diff --git a/.ipynb_checkpoints/Pseudo_aleatoriedade-checkpoint.ipynb b/.ipynb_checkpoints/Pseudo_aleatoriedade-checkpoint.ipynb new file mode 100644 index 0000000..084acb4 --- /dev/null +++ b/.ipynb_checkpoints/Pseudo_aleatoriedade-checkpoint.ipynb @@ -0,0 +1,522 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "ZlO2lOh3N0Tg", + "outputId": "46264a67-172f-4f81-a332-127f5e353daf" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5711513852214285" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "\n", + "np.random.rand()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "q1bQCtj1WMr1" + }, + "source": [ + "Von Neumann - Middle-square method" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "bq-ohAXOPIC6" + }, + "outputs": [], + "source": [ + "# semente = 5 # momoento que o primeiro rand é rodado\n", + "# formula(x) = x * 3 / 2\n", + "# formula(5) = 7.5\n", + "# formula(7.5) = 11.25" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iLk0cfiBQpkQ", + "outputId": "c0a4bc11-17b0-4d96-d083-1f3394bf2004" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "7.5" + ] + }, + "execution_count": 2, + "metadata": { + "tags": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "5*3/2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "BPpK-g0gQqdm", + "outputId": "4721dbcc-f9e2-4cff-8d86-207d5a807001" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "11.25" + ] + }, + "execution_count": 3, + "metadata": { + "tags": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "7.5*3/2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "RUxgeL6TQrT5" + }, + "outputs": [], + "source": [ + "seed = 150\n", + "# 12345\n", + "# 90000*90000\n", + "# 8100000000\n", + "\n", + "def middle_square():\n", + " global seed\n", + " result = seed * seed\n", + " result = \"{0:08d}\".format(result)\n", + " result = result[2:6]\n", + " # print(result)\n", + " result = int(result)\n", + " seed = result\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "oihDkv4zRk66", + "outputId": "3b95e424-bee4-4168-e071-814572af829a" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "225\n", + "506\n", + "2560\n", + "5536\n", + "6472\n" + ] + } + ], + "source": [ + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "HzHl4iz-RrpZ" + }, + "outputs": [], + "source": [ + "from tqdm import tqdm\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "def test_random(pseudo_random_generator):\n", + " results = np.array([pseudo_random_generator() for i in tqdm(range(10000000))])\n", + " results = pd.DataFrame(np.array([results]).T, columns=[\"middle_square\"])\n", + " print(results.mean())\n", + " results.plot(kind='hist')\n", + " plt.show()\n", + " display(results.value_counts().head())" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "1BF-aR0aaWK4", + "outputId": "ddaf71a8-0b59-4da7-a1ef-8ec7d30af46e" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 10000000/10000000 [00:10<00:00, 953302.45it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "middle_square 5099.997823\n", + "dtype: float64\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light", + "tags": [] + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "middle_square\n", + "4100 2499987\n", + "6100 2499987\n", + "8100 2499987\n", + "2100 2499986\n", + "3388 1\n", + "dtype: int64" + ] + }, + "metadata": { + "tags": [] + }, + "output_type": "display_data" + } + ], + "source": [ + "seed = 150\n", + "\n", + "test_random(middle_square)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "8Vi30jb6To1K", + "outputId": "5285b2d7-932b-4cf0-91c0-42b53b974de5" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "#1: 225\n", + "#2: 506\n", + "#3: 2560\n", + "#4: 5536\n", + "#5: 6472\n", + "#6: 8867\n", + "#7: 6236\n", + "#8: 