{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration\n",
    "\n",
    "#### scipy.integrate documentation at https://docs.scipy.org/doc/scipy/tutorial/integrate.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import  numpy as np\n",
    "import scipy as sp\n",
    "import scipy.integrate as integrate\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 5.4. \n",
    "\n",
    "Diffraction pattern $I(r) = \\left( \\frac{J_1(kr)}{kr} \\right )^2$. By definition $J_m(x) = \\frac{1}{\\pi} \\int_0^\\pi cos(m\\Theta - x sin \\Theta) d\\Theta$.\n",
    "\n",
    "a) Write a python function that calculates $J_m(x)$ . Use it to make a plot of $J_0$, $J_1$, $J_2$ in the x-interval [0,20]\n",
    "\n",
    "b) Make a density plot of the intensity of the diffraction pattern, for a point light source with $\\lambda = 500$ nm in a square region of the focal plane with r in the range [0,1] $\\mu$m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define integrand\n",
    "def integrand(theta,x,m):\n",
    "    integrand = (1.0/np.pi)*np.cos(m*theta - x*np.sin(theta))\n",
    "    return integrand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Bessel using general purpose integration routine from python\n",
    "# https://docs.scipy.org/doc/scipy/tutorial/integrate.html\n",
    "def bessel(func,x,m):\n",
    "    bes = integrate.quad(func,0.0,np.pi,args=(x,m))\n",
    "    return bes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Bessel using Romberg\n",
    "def bessel_rom(func,x,m):\n",
    "    bes = integrate.romberg(func,0.0,np.pi,args=(x,m))\n",
    "    return bes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Bessel using trapezoidal rule\n",
    "def bessel_trap(x,m,N):\n",
    "    dtheta = np.pi/float(N)\n",
    "    grid = np.arange(0.0,np.pi,dtheta)\n",
    "    y = integrand(grid,x,m)\n",
    "    bes = integrate.trapezoid(y,grid)\n",
    "\n",
    "    return bes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate Bessel using Simpson rule\n",
    "def bessel_simp(x,m,N):\n",
    "    dtheta = np.pi/float(N)\n",
    "    grid = np.arange(0.0,np.pi,dtheta)\n",
    "    y = integrand(grid,x,m)\n",
    "    bes = integrate.simpson(y,grid)\n",
    "\n",
    "    return bes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4859912606163224 0.4860912605858965\n"
     ]
    }
   ],
   "source": [
    "# Just a quick check that different methods \n",
    "# give consistent answers in a given x, for given m\n",
    "bes1 = bessel_simp(3,2,10000)\n",
    "bes2 = bessel_rom(integrand,3,2)\n",
    "print(bes1,bes2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xlist = np.arange(0,20,0.1)\n",
    "N = 1000\n",
    "\n",
    "for m in range(3):\n",
    "    \n",
    "    bes = [ ]\n",
    "    bes_rom = [ ]\n",
    "    bes_trap = [ ]\n",
    "    bes_simp = [ ]\n",
    "    \n",
    "    for x in xlist:\n",
    "        b1 = (bessel(integrand,x,m))\n",
    "        bes.append(b1[0])\n",
    "        bes_rom.append(bessel_rom(integrand,x,m))\n",
    "        bes_trap.append(bessel_trap(x,m,N))\n",
    "        bes_simp.append(bessel_simp(x,m,N))\n",
    "  \n",
    "    plt.plot(xlist,bes_trap,label='trapezoid, N =' + str(N))\n",
    "    plt.plot(xlist,bes_simp,label='Simpson, N=' + str(N))\n",
    "    plt.plot(xlist,bes_rom,label='Romberg')\n",
    "    plt.plot(xlist,bes,label='Python quad')\n",
    "    plt.xlabel('x',fontsize=16)\n",
    "    plt.ylabel('$J_m(x)$', fontsize=16)\n",
    "    plt.legend()\n",
    "    plt.title('Comparison between methods, m = ' + str(m),fontsize = 16)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# EXERCISE 5.4 FROM COMPUTATIONAL PHYSICS.\n",
