week3v2.ipynb

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  "metadata": {
    "colab": {
      "name": "week3.ipynb",
      "provenance": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyOILXWupQMZujQPxu90mOq7",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/xspronken/bigdataW1/blob/master/week3v2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qrGba3zpXTNs",
        "colab_type": "text"
      },
      "source": [
        "# **IMPORTS**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nZe2mNmCPLsB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import math as m\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vE5e9aTQ8BQt",
        "colab_type": "text"
      },
      "source": [
        "# FUNCTIONS AND VARIABLES"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oji3R7Zokxoy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "''' For conversion from natural units'''\n",
        "G = 6.67*10**(-11)    # (m**3)*(kg**-1)*(s**-2)\n",
        "c = 3*10**8    # m*(s**-1)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "####################################### DEFINING VARIABLES #######################################\n",
        "\n",
        "''' Defining waveform and fourrier transform variables'''\n",
        "m1 = 10**30 # kg\n",
        "m2 = 10**30 # kg\n",
        "\n",
        "M = (m1+m2) # kg\n",
        "n = m1*m2/(M**2) #dimensionless\n",
        "M_chirp = n**(3/5)*M # kg\n",
        "t_c = 100# secs\n",
        "phi_c = 100 #rads\n",
        "\n",
        "\n",
        "#alpha coefficients as given by eq 3.4 || note that only alpha 0 to 4 have been inserted, therefore highest PN possible is 2\n",
        "alpha = [1, 0, (20/9*(743/336 + n*11/4)), -16*m.pi, 10*(3058673/1016064 + n*5429/1008 + (n**2) * 617/144)]\n",
        "PN = 2 \n",
        "\n",
        "SNR = 10\n",
        "\n",
        "\n",
        "''' Defining Power Spectral Density S(f) of Initial Ligo and its variables'''\n",
        "# as given in the paper eq 3.8\n",
        "\n",
        "fs = 40 # Hz\n",
        "f0 = 150 # Hz\n",
        "s0 = 9**(-46) #Hz**-1\n",
        "\n",
        "def S(f):\n",
        "  x = f/f0\n",
        "  if (f >= fs):\n",
        "    return s0*((4.49*x)**(-56)+0.16*x**(-4.52)+0.52+0.32*x**2)\n",
        "  else: \n",
        "    return float('inf')\n",
        "\n",
        "\n",
        "''' defining upper and lower cut-off frequencies''' \n",
        "# Limits of  the integrals used to fill in the Fischer information Matrix and calulating A\n",
        "\n",
        "F_high = (6**(3/2)*m.pi*M*G*(c**-3))**-1 # eq 3.6 || assuming the to constants to be dimensionless and M being in kg we multiply by g*c**-3 to get Hz as a final result\n",
        "F_low = fs\n",
        "\n",
        "\n",
        "''' Computing the variable A '''\n",
        "\n",
        "def compute_A(SNR, dx):\n",
        "  #perform integral using trapezoidal sums\n",
        "  accumulator = 0\n",
        "  for i in range (int(F_low/dx), int(F_high/dx - 1)):\n",
        "   x = i*dx\n",
        "   fi = (x**(-7/6) / (S(x)))\n",
        "   fi2 = ((x + dx)**(-7/6) / (S(x + dx)))\n",
        "   accumulator += dx * (fi + fi2)/2\n",
        "  # divide SNR by integral multiplied by 4\n",
        "  A = m.sqrt(SNR/(4*accumulator))\n",
        "  \n",
        "  print (\"A = \", A, \"\\n\")\n",
        "  return A\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "''' Defining the list of independent parameters processed into the matrix''' \n",
        "\n",
        "teta = [t_c, phi_c, M_chirp, n]\n",
        "\n",