8876\n", + "#9: 7833\n", + "#10: 3558\n", + "#11: 6593\n", + "#12: 4676\n", + "#13: 8649\n", + "#14: 8052\n", + "#15: 8347\n", + "#16: 6724\n", + "#17: 2121\n", + "#18: 4986\n", + "#19: 8601\n", + "#20: 9772\n", + "#21: 4919\n", + "#22: 1965\n", + "#23: 8612\n", + "#24: 1665\n", + "#25: 7722\n", + "#26: 6292\n", + "#27: 5892\n", + "#28: 7156\n", + "#29: 2083\n", + "#30: 3388\n", + "#31: 4785\n", + "#32: 8962\n", + "#33: 3174\n", + "#34: 742\n", + "#35: 5505\n", + "#36: 3050\n", + "#37: 3025\n", + "#38: 1506\n", + "#39: 2680\n", + "#40: 1824\n", + "#41: 3269\n", + "#42: 6863\n", + "#43: 1007\n", + "#44: 140\n", + "#45: 196\n", + "#46: 384\n", + "#47: 1474\n", + "#48: 1726\n", + "#49: 9790\n", + "#50: 8441\n", + "#51: 2504\n", + "#52: 2700\n", + "#53: 2900\n", + "#54: 4100\n", + "#55: 8100\n", + "#56: 6100\n", + "#57: 2100\n", + "#58: 4100\n", + "We began with 150, and have repeated ourselves after 58 steps with 4100.\n" + ] + } + ], + "source": [ + "# From https://en.wikipedia.org/wiki/Middle-square_method\n", + "\n", + "seed_number = 150\n", + "\n", + "number = seed_number\n", + "already_seen = set()\n", + "counter = 0\n", + "\n", + "while number not in already_seen:\n", + " counter += 1\n", + " already_seen.add(number)\n", + " number = int(str(number * number).zfill(8)[2:6]) # zfill adds padding of zeroes\n", + " print(f\"#{counter}: {number}\")\n", + "\n", + "print(f\"We began with {seed_number}, and\"\n", + " f\" have repeated ourselves after {counter} steps\"\n", + " f\" with {number}.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "QuDRIHhjU0Q8" + }, + "outputs": [], + "source": [ + "x = 0\n", + "weil_counter = 0\n", + "k = int(\"0xb5ad4eceda1ce2a9\", 0)\n", + "\n", + "def msws():\n", + " global x, weil_counter, k\n", + " result = x * x\n", + " weil_counter += k\n", + " result += weil_counter\n", + " result = str(result).zfill(8)\n", + " result = result[2:6]\n", + " # print(result)\n", + " result = int(result)\n", + " x = result\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "4lbYR9QPZ65C", + "outputId": "c9d3b62b-944d-43d5-b287-1822eb53a62b" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "13091206342165455529" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "k" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "7OcZoJFIaDPr", + "outputId": "c842f056-b6ef-4b90-c414-21f0bb66479b" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 10000000/10000000 [00:14<00:00, 671183.45it/s]\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "middle_square 4967.842999\n", + "dtype: float64\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x=0\n", + "weil_counter=0\n", + "eixo_x=np.array([msws() for i in range(1000)])\n", + "eixo_y=np.array([msws() for i in range(1000)])\n", + "\n", + "plt.scatter(eixo_x,eixo_y,alpha=0.3)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [], + "name": "Pseudo aleatoriedade", + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/Pseudo_aleatoriedade.ipynb b/Pseudo_aleatoriedade.ipynb index f3e0f1f..fb26a92 100644 --- a/Pseudo_aleatoriedade.ipynb +++ b/Pseudo_aleatoriedade.ipynb @@ -1,490 +1,674 @@ { - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { "colab": { - "name": "Pseudo aleatoriedade", - "provenance": [], - "collapsed_sections": [] + "base_uri": "https://localhost:8080/" }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" + "id": "ZlO2lOh3N0Tg", + "outputId": "46264a67-172f-4f81-a332-127f5e353daf" + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5711513852214285" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" } + ], + "source": [ + "import numpy as np\n", + "\n", + "np.random.rand()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "q1bQCtj1WMr1" + }, + "source": [ + "Von