBpjgNYAMAW2frNuscd5pj\ngab+vj1v/mg8yOx9eSx068dU0I3rqSLz900WqjjG8B76EfY64XLYOD6PvNI6vfoNljo2VajBaScY\n87GdDksRC3lwMZFn/r6pfA2P7h9n/r68oVRBrIqIhfkYTF6TPyliIU+3roUVeHYG9L8va+8hma/C\nbiOY8LPvMAJ0j6fWZL+Qjlf7M0Us5GZOYHm2mgP82vtpCo1XXj4W8iBdZB+BTXNqfwZ6W7dZR054\nja6niHJKD+s7jNguWOyH3mXE9sy0C431fi4RsMjJAMQ4TaVM5mtcimEpYhwGKPFsfwaAMZ8LTjvh\nYjCjQTeXDiOAz0I6nkP6KHgMYut2j3Cs7wHYpxp4TeKliAbdaLQ0bJXYTYkt1/VIJs+QPY9UA+/I\nSX90jSVS+RrXjpdYyIMi49Ztnl1ovGGRkwGgBIJl54ve2srP4wGAeMiDbJnt0kLe6RGbjXCZdaIX\nDXIkghwILB3Sxze6xt7w8BpdT+Fx2hHyODhFMvmmWQG2MtIt0OSdHmYuIzRywimFFuDjUPJMswJ8\ndrnx7ELjDYucDACPivXNIp/lef3oefPsBL0XOeH4gIbYhzb1okG+Hg/AVkZ4F9/R994uN5i2bqcK\nNThsfIb0UfAoQNY3+wqQEYbRzCTnKBXQKeTlYOTHfE64HXxSaC6HDeN+F/NONF4ThCmiHNLavLvQ\neMIiJwPgdemeGkuBEWHk+SjDGvwuO4IePgVhgO4FMvfUCvxmswB8Ug2863v635upp9YJffNKoQHs\nNyrrW1t5R07Y704RMfkzFvKgUGuixHAhHW8jD9B0FDu5rjZayFUaQnQ2Dz3ylmwlfisgHmZrMHm3\ntgLoziJh2U7Ma2trP1inGqqNFrLlBtfQt8/FfiEd7/QI0BddY6oM+abQAPbRte1yXU+hcVTg9FlP\n5O4tw8OjnVhEa6veus3ueUwX+OvsKIdJwiIisLxgkZMhwDqMTB8a3gWxAHtB561UoiEP8tUmKnU2\nqQbe02EpWC+kEzFymkfrtoiBT9TwtBkN2eLdYQToqYYJv4tpxCeVr8LlsDEdcXAnYhycnDTHCcIU\n8ZCH6Znps82z64W2brPsMkoXaghyGuTIGxY5GQKsizQTOX7L8yjCXifcDhtTjydZqHKbDkvBenKp\niLw8wJ7AJvJVRHx8R07zILCJHH8ZoZ0v22U2nS88x5L3g3V3VKqgd6HxXPDO+nnUU2giIidubBZr\naLbYbN0WUXxMW7eZO5T3YEoHsMjJUIiH9V5/lp4ar+V5FHRpISvvQdM07u2WAPsJoKI2crIOI/Nc\nE0Ax5nPBYWPXul2p68MKeUYEAfadL6k8/xow+v4su/7ERKn092elR7bLdTTbfFNogE4E25o+jZYF\n7lUnJ8VxCSdvWORkCMRCns44ZHaCLqK1i2X9RrbcQL3Z5p8eYdwdJaJ2A+gV4LEassW7/Rmgrdvs\nZETUXbNeL8+7tZUifg8anqDHCb/Lzuzc3Xo7QRFYVrItogsNoDJybxFYXrDIyRBgLejJfFXIUByW\nMwoSgg0Pu7vmO3KagvVCOj09wl+pREMeZjlu3gsWKfrHk7NAMl/FuN/FrbWVIhryME01iDI8LLuj\neA9go2AdgRXRhQbod53orMIwC32QI7/9XLxhkZMhwIOc8A59A70QIQtBF2V4uvs8GBpMniOnKVgq\nw2ZnSB/vtA7ANrpGCSz3mhMOBFaMkXdD04B00byMVOotFKpNIYYnGnIzW4WREtCpCPCInPCPZAJ6\nCUG53kKRQet2vtJEvdm2Iiffy+jmXRkIOs3Li0jrxPuWFpqFqGE+eq0MQ4OZE0cEATbKcLNYR1vj\nH/oG2Oa4U4JC9m6HHWM+J1NvXkRePh5iVytDIxAiDE+cQ+SEdwptwu+CjbAjJ+mCKALLTo+IKvTm\nBYucDIGpgBuEsFEqSUHeJdA3HIyBoFNiJqRWhmF3VDLPv3sE6GvLZRDxESkjsZAHuQqbNQeJfBXe\nznh53tA76NhF13hHBAG2hkdUoTf9DHYR2BrCXr5daADgsNswxbieSiQ5YTEPp9dhZEVOvmfhsNsw\nGXAzNfL3mqcmKi8P0M4X82fWNA0JQcXHLFMNImVkiuE+D2rkeafQADqIzfxdt9r61lYRd81SRkR1\njwC6HNabbWTL5uup9M2+Yowlq6hgrdnCdrkhVGeziNL3ZMSKnHxPg1UboKjaDf0z2Aq6KKXCagKo\nvuGzJSQCwXIhXVdGwuJkhEXni4gJwhSsCGymWBOWQpv0u2G3ETaREwFzNyhYrsIQ2drKaj5VWuAI\neB7RNavm5HscrNoARbJZloKeEGx4irWm6aKwbnpEQM0JwM5TS+arsNsIJvxiijT1z2RxbnGGJxZi\nM3soKTD0TVu3WYTsk4UqXHYbIpy70AC2s05SgoqPgZ6MmIXIFBrLXW6pQhUBtwN+N/80Kw9Y5GRI\nsJrumMh1lucJEBiWgp7I1TAtzMizqZWhRkCsN8/mrqNB3cvmjRijuTI0hSaSCLKYPSRqNgtFlJGM\npDutrSJSaN3omkkCq7e2iul6AfRzb5Xqprdui1gl0Y94mM3wTJFEkAcscjIk4iEPMgwEnbYRi1Aq\nAJtZJ/Vmp7VVlOEJsqmVEdXaShENsdmEKlKBR3xOuOw20yH7XEXMkD4KVsP6kgWx5CTOqBON96bt\nfrCqldkq6QsWRUZOAPOkihIFsRFY8zKykatgOnJv1psAFjkZGlTQzQ6s2shVMB32sjjSUNA3Kps7\nM/X0REVOoozqIESndaJB3Ss229UgagAboLduTwXN1/gkBNZSAX2daKZlpAZCgMkA38mfFKxWSiRy\nVWHPo9thx7jfZbp2baPze88IMpis6qk28noKjfd0WApW6eFETlwqngcscjIkoiFG3rxggWFRFEaV\nqch6AsC8p5bIVYW0LVLEQnQhnbmuBlHtzxQs5srQ50LUuVnt10nlq5gMuOGwi1GFMQZbtzVNw0au\ninhInJND1zOYQc9ZEHNuVjKSyFURC/OfDksRD3mQLtbQMlFP1WprSBbEpeJ5wCInQ6LXlmtcicsQ\nGBaFg9TjERXxCbgd8DHY55EQbuTNe2q9IX1iz222cDApmMBOBdgQWFEzTihYyEi+qnehidUj5mtl\nenpENIE1f+5pgUQwFtbrqTZNTBLe7JAbUUSQByxyMiRYCHpPYMQplTgV9JJxQRedHqEblVkYHlF5\neYBN54voOhmATY5b5NwNAHA5bJjwu8yTqnxNSDsuBYvOF9E1EIAuj2bTUYmc3oU2GRAjI2M+J5x2\nwiRyIvqu6ecaRZcIWmmd732MdQoHzeRdE4I9B4DNkrSNXBU+l5jJnxRRFnUQObGRExZFmqK7RwCd\nUBSqTZTrxlu3E/kqxnxOIUP6KFh00IknsHRmiJnnsQJArB6JhdymlxZu5KqICepCA3Qnx2xam3ah\nib5rwJwekUFgWcMiJ0OCEGJ6ONiG4NA30BNOs55aPCSuwwgwvwm1uzxP4MPZm7ZqnpzEBQxgo2BB\nYEXOOKGImeyOqjZayJTqmBEY+u615d5bhicW9qCtwVTrdiJfEW4szdZTbZf1LjQZkRNz5EQ8gWUN\ni5yMALPhbxkC02XhJgy9yPkVFFSpGO18ocvzRBpMj9OOiM9pymDKGDnNwlMTtTyvH1GTu1O6kcyI\nOHIS8jjgcdpMh+wJ4b/Ztx809WX23CI7FQHzM0NkRKkmAnp0yUyUvtth5BfTYcQDFjkZAfGQ554T\nmEkGSwtF51wBnVRUG23DG5Vl1G4AuhI3UziYyNXgEzSkj6JXpGlSRoRHTjymUg3rWd3wzAiU7W49\nlcm7ngy44XKIU99ma+40TZOiR2bCXqznKoadnF6UShypstsIpgLmJgnTDiOR0W7WsMjJCDCb1klK\nEBhnZ2lh0qD30G5rSArOuQJ9s04MKkNZOddY2NNN3xlBsiAhhWayVoam0GISZMRMqmFdQuQE6ERg\nzXjzEp5HuufJqIzI6DACgJmIF9VG23B7v+gOI4pY2JyTI7rDiAdMkRNCyDgh5GuEkKud/4/t8roW\nIeS1zn9fNPOZMmF254ssgYmF3IbTOpulGpptTUIEwlzni4zCUgCYjXiwnjWXahBZoAkAIa/eum30\n3KmCvjxPtIzQTgSjZHAjKycvHwt5sJGvGP75RK4i/K4n/OZSDbKcBTrwjUbJRoXoDiOKeMhtvk7w\nHq43AcxHTn4ZwN9pmnYYwN91/r4TKpqmne7896TJz5QGs4VKMmo3AHNtgDLCmoD5MPJ6rgKXXW83\nFYmZsBebxRqqDWNDtjayFcwI9uQJIZiJeLGWLRv6eZqXFzX5k4Lek1HDs56rYsLvEjakj2Imoj+P\nRmcPbeSqwmXEbiOIhzzYMEhgZdRuAOZlRHSHEYWZEgIZHUY8YJacPAXgjzp//iMAHzH5fkrDzI4J\nOtVRhsBETQzZkhXWpHdt9AFdz1YxHfEIm+pIQZWhETLYbLWRyFcxK9jwAMBsxGs4crLW+TnR554d\n0z9vbduo4ZGze2Qu4kWjpSFtYMhWsdZEodqU4uTMRrxYMxGBAMQ7ObQA12h0TUaHEaCnGgvVJgrV\n0dNRtMPoXh5dD5gnJzFN0zY6f04AiO3yOg8h5Cwh5HlCyK4EhhDyyc7rzqbTaZNHYw8zkZOsRIGJ\nBY1v5xQ9up7C53Ig7HUajvisZytCW0QpKDkxosSTnfSIaK8Y0D/TcASCpkcEnzvkcSDgdhg2mBtZ\n8d0jQB+pMnBumS2iMxGP8bvudhiJTY9M+F1wOWymIidSZKQb8Rld/8mKUrHGQHJCCPk6IeTcDv89\n1f86TS+H3i1OuU/TtDMAfhzA7xBCDu70Ik3TPq1p2hlN085MTU2N+rtwh5n9OrIiEEBvZoaRYt5E\nvgqnnQhPjwDopBqMG0wZRn7WBDnpdo9IObe+ddvIzpf1bAVhrxMBgR1GgJ6OMuPN6wRWhpE3HvGh\nekR0zQmgk6pErmpo50siV8VUwA2noB1GFDYbwXTYGKmS1WEEmEtHfS8MYAOAgdpE07T37/Y9QkiS\nEDKtadoGIWQaQGqX91jr/P8GIeRbAB4EcN3YkeUh4NY9NSORk0SnAE50RwNw+5bf+XHfSD+7ka0g\nFhKfHgF0Q7+yNXodRKPVRjJfxayEkH087AEhxpQK/RkZ56be/HqugoNTgZF+dj1bkealzUQ8hu66\nUG2gUGvecwRW9J6rfsxGfGh2uvdGvTcZHUYUM2GvobSOrA4joCcjq/eYjLCEWRr7RQA/2fnzTwL4\nqztfQAgZI4S4O3+eBPA4gAsmP1cajE4cpF7SnARl2NvVMHrkZHW7grkxOUI+N2Ys1ZDMV6WlR1wO\nG6JBt0FyIk+p0BSYkXOvZeXUyQA6qTJl5CWcO+hxIuRxmPKKRXd0AeY6XxK5irQaCKMpS5oekXHu\naNANp50YdnL0DqN7dwAbYJ6c/AaADxBCrgJ4f+fvIIScIYT8Yec1xwGcJYS8DuCbAH5D07R7mJx4\nDKV1VrcrcDlswlvSAHOdL2vZCmYjo0VbWGEm4kGh1kSuMlpRGDXyMsgJ/VyjaZ2w1wm/4PQIYDbV\nICeFBujnzpYbKI3Y3i9jAFs/ZiJew3cto8MIQNdJGVW2NU3D2nalG50TjZmIPtl71GF9XYdSwrlt\nNoP0Bn0AABueSURBVIJ42FhUcC1bwUzEA4fgFBprmNKCmqZlALxvh6+fBfAznT8/B+Ckmc9RCbGQ\nBy/d2hr551a3K5iLeKWkR+jSwlFnndSbeveIrMgJJUVr27rRHhYyazfo515Yz4/8c7LqZAA9HWUz\nkI4q1ZrIlhvSzk0jNhu5Cg5Fg0P/nMzICaAbvFUD5GRlq4K5EVOzrED/jUc9d7bcQKnewtyYvHO3\nNb3gfJQI32qXnEg6d9gYgdVtjZwzs8S9Ta0kIBbyIJWvjTyjYDUrz3OgSwtHnUqZyFWhaZB2bqNd\nDWtdciLHK6ZFmqOOzNajVHLO7LTbEAt5um3Bw0LWjBOKWYMGcz1bgY30hv2JhtHo2up2WZqz4HM5\nMOZzjnzuVYkRCKDXhLAx8rnLcDts0tIjswbT2jJlhCUscjIiZiIe1DvjukfBmmSBiYc83XHdw2J1\nWy9GlRc5MVYHsZ6tYMznhM8lPj0C6OeuN9sjj1WXGTkBjOXm1ySn0LqFvCOSqvWsvqhQVuh7tjPH\nIj/CHIt2W8NatoJ5SZ480KnxGZEIriiiR4yQqrkxr7T9NLMRLxIjpqNqzRaS+Zq0aA9LWORkRNBu\nF/rADYNKvYXNYl2qwCyM+7A6YudL1+ORFCKkMwpGVSoqGHlgtPqNQrWBfFVO9wiFkbbc7owTSbUb\n0aAHDhsZebqtzA4joJ9UDX/fyUIVjZYm1cmZNUBge06OHD0yHTFGYHVyIk9n03TUKIMo6e9oRU7e\ngljokJPlEQw9VZyyOhoAYG7ch418daRBbKud0LesfnmbrTPHYkRPbU06ORm9q2FNcp0M/eyNXGWk\nlOXKVhmOzmhzGbB3CwdHMzzLW+XusywDRgis7PQI0EtHjZKyXN2uIORxjFQ3xhIBt8NQd9SK5Gi3\nkUFssqPdLGGRkxFBBWY5c28plYVxHzRtdEGPhTxCV7PfidmId6Ref03TsLJVkWp4jISRlzK6Utkn\n9dweNFraSCnLpS1dgcvsDBi186XebGMjJ1dG5gzICDU8o84qYonZiBflegvZEbb8yo5AAHrUZpRo\nd6HaQLbckHpuGl1bHeHc9DmQVSfIEhY5GREepx3xkGckQZdd9Q0YjPhInHFCMTfmxdoId50u1FBp\ntLBvQt5dh71O+Fz2kQzPMiUnEs/d7cYY4dwrW2WpxhLQDf0od72eraCtAQsTfo6n2huTATdc9tFS\nlqtbdEifxAisgSL1lS35BZqLk77uMzYM6O8n89x6vUvPcRkGq9uV7pLGex0WOTGA+XHvSEZ+dbsC\np50I3yvRDyPkZHW7IlURAsDChA+bxTqKQ86xWOr8fjK9YkIIFsZHU4bLW2WEPA5EfPIGJ3XrqUaQ\nkaVMWSqhAjpj1fNVNIYsHFRBRmw2gumIZ6Quo5XtMqaCbikzTii67f1DkhNN05SInCyM+7GyXR56\n9D4lgjLJidthx0zYi6VMaeifWd0uYzp87884ASxyYgjz476RFLguMHJmnFBEg264HLahi2IbLTrj\nRK5SWex4t8M+oN30iESvGNDPfWsEpbK0VZZ+Zmqsb20OJyO5cgO5SkOqkQf0f+tWWxva0C8rQE7o\n549CYFe3K5hXIJIJYOhzb5XqqDRa0iMn+yZ8aLS0buv7IMgu4qXYN+HrkulhIHOiN2tY5MQAFsZ9\nSIxQXLqUKWNxUq7hsdkI5saGj/isbOlehuxzU6982NDmUqYEG5Eb+gaAfZM+rGxVhvbUljMlLEiO\nQHicdsyEPUOTqp6Rl00EKaka7twrW/r8CpmRTADYP+nHrc3S0MWlKkQgxvwuRHxO3BxSRlYUqLcD\nerVcw+qRle0KPE55M04o9k2MRmCXtspSW81ZwiInBjA/pheXDlOEp2kabm6WsF+y4QE6ntqQ5ORm\nR9Hvl05O9M8f1mAuZcqYiXilFvECwP4JP+qt9lAdAs1WG6vbcgs0KRYnh4/4qBKBoAT65pDkZDmj\n18nIjGQCenStUGsONQ+n3mxjLauIjEz4hyaC9HWynZyFEZ2cm5slLE74pc04oVgY9yNTqqMwxDyc\nQrWBdKGGAyMu7lQVFjkxACroK0OQk3SxhmKtKd3IA/cmOQm4HZgMuIdWhnp6RL4C39dNRw2+741c\nFc22JrVTh2LfCIZnaUt/neyIz4TfhaDbMXzqT3IbMQV9toa57+VOJPPAlHw9QiM+w+DGZgmEyC30\nBvRlmi67rSuzg3AjXVTirhdHIFU0HStbZ7OCRU4MYKEbIhws6DfTHSOvAJtdGPehUG0iWx7sqd3c\nLCHsdWLMJ2c2QT8WJ3y4NaTHs5wpSU8zAHp3ADBcxKcbgVCAVO2f9GG73EBuiFbRla0yJvwuBCQs\nKuwHIQSLk37cHEJG9FZzNcjJKBGfG+kiACjhFe+f9GM9V0WlPjitfSNdxNyYF26HvCJeQJ+HMzfu\nHSpFUm+2sbJdwYFJ+Xc9SsTnxiaVEfn6jwUscmIA0aAbAbcD11LFga+liueAAmyWMurr6cHnvpUp\nYf+k/LAmoHvzwxDBfLWB7XJDupcGALGgBx6nbSgPU5Ui3v4zDEOqljJlJQgVoHvmw9z1Vknv/JLd\n/gzodRh2Gxnqrm9QPaKA4aGkapgoxI10SQkjD+h1J8M4ObSrR4UIRDcCO8Rd3+xEqVQg3ixgkRMD\nIITgYDQwHDnJlOCy26RO/qQ43NnaejU5xLnTJSUeTkCPnCTzNZTre7cTLyswyIzCZiPYN+4fShne\nypTgctiUmE3QTTUMYzDTJexXgFAB+rlXt8uoN/duJ76eVsfIO+02zI95h+qOupEuYjLgRsgjP5JJ\n/80HkUFab6fCXQO6oV/ODC5AvqGQjOhpbddQEZ8b6RJmI16preYsYZETgzg0NSQ5SZewb8IHu+Ti\nO0CfB+F22Aaeu9poYT1XVYac7Jscrn6D/l6Hoop4ahO+oSI+11JFHJj0KyEjw7YTF6oNJPJVHFTk\nrhcn/Ghrg3dedWVEgfQIoJOq4dI66hh5mrK8OUBGEvkqKo2WElFjQCcbpbq+GG8v3OykR1TRf4sT\n/i5h2gs3N9VxKFnAIicGcSgaQKpQG7hVVCWBsdsIDk4FcHUAOaFes+wKewqq3AY9oFdTBThsRIn0\nCADsn/JjKVMeuFX0aqqgDKGi7cRUQe8GGoFQ5dzdGp8Bhv56ugiv0y691ZyCdkcN9OY3SzioCDkJ\nepyYDLgHykgvAqGGjFBZvZoq7Pm6m5sljPtdUgci9uNwLIArqcKeMkKjVAcVuWsWsMiJQRzuCPpe\nUYhWW8NSpqwMOQH0B3RQ5KRbxKuIkT8UDcBGgMvJvZXK1WQR+yZ80tuIKY5Eg6i32nsOUarUW1jd\nrnRTbirgUCw4kMCqFqU6NNVJWQ5x7gNTfultxBQHpgIo11vYyO2+8ypbrmOrVFemdgPQHYZBzoJK\ndTLA8Gnt6+mSMtEeADgUDSJbbmCzuHsjg0pdoayghha/B0GV8rU9BH0pU0K91VaKzR6OBrCWrexZ\nv3E5WQAh6hgej9OOfRN+XB1ATq6likoZ+aNx/SxXEruf+3q6CE1T564B4FhcJyd7RXyupYpw2okS\n9T0AEPY5EQ95cHmPuwb0c6t010djuozsdW6V6mQojsQDuJzc25u/0YlSqVBLBQCTARfGfM6BBPZG\nuqiUkT8SGxzxoc6CSjJiFhY5MYj5cd1Dv7ZH58uljsI5Ph0SdayBoIr5emp3r+fSRgH7J/zwutQp\nrDoSC+wZOak1W1jaKuNwTB3DcygaACE9OdgJtHNKpXMfiQVRb+4d8bmWKmBxwq/UDo+j8eCeRr5Y\na2ItW1Gm3gTokZO9ZISScpVI1bF4CIVqE+t7RHwuJwo4HAso0fEH6I0Mh6NBXNvDyKcLNWwW6zim\nkM4eJuJzcUP/nY7F1Tm3WaijWe4x2G0EByb9e6ZILm7kYSNqGR56lmvp3R/QS4k8jk2rE4EAdCV+\na7OEamPn2QrXUkW02hoOx9Q5t8dpx+KEH1f2IFUXNvJw2W3dHUIq4Fh8sDd/YT2PEzNqKcJj8SCu\npXeP+FzcyAOAUucO+5yYCXtwOZHf9TXn1/MIuh1KjSWnMnJpY+dza5qGCxt53KfQXQO6/ruU2D3i\nQ2XkuEL6LxZyI+hx7OmcXdzIYzLgxpTklQwsYZETEzgWD+LC+u5K5eJGHgemAkq1du2b8MPlsHWZ\n9p0o1ZpY2iorx8CPxkNoa7vX+JxbywEATs6GRR5rII7EAnsa+fNreRyNB5WpkwF6NT67efOZYg3r\nuapyhudoXI/47NYGfb4jI/fNqCUjR+PBPSMnFzbyOD4dUqZOBgCOxPeO+GzkqsiWGzihUAQC0P/t\nC9XmrpOyL1ACq9C5CSG4byaE8wNsjUqEigXU0Yj3IE7ORZDIV5HK7xzavLhRUCqlA+izFY5Ph/D6\nSnbH7+t55J5npAoemNMNyuurO5/73FoeAbdDmRoIipOzYdzYLCFXuburS9M0nFvP4f5ZtWTE47Tj\n4FSgS/juBFWS9ytm5Omzdm5tZyV+fj2PCb8LsZBa3uWx6RCupYo7RgVbbQ0XN9SLUoU8TsyNebvG\n/E5Qp+2EYjJCnZc3d5Htixt5zIQ9ynTqUDwwF8HFjTwaO0QFG602riaLShEqFrDIiQmc6hjMN1bv\nFvR0oYa1bEU57xLQz31uLbfjxlxKWk7OqaVU5sa8GPM58cbKzkrlzbUc7ptRy7sEgFPzEQDAmzvI\nyFq2gmy5oZwnDwCn5yN4bSW7Y/ibkhPVzn0kFoTPZcdruxDv851UlCo1EBSn5yNotjWcX79bRm5l\nSijXW8qREwA4NRfBa8u73zUh6jk5R+IBuOy2XcnJubWccg4lANw/G0a92d4xRXwlWUC91VZSRszA\nIicmcGImBBsB3tjBm39leRsAcGbfmOhjDcQDcxGU6q3uvo5+vLy0jdmIF9NhNeZAUBBCcGo+smPk\npNFq4+JGHvcrltIB9LsGdo74UFKr4rlPL0SwVapjZevu5Zavr2QxP+5FWIG9S/2w2wgemAvj1c6z\n149yvYkryYJyaT8AeHBBl5FXdzD0ryzpv8upjhyphAcXIljLVpDcIXJ8dmkLR2NB+CXvXboTbocd\nR+PBHaOCW6U6rqdLeEhFnU0jPjs4OS93ZORtCp7bDCxyYgI+lwNHYkG8sotScdltShoeGvHZTRmq\n+HACuqG/kiygWLu9DfqN1SxqzbaSRDDsdeLAlH/Hu37hRgZep13JcCw1hq+u3G7o220NL97awiOL\nEzKONRAPLozhwkb+rhTJy0vbaLY1PHpAvXNHgx7MjXl3lJEXb24h4nN25yqpBGoMKYGiaLbaeGVp\nGw8vjss41kA8tBDBq8vZu1YdUCOv4rn3Tfgw5nPipVt3E++Xbm0jHvIoM1iQFSxyYhLvODiJl25t\n3aUMzy5t4/7ZkFLFsBQHpwKYDLjx7Wubt319PVvBeq6KhxbU89IA4LH942hrwPPXM7d9/budvz+m\noOEBgIf3jeOFm5m7ukiev7GFM4tjShXDUhyLBxFwO/D8jdvv+mqqiK1SHY8dUE+BA8BDC2NotLS7\nDP0LN7ZgtxFlvcsHF8bw0q2tu9JoL93awsOL48qlKwE9redy2HD2DnJycaOAUr2Fh/erKSNvPziJ\ncr11VzTz7K0tuOy2bn2bSiCE4O0HJ/Dc9c27ZOTlW1t42+KYculKs1BPK95jeOLwBGrNdpd1A/pE\nx9dWssoaS5uN4J2HJ/Gda5to99WdfPNyCoBOuFTE2xbH4HXa8czV9G1ff+56BsenQxjzq1XERvF9\nR6dQqDZvq4XIFGu4nCwoKyMOuw1PHJrEty6nb1OGL9xUmwi+/eAEnHaCb3VkmeKFmxncPxtGQLE0\nA8W7Dk8iVajd1pGxkavgVqaMRxT05AHA5bDh0f3jXb1B8d0butOj6rkfOzAOQoDnrt1OvL99bROn\n5sNKOpQA8PihSWzkqrftYrqeLmI9V8VjihJBM7DIiUk8un8CDhvB31/pGcxvXEqh1dbw/ffFJZ5s\nb7zz8CQypfptyvBrF5JYGPd1JxKqBrfDjscOjOOZKz2Dmas0cHZpG48fVNNYArpSsdsIvnW5JyN/\nd1FX6O88rCYRBIB3H53CRq6KK33Dn54+n8DihA9zY2qGkANuBx65w2Cm8lWcXdrG9x2ZkniyvfHu\no1EQousOiq++mQAAvPd4VNaxBuL9x2O4kS7dVr/2lTcTuH82hHhYjcmwdyLic+H+mTC+0Scjy5ky\nzq/n8YETMYkn2xtPHNJ1xTf79MjfnNNl5P0Kn9soTJETQshHCSHnCSFtQsiZPV73QULIZULINULI\nL5v5TNXgdzvwfUem8JevrnXbvJ4+n0A85OkWMamIdx+NwmW34S9eWQUA5KsNPHctgw+ciCkdHvzA\niThuZcrdOp+/fmMd9WYbT52elXyy3RH2OvHw4hi++Pp6t0PqL15Zxf5Jv5IFmhTUYP7Va2sAgESu\niueuZ/Dk6VmlZeS9x2K4kix258v89Rsb0DTgyVMzkk+2O6aCbpyai+Arb250ifdfv7GO49MhpdZf\n3In3dYjTVztGcnW7jNdWsviBk9MyjzUQHz41jddXst1psX9zfgMA8KH71T33vgk/7p8N4c9fXu3K\nyNPnEzg9H1GugYEFzEZOzgH4EQDP7PYCQogdwO8B+BCAEwA+QQg5YfJzlcInHllAulDD1y8ksbpd\nxt9dTOHDp6aVzBNTjPtd+NDJOP7i5VWUak18/qUV1FttPHVaXQUOAE+dnkHQ7cAff/cWNE3Dn720\ngiOxgHKzQu7EP35sEctbZXzjUgo30kW8cHMLP/yg2kY+Hvbg+0/E8LkXl1Gpt/Dfz65A06C8jPzI\ng7PwOu34g2dvoN3W8PmzKzgxHVJq/PtO+PFHF3ApUcAzVzdxKZHHK8tZfPiUusYSAObGfHji0CT+\n83duodpo4U9fXAEhwA+dVFtGfvjBOdhtBH/y4gpabQ1/8uIKTs1HMK/YnKQ78bGHF3BxI4/XVrJ4\nfSWLN1Zz+LDCpNsMTCVgNU27CGCQgn0EwDVN0250XvunAJ4CcMHMZ6uEdx+dwv5JP37tyxcRDbnh\nsBP81OP7ZR9rIH7qHYv4q9fW8XP/7RW8sryNJw5NdltfVYXf7cDHHp7HZ75zE82WhjdWc/jNHz2p\ntJEHgO+/L4bZiBe/9uULCHud8Lns+Pgj87KPNRA/+84DePp8Ej//uVfwwo0M3n88qrQnDwBjfhc+\n9vA8Pvv8Ekq1Ji4lCvj3Hz8t+1gD8ZHTs/jtr13Br3zpPFx2G4IeB378kQXZxxqIT733ED7+6efx\nqc+9imevpvEDJ6exMKG2kZ8KuvHkqRn81+8uYWWrjJubJfz+//Q22ccaiKdOz+C3/vYyfvkv3oQG\nDRN+F37szJzsY3GBiJqTWQArfX9f7XztLhBCPkkIOUsIOZtOp3d6iZJw2G347Y+dRqnexLm1HP71\nR07eE21dDy6M4Z9/4AieuZpG2OvEr//ISdlHGgr/+weO4MH5CL785gY+cnoGH32b+kbeabfhdz5+\nGtulOi4nCvjNH30A0aCaOfl+nFkcx6fecwjfuJRCNOTBr33k3pCRX/zAERyfDuGr5xL42Jl5pVM6\nFC6HDf/2o6eQztdwK1PCb/3YaeUmle6Exw5M4Kef2I+vX9Rr1v7vD98n+0hD4V/+4HEcmPLjby8k\n8RNv34d/cJ/6dRshjxO/9WOnsbxVxup2Bf/ux07h/2/vXkOsqOMwjn8fd71kSReCKJX0hRQSRCFd\nISJ9YReyIKKgkKh32Y0iurzobS8i6kUE0U1IDDElKcnKit6JtyAvRdHFVi2NsCKNXd2nF2eCxdQ1\nds/MnJnn8+ac+XP2zLM/hnN+c2b+M9Om1Ot6Q+NFJ7rlNYCkj4Fjndn5tO13i9d8Bjxme9Mx/v42\nYKHt+4rlu4HLbS850XrnzZvnTZv+83a19vfQEQ4Pu7YzAo7n94NDTJ3cx8Qa3WF2NMPD5sChIc6q\n6Qyd4+nVbeTAwUFOm9xfq7sQj6ZXt5FDg0cwZuqk3ttGpk2ZSF+ND2cf7ciw+ePQUG1n+h3PwcHO\ntZ56bRsBkLTZ9nHPUf3XqP+Z7QVjzLIbGLlrO6MYa5y6TkEbTd2u9HkyJkxQz33pQO9uI72wB3+0\nXt1GTpmUbaQsfRPUc40J9GZT8n+VsRu0EZgjabakScAdwJoS1hsRERE9aKxTiW+VNABcCbwvaV0x\nfp6ktQC2DwNLgHXATmCF7e1jix0RERFNNdbZOquB1ccY3wPcMGJ5LbB2LOuKiIiIduids9siIiKi\nFdKcRERERK2MOpW4KpL2Az926e3PBn4d9VUxXlLv8qTW5Umty5V6l6ebtT7f9qg3uqptc9JNkjad\nzDzrGB+pd3lS6/Kk1uVKvctTh1rnsE5ERETUSpqTiIiIqJW2NievVB2gZVLv8qTW5Umty5V6l6fy\nWrfynJOIiIior7b+chIRERE1leYkIiIiaqV1zYmkhZK+lvStpCeqztNUkmZK+lTSDknbJT1Udaam\nk9Qnaauk96rO0nSSzpC0UtJXknZKurLqTE0l6ZHiM2SbpOWSplSdqUkkvS5pn6RtI8bOkvSRpG+K\nxzPLztWq5kRSH/AScD0wF7hT0txqUzXWYeBR23OBK4D7U+uue4jOzTWj+14EPrB9IXAxqXtXSJoO\nPAjMs30R0EfnzvYxft4EFh419gSw3vYcYH2xXKpWNSfAZcC3tr+zPQi8DSyqOFMj2d5re0vx/E86\nH97Tq03VXJJmADcCr1adpekknQ5cA7wGYHvQ9oFqUzVaP3CKpH5gKrCn4jyNYvtz4LejhhcBS4vn\nS4FbSg1F+5qT6cBPI5YHyBdm10maBVwCbKg2SaO9ADwODFcdpAVmA/uBN4rDaK9KOrXqUE1kezfw\nHLAL2Av8bvvDalO1wjm29xbPfwbOKTtA25qTKJmk04B3gIdt/1F1niaSdBOwz/bmqrO0RD9wKfCy\n7UuAv6jgZ+82KM51WESnITwPOFXSXdWmahd3rjdS+jVH2tac7AZmjlieUYxFF0iaSKcxWWZ7VdV5\nGuxq4GZJP9A5VHmdpLeqjdRoA8CA7X9/CVxJp1mJ8bcA+N72fttDwCrgqooztcEvks4FKB73lR2g\nbc3JRmCOpNmSJtE5sWpNxZkaSZLoHJPfafv5qvM0me0nbc+wPYvONv2J7exddontn4GfJF1QDM0H\ndlQYqcl2AVdImlp8pswnJx+XYQ2wuHi+GHi37AD9Za+wSrYPS1oCrKNz1vfrtrdXHKuprgbuBr6U\n9EUx9pTttRVmihgvDwDLip2c74B7Ks7TSLY3SFoJbKEzA3ArNbi0epNIWg5cC5wtaQB4BngWWCHp\nXuBH4PbSc+Xy9REREVEnbTusExERETWX5iQiIiJqJc1JRERE1Eqak4iIiKiVNCcRERFRK2lOIiIi\nolbSnERERESt/AMeoljaZ3hw0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa1a37ddd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(t, y1[:,0]);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa19da9810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(w, abs(F));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the signal is real, the spectrum is symmetric. We therefore only need to plot the part that corresponds to the postive frequencies. To extract that part of the `w` and `F` we can use some of the indexing tricks for NumPy arrays that we saw in Lecture 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "indices = where(w > 0) # select only indices for elements that corresponds to positive frequencies\n",
    "w_pos = w[indices]\n",
    "F_pos = F[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9jwnpV0Iys8puSZJqyBBSM2UlZM9Pxyw02OglP1/vVtktSVINDQ0hEfG5iDgbEd/b0nZt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffa1a52f5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(9,3))\n",
    "ax.plot(w_pos, abs(F_pos))\n",
    "ax.set_xlim(0, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, we now see a peak in the spectrum that is centered around 1, which is the frequency we used in the damped oscillator example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise 03 : forecasting using fourier transform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose we have a data series as follows "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dONxwQ+G2N95A0YR1NEydYFgBwqNOOEcj64StoxEoTIQQ7QBOzf0ztfkCUmz4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x6431810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([669, 592, 664, 1005, 699, 401, 646, 472, 598, 681, 1126, 1260, 562, 491, 714, 530, 521, 687, 776, 802, 499, 536, 871, 801, 965, 768, 381, 497, 458, 699, 549, 427, 358, 219, 635, 756, 775, 969, 598, 630, 649, 722, 835, 812, 724, 966, 778, 584, 697, 737, 777, 1059, 1218, 848, 713, 884, 879, 1056, 1273, 1848, 780, 1206, 1404, 1444, 1412, 1493, 1576, 1178, 836, 1087, 1101, 1082, 775, 698, 620, 651, 731, 906, 958, 1039, 1105, 620, 576, 707, 888, 1052, 1072, 1357, 768, 986, 816, 889, 973, 983, 1351, 1266, 1053, 1879, 2085, 2419, 1880, 2045, 2212, 1491, 1378, 1524, 1231, 1577, 2459, 1848, 1506, 1589, 1386, 1111, 1180, 1075, 1595, 1309, 2092, 1846, 2321, 2036, 3587, 1637, 1416, 1432, 1110, 1135, 1233, 1439, 894, 628, 967, 1176, 1069, 1193, 1771, 1199, 888, 1155, 1254, 1403, 1502, 1692, 1187, 1110, 1382, 1808, 2039, 1810, 1819, 1408, 803, 1568, 1227, 1270, 1268, 1535, 873, 1006, 1328, 1733, 1352, 1906, 2029, 1734, 1314, 1810, 1540, 1958, 1420, 1530, 1126, 721, 771, 874, 997, 1186, 1415, 973, 1146, 1147, 1079, 3854, 3407, 2257, 1200, 734, 1051, 1030, 1370, 2422, 1531, 1062, 530, 1030, 1061, 1249, 2080, 2251, 1190, 756, 1161, 1053, 1063, 932, 1604, 1130, 744, 930, 948, 1107, 1161, 1194, 1366, 1155, 785, 602, 903, 1142, 1410, 1256, 742, 985, 1037, 1067, 1196, 1412, 1127, 779, 911, 989, 946, 888, 1349, 1124, 761, 994, 1068, 971, 1157, 1558, 1223, 782, 2790, 1835, 1444, 1098, 1399, 1255, 950, 1110, 1345, 1224, 1092, 1446, 1210, 1122, 1259, 1181, 1035, 1325, 1481, 1278, 769, 911, 876, 877, 950, 1383, 980, 705, 888, 877, 638, 1065, 1142, 1090, 1316, 1270, 1048, 1256, 1009, 1175, 1176, 870, 856, 860])\n",
    "pl.plot(np.arange(0, x.size), x, 'b', label = 'x', linewidth = 3)\n",
    "pl.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please use Fourier transform to predict next 100 values. Hint: first we need to remove linear trends, then we can find the Fourier components, finally we can reconstruct the new values as linear combination of Fourier components plus linear trend. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Special functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A large number of mathematical special functions are important for many computional physics problems. SciPy provides implementations of a very extensive set of special functions. For details, see the list of functions in the reference documention at http://docs.scipy.org/doc/scipy/reference/special.html#module-scipy.special. \n",
    "\n",
    "To demonstrate the typical usage of special functions we will look in more detail at the Bessel functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# The scipy.special module includes a large number of Bessel-functions\n",
    "# Here we will use the functions jn and yn, which are the Bessel functions \n",
    "# of the first and second kind and real-valued order. We also include the \n",
    "# function jn_zeros and yn_zeros that gives the zeroes of the functions jn\n",
    "# and yn.\n",
    "#\n",
    "from scipy.special import jn, yn, jn_zeros, yn_zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J_0(0.000000) = 1.000000\n",
      "Y_0(1.000000) = 0.088257\n"
     ]
    }
   ],
   "source": [
    "n = 0    # order\n",
    "x = 0.0\n",