    "# CALCULATE AND PLOT THE DIFFRACTION PATTERN\n",
    "############################################\n",
    "\n",
    "import  numpy as np\n",
    "import scipy as sp\n",
    "import scipy.integrate as integrate\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "\n",
    "# Calculate Bessel function using Simpson rule\n",
    "def bessel_simp(x,m,N):\n",
    "    \n",
    "    # Define integrand\n",
    "    def integrand(theta,x,m):\n",
    "        integrand = (1.0/np.pi)*np.cos(m*theta - x*np.sin(theta))\n",
    "        return integrand\n",
    "    \n",
    "    # Evaluate in a grid\n",
    "    dtheta = np.pi/float(N)\n",
    "    grid = np.arange(0.0,np.pi,dtheta)\n",
    "    y = integrand(grid,x,m)\n",
    "    #Integrate\n",
    "    bes = integrate.simpson(y,grid)\n",
    "\n",
    "    return bes\n",
    "\n",
    "\n",
    "# Use Bessel evaluation above to compute the \n",
    "# intensity of the diffraction pattern as \n",
    "# a function of the coordinates (x,y) in the \n",
    "# focal plane of the telescope\n",
    "def diffraction(x,y,N):\n",
    "    \n",
    "    twopi = 2*np.pi\n",
    "    # Light wavelength (could be passed as input)\n",
    "    wavelength = 500 # nm units\n",
    "    # Frequency\n",
    "    k = twopi/wavelength\n",
    "    # Distance from center of the point (x,y)\n",
    "    r = np.sqrt(x**2 + y**2)\n",
    "    kr = k*r\n",
    "    # Bessel J_1, m=1\n",
    "    m = 1\n",
    "    \n",
    "    if (kr < 1e-20):\n",
    "        # Limit of (J_1(kr)/kr)^2, when kr -> 0\n",
    "        intensity = 1./4.\n",
    "    else:\n",
    "        # intensity = (J_1(kr)/kr)^2\n",
    "        J1 = bessel_simp(kr,m,N)\n",
    "        intensity = (J1/kr)**2\n",
    "    \n",
    "    return intensity\n",
    "\n",
    "\n",
    "# Define grid of x,y coordinates in the focal plane\n",
    "# in which we want to evaluate the intensity\n",
    "xlist = np.arange(-1000,1000,5)\n",
    "ylist = np.arange(-1000,1000,5)\n",
    "\n",
    "# Number of points for Simpson integration scheme\n",
    "N = 1000\n",
    "\n",
    "# Compute diffraction intensity in all poins \n",
    "# of the (x,y) grid\n",
    "z = [ ]\n",
    "for x in xlist:\n",
    "    for y in ylist:\n",
    "        z.append(diffraction(x,y,N))\n",
    "\n",
    "# Rearrange x,y in meshgrid for plotting\n",
    "x = np.array(xlist)\n",
    "y = np.array(ylist)\n",
    "X, Y = np.meshgrid(x,y)\n",
    "# Reshape z to adapt it to meshgrid\n",
    "z = np.array(z)\n",
    "Z = z.reshape(len(ylist),len(xlist))\n",
    "\n",
    "# Produce intensity plot\n",
    "fig1, ax = plt.subplots()\n",
    "c = ax.pcolormesh(X,Y,Z,cmap='gray',vmax=0.004)\n",
    "plt.colorbar(c)\n",
    "\n",
    "# Axes limits\n",
    "ax.set_xlim(-1000,1000)\n",
    "ax.set_ylim(-1000,1000)\n",
    "\n",
    "# This is to show a square box (and not a rectangular one)\n",
    "ax.set_box_aspect(1)\n",
    "\n",
    "# Title and labels\n",
    "ax.set_title('Diffraction pattern',fontsize = 16)\n",
    "ax.set_xlabel('X (nm)',fontsize=16)\n",
    "ax.set_ylabel('Y (nm)',fontsize=16)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise, implement the trapezoidal rule: \n",
    "Write your own function for trapezoidal integration. The function should double the number of points in the sampled interval until a specifified level of accuracy is reached"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trap(func,a,b,tol):\n",
    "        \n",
    "    demomode = False\n",
    "        \n",
    "    # Initial number of sampled points\n",
    "    N = 10\n",
    "    \n",