        "''' Defining the Fourrier transform h(f) and it's waveform psi'''\n",
        "\n",
        "def h(f, A, params, x):\n",
        "  #defining the waveform's variables with respect to which h(f) will be partially derived \n",
        "  #make sure they correspond to the values inserted previously into teta\n",
        "  \n",
        "  t_c, phi_c, M_chirp, n = params\n",
        "  \n",
        "  M = M_chirp*n**(-3/5)  \n",
        "  \n",
        "  v = (m.pi*M*f*G/c**3)**(1/3) # eq. 3.3 || v is dimensionless, M in kg, F in Hz || multiplying by G/c**3 converts to the right units\n",
        "  \n",
        "  #sum of all coefficients (alpha) in the fourrier phase\n",
        "  x *= 2\n",
        "  sum_alpha = 0\n",
        "  for i in range(x):\n",
        "    sum_alpha += (alpha[i] * (v**i))\n",
        "  \n",
        "  #defining the waveform psi(f) || this waveform can be modified along with the variables defined previously \n",
        "  psi =  2*m.pi*f*t_c - phi_c - m.pi/4 + 3/(128*n*v**5)*sum_alpha\n",
        "\n",
        "  return  A * f**(-7/6) * m.e**(1j * psi)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "####################################### COMPUTATIONS #######################################\n",
        "\n",
        "''' Calculating the partial derivative of h(f) '''\n",
        "def h_partial(f, A, params, x):   \n",
        "  dx = params[x]/100\n",
        "  dparams = params.copy()\n",
        "  dparams[x] += dx\n",
        "  dy = h(f, A, dparams, PN)-h(f, A, params, PN)\n",
        "  return dy/dx\n",
        "\n",
        "''' Generating the Fischer information matrix '''\n",
        "def generate_matrix(A, params, dx):\n",
        "  \n",
        "# create a  n*n matrix where n is the number of observables\n",
        "  n = len(params)\n",
        "  matrix = np.empty([n,n]) \n",
        "  \n",
        "# Start filling the matrix\n",
        "  for i in range (n):\n",
        "    for j in range (n):\n",
        "      \n",
        "      #start integration (again with trap sums) using eq 2.11 of the paper as a reference instead of the plug and play\n",
        "      accumulator = 0\n",
        "      for k in range(int(F_low/dx), int(F_high/dx-1)):\n",
        "        x1 = k*dx\n",
        "        part_i1 = h_partial(x1, A, params,i)\n",
        "        part_j1 = h_partial(x1, A, params,j)\n",
        "        f1 = ((part_i1 * np.conj(part_j1))+(np.conj(part_i1) * part_j1))/S(x1)  \n",
        "        \n",
        "        x2 = k*dx + dx \n",
        "        part_i2 = h_partial(x2, A, params,i)\n",
        "        part_j2 = h_partial(x2, A, params,j)\n",
        "        f2 = ((part_i2 * np.conj(part_j2))+(np.conj(part_i2) * part_j2))/S(x2)\n",
        "        \n",
        "        accumulator += np.real(dx * (f1 + f2)/2)\n",
        "      \n",
        "      #once integration is done add it to the matrix\n",
        "      matrix[i][j] = accumulator*2\n",
        "  print(\"Fischer matrix : \\n\",  matrix)\n",
        "  return matrix\n",
        "\n",
        "\n",
        "''' Extract the diagonal elements from the inverted Fischer matrix'''\n",
        "\n",
        "def extract_from_matrix(matrix):\n",
        "  #invert matrix\n",
        "  y = np.linalg.inv(matrix) \n",
        "  z = []\n",
        "  \n",
        "  #fetch the square root of diagonal elements\n",
        "  for i in range (len(y)):\n",
        "    z.append(m.sqrt(y[i][i]))\n",
        "  \n",
        "  return z\n",
        "\n",
        "\n",
        "####################################### Exercise 3 functions ############################################\n",