    "\n",
    "# Bessel function of first kind\n",
    "print \"J_%d(%f) = %f\" % (n, x, jn(n, x))\n",
    "\n",
    "x = 1.0\n",
    "# Bessel function of second kind\n",
    "print \"Y_%d(%f) = %f\" % (n, x, yn(n, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zzh54OHjIHRZjzEgu5ObCW6k0eD1Kb294aTEAsrQOHz6MDh06FN//5ZdfUKFC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4fdf890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(0, 10, 100)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "for n in range(4):\n",
    "    ax.plot(x, jn(n, x), label=r\"$J_%d(x)$\" % n)\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.40482556,   5.52007811,   8.65372791,  11.79153444])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# zeros of Bessel functions\n",
    "n = 0 # order\n",
    "m = 4 # number of roots to compute\n",
    "jn_zeros(n, m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical integration: quadrature"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numerical evaluation of a function of the type\n",
    "\n",
    "$\\displaystyle \\int_a^b f(x) dx$\n",
    "\n",
    "is called *numerical quadrature*, or simply *quadature*. SciPy provides a series of functions for different kind of quadrature, for example the `quad`, `dblquad` and `tplquad` for single, double and triple integrals, respectively.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import quad, dblquad, tplquad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `quad` function takes a large number of optional arguments, which can be used to fine-tune the behaviour of the function (try `help(quad)` for details).\n",
    "\n",
    "The basic usage is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function quad in module scipy.integrate.quadpack:\n",
      "\n",
      "quad(func, a, b, args=(), full_output=0, epsabs=1.49e-08, epsrel=1.49e-08, limit=50, points=None, weight=None, wvar=None, wopts=None, maxp1=50, limlst=50)\n",
      "    Compute a definite integral.\n",
      "    \n",
      "    Integrate func from `a` to `b` (possibly infinite interval) using a\n",
      "    technique from the Fortran library QUADPACK.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    func : function\n",
      "        A Python function or method to integrate.  If `func` takes many\n",
      "        arguments, it is integrated along the axis corresponding to the\n",
      "        first argument.\n",
      "        If the user desires improved integration performance, then f may\n",
      "        instead be a ``ctypes`` function of the form:\n",
      "    \n",
      "            f(int n, double args[n]),\n",
      "    \n",
      "        where ``args`` is an array of function arguments and ``n`` is the\n",
      "        length of ``args``. ``f.argtypes`` should be set to\n",
      "        ``(c_int, c_double)``, and ``f.restype`` should be ``(c_double,)``.\n",
      "    a : float\n",
      "        Lower limit of integration (use -numpy.inf for -infinity).\n",
      "    b : float\n",
      "        Upper limit of integration (use numpy.inf for +infinity).\n",
      "    args : tuple, optional\n",
      "        Extra arguments to pass to `func`.\n",
      "    full_output : int, optional\n",
      "        Non-zero to return a dictionary of integration information.\n",
      "        If non-zero, warning messages are also suppressed and the\n",
      "        message is appended to the output tuple.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    y : float\n",
      "        The integral of func from `a` to `b`.\n",
      "    abserr : float\n",
      "        An estimate of the absolute error in the result.\n",
      "    infodict : dict\n",
      "        A dictionary containing additional information.\n",
      "        Run scipy.integrate.quad_explain() for more information.\n",
      "    message\n",
      "        A convergence message.\n",
      "    explain\n",
      "        Appended only with 'cos' or 'sin' weighting and infinite\n",
      "        integration limits, it contains an explanation of the codes in\n",
      "        infodict['ierlst']\n",
      "    \n",
      "    Other Parameters\n",
      "    ----------------\n",
      "    epsabs : float or int, optional\n",
      "        Absolute error tolerance.\n",
      "    epsrel : float or int, optional\n",
      "        Relative error tolerance.\n",
      "    limit : float or int, optional\n",
      "        An upper bound on the number of subintervals used in the adaptive\n",
      "        algorithm.\n",
      "    points : (sequence of floats,ints), optional\n",
      "        A sequence of break points in the bounded integration interval\n",
      "        where local difficulties of the integrand may occur (e.g.,\n",
      "        singularities, discontinuities). The sequence does not have\n",
      "        to be sorted.\n",
      "    weight : float or int, optional\n",
      "        String indicating weighting function. Full explanation for this\n",
      "        and the remaining arguments can be found below.\n",
      "    wvar : optional\n",
      "        Variables for use with weighting functions.\n",
      "    wopts : optional\n",
      "        Optional input for reusing Chebyshev moments.\n",
      "    maxp1 : float or int, optional\n",
      "        An upper bound on the number of Chebyshev moments.\n",
      "    limlst : int, optional\n",
      "        Upper bound on the number of cycles (>=3) for use with a sinusoidal\n",
      "        weighting and an infinite end-point.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    dblquad : double integral\n",
      "    tplquad : triple integral\n",
      "    nquad : n-dimensional integrals (uses `quad` recursively)\n",
      "    fixed_quad : fixed-order Gaussian quadrature\n",
      "    quadrature : adaptive Gaussian quadrature\n",
      "    odeint : ODE integrator\n",
      "    ode : ODE integrator\n",
      "    simps : integrator for sampled data\n",
      "    romb : integrator for sampled data\n",
      "    scipy.special : for coefficients and roots of orthogonal polynomials\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    \n",
      "    **Extra information for quad() inputs and outputs**\n",
      "    \n",
      "    If full_output is non-zero, then the third output argument\n",
      "    (infodict) is a dictionary with entries as tabulated below.  For\n",
      "    infinite limits, the range is transformed to (0,1) and the\n",
      "    optional outputs are given with respect to this transformed range.\n",
      "    Let M be the input argument limit and let K be infodict['last'].\n",
      "    The entries are:\n",
      "    \n",
      "    'neval'\n",
      "        The number of function evaluations.\n",
      "    'last'\n",
      "        The number, K, of subintervals produced in the subdivision process.\n",
      "    'alist'\n",
      "        A rank-1 array of length M, the first K elements of which are the\n",
      "        left end points of the subintervals in the partition of the\n",
      "        integration range.\n",
      "    'blist'\n",
      "        A rank-1 array of length M, the first K elements of which are the\n",
      "        right end points of the subintervals.\n",
      "    'rlist'\n",
      "        A rank-1 array of length M, the first K elements of which are the\n",
      "        integral approximations on the subintervals.\n",
      "    'elist'\n",
      "        A rank-1 array of length M, the first K elements of which are the\n",
      "        moduli of the absolute error estimates on the subintervals.\n",
      "    'iord'\n",
      "        A rank-1 integer array of length M, the first L elements of\n",
      "        which are pointers to the error estimates over the subintervals\n",
      "        with ``L=K`` if ``K<=M/2+2`` or ``L=M+1-K`` otherwise. Let I be the\n",
      "        sequence ``infodict['iord']`` and let E be the sequence\n",
      "        ``infodict['elist']``.  Then ``E[I[1]], ..., E[I[L]]`` forms a\n",
      "        decreasing sequence.\n",
      "    \n",
      "    If the input argument points is provided (i.e. it is not None),\n",
      "    the following additional outputs are placed in the output\n",
      "    dictionary.  Assume the points sequence is of length P.\n",
      "    \n",
      "    'pts'\n",
      "        A rank-1 array of length P+2 containing the integration limits\n",
      "        and the break points of the intervals in ascending order.\n",
      "        This is an array giving the subintervals over which integration\n",
      "        will occur.\n",
      "    'level'\n",
      "        A rank-1 integer array of length M (=limit), containing the\n",
      "        subdivision levels of the subintervals, i.e., if (aa,bb) is a\n",
      "        subinterval of ``(pts[1], pts[2])`` where ``pts[0]`` and ``pts[2]``\n",
      "        are adjacent elements of ``infodict['pts']``, then (aa,bb) has level l\n",
      "        if ``|bb-aa| = |pts[2]-pts[1]| * 2**(-l)``.\n",
      "    'ndin'\n",
      "        A rank-1 integer array of length P+2.  After the first integration\n",
      "        over the intervals (pts[1], pts[2]), the error estimates over some\n",
      "        of the intervals may have been increased artificially in order to\n",
      "        put their subdivision forward.  This array has ones in slots\n",
      "        corresponding to the subintervals for which this happens.\n",
      "    \n",
      "    **Weighting the integrand**\n",
      "    \n",
      "    The input variables, *weight* and *wvar*, are used to weight the\n",
      "    integrand by a select list of functions.  Different integration\n",
      "    methods are used to compute the integral with these weighting\n",
      "    functions.  The possible values of weight and the corresponding\n",
      "    weighting functions are.\n",
      "    \n",
      "    ==========  ===================================   =====================\n",
      "    ``weight``  Weight function used                  ``wvar``\n",