Neumann - Middle-square method" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "bq-ohAXOPIC6" + }, + "outputs": [], + "source": [ + "# semente = 5 # momoento que o primeiro rand é rodado\n", + "# formula(x) = x * 3 / 2\n", + "# formula(5) = 7.5\n", + "# formula(7.5) = 11.25" + ] }, - "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "iLk0cfiBQpkQ", + "outputId": "c0a4bc11-17b0-4d96-d083-1f3394bf2004" + }, + "outputs": [ { - "cell_type": "code", - "metadata": { - "id": "ZlO2lOh3N0Tg", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "46264a67-172f-4f81-a332-127f5e353daf" - }, - "source": [ - "import numpy as np\n", - "\n", - "np.random.rand()" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "0.2565472028882839" - ] - }, - "metadata": { - "tags": [] - }, - "execution_count": 1 - } + "data": { + "text/plain": [ + "7.5" ] + }, + "execution_count": 2, + "metadata": { + "tags": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "5*3/2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, + "id": "BPpK-g0gQqdm", + "outputId": "4721dbcc-f9e2-4cff-8d86-207d5a807001" + }, + "outputs": [ { - "cell_type": "markdown", - "metadata": { - "id": "q1bQCtj1WMr1" - }, - "source": [ - "Von Neumann - Middle-square method" + "data": { + "text/plain": [ + "11.25" ] + }, + "execution_count": 3, + "metadata": { + "tags": [] + }, + "output_type": "execute_result" + } + ], + "source": [ + "7.5*3/2" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "RUxgeL6TQrT5" + }, + "outputs": [], + "source": [ + "seed = 150\n", + "# 12345\n", + "# 90000*90000\n", + "# 8100000000\n", + "\n", + "def middle_square():\n", + " global seed\n", + " result = seed * seed\n", + " result = \"{0:08d}\".format(result)\n", + " result = result[2:6]\n", + " # print(result)\n", + " result = int(result)\n", + " seed = result\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "oihDkv4zRk66", + "outputId": "3b95e424-bee4-4168-e071-814572af829a" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "225\n", + "506\n", + "2560\n", + "5536\n", + "6472\n" + ] + } + ], + "source": [ + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())\n", + "print(middle_square())" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "id": "HzHl4iz-RrpZ" + }, + "outputs": [ + { + "ename": "IndentationError", + "evalue": "unindent does not match any outer indentation level (, line 8)", + "output_type": "error", + "traceback": [ + "\u001b[1;36m File \u001b[1;32m\"\"\u001b[1;36m, line \u001b[1;32m8\u001b[0m\n\u001b[1;33m results = pd.DataFrame(np.array([results]).T, columns=[\"middle_square\"])\u001b[0m\n\u001b[1;37m ^\u001b[0m\n\u001b[1;31mIndentationError\u001b[0m\u001b[1;31m:\u001b[0m unindent does not match any outer indentation level\n" + ] + } + ], + "source": [ + "from tqdm import tqdm\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "def test_random(pseudo_random_generator):\n", + " results = np.array([pseudo_random_generator() for i in tqdm(range(10000000))])\n", + " results = pd.DataFrame(np.array([results]).T, columns=[\"middle_square\"])\n", + " print(results.mean())\n", + " results.plot(kind='hist')\n", + " plt.show()\n", + " display(results.value_counts().head())\n", + " results.describe()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 }, + "id": "1BF-aR0aaWK4", + "outputId": "ddaf71a8-0b59-4da7-a1ef-8ec7d30af46e" + }, + "outputs": [ { - "cell_type": "code", - "metadata": { - "id": "bq-ohAXOPIC6" - }, - "source": [ - "# semente = 5 # momoento que o primeiro rand é rodado\n", - "# formula(x) = x * 3 / 2\n", - "# formula(5) = 7.5\n", - "# formula(7.5) = 11.25" - ], - "execution_count": null, - "outputs": [] + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 10000000/10000000 [00:10<00:00, 