        "\n",
        "def fetch_ligo(nb_col):\n",
        "  if nb_col > 6 or nb_col < 1:\n",
        "    print('invalid column number, column number was reset to default (6)')\n",
        "    nb_col = 6\n",
        "  data = []\n",
        "  freq = []\n",
        "  sens = []\n",
        "  f = open('LIGO.txt')\n",
        "  lines = f.readlines()\n",
        "  for x in range(len(lines)):\n",
        "    line = list(map(float,lines[x].split()))\n",
        "    data.append(line)\n",
        "  for y in range(len(data)):\n",
        "    freq.append(data[y][0])\n",
        "    sens.append(data[y][nb_col])\n",
        "  \n",
        "  return freq, sens\n",
        "\n",
        "\n",
        "def fetch_einstein(nb_col):\n",
        "  if nb_col > 3 or nb_col < 1:\n",
        "    print('invalid column number, column number was reset to default (3)')\n",
        "    nb_col = 3\n",
        "  data = []\n",
        "  freq = []\n",
        "  sens = []\n",
        "  final = []\n",
        "  f = open('EINSTEIN.txt')\n",
        "  lines = f.readlines()\n",
        "  for x in range(len(lines)):\n",
        "    line = list(map(float,lines[x].split()))\n",
        "    data.append(line)\n",
        "  for y in range(len(data)):\n",
        "    freq.append(data[y][0])\n",
        "    sens.append(data[y][nb_col])\n",
        "  \n",
        "  return freq, sens\n",
        "\n",
        "  ''' the functions defining A and the fischer matrix are modified to accept data loaded from eintein telescope or ligo '''\n",
        "\n",
        "def compute_A_2(data, SNR):\n",
        "  #perform integral using trapezoidal sums\n",
        "  accumulator = 0\n",
        "  for x in range(len(data[0])-1) : # possible to do this because data[0] and data[1] ahve the same length\n",
        "   freq = data[0][x]\n",
        "   sens = data[1][x]\n",
        "   fi = (freq**(-7/6) / sens)\n",
        "  \n",
        "   freq2 = data[0][x+1]\n",
        "   sens2 = data[1][x+1]\n",
        "   fi2 = (freq2**(-7/6) / sens2)\n",
        "     \n",
        "   accumulator += (freq2-freq) * (fi + fi2)/2\n",
        "  \n",
        "  # divide SNR by integral multiplied by 4\n",
        "  A = m.sqrt(SNR/(4*accumulator))\n",
        "  \n",
        "  print (\"A = \", A, \"\\n\")\n",
        "  return A\n",
        "\n",
        "\n",
        "def generate_matrix_2(A, params, data):\n",
        " \n",
        "# create a  n*n matrix where n is the number of observables\n",
        "  n = len(params)\n",
        "  matrix = np.empty([n,n]) \n",
        "  \n",
        "# Start filling the matrix\n",
        "  for i in range (n):\n",
        "    for j in range (n):\n",
        "      \n",
        "      #start integration (again with trap sums) using eq 2.11 of the paper as a reference instead of the plug and play\n",
        "      accumulator = 0\n",
        "      for k in range(len(data[0])-1):\n",
        "        freq = data[0][k]\n",
        "        sens = data[1][k]\n",
        "        part_i1 = h_partial(freq, A, params,i)\n",
        "        part_j1 = h_partial(freq, A, params,j)\n",
        "        f1 = (part_i1*np.conj(part_j1) + np.conj(part_i1)*part_j1)/sens  \n",
        "        \n",
        "        freq2 = data[0][k+1]\n",
        "        sens2 = data[1][k+1]\n",
        "        part_i2 = h_partial(freq2, A, params,i)\n",
        "        part_j2 = h_partial(freq2, A, params,j)\n",
        "        f2 = ((part_i2 * np.conj(part_j2))+(np.conj(part_i2) * part_j2))/sens2\n",
        "        \n",
        "        accumulator += np.real((freq2-freq) * (f1 + f2)/2)\n",
