{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "numpy_random.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lhmyI7sB_bKJ",
        "colab_type": "text"
      },
      "source": [
        "# Generate Random Numbers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MulyzIdD_kxf",
        "colab_type": "text"
      },
      "source": [
        "`numpy.random` is frequently used for generating random numbers.\n",
        "\n",
        "For more details, please refer to [Random sampling (numpy.random)](https://docs.scipy.org/doc/numpy/reference/routines.random.html)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vtrQ-n7PAoYJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLB8lH051pDg",
        "colab_type": "text"
      },
      "source": [
        "`np.random.seed` sets the seed for the generator.\n",
        "\n",
        "With the seed reset (every time), the same set of numbers will appear every time.\n",
        "\n",
        "If the random seed is not reset, different numbers appear with every invocation:\n",
        "\n",
        "It is useful for debugging as output will not change\n",
        "\n",
        "Explainer: https://stackoverflow.com/questions/21494489/what-does-numpy-random-seed0-do"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PzxXe5pR3QI0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cSSX-VCBAnuJ",
        "colab_type": "text"
      },
      "source": [
        "`np.random.rand` randomly generates numbers from a uniform distribution over $[0, 1)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ran81EdeAKl6",
        "colab_type": "code",
        "outputId": "9adb1089-0417-490b-f31e-6730df35d688",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        }
      },
      "source": [
        "np.random.rand(2, 3) # Generates a 2x3 array with random numbers"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4.17022005e-01, 7.20324493e-01, 1.14374817e-04],\n",
              "       [3.02332573e-01, 1.46755891e-01, 9.23385948e-02]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g_jgVxcfAi00",
        "colab_type": "text"
      },
      "source": [
        "`np.random.randn` generates numbers following standard normal distribution."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OG-suj-PA72b",
        "colab_type": "code",
        "outputId": "6fda962e-bc37-4f93-9bdf-aa82b5502117",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        }
      },
      "source": [
        "np.random.randn(2, 3) # Generate 2 * 3 random numbers"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.52817175, -1.07296862,  0.86540763],\n",
              "       [-2.3015387 ,  1.74481176, -0.7612069 ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SLw958olA9Uu",
        "colab_type": "text"
      },
      "source": [
        "`np.random.randint(low, high)` generates integers ranging from `low` (inclusive) to `high` (exclusive)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SkRVwD_yCd7r",
        "colab_type": "code",
        "outputId": "72c58ee8-4ed7-433e-8a95-60e58293f827",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "np.random.randint(low = 0, high = 4, size = (3, 3))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3, 0, 2],\n",
              "       [0, 1, 2],\n",
              "       [2, 0, 3]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MLSvOE4UEA6n",
        "colab_type": "text"
      },
      "source": [
        "`np.random.choice` generates random numbers following a given pmf."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NidDNwzK4FRY",
        "colab_type": "code",
        "outputId": "13962d5d-09fb-41cb-fe32-e90186c6bfcd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "a = np.arange(4)  # 3 has prob=0.4\n",
        "p = [0.1, 0.2, 0.3, 0.4]\n",
        "np.random.choice(a = a, size=(3, 4), p = p)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2, 2, 3, 3],\n",
              "       [3, 3, 0, 2],\n",
              "       [3, 3, 3, 1]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Arc1wQq5a2V",
        "colab_type": "text"
      },
      "source": [
        "The sample space is not necessary to be number sets."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7JqVclm44hgH",
        "colab_type": "code",
        "outputId": "fc86099d-f55f-4d9c-f75f-930e91160710",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "a = ['Spade', 'Heart', 'Club', 'Diamond']\n",
        "p = [0.25, 0.25, 0.25, 0.25]\n",
        "np.random.choice(a = a, size=(3, 4), p = p)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([['Spade', 'Clud', 'Clud', 'Clud'],\n",
              "       ['Heart', 'Spade', 'Heart', 'Spade'],\n",
              "       ['Diamond', 'Heart', 'Spade', 'Clud']], dtype='<U7')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O7pLtNHP5XbL",
        "colab_type": "text"
      },
      "source": [
        "It is also possible to draw random samples from other distributions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wa7KH_rW6WaU",
        "colab_type": "text"
      },
      "source": [
        "Exponential: $f_X(x; \\beta) = \\frac{1}{\\beta}e^{-\\frac{x}{\\beta}}$, $\\beta$ is the scale parameter.\n",
        "\n",
        "$\\lambda$ = 1/$\\beta$\n",
        "\n",
        "Draws a sample from an exponential distribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fstao_qt6Yn7",
        "colab_type": "code",
        "outputId": "e44f81bf-1d3f-4e52-c19b-969cd1da70e0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        }
      },
      "source": [
        "# x value is randomly selected\n",
        "np.random.exponential(scale = 2, size = (2, 3))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[2.16136241, 0.70905534, 1.18166682],\n",
              "       [0.50237771, 0.15238928, 1.26688512]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cS-2YNh162s8",
        "colab_type": "text"
      },
      "source": [
        "Binomial: $P_X(k; n,p) = \\binom{n}{k} p^k (1 - p)^{n - k}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QCNVWxTx7Utf",
        "colab_type": "code",
        "outputId": "31fbcc4b-4710-4c67-9ffc-2921a5ddf7e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "# k value is randomly selected\n",
        "n = 10\n",
        "p = 0.8\n",
        "np.random.binomial(n = n, p = p, size = (3, 3))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[10,  6,  9],\n",
              "       [ 8, 10,  6],\n",
              "       [ 6,  9,  8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e16J3-el71gV",
        "colab_type": "text"
      },
      "source": [
        "More distribution types are shown in the docs. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jkt_2jWu8DBe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}