      "    ==========  ===================================   =====================\n",
      "    'cos'       cos(w*x)                              wvar = w\n",
      "    'sin'       sin(w*x)                              wvar = w\n",
      "    'alg'       g(x) = ((x-a)**alpha)*((b-x)**beta)   wvar = (alpha, beta)\n",
      "    'alg-loga'  g(x)*log(x-a)                         wvar = (alpha, beta)\n",
      "    'alg-logb'  g(x)*log(b-x)                         wvar = (alpha, beta)\n",
      "    'alg-log'   g(x)*log(x-a)*log(b-x)                wvar = (alpha, beta)\n",
      "    'cauchy'    1/(x-c)                               wvar = c\n",
      "    ==========  ===================================   =====================\n",
      "    \n",
      "    wvar holds the parameter w, (alpha, beta), or c depending on the weight\n",
      "    selected.  In these expressions, a and b are the integration limits.\n",
      "    \n",
      "    For the 'cos' and 'sin' weighting, additional inputs and outputs are\n",
      "    available.\n",
      "    \n",
      "    For finite integration limits, the integration is performed using a\n",
      "    Clenshaw-Curtis method which uses Chebyshev moments.  For repeated\n",
      "    calculations, these moments are saved in the output dictionary:\n",
      "    \n",
      "    'momcom'\n",
      "        The maximum level of Chebyshev moments that have been computed,\n",
      "        i.e., if ``M_c`` is ``infodict['momcom']`` then the moments have been\n",
      "        computed for intervals of length ``|b-a| * 2**(-l)``,\n",
      "        ``l=0,1,...,M_c``.\n",
      "    'nnlog'\n",
      "        A rank-1 integer array of length M(=limit), containing the\n",
      "        subdivision levels of the subintervals, i.e., an element of this\n",
      "        array is equal to l if the corresponding subinterval is\n",
      "        ``|b-a|* 2**(-l)``.\n",
      "    'chebmo'\n",
      "        A rank-2 array of shape (25, maxp1) containing the computed\n",
      "        Chebyshev moments.  These can be passed on to an integration\n",
      "        over the same interval by passing this array as the second\n",
      "        element of the sequence wopts and passing infodict['momcom'] as\n",
      "        the first element.\n",
      "    \n",
      "    If one of the integration limits is infinite, then a Fourier integral is\n",
      "    computed (assuming w neq 0).  If full_output is 1 and a numerical error\n",
      "    is encountered, besides the error message attached to the output tuple,\n",
      "    a dictionary is also appended to the output tuple which translates the\n",
      "    error codes in the array ``info['ierlst']`` to English messages.  The\n",
      "    output information dictionary contains the following entries instead of\n",
      "    'last', 'alist', 'blist', 'rlist', and 'elist':\n",
      "    \n",
      "    'lst'\n",
      "        The number of subintervals needed for the integration (call it ``K_f``).\n",
      "    'rslst'\n",
      "        A rank-1 array of length M_f=limlst, whose first ``K_f`` elements\n",
      "        contain the integral contribution over the interval\n",
      "        ``(a+(k-1)c, a+kc)`` where ``c = (2*floor(|w|) + 1) * pi / |w|``\n",
      "        and ``k=1,2,...,K_f``.\n",
      "    'erlst'\n",
      "        A rank-1 array of length ``M_f`` containing the error estimate\n",
      "        corresponding to the interval in the same position in\n",
      "        ``infodict['rslist']``.\n",
      "    'ierlst'\n",
      "        A rank-1 integer array of length ``M_f`` containing an error flag\n",
      "        corresponding to the interval in the same position in\n",
      "        ``infodict['rslist']``.  See the explanation dictionary (last entry\n",
      "        in the output tuple) for the meaning of the codes.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    Calculate :math:`\\int^4_0 x^2 dx` and compare with an analytic result\n",
      "    \n",
      "    >>> from scipy import integrate\n",
      "    >>> x2 = lambda x: x**2\n",
      "    >>> integrate.quad(x2, 0, 4)\n",
      "    (21.333333333333332, 2.3684757858670003e-13)\n",
      "    >>> print(4**3 / 3.)  # analytical result\n",
      "    21.3333333333\n",
      "    \n",
      "    Calculate :math:`\\int^\\infty_0 e^{-x} dx`\n",
      "    \n",
      "    >>> invexp = lambda x: np.exp(-x)\n",
      "    >>> integrate.quad(invexp, 0, np.inf)\n",
      "    (1.0, 5.842605999138044e-11)\n",
      "    \n",
      "    >>> f = lambda x,a : a*x\n",
      "    >>> y, err = integrate.quad(f, 0, 1, args=(1,))\n",
      "    >>> y\n",
      "    0.5\n",
      "    >>> y, err = integrate.quad(f, 0, 1, args=(3,))\n",
      "    >>> y\n",
      "    1.5\n",
      "    \n",
      "    Calculate :math:`\\int^1_0 x^2 + y^2 dx` with ctypes, holding\n",
      "    y parameter as 1::\n",
      "    \n",
      "        testlib.c =>\n",
      "            double func(int n, double args[n]){\n",
      "                return args[0]*args[0] + args[1]*args[1];}\n",
      "        compile to library testlib.*\n",
      "    \n",
      "    ::\n",
      "    \n",
      "       from scipy import integrate\n",
      "       import ctypes\n",
      "       lib = ctypes.CDLL('/home/.../testlib.*') #use absolute path\n",
      "       lib.func.restype = ctypes.c_double\n",
      "       lib.func.argtypes = (ctypes.c_int,ctypes.c_double)\n",
      "       integrate.quad(lib.func,0,1,(1))\n",
      "       #(1.3333333333333333, 1.4802973661668752e-14)\n",
      "       print((1.0**3/3.0 + 1.0) - (0.0**3/3.0 + 0.0)) #Analytic result\n",
      "       # 1.3333333333333333\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(quad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define a simple function for the integrand\n",
    "def f(x):\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "integral value = 0.5 , absolute error = 5.55111512313e-15\n"
     ]
    }
   ],
   "source": [
    "x_lower = 0 # the lower limit of x\n",
    "x_upper = 1 # the upper limit of x\n",
    "\n",
    "val, abserr = quad(f, x_lower, x_upper)\n",
    "\n",
    "print \"integral value =\", val, \", absolute error =\", abserr "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we need to pass extra arguments to integrand function we can use the `args` keyword argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.736675137081 9.3891268825e-13\n"
     ]
    }
   ],
   "source": [
    "def integrand(x, n):\n",
    "    \"\"\"\n",
    "    Bessel function of first kind and order n. \n",
    "    \"\"\"\n",
    "    return jn(n, x)\n",
    "\n",
    "\n",
    "x_lower = 0  # the lower limit of x\n",
    "x_upper = 10 # the upper limit of x\n",
    "\n",
    "val, abserr = quad(integrand, x_lower, x_upper, args=(3,))\n",
    "\n",
    "print val, abserr "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simple functions we can use a lambda function (name-less function) instead of explicitly defining a function for the integrand:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerical  = 1.77245385091 1.42026367809e-08\n",
      "analytical = 1.77245385091\n"
     ]
    }
   ],
   "source": [
    "val, abserr = quad(lambda x: exp(-x ** 2), -Inf, Inf)\n",
    "\n",
    "print \"numerical  =\", val, abserr\n",
    "\n",
    "analytical = sqrt(pi)\n",
    "print \"analytical =\", analytical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As show in the example above, we can also use 'Inf' or '-Inf' as integral limits.\n",
    "\n",
    "Higher-dimensional integration works in the same way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.785398163397 1.37530985102e-08\n"
     ]
    }
   ],
   "source": [
    "def integrand(x, y):\n",
    "    return exp(-x**2-y**2)\n",
    "\n",
    "x_lower = 0  \n",
    "x_upper = 10\n",
    "y_lower = 0\n",
    "y_upper = 10\n",
    "\n",
    "val, abserr = dblquad(integrand, x_lower, x_upper, lambda x : y_lower, lambda x: y_upper)\n",
    "\n",
    "print val, abserr "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how we had to pass lambda functions for the limits for the y integration, since these in general can be functions of x."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linear algebra module contains a lot of matrix related functions, including linear equation solving, eigenvalue solvers, matrix functions (for example matrix-exponentiation), a number of different decompositions (SVD, LU, cholesky), etc. \n",
    "\n",
    "Detailed documetation is available at: http://docs.scipy.org/doc/scipy/reference/linalg.html\n",
    "\n",
    "Here we will look at how to use some of these functions:\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear equation systems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear equation systems on the matrix form\n",
    "\n",
    "$A x = b$\n",
    "\n",
    "where $A$ is a matrix and $x,b$ are vectors can be solved like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.linalg import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = array([[1,2,3], [4,2,6], [7,5,9]])\n",
    "b = array([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.26882631e-16,   0.00000000e+00,   3.33333333e-01])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = solve(A, b)\n",
    "\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -1.11022302e-16,   0.00000000e+00,   0.00000000e+00])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check\n",
    "dot(A, x) - b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also do the same with\n",
    "\n",
    "$A X = B$\n",
    "\n",
    "where $A, B, X$ are matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = rand(3,3)\n",
    "B = rand(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = solve(A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.00439176, -1.52144589, -1.20718674],\n",
       "       [ 0.39740767,  1.70749784,  0.86609476],\n",
       "       [ 0.76481801,  0.70292475,  0.69137781]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3966823025038029e-16"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check\n",