953302.45it/s]\n" + ] }, { - "cell_type": "code", - "metadata": { - "id": "iLk0cfiBQpkQ", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "c0a4bc11-17b0-4d96-d083-1f3394bf2004" - }, - "source": [ - "5*3/2" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "7.5" - ] - }, - "metadata": { - "tags": [] - }, - "execution_count": 2 - } + "name": "stdout", + "output_type": "stream", + "text": [ + "middle_square 5099.997823\n", + "dtype: float64\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" ] + }, + "metadata": { + "needs_background": "light", + "tags": [] + }, + "output_type": "display_data" }, { - "cell_type": "code", - "metadata": { - "id": "BPpK-g0gQqdm", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "4721dbcc-f9e2-4cff-8d86-207d5a807001" - }, - "source": [ - "7.5*3/2" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "11.25" - ] - }, - "metadata": { - "tags": [] - }, - "execution_count": 3 - } + "data": { + "text/plain": [ + "middle_square\n", + "4100 2499987\n", + "6100 2499987\n", + "8100 2499987\n", + "2100 2499986\n", + "3388 1\n", + "dtype: int64" ] + }, + "metadata": { + "tags": [] + }, + "output_type": "display_data" + } + ], + "source": [ + "seed = 150\n", + "\n", + "test_random(middle_square)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, + "id": "8Vi30jb6To1K", + "outputId": "5285b2d7-932b-4cf0-91c0-42b53b974de5" + }, + "outputs": [ { - "cell_type": "code", - "metadata": { - "id": "RUxgeL6TQrT5" - }, - "source": [ - "seed = 150\n", - "# 12345\n", - "# 90000*90000\n", - "# 8100000000\n", - "\n", - "def middle_square():\n", - " global seed\n", - " result = seed * seed\n", - " result = \"{0:08d}\".format(result)\n", - " result = result[2:6]\n", - " # print(result)\n", - " result = int(result)\n", - " seed = result\n", - " return result" - ], - "execution_count": null, - "outputs": [] + "name": "stdout", + "output_type": "stream", + "text": [ + "#1: 225\n", + "#2: 506\n", + "#3: 2560\n", + "#4: 5536\n", + "#5: 6472\n", + "#6: 8867\n", + "#7: 6236\n", + "#8: 8876\n", + "#9: 7833\n", + "#10: 3558\n", + "#11: 6593\n", + "#12: 4676\n", + "#13: 8649\n", + "#14: 8052\n", + "#15: 8347\n", + "#16: 6724\n", + "#17: 2121\n", + "#18: 4986\n", + "#19: 8601\n", + "#20: 9772\n", + "#21: 4919\n", + "#22: 1965\n", + "#23: 8612\n", + "#24: 1665\n", + "#25: 7722\n", + "#26: 6292\n", + "#27: 5892\n", + "#28: 7156\n", + "#29: 2083\n", + "#30: 3388\n", + "#31: 4785\n", + "#32: 8962\n", + "#33: 3174\n", + "#34: 742\n", + "#35: 5505\n", + "#36: 3050\n", + "#37: 3025\n", + "#38: 1506\n", + "#39: 2680\n", + "#40: 1824\n", + "#41: 3269\n", + "#42: 6863\n", + "#43: 1007\n", + "#44: 140\n", + "#45: 196\n", + "#46: 384\n", + "#47: 1474\n", + "#48: 1726\n", + "#49: 9790\n", + "#50: 8441\n", + "#51: 2504\n", + "#52: 2700\n", + "#53: 2900\n", + "#54: 4100\n", + "#55: 8100\n", + "#56: 6100\n", + "#57: 2100\n", + "#58: 4100\n", + "We began with 150, and have repeated ourselves after 58 steps with 4100.\n" + ] + } + ], + "source": [ + "# From https://en.wikipedia.org/wiki/Middle-square_method\n", + "\n", + "seed_number = 150\n", + "\n", + "number = seed_number\n", + "already_seen = set()\n", + "counter = 0\n", + "\n", + "while number not in already_seen:\n", + " counter += 1\n", + " already_seen.add(number)\n", + " number = int(str(number * number).zfill(8)[2:6]) # zfill adds padding of zeroes\n", + " print(f\"#{counter}: {number}\")\n", + "\n", + "print(f\"We began with {seed_number}, and\"\n", + " f\" have repeated ourselves after {counter} steps\"\n", + " f\" with {number}.