LaborReplacement.ipynb

laborreplacement.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOTE3QxnuvKMrzWIGc+94PM",
      "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/gist/mfbalin/096dcad5e3b1f6a59ff7ff2f9f541618/laborreplacement.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "6jh4PjthSDrb"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "\n",
        "def invcdf(u, n, s):\n",
        "    return s * (1 - (1 - u) ** (1 / n))\n",
        "\n",
        "def get(n, seed):\n",
        "    rng = np.random.default_rng(seed)\n",
        "    numbers = [0]\n",
        "    sum = 1.0\n",
        "    rem = sum\n",
        "    for n in range(n, 0, -1):\n",
        "        x = invcdf(rng.random(), n, rem)\n",
        "        numbers.append(x + numbers[-1])\n",
        "        rem -= x\n",
        "    return numbers[1:]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from itertools import repeat\n",
        "\n",
        "fanout = 10\n",
        "trials = 10000\n",
        "P = [0.1, 0.2, 0.3, 0.4]\n",
        "for z in range(20):\n",
        "    R = np.zeros(len(P), dtype=np.int64)\n",
        "    for i in range(z * trials, (z + 1) * trials):\n",
        "        A = []\n",
        "        for j, p in enumerate(P):\n",
        "            A += list(zip([r_t / p for r_t in get(fanout, i * len(P) + j)], repeat(j)))\n",
        "        A = sorted(A)[:fanout]\n",
        "        i, c = np.unique([i for r, i in A], return_counts=True)\n",
        "        R[i] += c\n",
        "    print(R / R.sum())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y6Tek2MFSFmt",
        "outputId": "820950ac-1816-45d7-e31d-5050bce5b6ff"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.09875 0.19661 0.29995 0.40469]\n",
            "[0.09871 0.19899 0.29906 0.40324]\n",
            "[0.09832 0.19805 0.29959 0.40404]\n",
            "[0.09808 0.19704 0.30089 0.40399]\n",
            "[0.09801 0.198   0.30085 0.40314]\n",
            "[0.09779 0.19795 0.3031  0.40116]\n",
            "[0.09825 0.19793 0.29992 0.4039 ]\n",
            "[0.09866 0.19855 0.29957 0.40322]\n",
            "[0.09757 0.19807 0.3007  0.40366]\n",
            "[0.09706 0.19917 0.29897 0.4048 ]\n",
            "[0.09853 0.19722 0.29857 0.40568]\n",
            "[0.09835 0.19805 0.29955 0.40405]\n",
            "[0.09588 0.19735 0.30219 0.40458]\n",
            "[0.09746 0.19887 0.30023 0.40344]\n",
            "[0.09787 0.19775 0.30004 0.40434]\n",
            "[0.09533 0.19804 0.3002  0.40643]\n",
            "[0.10017 0.20008 0.29685 0.4029 ]\n",
            "[0.0977  0.19713 0.3008  0.40437]\n",
            "[0.0972  0.19699 0.30176 0.40405]\n",
            "[0.0979  0.19775 0.29741 0.40694]\n"
          ]
        }
      ]
    }
  ]
}