    "norm(dot(A, X) - B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Eigenvalues and eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The eigenvalue problem for a matrix $A$:\n",
    "\n",
    "$\\displaystyle A v_n = \\lambda_n v_n$\n",
    "\n",
    "where $v_n$ is the $n$th eigenvector and $\\lambda_n$ is the $n$th eigenvalue.\n",
    "\n",
    "To calculate eigenvalues of a matrix, use the `eigvals` and for calculating both eigenvalues and eigenvectors, use the function `eig`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "evals = eigvals(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.57238398+0.j        ,  0.49338229+0.18737521j,\n",
       "        0.49338229-0.18737521j])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "evals, evecs = eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.57238398+0.j        ,  0.49338229+0.18737521j,\n",
       "        0.49338229-0.18737521j])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.68576923+0.j        ,  0.60598757-0.27810317j,\n",
       "         0.60598757+0.27810317j],\n",
       "       [ 0.68895223+0.j        , -0.68912267+0.j        , -0.68912267-0.j        ],\n",
       "       [ 0.23466015+0.j        ,  0.18374440+0.21629988j,\n",
       "         0.18374440-0.21629988j]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evecs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The eigenvectors corresponding to the $n$th eigenvalue (stored in `evals[n]`) is the $n$th *column* in `evecs`, i.e., `evecs[:,n]`. To verify this, let's try mutiplying eigenvectors with the matrix and compare to the product of the eigenvector and the eigenvalue:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.3199839306544087e-16"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1\n",
    "\n",
    "norm(dot(A, evecs[:,n]) - evals[n] * evecs[:,n])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are also more specialized eigensolvers, like the `eigh` for Hermitian matrices. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.67450769, -0.34939337, -2.00919104],\n",
       "       [-0.91765852,  1.22126308,  0.96338391],\n",
       "       [ 0.06456633, -0.2846109 ,  1.28289428]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the matrix inverse\n",
    "inv(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4379648377741537"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# determinant\n",
    "det(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.6861217367383297, 2.1802609189713564)"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# norms of various orders\n",
    "norm(A, ord=2), norm(A, ord=Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sparse matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sparse matrices are often useful in numerical simulations dealing with large systems, if the problem can be described in matrix form where the matrices or vectors mostly contains zeros. Scipy has a good support for sparse matrices, with basic linear algebra operations (such as equation solving, eigenvalue calculations, etc).\n",
    "\n",
    "There are many possible strategies for storing sparse matrices in an efficient way. Some of the most common are the so-called coordinate form (COO), list of list (LIL) form,  and compressed-sparse column CSC (and row, CSR). Each format has some advantanges and disadvantages. Most computational algorithms (equation solving, matrix-matrix multiplication, etc) can be efficiently implemented using CSR or CSC formats, but they are not so intuitive and not so easy to initialize. So often a sparse matrix is initially created in COO or LIL format (where we can efficiently add elements to the sparse matrix data), and then converted to CSC or CSR before used in real calcalations.\n",
    "\n",
    "For more information about these sparse formats, see e.g. http://en.wikipedia.org/wiki/Sparse_matrix\n",
    "\n",
    "When we create a sparse matrix we have to choose which format it should be stored in. For example, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 3, 0, 0],\n",
       "       [0, 1, 1, 0],\n",
       "       [1, 0, 0, 1]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dense matrix\n",
    "M = array([[1,0,0,0], [0,3,0,0], [0,1,1,0], [1,0,0,1]]); M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<type 'numpy.int64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert from dense to sparse\n",
    "A = csr_matrix(M); A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 0, 0, 0],\n",
       "        [0, 3, 0, 0],\n",
       "        [0, 1, 1, 0],\n",
       "        [1, 0, 0, 1]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert from sparse to dense\n",
    "A.todense()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "More efficient way to create sparse matrices: create an empty matrix and populate with using matrix indexing (avoids creating a potentially large dense matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<type 'numpy.float64'>'\n",
       "\twith 6 stored elements in LInked List format>"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = lil_matrix((4,4)) # empty 4x4 sparse matrix\n",
    "A[0,0] = 1\n",
    "A[1,1] = 3\n",
    "A[2,2] = A[2,1] = 1\n",
    "A[3,3] = A[3,0] = 1\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Converting between different sparse matrix formats:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<type 'numpy.float64'>'\n",
       "\twith 6 stored elements in LInked List format>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<type 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = csr_matrix(A); A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<type 'numpy.float64'>'\n",
       "\twith 6 stored elements in Compressed Sparse Column format>"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = csc_matrix(A); A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute with sparse matrices like with dense matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  9.,  0.,  0.],\n",
       "        [ 0.,  4.,  1.,  0.],\n",
       "        [ 2.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(A * A).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  3.,  0.,  0.],\n",
       "        [ 0.,  1.,  1.,  0.],\n",
       "        [ 1.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.,  0.,  0.,  0.],\n",
       "        [ 0.,  9.,  0.,  0.],\n",
       "        [ 0.,  4.,  1.,  0.],\n",
       "        [ 2.,  0.,  0.,  1.]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(A).todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = array([1,2,3,4])[:,newaxis]; v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.],\n",
       "       [ 6.],\n",
       "       [ 5.],\n",
       "       [ 5.]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sparse matrix - dense vector multiplication\n",
    "A * v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.],\n",
       "        [ 6.],\n",
       "        [ 5.],\n",
       "        [ 5.]])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# same result with dense matrix - dense vector multiplcation\n",
    "A.todense() * v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Singular value decomposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Singular value decomposition is essentially trying to reduce a rank R  matrix to a rank K matrix. It means that we can take a list of R  unique vectors, and approximate them as a linear combination of K  unique vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more information about these svd , see e.g. https://en.wikipedia.org/wiki/Singular_value_decomposition\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "in python we can use svd function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function svd in module scipy.linalg.decomp_svd:\n",
      "\n",
      "svd(a, full_matrices=True, compute_uv=True, overwrite_a=False, check_finite=True, lapack_driver='gesdd')\n",
      "    Singular Value Decomposition.\n",
      "    \n",
      "    Factorizes the matrix a into two unitary matrices U and Vh, and\n",
      "    a 1-D array s of singular values (real, non-negative) such that\n",
      "    ``a == U*S*Vh``, where S is a suitably shaped matrix of zeros with\n",
      "    main diagonal s.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    a : (M, N) array_like\n",
      "        Matrix to decompose.\n",
      "    full_matrices : bool, optional\n",
      "        If True, `U` and `Vh` are of shape ``(M,M)``, ``(N,N)``.\n",
      "        If False, the shapes are ``(M,K)`` and ``(K,N)``, where\n",
      "        ``K = min(M,N)``.\n",
      "    compute_uv : bool, optional\n",
      "        Whether to compute also `U` and `Vh` in addition to `s`.\n",
      "        Default is True.\n",
      "    overwrite_a : bool, optional\n",
      "        Whether to overwrite `a`; may improve performance.\n",
      "        Default is False.\n",
      "    check_finite : bool, optional\n",
      "        Whether to check that the input matrix contains only finite numbers.\n",
      "        Disabling may give a performance gain, but may result in problems\n",
      "        (crashes, non-termination) if the inputs do contain infinities or NaNs.\n",
      "    lapack_driver : {'gesdd', 'gesvd'}, optional\n",
      "        Whether to use the more efficient divide-and-conquer approach\n",
      "        (``'gesdd'``) or general rectangular approach (``'gesvd'``)\n",
      "        to compute the SVD. MATLAB and Octave use the ``'gesvd'`` approach.\n",
      "        Default is ``'gesdd'``.\n",
      "    \n",
      "        .. versionadded:: 0.18\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    U : ndarray\n",
      "        Unitary matrix having left singular vectors as columns.\n",
      "        Of shape ``(M,M)`` or ``(M,K)``, depending on `full_matrices`.\n",
      "    s : ndarray\n",
      "        The singular values, sorted in non-increasing order.\n",
      "        Of shape (K,), with ``K = min(M, N)``.\n",
      "    Vh : ndarray\n",
      "        Unitary matrix having right singular vectors as rows.\n",