    "    # 1/2*f(a) + 1/2*f(b)\n",
    "    s = 0.5*func(a) + 0.5*func(b)\n",
    "    \n",
    "    # Starting with N points\n",
    "    h = (b-a)/N\n",
    "    s1 = 0.\n",
    "    for k in range(1,N):\n",
    "        s1 += func(a + k*h)\n",
    "    # Trapezoidal rule with N points in [a,b]\n",
    "    trap1N = h*(s + s1)\n",
    "    \n",
    "    acc = tol+1.\n",
    "    \n",
    "    if demomode:\n",
    "        print(N,trap1N)\n",
    "    \n",
    "    while (acc > tol):\n",
    "        # Now doubling the number of points and updating h\n",
    "        N = 2*N\n",
    "        h = (b-a)/N\n",
    "        # Computing \\sum f(x), only in the new sampled points \n",
    "        s2 = 0.\n",
    "        for k in range(1,N,2):\n",
    "            s2 += func(a + k*h)\n",
    "        # Trapezoidal rule with 2N points\n",
    "        trap2N = h*(s + s1 + s2)\n",
    "        \n",
    "        acc = ((1./3.)*abs(trap2N-trap1N))/abs(trap2N)\n",
    "\n",
    "        if demomode:\n",
    "            print(N, trap2N)\n",
    "               \n",
    "        # Update and loop\n",
    "        s1, trap1N = s1 + s2, trap2N\n",
    "        \n",
    "        # Exit loop if N > 1e6\n",
    "        if (N > 1e6):\n",
    "            print(' ')\n",
    "            print('The required accuracy could not be reached with N=1e6 points.')\n",
    "            print('Stopping here, N =', N, '; acc =', acc)\n",
    "            break\n",
    "    \n",
    "    return trap2N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise, implement the Simpson's rule: \n",
    "Write your own function for Simpson's integration. The function should double the number of points in the sampled interval until a specifified level of accuracy is reached"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simp(func,a,b,tol):\n",
    "    \n",
    "    demomode = False\n",
    "        \n",
    "    # Initial number of sampled points\n",
    "    N = 10\n",
    "    \n",
    "    # 1/3*f(a) + 1/3*f(b)\n",
    "    s = (1./3.)*func(a) + (1./3.)*func(b)\n",
    "    \n",
    "    # Starting with N points\n",
    "    h = (b-a)/N\n",
    "    s1odd = 0.\n",
    "    for k in range(1,N,2):\n",
    "        s1odd += func(a + k*h)\n",
    "    s1even = 0.\n",
    "    for k in range(2,N,2):\n",
    "        s1even += func(a+k*h)\n",
    "    \n",
    "    # Simpson's rule with N points in [a,b]\n",
    "    simp1N = h*(s + (4./3.)*s1odd + (2./3.)*s1even)\n",
    "    \n",
    "    if demomode:\n",
    "            print(N, simp1N)\n",
    "    \n",
    "    acc = tol+1.\n",
    "    \n",
    "    while (acc > tol):\n",
    "        # Now doubling the number of points and updating h\n",
    "        N = 2*N\n",
    "        h = (b-a)/N\n",
    "        # All points in previous interval (odd+even) are\n",
    "        # now the even points in the new interval.\n",
    "        s2even = s1odd + s1even\n",
    "        # Now getting s2odd\n",
    "        s2odd = 0.\n",
    "        for k in range(1,N,2):\n",
    "            s2odd += func(a+k*h)\n",
    "        # Simpson's rule with 2N points in the sample\n",
    "        simp2N = h*(s + (4./3.)*s2odd + (2./3.)*s2even)\n",
    "    \n",
    "        acc = ((1./15.)*abs(simp2N-simp1N))/abs(simp2N)\n",
    "        \n",
    "        # Update and loop\n",
    "        s1even, s1odd = s2even, s2odd\n",
    "        simp1N = simp2N\n",
    "        \n",
    "        if demomode:\n",
    "            print(N, simp2N)\n",
    "        \n",
    "        # Exit loop if N > 1e6\n",
    "        if (N > 1e6):\n",
    "            print(' ')\n",