        "      \n",
        "      #once integration is done add it to the matrix\n",
        "      matrix[i][j] = accumulator*2\n",
        "  print(\"Fischer matrix : \\n\",  matrix, \"\\n\")\n",
        "  return matrix\n",
        "\n",
        "def compare_ligo_einstein(diagLigo, diagEinstein):\n",
        "  y = list(zip(diagLigo, diagEinstein))\n",
        "  x = [\"Ligo\", \"Einstein\"]\n",
        "  for i in range(len(y)):\n",
        "    plt.figure()\n",
        "    plt.title(\"Parameter %i\" %i)\n",
        "    plt.plot(x, y[i],'o')\n",
        "    plt.ylabel('Measurability')\n",
        "    plt.xlabel(\"Telescope\")\n",
        "    plt.show \n",
        "  return None\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P5vhMeXt8IB1",
        "colab_type": "text"
      },
      "source": [
        "# EXERCISE 1 / 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j8EwcOytH4hT",
        "colab_type": "text"
      },
      "source": [
        "The different code blocks in this section were run with different tetas. Yielding different results, however if you re-run them now they will take the current values to which all variables are set to in the Functions and Variables section. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IFkeaXiDp9Bh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 168
        },
        "outputId": "c1038466-91d1-4d31-d3e6-c320ac42355d"
      },
      "source": [
        "print(\"teta : t_c, phi_c, M, n: \", teta)\n",
        "A = compute_A(10, 0.001)  # Inputs are SNR and increment used for integrating with trap sums\n",
        "fischer = generate_matrix(A, teta, 0.1)\n",
        "Results = extract_from_matrix(fischer)\n",
        "print(\"Results for PN =\", PN, \" : \" ,Results)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "teta : t_c, phi_c, M, n:  [100, 100, 2000000000000000000000000000000, 0.25]\n",
            "A =  2.331029579377938e-22 \n",
            "\n",
            "Fischer matrix : \n",
            " [[5.65236943e-02 1.29855392e-02 1.43440504e-30 1.14343116e+01]\n",
            " [1.29855392e-02 2.59837484e-02 6.50297090e-31 5.21538539e+00]\n",
            " [1.43440504e-30 6.50297090e-31 1.41439798e-58 5.63737301e-28]\n",
            " [1.14343116e+01 5.21538539e+00 5.63737301e-28 9.07077481e+03]]\n",
            "Results for PN = 1  :  [5.242343341038053, 6.817949829675521, 1.0434526672746667e+29, 0.013012671068597343]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BBCyNzqjl35x",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 151
        },
        "outputId": "dcf4cbe5-2226-48a3-883e-152c21e11c6a"
      },
      "source": [
        "print(\"teta : t_c, phi_c, M: \", teta)\n",
        "A = compute_A(10, 0.001)  \n",
        "fischer = generate_matrix(A, teta, 0.1)\n",
        "Results = extract_from_matrix(fischer)\n",
        "print(\"Results for PN =\", PN, \" : \" ,Results)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "teta : t_c, phi_c, M:  [100, 100, 2000000000000000000000000000000]\n",
            "A =  2.331029579377938e-22 \n",
            "\n",
            "Fischer matrix : \n",
            " [[5.65236943e-02 1.29855392e-02 1.43440504e-30]\n",
            " [1.29855392e-02 2.59837484e-02 6.50297090e-31]\n",
            " [1.43440504e-30 6.50297090e-31 1.41439798e-58]]\n",
            "Results for PN = 1  :  [4.987507066625157, 6.7387874596557005, 9.971844129541572e+28]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VHt2qyReGfQy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 168
        },