      "        Of shape ``(N,N)`` or ``(K,N)`` depending on `full_matrices`.\n",
      "    \n",
      "    For ``compute_uv=False``, only `s` is returned.\n",
      "    \n",
      "    Raises\n",
      "    ------\n",
      "    LinAlgError\n",
      "        If SVD computation does not converge.\n",
      "    \n",
      "    See also\n",
      "    --------\n",
      "    svdvals : Compute singular values of a matrix.\n",
      "    diagsvd : Construct the Sigma matrix, given the vector s.\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> from scipy import linalg\n",
      "    >>> a = np.random.randn(9, 6) + 1.j*np.random.randn(9, 6)\n",
      "    >>> U, s, Vh = linalg.svd(a)\n",
      "    >>> U.shape, Vh.shape, s.shape\n",
      "    ((9, 9), (6, 6), (6,))\n",
      "    \n",
      "    >>> U, s, Vh = linalg.svd(a, full_matrices=False)\n",
      "    >>> U.shape, Vh.shape, s.shape\n",
      "    ((9, 6), (6, 6), (6,))\n",
      "    >>> S = linalg.diagsvd(s, 6, 6)\n",
      "    >>> np.allclose(a, np.dot(U, np.dot(S, Vh)))\n",
      "    True\n",
      "    \n",
      "    >>> s2 = linalg.svd(a, compute_uv=False)\n",
      "    >>> np.allclose(s, s2)\n",
      "    True\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from scipy.linalg import svd\n",
    "help(svd) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Exercise 04 : Image compression using SVD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Images are represented in a rectangular array where each element corresponds to the grayscale value for that pixel. For coloured images we have a 3-dimensional array of size n×m×3, where n and m represent the number of pixels vertically and horizontally, respectively, and for each pixel we store the intensity for colours red, green and blue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use SVD to create a low-rank approximation for the larger matrix of image. Create low-rank approximation for each color of the image and using resulting 3-dimensional array we can reconstruct the original image."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a code segment to perform SVD and use this to create compress image. Use sample images in your current directory. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimization (finding minima or maxima of a function) is a large field in mathematics, and optimization of complicated functions or in many variables can be rather involved. Here we will only look at a few very simple cases. For a more detailed introduction to optimization with SciPy see: http://scipy-lectures.github.com/advanced/mathematical_optimization/index.html\n",
    "\n",
    "To use the optimization module in scipy first include the `optimize` module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding a minima"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first look at how to find the minima of a simple function of a single variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 4*x**3 + (x-2)**2 + x**4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uwFrNMb0UGLJcp05w110+aKe0NHY1IiLZ6557fJbZ3XfDEUfErib/KDDkgJIS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\nwCAiIiIp/T8710MLkde1IAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5e9dfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots()\n",
    "x = linspace(-5, 3, 100)\n",
    "ax.plot(x, f(x));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the `fmin_bfgs` function to find the minima of a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: -3.506641\n",
      "         Iterations: 5\n",
      "         Function evaluations: 24\n",
      "         Gradient evaluations: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-2.67298151])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_min = optimize.fmin_bfgs(f, -2)\n",
    "x_min "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 2.804988\n",
      "         Iterations: 3\n",
      "         Function evaluations: 27\n",
      "         Gradient evaluations: 9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.46961743])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fmin_bfgs(f, -0.79) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use the `brent` or `fminbound` functions. They have a bit different syntax and use different algorithms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46961743402759754"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.brent(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.6729822917513886"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fminbound(f, -4, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding a solution to a function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find the root for a function of the form $f(x) = 0$ we can use the `fsolve` function. It requires an initial guess: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "omega_c = 3.0\n",
    "def f(omega):\n",
    "    # a transcendental equation: resonance frequencies of a low-Q SQUID terminated microwave resonator\n",
    "    return tan(2*pi*omega) - omega_c/omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python2.7/site-packages/ipykernel/__main__.py:4: RuntimeWarning: divide by zero encountered in divide\n"
     ]
    },
    {
     "data": {
      "image/png": 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e4L0fvulMn96Q5W9zAZzvvc9O9GsnA57zYweTHxuWLgU2bmTyY0FNjSQ/V17J\nSSwLVq0C3nsPePZZoFEj7WgoCL16Abm5wIAB/B2PkoQnPwDgvR8AYEAQr5VsWPmxwXtpi9qcR/tG\nXlqaXJn8RN+0aTIgvvZa7UgoCH36SNLDvV02/PCDHGjaty9w4IHa0VA8seagzHsmPxYUFQEVFUx+\nLEhLA/bfn++1BUOGAG3bAqedph0JJVpWFvDuu3K4ZePG2tFQopWUyAG2xx0HPPSQdjQUb4FUfmjb\nqqvZLcaC7E2LPFu00I2DEi8tjVUfC8rLgeHD5cBDLl2Ovueek6rPAw9oR0JBePxxYPlyYPZsYHeO\nlCOHj2xlNTVMfixg8mOD90x+rPjqKyA/H4hzB1YKofnzZa/PM88Ae+6pHQ0l2tixQP/+stztiCO0\no6FEYPKjrLqas4YW5OTIlclPtGVlSaLL5Cf6Bg2S95mDo2jzXpa6HXqoVPko2rKygO7d5eyuHj20\no6FEYTFPGSs/NsQqP9wHEm3Tp8v1lFN046DEysoCvvgCePNN7Ugo0caMASZOBEaN4uGWUVdRAXTt\nKu/zhx9yYjrKmPwoY+XHhuxsoGlTfnhGXWqqHGS7zz7akVAivf8+UK8ecMMN2pFQIpWWAj17Al26\nAJdcoh0NJdpf/yod3r79FmjVSjsaSiQmP8pY+bEhO5tL3iyYPh3o1Ek7Ckqk6mpg4ECgWzfu/4i6\n558HVqwARo9mV9aoGzoUeP11qebyGR59rDkoY+XHBiY/0VdWBsyZA5x6qnYklEgjR8qA+J57tCOh\nRFqwAHjxReCpp4DDD9eOhhJp5kzgjjukeQn3ddnAYbcyVn5sYPITfbNnA5WVnDWMupdfBs48Ezjh\nBO1IKFGqq4G77pImB48/rh0NJVJmJnDppXKezzvvsMJnBZe9KWPlx4bsbODYY7WjoERKTQUaNACO\nOUY7EkqU6dPlfR41SjsSSqSXXgJmzACmTAHq1tWOhhIlLw+46CI5tHbkSKB+fe2IKChMfpSx8mMD\nKz/RN3UqcNJJPBAvyl5+GTjsMODii7UjoUSZOxfo1Us2v59+unY0lChlZcCVVwLr18ukBj+fbWHN\nQRkrPzZkZ7PNdZRVVUmHoM6dtSOhRFm2DPjsM+n+xWd2NJWVyb6PI44AevfWjoYSpbJSWlp//71U\nfNq1046IgsY5SmXV1az8RF1pKVBczJmlKEtLAwoKpCUuRdMLL8jv8M03a0dCidKzJ7B0KTBrFpe7\nRVV1tRwK6FF2AAAgAElEQVRiOnasJD6s7tnE5EdZTQ1nEaMudsApk5/omjgRaNgQOPFE7UgoEZYu\nBT74QPaCcF9ANH34IfDWW8C77wJHHaUdDSWC99LNbdgwYPhw4MILtSMiLUx+lLHyE31MfqJv0iTp\nALbHHtqRUCI895wcXMv21tE0f768t7feCtx+u3Y0lAg1NZL4vPuuTGRcfbV2RKSJNQdlrPxEH5Of\naCsvl2YHXPIWTQsXAh99JOe91KunHQ3FW36+DITbtZMDLtnqOHqqq4HbbpPEZ9AgWfZGtrHyo4yV\nn+hj8hNt06bJvq5zztGOhBLh6aeBAw5gRSCKqqqAG26QZ/TYsVzSGEVVVbJPb/hwYMgQeb+JmPwo\nY+Un+rKzZT8IP1ijacwYYN995ZA8ipbJk4HPPwf+8x8uaYwa74GHHgLGjwe++go45BDtiCjeysuB\nG2+UxgYffwxcc412RBQWTH6UsfITfWvWyOCYomnMGDn3hctloqWqCnj4YaBTJxlAUbS89howYADw\nzjvAuedqR0PxVlAg5/ikpgKffgpcdpl2RBQmTH6UsfITfVlZQOvW2lFQIixdCixeDLz4onYkFG8D\nB8pG+JkzmdhGzciRwCOPyEGmd96pHQ3F25o10sntl1+Ar78GzjhDOyIKGyY/ylj5ib6sLGD//bWj\noEQYM0aWQ7HZQbTk5spen1tuYfvyqJk0CbjuOmly0KePdjQUb4sXAxdcIAeZfvcd25bT1rHmoIyV\nn+jLygL22087CkqE0aOBs88GGjXSjoTi6ZFH5Nn8wgvakVA8ff+9LH866yzZ/M7P3mj5/nvgtNNk\nf21qKhMf2jb+6itj5SfavAdWr+aytyjKyQG++Qa46irtSCiexo+XAy9fflnO9qFo+PFHWQp13HHA\nZ58BdetqR0TxNHSoJLWHHSZHDxxwgHZEFGZMfpSx8hNt+fnSBpnJT/R8/rkkt1deqR0JxUtxMXD3\n3dK2/JZbtKOhePn5Z+C884C2bYEvvpDumxQNNTXAk09KU5KuXYGJE4G99tKOisKOe36UVVdzBirK\nsrLkyuQnev77X1ny1rKldiQUL489BqxbB0yYwCYHUbF4sSSzTZsC48bJlaKhqAj485+BUaOAvn2B\nRx/l720UZWbG/+9k8qOMlZ9oY/ITTTk5snG6f3/tSChevvhCWh8PGMAzX6Ji4UJpRrLXXlIR4ERF\ndGRmyv6tX36R5OeSS7QjokQYMUIOqY03DruVcc9PtMWSH57zEy2ffMIlb1Gydi1w220ygLrnHu1o\nKB5+/PHXyuw333D/VpRMmQKcdBJQUgJMn87EJ4pqaoBeveQz9pRT4v/3M/lRxspPtK1eDbRowdPh\no2bQINk83aqVdiT0e3kP3HqrPIffe4/LZqJgzhygc2c5YmDSJHkGUzS8+65U8446Ss7gOvJI7Ygo\n3goKgMsvB55/Xjpu9u0b/9fgsFsZKz/RxgNOo2fhQvnQvfVW7UgoHl59FRg7FvjgAy6LioJJk6Ti\nc8ghstRt7721I6J4qKoCHnoIuOsuOZh2/Hi+t1G0ZIlUer77Ts7R+9vfEjMhxeRHWU0Nk58oY/IT\nPR98IHsIuNQi+U2ZAvz1r8Bf/iIHI1Jy+/RTqch26iSJT7Nm2hFRPOTlARddBLz5pvwZMACoU0c7\nKoq3r76S5YyATDBeeGHiXovJj7Lqai57izImP9FSVQX85z/SVpVdGpNbVpa0xj3jDKBPH+1o6Pd6\n+23g2mvl3K3Ro3nwcFQsXgycfDIwa5ZUe+67TzsiijfvZWnbxRcDp58OzJgBtGuX2NfksFsZKz/R\nxuQnWsaOlc3xXPKW3MrLgWuukdnjYcOA3dn3NGl5D/zjH9KookcP4KOPuMcyKsaNk8Rn992lEnDO\nOdoRUbyVlMhk4uOPA088AYwcCTRpkvjX5SNfGSs/0VVRAaxfD+y3n3YkFC8DBwLHHgscf7x2JLSr\nvAfuv182xU+Zwn0+yayyErj3XmlU0bs38PTTbFgRBd4Dr78OPPKILEcdOjSYATEFKytL2pWnp8sk\nVNeuwb02kx9lbHgQXStWyEP8wAO1I6F4yMiQ8yTeeks7Evo9+vaVJHbQIJlVpuRUUCDVu2+/lX14\n3btrR0TxUFEhS9vee08OLe3Th2OkKJo3T5a5OQdMmwYcd1ywr8/kRxlbXUdX7FTigw7SjYPio39/\n2UB9003akdCuGjZMugc9/TRwyy3a0dCu+uUXGThlZcnSqM6dtSOieMjOBq6+Gvj+eya0Ufbll8B1\n18m+ntGjdVbHcNitjJWf6MrMlMT2gAO0I6Hfq6hIZiLvvBNo0EA7GtoV06bJYOqGG2SJFCWnWbOk\nFW5JCZCaysQnKhYskE5f6enA5MlMfKLq3/8GLr1U9m9NmaK3LYDJjzJWfqIrM1MO2WNLzuQ3eDBQ\nXCwbqin5/PyzHJp38snA++9zX0iyGjkSOPNMoG1b6QjVvr12RBQPY8YAp54KNG4M/PCD/DNFS02N\nHCtw333AAw8An30GNGyoFw+H3cpY+YmuzEwueYuC6mrZfHv11UCbNtrRUG2tWgWcey7QvDnw+eds\nUZ6MvJfDaK+8Upa7TZ7MRhVR4D3wyitSCejcWaqzbdtqR0XxVlkpHVJffhl47TX5XdYe93LPjzJW\nfqIrMxM44gjtKOj3+vRTqRwMGaIdCdVWdrYkPt4DX38th9NScqmqAnr2lD13jz0GvPACPzOjoKJC\nOvW9/768r//8p/6AmOKvtFT293z1lbSh79ZNOyLB5EcZKz/RlZkps5SUvGpq5AyR88779eRpSg75\n+cD558vp8N99x6pdMiosBK6/Xg63fOst4O67tSOieMjPlypeaiobG0RZQYFU9WbNkk6pF16oHdGv\nmPwoY+UnmjZulFlnLntLbqNGAT/+CAwYoB0J1UZxMXDJJTIB8e23wB//qB0R1daKFfIerlghs8bn\nnqsdEcXDypUyCF69GpgwATjjDO2IKBHy8mTScOlSeZ/Dto+LyY8yVn6iiW2uk5/3wN//Dpx9NnD6\n6drR0M6KJT5z58qH7jHHaEdEtTVzphx+2KCBVAe4fDga5s8HLroI2H132d/DhhXRlJ8viU9GBjBp\nUjgPBWfNQRkrP9HE5Cf5ffEFMGcO0KuXdiS0szZulFnlWbOAsWOlJTIll08+Ac46Czj4YOnoxsQn\nGiZOlCpPy5bA9OlMfKIqlvgsWyaTT2FMfAAmP+pY+YmmzEzpKrXvvtqR0K6orgaeeEI6EPEckeRQ\nVARccIFUfMaNY7Uu2XgvzQyuvVb2g0yaxI5uUTF8uExKdOoky1D5uRhNBQWyz3LpUkl2w5r4AEx+\n1LHyE02ZmdKyk+9tcvrwQ+Cnn4C+fXkmTDIoLJQP3R9/lM3xYVtfTttXUQHcdhvw5JPAM89IV6h6\n9bSjonh4/33p8NW1KzB6tJzlQ9FTWirLjX/+OfyJD8A9P+pY+YmmxYuBww7TjoJ2RWkp8H//J+05\nTzhBOxrakYICqfgsWiTtrNmVL7ls2ABcdZUshRoyBLjxRu2IKF5eew14+GHgnnuAN9/kZGBUVVVJ\nV8bZs8O7x2dLvBWVsfITTenpwOGHa0dBu+K114B164Dnn9eOhHYkN1e6gKWny/pyJj7JJSNDlkL9\n9JPMFjPxiQbv5YiAhx8GHn1UumVynBNN3ktyO2aM7NdLln2WvB2VsfITPaWlwC+/MPlJRqtWyYd2\njx7AIYdoR0Pbk5UFnHkmsHy5zDaySpdcZs+WxMd7aWzAPVrR8Y9/SKOY3r25dDjqnnsOeO89Wd54\n0UXa0ew8Jj/KWPmJnp9/lg90LntLPn/5C9CoEfDss9qR0PYsXQqcdpo0OZg6NTmWWdCvxo2Tjm4H\nHigtjznREB19+8qy4VgCxMQnuoYPl+Tn+eeBm2/WjqZ2OOxWxspP9KSny5WVn+QyYYI8zF96CWjS\nRDsa2pb586VKUK+eDJzbtdOOiGrjww9lY3TnzlKxa9FCOyKKl9dfBx5/HHj6aeCpp7SjoURKSwNu\nuUX2+jzxhHY0tcfkRxkrP9GzeDHQvDmw997akdDOqqgA7r9fzqHgvoPwSk2VikHr1sB33wFt2mhH\nRDvLe6BPH6B7dxk0ff450LChdlQUL++8Azz0kOzx6d1bOxpKpHXrgMsvlzO43nsvOat7CRl2O+fa\nOucGOucynHMlzrmfnXPPOufqJOL1khkrP9GTns4lb8nmlVdkKdWbbybng9yCceOkucExxwCTJ7Ni\nkEy8B3r2lBniZ5+VgfLu7DUbGZ98IpveH3iAe3yirqpK2pZXVAAjRgANGmhHtGsS9fg5HIADcCeA\nZQCOAjAQQAMAjyXoNZMSKz/Rk57OPQjJZPFiWbf80EPA0UdrR0Nb89//SkXu/PNlaWL9+toR0c6q\nrpaB8cCB0vXr3nu1I6J4mjoVuOkmWf706qtMfKKud295zydPBvbfXzuaXZeQYbf3fpz3/nbv/UTv\n/XLv/RcAXgJwVSJeL1l5L8kPKz/R4b0MprnfJzlUV8vhivvvD/z979rR0NYMHCgDq65dgc8+Y+KT\nTKqqZCP0++8Dgwcz8Yma9HTgssuka9+gQZzIjbpJk6SRxXPPSafNZBZk4bkpgA0Bvl7o1dTIlQ+M\n6Fi1Cigu5rK3ZPH663K44rffJm/5Pqq8B158UZZK9egh7xWflcmjvBzo1g0YPRoYNgy45hrtiCie\n1q8HLrwQ2G8/2b9Vt652RJRIublS4TvnnORscLClQJIf59yhAO4H8EgQr5csYskPKz/R8eOPcuXy\nqfD7+WfgySeBBx+URgcUHjU1wF//KnuxnnlG/nA5TfIoLQWuukqWxowYAVx8sXZEFE9VVcB11wEl\nJTJx1LSpdkSUaA88AJSVAf/5TzTGrLVKfpxzLwB4fDvf4gG0994v2exnWgP4CsAw7/37O/M6PXv2\nRJMtes1269YN3bp1q024oVddLVfOZkbHvHnAnnsCbdtqR0LbU1UlHadat5YzCig8qqqAO+6QZVJv\nvCFd+Ch5lJcDV18tg+IxY4AuXbQjonh77DHZ9zFxInDAAdrRUKJ99hmQkgJ89BGw776Jfa2UlBSk\npKT85msFBQVxf53aVn5eAjBoB9+TEfsH59x+ACYBmOq9v3tnX6Rfv37o0KFDLUNLPqz8RM/8+dKN\nirPU4fb3v8up8lOmsN1umJSWyv6eL7+UD9obbtCOiGqjqkqWuk2aJMvdmPhEz0cfAf36ycREsu/7\noB3LyZGGJVdeKb/biba1QsecOXPQsWPHuL5OrZIf730ugNyd+d5NFZ9JAH4AcFvtQ4s+Vn6iZ/58\nObyPwuvbb2XT5rPPAqedph0NxRQUyObpH34ARo2S/QSUPKqr5Qyf0aNlD8i552pHRPH244/AnXdK\nE4sePbSjoSA89phMavz739Ga1E3UOT/7AvgGwApIa+uWzrlWzrlWiXi9ZMXKT7SUlUmnt2OO0Y6E\ntiW2afOMM2S/D4XDunXA2WfL5MGECUx8ko33wN13Ax9/LMtjLrlEOyKKt1hV9tBDgbfeitZAmLZu\n+nTp4vfCC0CriI3eE9Xw4DwAB2/6s3LT1xxkTxCH+puw8hMtCxfKe8rkJ5y8l70kJSXAkCGcdAiL\nzEypEpSUyDJENgtJPr16yUnvH37Irm5R9eijQEYGMGsW281bUF0t1b2OHeVzM2oSkvx47wcDGJyI\nvztKWPmJlnnzZDbsqKO0I6Gt+fe/pfPUiBHJfThblPz4oxxc2rAhMG0acNBB2hFRbb39tjQN+de/\ngD//WTsaSoTRo+WA2gEDgCOP1I6GgvD228DcubI3NopjVNYcFLHyEy3z5wOHHAI0aqQdCW3p+++B\nnj1lJuvyy7WjIUD29px1liynmDqViU8y+uIL4L77pA3uX/6iHQ0lQl4ecNdd0q78nnu0o6EgFBXJ\n8QK33AKcdJJ2NInBYbciVn6iZc4c4LjjtKOgLa1fL613O3SQc2NI37Rp0gns8MPlLJiorSe3IC1N\nznq5/HLp/sU9INH06KOyJPXtt/keW9GvnyRAzz2nHUniMPlRxMpPdFRXA7NnAyeeqB0JbS52GF9l\nJfDJJ8Aee2hHRJMmAeedJ2vJx4/nAYnJKDsbuOIKoH17aX3MCbxo+vpr4P33gZdekjPRKPpycuT9\n7tEDaNNGO5rESVTDA9oJrPxEx6JFQHFxdEvEyepvfwO++04G3Pzw1jd2rJwXceaZ0g65QQPtiKi2\nKitlQqG0VN5Dbn6PptJS6eDXuXM0N7zT1r3wglyfeEI3jkRj8qOIlZ/o+OEHWRIQ53O46HcYNgx4\n+WUp4fMwPn0jRgBdu0ob6+HDgbp1tSOiXfHXv8qEwsSJ0Z4Ztu7ll4FVq2TCgsvdbFi3DnjzTUl8\nmjfXjiaxOOxWxMpPdPzwgywBadxYOxICpB3rrbcCN9wAPPSQdjT06afSAvmKK2T5IROf5DRsGPDa\na/KHEwrRtWqVVAAeegho1047GgrKG28AdeoADz6oHUniMflRxMpPdMycyf0+YZGVBVx2mZy3NHAg\nZy21jRolhyN27QoMHSofrpR8li+Xrl/XXw/ce692NJRIjz8uE3m9emlHQkHZuFFamd95J9CsmXY0\nicdhtyJWfqKhrEzaXDP50VdSIonP7rvLMivuR9A1dixw7bXSEezDD+V9oeRTVQXceCOw117AW29x\nQiHKvv9eJileeAHYc0/taCgo770HFBYCDz+sHUkw+FGkiJWfaJg7VzYBs9mBrpoaoHt3YPFiaaW8\nzz7aEdk2caIsc7vgAhlMMfFJXv/4hwyKp0wBmjTRjoYS6emn5aDu7t21I6GgVFbKMRDdugEHHKAd\nTTD4caSIlZ9omDZNKgw840fXM8/I3pLPPweOPVY7GtumTAEuvRQ45xxpbsAW48krNRX4+9+BZ58F\nTj1VOxpKpClTgAkT5DnKSVk7PvsMWLFCznSygsmPIlZ+omHqVOCUU7iXQdPgwTI7/eKLssSK9MyZ\nI6fBn3aaDKLY3CB5lZUBt90mVe0nn9SOhhLJe+D//k8m8a64QjsaCtJbb0kDE0uThkx+FLHyk/y8\nl+SHG4D1jBsn51DccYe04SU9y5ZJK+sjjuAZMFHwj38AGRlAWho/p6Ju0iTg22+lQQknZO1YvBj4\n5htgyBDtSILFW1xRrPLDD5XktWSJnIh8+unakdg0ezZw9dWyr+Tf/+ZGbE3r1gHnnw80bQqMGQM0\naqQdEf0e8+dLJfWpp4Ajj9SOhhLthRfknLpLLtGOhIL0zjvA3nvL56glrPwo4rK35Dd1qrx/p5yi\nHYk9GRnARRfJwOzjj7mhXlNRkbwXxcWyRyTqB+RFXU0NcPfdwGGHRf+kdwLmzZMGJSkpnECypLJS\nunDefDNQr552NMHicEERl70lv6lTZZ0sW4IGKydHqj177gl88QXQsKF2RHZVVUk766VLZcP0QQdp\nR0S/19ChwIwZwOTJbFZhwauvAm3a2Jv9t27cOPksveUW7UiCx5qDIlZ+kpv3slb2jDO0I7GlpESW\nZhQUyDkyLVpoR2TbI4/IrPFnn9naMBtVGzfKIZfXXAOcfbZ2NJRoa9dKsvvAA2zaY82QIcDRR8uB\n4NZw2K2IlZ/ktmyZnHr+pz9pR2JHVZWcRbBggewrOeQQ7Yhse/tt4I035E+XLtrRUDz06QNs2AD8\n61/akVAQBgyQpOfOO7UjoSAVFgIjR8rhxRZx2ZsiVn6S24QJkrhydjQY3gM9ekjSM3o0cMIJ2hHZ\nNnkycP/98ueee7SjoXhYtQp46SXpmnjggdrRUKJVVEib41tvlUYlZMeIEdLK/oYbtCPRweRHUSz5\n4Ubt5DRhgjQ6aNxYOxIbnn9eOtO8/760UyY9K1bIPp+zzwb69dOOhuLl+eelSx9bxtswejSQnc3J\nC4s+/VQOLW7TRjsSHaw5KKqqkiuXvSWf6mo5F4FL3oIxaBDQq5ecNH/rrdrR2FZRAXTtKoPkYcM4\neRMVy5cD770HPPYYG7hYMXCgTOCxlbktxcXA+PHAlVdqR6KHH1uKWPlJXnPmAHl5wLnnakcSfV99\nJevR775bzhwhXY89Jvf/1KnAXntpR0Px8ve/A82aydJSir6VK6Xb1zvvaEdCQRs7Vpa8MfkhFaz8\nJK+vv5blbiedpB1JtP3wg3SduvhioH9/nkGh7b//BV57TRoc8N6PjqVLgcGDZb8P28bb8J//APXr\nA9ddpx0JBW3ECOnyZrlhEJe9KWLlJ3lNmCD7HdgaNHGWLZOk55hj5PA9/p7oWr4cuP12WfLG6kC0\nvPyynPJ+993akVBQUlKAK67gnlVrqqrkbLwrrtCORBeTH0Wxyg8HdcmlpASYNo37fRIpO1sOMW3a\nVDblNmigHZFtNTVA9+6yLOqdd1iBi5KcHKn63H+/VAIo+hYskD/XX68dCQXt+++B/HyZWLSMw25F\nXPaWnCZMkE3fF1ygHUk0FRfLIaZFRUBqKtC8uXZE1K8fMGWKtLdu0kQ7Goqnt96SNvL33qsdCQVl\n2DCZWDrvPO1IKGjjx8sklvWjIpj8KOKyt+Q0ahRw2GFAu3bakURPVZXMRv70E/Dtt8DBB2tHRAsW\nAE8+CfTsyTOtoqa8XPbSde/OSQYrvAc+/hi4+mqgbl3taCho48bJqhXrk+5c9qaIlZ/kU1Mjy7Au\nv1w7kuiJHWL61VdyBkHHjtoRUWUlcPPNwKGHAv/8p3Y0FG8pKcC6dcDDD2tHQkH56SdpcHHNNdqR\nUNA2bJAmQuefrx2JPtYcFMUqP39gCpo0Zs4E1q8HLrtMO5Lo+ec/fz3ElA/ncHjlFWDePLnv69XT\njobirX9/4KKLgMMP146EgjJqlJzR1bmzdiQUtEmTZAKXyx2Z/KiqqpIlb9w8nDxGjZLlIaecoh1J\ntAweDDz9NPDcczzENCwyM+X9eOghVuGiKC0NmD0bGDlSOxIK0qhRMrnEJW/2TJggS/bbtNGORB9r\nDoqqq7nkLdmMHCmb8fm+xc/XXwN33CF/evXSjoYAWYJ4//3S/rh3b+1oKBHefRfYd1+p/JANa9dK\nty+uXLBp6lTgrLO0owgHJj+KYpUfSg5LlwILF/KDI57mzpWNt+edB/z736yChsXnnwNffimHmTZq\npB0NxVtJCfDRR1Jl5WeQHWPGyDJ7Jrz25ObKfq/TT9eOJByY/CiqqmIFIZmMHClLBc49VzuSaPjl\nF/kQbtdOWq9yEBYO5eXAo48CF17Ig/CiauRIoLAQuO027UgoSGPHAiefzM5+FqWmyvWMM3TjCAsO\nNxRVV3PAl0yGDZPBOmfCf7+8PBlc16sns5H8bxoeb7wBrFghp4BTNA0dKvsWDzlEOxIKSk2NbHjv\n0UM7EtLw3XdA69ZA27bakYQDKz+KWPlJHhkZ0iKya1ftSJJfZaUsdVu3TmYiW7XSjohicnKAf/wD\nuOsu4IgjtKOhRMjNld+7G27QjoSCNHeutDr+05+0IyENU6dK1YdLywWTH0Ws/CSP4cOB+vWl2QHt\nOu+B++6TB/Hnn/Og2LDp3Vveo2ef1Y6EEuXTT6UKwIkcWyZMABo0YKdSi0pLgVmzuN9nc0x+FLHh\nQfIYNkwSHy7P+n369QMGDpTzfM48Uzsa2tzKlcBbbwGPPw60bKkdDSXKxx8DXbqw4mrNxInyzN1j\nD+1IKGhz58qKCya+v2Lyo4itrpPDkiXy8LjuOu1Iktvo0bKR/vHHgVtu0Y6GtvTCC8CeewIPPKAd\nCSVKbi7w7bey7JTsKC+XPR9dumhHQhpmz5ak9+ijtSMJDyY/ilj5SQ7DhknFh+1Bd928eUC3bsDl\nlwP//Kd2NLSllSulIvfoo0DjxtrRUKKMGSNL3tiu35bZs2XpE894sWn2bEl8WPX7FZMfRWx4EH7e\nAykpMlioX187muS0di1w6aWyv2fIEDlngsIlVvVhJ6hoGzlSWh3vu692JBSk6dPl8+u447QjIQ2z\nZwMdO2pHES4chihiw4PwmzULWLQIuPlm7UiSU3m5nBVTVQWMGgU0bKgdEW1p9WpWfSwoLZUub5df\nrh0JBS01FTjpJKBOHe1IKGilpXI4O5Of32Lyo4jL3sJv8GBgv/3YHnRXPfggkJYGjBgB7L+/djS0\nNW++Kect3XefdiSUSJMnAyUlTH6s8V6Sn1NP1Y6ENMybJxPtTH5+i8mPIjY8CLfycjkM8M9/5vu0\nK2Jd3QYMkFlHCp+SEuDtt4Hbb5dlbxRd48YBBxwAtG+vHQkFaflyWXrM5MemWLODo47SjiRcmPwo\nYuUn3L74AsjLA7p3144k+cycKftH7rpLBtYUTkOGyMGH7PAWfV9/DZx3Hg85tGb6dLmyzbFNc+ZI\n4lO3rnYk4cLkRxErP+E2eDBw4omcKa2t9eulle7xxwOvv64dDW2L98Crr8oyqIMP1o6GEmnVKtm7\neO652pFQ0FJTpdlM8+bakZCGBQuAY47RjiJ8mPwoYuUnvNatA776ilWf2qqqAq6/HqioAD75hLNN\nYfb11zIgfvhh7Ugo0b7+Wio+POfFntmzZRKP7PFemh0ccYR2JOHD5EcRk5/wev996Yxzww3akSSX\nXr2AKVOA4cPZ4CDs3nlHlkOceaZ2JJRoX38tG5733ls7EgpSdTUwf75U4cmelSuBjRuBI4/UjiR8\nmPwo4rK3cKqpkYHhddcBzZppR5M8xo8H+vSRQ0x5mF645eZK6/HbbuMekKjzHpg0iR0rLVqyRJqa\nMPmx6aef5MrKz/9i8qOIlZ9wGj9eOuTcfbd2JMlj7Vrpinf++XJeDIXb0KEyKL7pJu1IKNGWLZNl\nvKzw2TN3rlx5uKlNCxcCDRpIl0f6LSY/ilj5Cae33waOPVZOQqcdq6mRxMc5aRLxBz5VQm/QIOCS\nS4AWLbQjoUSbOlV+Nzt10o6EgpaWJgPfvfbSjoQ0/PSTVH34mfy/+J9EESs/4ZOVBYweLVUfLgfa\nOfcoLO0AABEySURBVH37AhMnStvkVq20o6EdmTdPBkW33qodCQVh2jTZ29W0qXYkFLS0NC55s4zN\nDraNyY+i6momP2Hz3nty2v2NN2pHkhxmzACefhr429+4pyBZfPAB0LIlcOGF2pFQEKZOBU47TTsK\nCpr3kvxwyZtNsU5vbHawdQlPfpxzezjn5jrnapxz7Da+maoqLnsLk6oq4N13pcMbT7vfseJi4Oab\npYvUc89pR0M7o7oa+Phjucfr1NGOhhItJwdITwdOP107EgpaVpY0NmHlx6ZVq4CiIlZ+tiWIyk9f\nAKsA+ABeK6lw2Vu4fPGFPDDY6GDnPPGEtNIcPJgD6WQxbZo0p+jaVTsSCkJqqlyZ/NizYIFcjz5a\nNw7SsWSJXA87TDeOsEpo8uOcuxDAuQAeBcAdFFtgw4NwefVV4NRTpZJB2zdxIvDGG9La+vDDtaOh\nnfXJJ0Dr1mzmYcXMmcA++7Dbk0Xp6bKEu21b7UhIQ0aGNDrg+791Cas7OOdaAXgHwGUAShP1OsmM\nlZ/wmDsX+PZbYNgw7UjCr6BAzoc5+2zggQe0o6GdVVMDfPopcO217P5jxezZMpnD5i32pKfLrD8n\nWG1atgxo0wbYYw/tSMIpkR+BgwAM8N6nJfA1khorP+Hx+uvyoLjqKu1Iwu+xx4ANG6RdMgfRyWP6\ndGD1auCaa7QjoSB4/2vyQ/akp7Mqb1lGBnDIIdpRhFet6g7OuRcAPL6db/EA2gO4AEBjAC/GfrQ2\nr9OzZ080adLkN1/r1q0bunXrVpu/JvRY+QmH9evl0MfnnuP7sSNTpwLvvAP07w8ceKB2NFQbo0fL\nuT6nnqodCQUhKwvIzgY6dNCOhDQsWiTVebIpIyM5m12kpKQgJSXlN18rKCiI++vUdqj3EqSisz2Z\nADoDOAVAufttvX2Wc+4j7/12T5jo168fOhh4YrPVdTi8/bZUMO68UzuScCsvB+66S/aL3HOPdjRU\nW19+Ke2tWa2zYfZsubLyY8+GDTKpx8qPXcuWAVdfrR1F7W2t0DFnzhx0jPODrFZDb+99LoDcHX2f\nc+4BAE9t9qX9AIwD0BXAzNq8ZpSx1bW+igpgwADgz3/mKdg70rcv8PPPMqjifZtcVqwAfvxRzmQi\nG+bMkUpf69bakVDQFi+Wa/v2unGQjrw8ID+fy962JyF1B+/9qs3/3TlXDFn6luG9X52I10xGXPam\nb9gwaf374IPakYTbkiXA888Djz4KHMPTupLOl19KwnreedqRUFDY7MCu9HR53//4R+1ISENGhlwP\nPlg3jjALcgEEz/nZAhse6PJeqhkXXcRTkLfHe+nq1ro10KuXdjS0K778EjjtNKBpU+1IKChz5nC/\nj1Xp6dLiuEED7UhIA5OfHQuk7uC9/wUAh/lbYOVH19ixchBc//7akYTbmDHA+PHAiBH8ME1GlZXA\npElc8mZJTg6wZg2rtFax05tty5bJRBeX8m8bt74qYsMDXX37AiedBJx5pnYk4VVRATzyCNClC3DZ\nZdrR0K6YNQsoLgbOOUc7EgrKokVyZUXbpqVLueTNsowMVn12hENvRWx4oGfmTOCbb+TEe66J37b+\n/WUW6dNP+d8pWU2aBDRuzCVQlixcKJ8tHADb4z2wfDmPIrAsIwM46CDtKMKNlR9FrPzo+de/gEMP\nBa64QjuS8MrOBnr3Bu6+Gzj6aO1oaFdNnizVTT5r7Fi4UJ5vdetqR0JBy8kBSkqY/Fi2ahVwwAHa\nUYQbkx9FrPzoWLpUKhmPPsr//tvzzDNS7endWzsS2lXl5cC0aUDnztqRUJAWLgSOOEI7CtKQmSlX\nzvzblZXFFvc7wuRHERse6Hj5ZTn/4uabtSMJr2XLgHffBZ58EmjeXDsa2lXffw+UlTH5sYbJj13L\nl8uVlR+bCguBjRuZ/OwIkx9FXPYWvHXrgA8+kHN96tfXjia8nn0WaNkSuP9+7Ujo9/juO6BJE+DY\nY7UjoaDk5wOrVzP5sSozU37nmzXTjoQ0ZGXJlcnP9nHorYjL3oL3yitAnTrAvfdqRxJeCxYAH30E\nvPkmE8RkN2MGcPLJfM5YEuv0xuTHJjY7sI3Jz85h5UcRKz/BysmRAf3997P//fb06iUfnrffrh0J\n/R7eS/JzyinakVCQFi6UvXqHHaYdCWlg8mNbLPnZbz/dOMKOyY8iVn6C9eqrMiDs2VM7kvCaO1cO\nM33mGWCPPbSjod8jI0MSfiY/tqSny+CXVVubMjPZ7MCyVauAvfcG6tXTjiTcmPwoqamRKys/wcjP\nB954A7jvPml2QFvXp48MnG68UTsS+r2mT5frSSfpxkHBysiQNtdkj/fAL7+w8mMZO73tHCY/Sqqq\n5MrKTzBefx2oqAD+8hftSMJryRJg+HDg8ceZlEfBjBlAu3YyC0h28HR3u9aule6OTH7sYvKzc5j8\nKIklP3Xq6MZhQWGhLHm76y