\")" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "id": "QuDRIHhjU0Q8" + }, + "outputs": [], + "source": [ + "x = 0\n", + "weil_counter = 0\n", + "k = int(\"0xb5ad4eceda1ce2a9\", 0)\n", + "\n", + "def msws():\n", + " global x, weil_counter, k\n", + " result = x * x\n", + " weil_counter += k\n", + " result += weil_counter\n", + " result = str(result).zfill(8)\n", + " result = result[2:6]\n", + " # print(result)\n", + " result = int(result)\n", + " x = result\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" }, + "id": "4lbYR9QPZ65C", + "outputId": "c9d3b62b-944d-43d5-b287-1822eb53a62b" + }, + "outputs": [ { - "cell_type": "code", - "metadata": { - "id": "oihDkv4zRk66", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "3b95e424-bee4-4168-e071-814572af829a" - }, - "source": [ - "print(middle_square())\n", - "print(middle_square())\n", - "print(middle_square())\n", - "print(middle_square())\n", - "print(middle_square())" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "stream", - "text": [ - "225\n", - "506\n", - "2560\n", - "5536\n", - "6472\n" - ], - "name": "stdout" - } + "data": { + "text/plain": [ + "13091206342165455529" ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "k" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 447 + }, + "id": "7OcZoJFIaDPr", + "outputId": "c842f056-b6ef-4b90-c414-21f0bb66479b" + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 10000000/10000000 [00:18<00:00, 542774.74it/s]\n" + ] }, { - "cell_type": "code", - "metadata": { - "id": "HzHl4iz-RrpZ" - }, - "source": [ - "from tqdm import tqdm\n", - "import pandas as pd\n", - "import matplotlib.pyplot as plt\n", - "\n", - "\n", - "def test_random(pseudo_random_generator):\n", - " results = np.array([pseudo_random_generator() for i in tqdm(range(10000000))])\n", - " results = pd.DataFrame(np.array([results]).T, columns=[\"middle_square\"])\n", - " print(results.mean())\n", - " results.plot(kind='hist')\n", - " plt.show()\n", - " display(results.value_counts().head())" - ], - "execution_count": null, - "outputs": [] + "name": "stdout", + "output_type": "stream", + "text": [ + "middle_square 4967.842999\n", + "dtype: float64\n" + ] }, { - "cell_type": "code", - "metadata": { - "id": "1BF-aR0aaWK4", - "colab": { - "base_uri": "https://localhost:8080/", - "height": 447 - }, - "outputId": "ddaf71a8-0b59-4da7-a1ef-8ec7d30af46e" - }, - "source": [ - "seed = 150\n", - "\n", - "test_random(middle_square)" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "stream", - "text": [ - "100%|██████████| 10000000/10000000 [00:10<00:00, 953302.45it/s]\n" - ], - "name": "stderr" - }, - { - "output_type": "stream", - "text": [ - "middle_square 5099.997823\n", - "dtype: float64\n" - ], - "name": "stdout" - }, - { - "output_type": "display_data", - "data": { - "image/png": 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\n", 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\n", + "text/plain": [ + "
" ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" }, { - "cell_type": "code", - "metadata": { - "id": "8Vi30jb6To1K", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "5285b2d7-932b-4cf0-91c0-42b53b974de5" - }, - "source": [ - "# From https://en.wikipedia.org/wiki/Middle-square_method\n", - "\n", - "seed_number = 150\n", - "\n", - "number = seed_number\n", - "already_seen = set()\n", - "counter = 0\n", - "\n", - "while number not in already_seen:\n", - " counter += 1\n", - " already_seen.add(number)\n", - " number = int(str(number * number).zfill(8)[2:6]) # zfill adds padding of zeroes\n", - " print(f\"#{counter}: {number}\")\n", - "\n", - "print(f\"We began with {seed_number}, and\"\n", - " f\" have repeated ourselves after {counter} steps\"\n", - " f\" with {number}.