        "outputId": "b8d5a63a-5743-4364-9df8-82a0d30906f5"
      },
      "source": [
        "print(\"teta : t_c, phi_c, M_chirp, n: \", teta)\n",
        "A = compute_A(10, 0.001)  \n",
        "fischer = generate_matrix(A, teta, 0.1)\n",
        "Results = extract_from_matrix(fischer)\n",
        "print(\"Results for PN =\", PN, \" : \" ,Results)"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "teta : t_c, phi_c, M_chirp, n:  [100, 100, 8.705505632961241e+29, 0.25]\n",
            "A =  2.331029579377938e-22 \n",
            "\n",
            "Fischer matrix : \n",
            " [[ 5.65236943e-02  1.29855392e-02  3.29539742e-30  8.38924171e-13]\n",
            " [ 1.29855392e-02  2.59837484e-02  1.49399040e-30  5.61986189e-12]\n",
            " [ 3.29539742e-30  1.49399040e-30  7.46523730e-58 -9.66022611e-41]\n",
            " [ 8.38924171e-13  5.61986189e-12 -9.66022611e-41  6.51663286e-20]]\n",
            "Results for PN = 1  :  [4.98762658145094, 6.814268282450041, 4.34704216046072e+28, 3962731645.739399]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JU0H5CchYRFc",
        "colab_type": "text"
      },
      "source": [
        "# EXERCISE 3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xhdz8bxpqp-3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "4711d7f2-5cae-4b60-e8be-64febf7933d0"
      },
      "source": [
        "A1 = compute_A_2(fetch_ligo(6), 10)\n",
        "fischer1 = generate_matrix_2(A1, teta, fetch_ligo(6))\n",
        "results1 = extract_from_matrix(fischer1)\n",
        "print(\"Ligo results for PN =\", PN, \" : \" , results1 , \"\\n\\n\")\n",
        "\n",
        "\n",
        "A2 = compute_A_2(fetch_einstein(3), 10)\n",
        "fischer2 = generate_matrix_2(A2, teta, fetch_einstein(3))\n",
        "results2 = extract_from_matrix(fischer2)\n",
        "print(\"Einstein results for PN =\", PN, \" : \" , results2)\n",
        "\n",
        "print(compare_ligo_einstein(results1,results2))"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A =  2.3881660193922547e-12 \n",
            "\n",
            "Fischer matrix : \n",
            " [[1.11197721e-01 2.54916905e-02 6.35254068e-30 7.91935516e+00]\n",
            " [2.54916905e-02 5.11531396e-02 2.93297211e-30 2.56391910e+00]\n",
            " [6.35254068e-30 2.93297211e-30 1.48364768e-57 9.45987385e-28]\n",
            " [7.91935516e+00 2.56391910e+00 9.45987385e-28 6.32545624e+03]] \n",
            "\n",
            "Ligo results for PN = 2  :  [3.5817146115038554, 4.802263717906446, 3.1093672147021856e+28, 0.013430548478467221] \n",
            "\n",
            "\n",
            "A =  7.03025537640848e-13 \n",
            "\n",
            "Fischer matrix : \n",
            " [[3.38989147e-01 7.81754782e-02 1.95095907e-29 5.34310877e+01]\n",
            " [7.81754782e-02 1.55944384e-01 8.65215930e-30 2.82499054e+01]\n",
            " [1.95095907e-29 8.65215930e-30 4.44215835e-57 6.97101673e-27]\n",
            " [5.34310877e+01 2.82499054e+01 6.97101673e-27 4.68227288e+04]] \n",
            "\n",
            "Einstein results for PN = 2  :  [2.077708707527783, 2.7830628326472784, 1.8649899018584787e+28, 0.005512534487494858]\n",
            "None\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TbV84yLrzgfkAO+2007qUGRERlWrvCD+DAY4SbP/vodazvRaYLWkacIGkPWz/ZICu82jG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\nxK5kTAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MtgC/S/Xk+T831aiIiOgunYbJDNvfAWT7TtsfBF7RXLMiIqKbdHpr8COSngLcVm73XU81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\nMImIiNoSJhERUdv/B7f4NX1edzC1AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}