Homework_2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Homework_2.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyP329ATkeI+98UQGzObAZAW",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/palia95/ML_Physics/blob/master/Homework_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "wl5dgTCqbgAB",
        "outputId": "49f829c1-e7d9-4e40-b950-1821150776ba"
      },
      "source": [
        "\n",
        "from __future__ import print_function\n",
        "__author__= 'fbb'\n",
        "\n",
        "import pylab as pl\n",
        "from scipy.optimize import curve_fit, minimize\n",
        "    \n",
        "%pylab inline\n",
        "# this package sets up pretty plots\n",
        "import seaborn\n",
        "seaborn.set_style(\"darkgrid\")\n",
        "\n",
        "#distributions = ['pois', 'gaus', 'chisq', 'cauchy', 'lnorm', 'binomial']\n",
        "distributions = ['pois']\n",
        "\n",
        "mymean = 100\n",
        "df = mymean\n",
        "\n",
        "import numpy as np\n",
        "np.random.seed(69)\n",
        "md = {}\n",
        "# md is an empty disctionary; \n",
        "# if you are not familiar with python dictionaries see https://www.pythonforbeginners.com/dictionary/how-to-use-dictionaries-in-python\n",
        "md['pois'] = np.random.poisson(df, size=100)\n",
        "# md now is a dictionary with one object: an array by the key 'chisq'\n",
        "pl.hist(md['pois'], bins = 30)\n",
        "pl.ylabel('N')\n",
        "pl.xlabel('x');"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_YRNssqNds1-",
        "outputId": "03a043de-96fa-4a0f-f8de-23c88a768038"
      },
      "source": [
        "print (\"Pois mean: %.2f, standard deviation: %.2f\"%(md['pois'].mean(), md['pois'].std()))\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Pois mean: 99.90, standard deviation: 10.46\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oNgmGFA5d3vI",
        "outputId": "668459b3-267f-41d1-d69c-55801e7808c1"
      },
      "source": [
        "mysize = (2000 / (np.array(range(1, 100)))).astype(int)\n",
        "# mysize = 1000 / (np.array(range(1, 100) + [10]))\n",
        "# mysize = (np.random.rand(100) * 1000).astype(int)\n",
        "print (\"shape of the 'size' list that contains the size of each distribution\", mysize.shape)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "shape of the 'size' list that contains the size of each distribution (99,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 436
        },
        "id": "DK0JcdaoeIKX",
        "outputId": "6c639d41-d884-4cf5-d115-4e57195ef78d"
      },
      "source": [
        "\n",
        "# I am gonna overwrite the disctionary entry created into a nested dictionary \n",
        "# the outside dictionary hosts the distributions as dictionary, \n",
        "# and each distribution dictionary contains the 100 distribution (arrays of diferent sizes)\n",
        "\n",
        "md['pois'] = {} \n",
        "\n",
        "#and do it in a for loop. not pythonic, but easily readable\n",
        "\n",
        "for n in mysize:\n",
        "    md['pois'][n] = np.random.chisquare(df, size = n)\n",
        "    \n",
        "# save the means for plotting later    \n",
        "\n",
        "md['pois']['means'] = {}\n",
        "axpois_mu_n = pl.figure(figsize=(10,6)).add_subplot(111)\n",
        "\n",
        "for nn in md['pois']:\n",
        "    if not type(nn) == str:\n",
        "        md['pois']['means'][nn] = md['pois'][nn].mean()\n",
        "        #and plot it\n",
        "        axpois_mu_n.plot(nn, md['pois']['means'][nn], 'o')\n",
        "        axpois_mu_n.set_xlabel('sample size', fontsize=18)\n",
        "        axpois_mu_n.set_ylabel('sample mean', fontsize=18)\n",
        "        axpois_mu_n.set_title('Pois dist', fontsize=18)\n",
        "        axpois_mu_n.plot([min(mysize), max(mysize)], [df, df], 'k')\n",
        "axpois_mu_n.text(axpois_mu_n.get_xlim()[1] * .6, 100, \"expected mean\", \n",
        "                  va=\"bottom\", fontsize=20)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(1259.3999999999999, 100, 'expected mean')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 634
        },
        "id": "bGq_xN3Meq5B",
        "outputId": "e2207a65-e034-46cb-a2d9-a5e7ee467c77"
      },
      "source": [
        "\n",
        "allmeans = list(md['pois']['means'].values())\n",
        "\n",
        "pl.figure(figsize=(10, 10))\n",
        "pl.hist(allmeans,bins=30)\n",
        "pl.xlabel('sample mean', fontsize = 18)\n",
        "pl.ylabel('N', fontsize = 18)\n",
        "\n",
        "def mygauss(x, mu, sig):\n",
        "  return 1/np.sqrt(2)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'N')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}