    "            print('The required accuracy could not be reached with N=1e6 points.')\n",
    "            print('Stopping here, N =', N, '; acc =', acc)\n",
    "            break\n",
    "    \n",
    "    return simp2N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise from slides: integration of NFW profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.integrate as integrate\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Parameters\n",
    "rho0 = 1e8  # Solar masses kpc^-3\n",
    "rs = 10.0   # kpc\n",
    "rmax = 100.*rs\n",
    "\n",
    "# Function that computes NFW profile as a function of r\n",
    "def NFW(r):\n",
    "       \n",
    "    x = r/rs   \n",
    "    rho = rho0/(x*(1.+ x)**2)\n",
    "    \n",
    "    return rho\n",
    "\n",
    "# Function to integrate\n",
    "def integrand(r):\n",
    "    \n",
    "    fourpi = 4.0*np.pi\n",
    "    \n",
    "    # For r=0, integrand=0, otherwise call NFW(r)\n",
    "    if (r < 1e-30):\n",
    "        integrand = 0.\n",
    "    else:\n",
    "        rho = NFW(r)\n",
    "        integrand = fourpi*r**2*rho\n",
    "        \n",
    "    return integrand\n",
    "\n",
    "# Romberg integration to get mass, using parameters at the beginning of the box\n",
    "#M = integrate.romberg(integrand,0.0,rmax)\n",
    "#print(' ')\n",
    "\n",
    "# Same integral, using my own trapezoidal rule function\n",
    "#tol = 1e-4\n",
    "#M = trap(integrand,0.0,rmax,tol)\n",
    "#print('Trapezoidal rule \\n')\n",
    "\n",
    "# Same integral, using my own trapezoidal rule function\n",
    "tol = 1e-4\n",
    "M = simp(integrand,0.0,rmax,tol)\n",
    "print('Simpsons rule \\n')\n",
    "\n",
    "print(\"The answer is:\")\n",
    "print(\"M =\", \"{:.2E}\".format(M), \"Msun\")\n",
    "print(' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise: \n",
    "Do again exercise 5.4 (bessel function) using your own Simpson's rule integration function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import  numpy as np\n",
    "import scipy as sp\n",
    "import scipy.integrate as integrate\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "# Define integrand\n",
    "def integrand(theta,x,m):\n",
    "    integrand = (1.0/np.pi)*np.cos(m*theta - x*np.sin(theta))\n",
    "    return integrand\n",
    "\n",
    "def bessel(x,m):\n",
    "    integ = lambda theta: integrand(theta,x,m)\n",
    "    tol = 1e-4\n",
    "    bes = simp(integ, 0., np.pi,tol)\n",
    "    return bes\n",
    "\n",
    "# Calculate Bessel using Simpson rule from scipy\n",
    "N = 100\n",
    "def bessel_simp(x,m,N):\n",
    "    dtheta = np.pi/float(N)\n",
    "    grid = np.arange(0.0,np.pi,dtheta)\n",
    "    y = integrand(grid,x,m)\n",
    "    bes = integrate.simpson(y,grid)\n",
    "\n",
    "    return bes\n",
    "\n",
    "x = 3\n",
    "m = 2\n",
    "bes = bessel(x,m)\n",
    "bes2 = bessel_simp(x,m,N)\n",
    "print(bes)\n",
    "\n",
    "\n",
    "xlist = np.arange(0,20,0.1)\n",
    "for m in range(3):\n",
    "    \n",
    "    bes = [ ]\n",
    "    bes2 = [ ]\n",
    "    \n",
    "    for x in xlist:\n",
    "        b1 = bessel(x,m)\n",
    "        b2 = bessel_simp(x,m,N)\n",
    "        bes.append(b1)\n",
    "        bes2.append(b2)\n",
    "        \n",
    "    plt.plot(xlist,bes,label='Simpson, my function')\n",
    "    plt.plot(xlist,bes2,label='Simpson, scipy')\n",
    "    plt.xlabel('x',fontsize=16)\n",
    "    plt.ylabel('$J_m(x)$', fontsize=16)\n",
    "    plt.legend()\n",
    "    plt.title('Bessel function, m = ' + str(m),fontsize = 16)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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