\")" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "stream", - "text": [ - "#1: 225\n", - "#2: 506\n", - "#3: 2560\n", - "#4: 5536\n", - "#5: 6472\n", - "#6: 8867\n", - "#7: 6236\n", - "#8: 8876\n", - "#9: 7833\n", - "#10: 3558\n", - "#11: 6593\n", - "#12: 4676\n", - "#13: 8649\n", - "#14: 8052\n", - "#15: 8347\n", - "#16: 6724\n", - "#17: 2121\n", - "#18: 4986\n", - "#19: 8601\n", - "#20: 9772\n", - "#21: 4919\n", - "#22: 1965\n", - "#23: 8612\n", - "#24: 1665\n", - "#25: 7722\n", - "#26: 6292\n", - "#27: 5892\n", - "#28: 7156\n", - "#29: 2083\n", - "#30: 3388\n", - "#31: 4785\n", - "#32: 8962\n", - "#33: 3174\n", - "#34: 742\n", - "#35: 5505\n", - "#36: 3050\n", - "#37: 3025\n", - "#38: 1506\n", - "#39: 2680\n", - "#40: 1824\n", - "#41: 3269\n", - "#42: 6863\n", - "#43: 1007\n", - "#44: 140\n", - "#45: 196\n", - "#46: 384\n", - "#47: 1474\n", - "#48: 1726\n", - "#49: 9790\n", - "#50: 8441\n", - "#51: 2504\n", - "#52: 2700\n", - "#53: 2900\n", - "#54: 4100\n", - "#55: 8100\n", - "#56: 6100\n", - "#57: 2100\n", - "#58: 4100\n", - "We began with 150, and have repeated ourselves after 58 steps with 4100.\n" - ], - "name": "stdout" - } + "data": { + "text/plain": [ + "middle_square\n", + "776 1079\n", + "658 1078\n", + "632 1077\n", + "552 1077\n", + "493 1077\n", + "dtype: int64" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_random(msws)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting random numbers Middle-Square Weil Counter" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "id": "Xf1_5EF_aizz" + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x=0\n", + "weil_counter=0\n", + "x_axis=np.array([msws() for i in range(1000)])\n", + "y_axis=np.array([msws() for i in range(1000)])\n", + "\n", + "plt.scatter(x_axis,y_axis,alpha=0.3)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting random numbers Random" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x_axis=np.random.random(1000)\n", + "y_axis=np.random.random(1000)\n", + "\n", + "plt.scatter(x_axis,y_axis,alpha=0.3)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suggested alteration MSWS" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "x = 0\n", + "weil_counter = 0\n", + "k = int(\"0xb5ad4eceda1ce2a9\", 0)\n", + "def msws_adjusted():\n", + " global x, weil_counter, k\n", + " result = x * x\n", + " weil_counter += k\n", + " result += weil_counter\n", + " result = str(result).zfill(8)\n", + " #Using the second and sixth from right to left\n", + " result = result[-6:-2]\n", + " result = int(result)\n", + " x = result\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 10000000/10000000 [00:15<00:00, 654749.71it/s]\n" + ] }, { - "cell_type": "code", - "metadata": { - "id": "QuDRIHhjU0Q8" - }, - "source": [ - "x = 0\n", - "weil_counter = 0\n", - "k = int(\"0xb5ad4eceda1ce2a9\", 0)\n", - "\n", - "def msws():\n", - " global x, weil_counter, k\n", - " result = x * x\n", - " weil_counter += k\n", - " result += weil_counter\n", - " result = str(result).zfill(8)\n", - " result = result[2:6]\n", - " # print(result)\n", - " result = int(result)\n", - " x = result\n", - " return result" - ], - "execution_count": null, - "outputs": [] + "name": "stdout", + "output_type": "stream", + "text": [ + "middle_square 5002.164908\n", + "dtype: float64\n" + ] }, { - "cell_type": "code", - "metadata": { - "id": "4lbYR9QPZ65C", - "colab": { - "base_uri": "https://localhost:8080/" - }, - "outputId": "c9d3b62b-944d-43d5-b287-1822eb53a62b" - }, - "source": [ - "k" - ], - "execution_count": null, - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": [ - "13091206342165455529" - ] - }, - "metadata": { - "tags": [] - }, - "execution_count": 82 - } + "data": { + "image/png": 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\n", 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\n", 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