5gn320owmvvn2BVq2AW27RjoTigft97PGeyY9lsTbXXPZmV1YWsP/+\n2lGEH5MfJZWVcuUMe+K9+SZQXAw89ph2JOG1ahXw4YfAI49wrXAUlJcD8+ZJpzeyY8MGmexh8mPT\nihVybdNGNw7Sw8rPzmHyoySW/LDyk1jFxdLe+vbb+UDYnv79gQYNgHvu0Y6E4mHhQqkuH3+8diQU\npGXL5HrIIbpxkI41a2TyqmlT7UhIQ2WlnGXIsc6OMflRwuQnGG+9Jc0OHn9cO5LwKi0F3n1XEsTG\njbWjoXiYO1faHR99tHYkFKSMDLmy8mPTmjXS4tg57UhIw9q1svSVyc+OMflRwuQn8UpLgX/9C+je\nHWjbVjua8Bo6FMjLA3r00I6E4mXePOn41aiRdiQUpIwMOcOsSRPtSEjD6tXAvvtqR0FaeMDpzmPy\noyTW8IB7fhLn3XflnJMnntCOJLy8l054l1zC2eIomTsXOPZY7SgoaGx2YFus8kM2rVkjVybAO8bk\nRwkrP4lVXi7dy268kevft2fKFGD+fODBB7UjoXjxXio/xx2nHQkFjcmPbWvWcOBrWXY28Ic/SPWX\nto/JjxImP4k1aJAsAXjySe1Iwq1/f6B9e6BLF+1IKF5WrpR9bqz82MPkxzYmP7ZlZ0viw/Mjd4zJ\njxImP9uWkpLyu36+shLo0we47jrgsMPiFFQE5eQAI0cCd94Zvg2yv/cesGzuXLkme/LDe6B2Kiok\n8Y1a8sP7YOeUlsrezSgue+M9sHNycoAWLbSjSA5MfpTwkNNt+70Puv/8B/jlF+Cpp+IUUEQNHSpL\npG66STuS/8UPu103bx7QrFnyH3THe6B2srKAmproNXfhfbBz1q6VaxQrP7wHdk52NtC8uXYUyYHJ\njxIecpoYVVXA888DV18NHHWUdjThNmgQcOmlnCmKmkWLgCOPDF81jxKLnZ5s42Z3ys7m5/nOYvKj\nhMveEiMlRda9P/20diThlpYmy6NuvVU7Eoq3xYuBww/XjoKCxuTHttWr5RrFZW+0c7jsbecx+VHC\n5Cf+qqul6nPppex0tSODBgGtWgEXXqgdCcWT95L8cK+bPVlZQIMGPOPHqjVrgLp1Zckr2cRlbzsv\nbIuu6gHAokWLtONIuPT0X68bNujGEjYFBQWYM2dOrX9u/HgZ+D31FLALP25GVRUweDBw+eXS5jqM\ndvUesG7dOqC4WJbTJvt/Pt4DtZOWBuy9t1yjhPfBzklLk8Qnau8/wHtgZ61fD5SVJf+zf0ub5QT1\n4vV3Ou99vP6u3805dwOAj7TjICIiIiKi0LjRez80Hn9R2JKfvQGcD2A5gDLdaIiIiIiISFE9AAcC\nGOe9z43HXxiq5IeIiIiIiChR2PCAiIiIiIhMYPJDREREREQmMPkhIiIiIiITmPwQEREREZEJTH6I\niIiIiMiEwJMf51wP51ymc67UOTfDOXfiDr7/Wufcok3fP885xzPpk1xt7gHnXHfnXI1zrnrTtcY5\nVxJkvBRfzrkznHOjnHNZm97Py3biZ852zs12zpU555Y457oHESslRm3vAefcWZv9/tds9kxoGVTM\nFF/OuSecczOdc4XOuXXOuc+dc+124uc4JoiIXbkHOCaIFufcPZt+jws2/Ul1zl2wg5/53c+AQJMf\n59x1AF4G8AyA4wHMAzDOOdd8G9/fCcBQAO8COA7ACAAjnHNHBBMxxVtt74FNCgDss9mftomOkxKq\nIYC5AHoA2GGvfefcgQC+ADARwLEAXgMw0Dl3buJCpASr1T2wiQfwR/z6HNjXe78+MeFRAM4A8AaA\nkwH8CUAdAOOdc/W39QMcE0ROre+BTTgmiI6VAB4H0HHTn0kARjrn2m/tm+P1DAj0nB/n3AwA33vv\nH9r07w7yf/x1733frXz/xwAaeO8v2+xr0wGkee/vCyhsiqNduAe6A+jnvd8r2EgpCM65GgBXeO9H\nbed7XgRwoff+mM2+lgKgiff+ogDCpATayXvgLMiHYjPvfWFgwVFgNk2ArQdwpvd+6ja+h2OCCNvJ\ne4BjgohzzuUCeNR7P2gr/1tcngGBVX6cc3UgWd3E2Ne8ZF4TAHTaxo912vS/b27cdr6fQmwX7wEA\naOScW+6cW+Gc4yyfPaeAzwECHIC5zrnVzrnxzrlTtQOiuGoKqe5t2M73cEwQbTtzDwAcE0SSc+4P\nzrnrATQAMH0b3xaXZ0CQy96aA9gNwLotvr4OUrbcmn1q+f0UbrtyDywGcBuAywDcCLlnU51zrRMV\nJIXOtp4Dezrn6irEQ8FbA+BuAFcDuApSLf7GOXecalQUF5tWALwKYKr3fuF2vpVjgoiqxT3AMUHE\nOOeOcs4VASgHMADAld779G18e1yeAbvXOsr4c9j5Nd+78v0Uftt8T733MwDM+P/fKOXNRQDuguwb\nIpvcpiufBQZ475cAWLLZl2Y45w4B0BMAm18kvwEAjgBw2i78LMcE0bBT9wDHBJGUDtnP2xQywfWh\nc+7M7SRAW6r1MyDIyk8OgGoArbb4ekv8bxYXs7aW30/htiv3wG9476sApAE4NL6hUYht6zlQ6L2v\nUIiHwmEm+BxIes65/gAuAnC2937NDr6dY4IIquU98BscEyQ/732V9z7Dez/He/8UpBHWQ9v49rg8\nAwJLfrz3lQBmA+gS+9qmMmcXAKnb+LHpm3//Judi22sBKcR28R74DefcHwAcBVkGQzZs7TlwHvgc\nsO448DmQ1DYNei8H0Nl7v2InfoRjgojZhXtgy5/nmCB6/gBgW0va4/IMCHrZ2ysABjvnZkNm7XpC\nNjZ9AADOuQ8BrPLeP7np+18D8K1z7hEAYwB0g2yYvzPguCl+anUPOOd6QUrcSyEl0ccgbS0HBh45\nxYVzriFkli62dO1g59yxADZ471c6514AsJ/3Prac6S0A92/q+vY+5MF3DWSmkJJQbe8B59xDADIB\n/ASgHuQzoDPkQ4+SkHNuAOQz/TIAxc652Gxugfe+bNP3DAaQxTFBNO3KPcAxQbQ4554H8BVkH2dj\nyD6usyATnAnLCwJNfrz3wze1MuwNKVvNBXC+9z5707fsD6Bqs++f7pzrBuD5TX9+BnD5DjbDUYjV\n9h4A0AzAO5DNbHmQylGnWqwFpfA5AcBkyBpdDzn3CQAGQzay7gOgTeybvffLnXMXQxLnBwGsAnC7\n937Lji+UPGp1DwDYY9P37AegBMB8AF2891OCCpji7h7Ie//NFl+/FcCHm/65DWSpNACOCSKo1vcA\nOCaImlaQ93pfyPlN8wGc572ftOl/T0heEOg5P0RERERERFqCbHhARERERESkhskPERERERGZwOSH\niIiIiIhMYPJDREREREQmMPkhIiIiIiITmPwQEREREZEJTH6IiIiIiMgEJj9ERERERGQCkx8iIiIi\nIjKByQ8REREREZnA5IeIiIiIiEz4f4hgKGq6E5+FAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x53c9590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots(figsize=(10,4))\n",
    "x = linspace(0, 3, 1000)\n",
    "y = f(x)\n",
    "mask = where(abs(y) > 50)\n",
    "x[mask] = y[mask] = NaN # get rid of vertical line when the function flip sign\n",
    "ax.plot(x, y)\n",
    "ax.plot([0, 3], [0, 0], 'k')\n",
    "ax.set_ylim(-5,5);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.23743014])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.75000001])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 0.75000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.18990285])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize.fsolve(f, 1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interpolation is simple and convenient in scipy: The `interp1d` function, when given arrays describing X and Y data, returns and object that behaves like a function that can be called for an arbitrary value of x (in the range covered by X), and it returns the corresponding interpolated y value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = arange(0, 10)  \n",
    "x = linspace(0, 9, 100)\n",
    "\n",
    "y_meas = f(n) + 0.1 * randn(len(n)) # simulate measurement with noise\n",
    "y_real = f(x)\n",
    "\n",
    "linear_interpolation = interp1d(n, y_meas)\n",
    "y_interp1 = linear_interpolation(x)\n",
    "\n",
    "cubic_interpolation = interp1d(n, y_meas, kind='cubic')\n",
    "y_interp2 = cubic_interpolation(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/SHsCqnaHvKsol70c/8v/PwZ1GcSePXusTVKmTMnAgQNp37499k+6dWyxmHdb/stdmif9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BB+fn7Mnj07yX5X165dS1dmDw8PtNYJth8XF8c333yTrvWBcYS+q1evMn369GTnsbGxAVJ3rAID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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x65e5e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,4))\n",
    "ax.plot(n, y_meas, 'bs', label='noisy data')\n",
    "ax.plot(x, y_real, 'k', lw=2, label='true function')\n",
    "ax.plot(x, y_interp1, 'r', label='linear interp')\n",
    "ax.plot(x, y_interp2, 'g', label='cubic interp')\n",
    "ax.legend(loc=3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `scipy.stats` module contains a large number of statistical distributions, statistical functions and tests. For a complete documentation of its features, see http://docs.scipy.org/doc/scipy/reference/stats.html.\n",
    "\n",
    "There is also a very powerful python package for statistical modelling called statsmodels. See http://statsmodels.sourceforge.net for more details."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a (discreet) random variable with poissionian distribution\n",
    "\n",
    "X = stats.poisson(3.5) # photon distribution for a coherent state with n=3.5 photons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zOHTUoWxHg/XXA+cBjwJ7muqlmZnZ4WkyKYhYn0djStMX8iXpbuCeiLgoOxaw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7198410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = arange(0,20)\n",
    "\n",
    "fig, axes = plt.subplots(3,1, sharex=True)\n",
    "\n",
    "# plot the probability mass function (PMF)\n",
    "axes[0].step(n, X.pmf(n))\n",
    "\n",
    "# plot the commulative distribution function (CDF)\n",
    "axes[1].step(n, X.cdf(n))\n",
    "\n",
    "# plot histogram of 1000 random realizations of the stochastic variable X\n",
    "axes[2].hist(X.rvs(size=1000));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a (continous) random variable with normal distribution\n",
    "Y = stats.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SKEoaREREpFGUNIiIiEijKGkQERGRRlHSICIiIo2ipEFEREQaRUmDiIiINErG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x65e1810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = linspace(-5,5,100)\n",
    "\n",
    "fig, axes = plt.subplots(3,1, sharex=True)\n",
    "\n",
    "# plot the probability distribution function (PDF)\n",
    "axes[0].plot(x, Y.pdf(x))\n",
    "\n",
    "# plot the commulative distributin function (CDF)\n",
    "axes[1].plot(x, Y.cdf(x));\n",
    "\n",
    "# plot histogram of 1000 random realizations of the stochastic variable Y\n",
    "axes[2].hist(Y.rvs(size=1000), bins=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Statistics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.5, 1.8708286933869707, 3.5)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.mean(), X.std(), X.var() # poission distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 1.0, 1.0)"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.mean(), Y.std(), Y.var() # normal distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test if two sets of (independent) random data comes from the same distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistic = -0.0482845462453\n",
      "p-value = 0.961494296312\n"
     ]
    }
   ],
   "source": [
    "t_statistic, p_value = stats.ttest_ind(X.rvs(size=1000), X.rvs(size=1000))\n",
    "\n",
    "print \"t-statistic =\", t_statistic\n",
    "print \"p-value =\", p_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the p value is very large we cannot reject the hypothesis that the two sets of random data have *different* means."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test if the mean of a single sample of data has mean 0.1 (the true mean is 0.0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-1.8895954172910594, pvalue=0.059101437300419203)"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Y.rvs(size=1000), 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Low p-value means that we can reject the hypothesis that the mean of Y is 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-1.5461029124085754, pvalue=0.12239642231324205)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(Y.rvs(size=1000), Y.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* http://www.scipy.org - The official web page for the SciPy project.\n",
    "* http://docs.scipy.org/doc/scipy/reference/tutorial/index.html - A tutorial on how to get started using SciPy. \n",
    "* https://github.com/scipy/scipy/ - The SciPy source code. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Credit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on J.R. Johansson (jrjohansson at gmail.com) online training materials\n",
    "The latest version of this IPython notebook lecture is available at http://github.com/jrjohansson/scientific-python-lectures.\n",
    "The other notebooks in this lecture series are indexed at http://jrjohansson.github.io."
   ]
  }
 ],
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