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kvedala/c-algorithms.ipynb

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c-algorithms.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Compile and run C Algorithms",
"provenance": [],
"collapsed_sections": [],
"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/gist/kvedala/27f1b0b6502af935f6917673ec43bcd7/plot-durand_kerner-log.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "b29wElh1z2Ye",
"colab_type": "text"
},
"source": [
"# Initializer\n",
"Documentation available here: https://kvedala.github.io/C"
]
},
{
"cell_type": "code",
"metadata": {
"id": "WJLeiiCj6UZs",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import widgets, animation\n",
"from IPython.display import display\n",
"import ipywidgets\n",
"from plotly import express as px\n",
"from plotly import graph_objects as go\n",
"from matplotlib.animation import FuncAnimation\n",
"rand = np.random.default_rng()"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "gALUN9Dbz4iK",
"colab_type": "text"
},
"source": [
"# Setup environment\n",
"1. Clone the [GitHub repository](https://github.com/kvedala/C.git) \n",
"2. Compile and build the code"
]
},
{
"cell_type": "code",
"metadata": {
"id": "f6IiAkSWVNgI",
"colab_type": "code",
"colab": {}
},
"source": [
"%%bash\n",
"apt -qq update\n",
"apt -qq install ninja-build cmake\n",
"git clone https://github.com/kvedala/C.git\n",
"mkdir C/build\n",
"cd C/build\n",
"cmake -G Ninja ..\n",
"cmake --build ."
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "m8oQJFVe0SkS",
"colab_type": "text"
},
"source": [
"# [Durand Kerner Roots](https://kvedala.github.io/C/da/d38/durand__kerner__roots_8c.html)\n",
"## Setup variables\n",
"For Durand-Kerner algorithm, this creates a polynomial of degree `N`. The coefficients are randomly distributed in the interval `[a,b]`. The "
]
},
{
"cell_type": "code",
"metadata": {
"id": "AbQQ_sMSUzAq",
"colab_type": "code",
"outputId": "8b6cdfa0-2c9b-4697-c368-95116b4f7d42",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 51
}
},
"source": [
"a = -2\n",
"b = 2\n",
"N = 10\n",
"coeffs = rand.random(size=(N,)) * (b - a) + a \n",
"\n",
"print(\"The polynomial to find roots is: \")\n",
"coeffs_str = \"\"\n",
"for i, c in enumerate(coeffs):\n",
" coeffs_str += \"%.4g \" % c\n",
" print(\"%.4g x^%d\" %(c, N-i-1), end=\" + \")\n",
"print(\"\\b\\b= 0\")"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"The polynomial to find roots is: \n",
"1.208 x^9 + 1.19 x^8 + 1.699 x^7 + -0.727 x^6 + -0.8313 x^5 + 1.535 x^4 + 1.814 x^3 + -1.277 x^2 + 1.899 x^1 + 1.384 x^0 + \b\b= 0\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aDrGH8hs3uLh",
"colab_type": "text"
},
"source": [
"## Execute the compiled C-function"
]
},
{
"cell_type": "code",
"metadata": {
"id": "a0oTYsz_Y633",
"colab_type": "code",
"outputId": "a1398b85-350c-472a-baec-675309871b96",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 272
}
},
"source": [
"!./build/numerical_methods/durand_kerner_roots $coeffs_str"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"Computing the roots for:\n",
"\t(1.208) x^9 + (1.19) x^8 + (1.699) x^7 + (-0.727) x^6 + (-0.8313) x^5 + (1.535) x^4 + (1.814) x^3 + (-1.277) x^2 + (1.899) x^1 + (1.384) x^0 = 0\n",
"\n",
"Iterations: 149\n",
"\t 0.902+0.4628j\n",
"\t 0.902-0.4628j\n",
"\t 0.36-0.8036j\n",
"\t-0.5329 +1.444j\n",
"\t-0.9732 -0.524j\n",
"\t-0.5329 -1.444j\n",
"\t-0.9732 +0.524j\n",
"\t 0.36+0.8036j\n",
"\t-0.4969+2.816e-17j\n",
"absolute average change: 1.065e-13\n",
"Time taken: 0.006181 sec\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4sMFnaiZ3vy1",
"colab_type": "text"
},
"source": [
"## Read stored log file\n",
"Convert the log file into a pandas data frame and convert complex number values from string format to complex numbers. Save the real and imaginary components of the complex root approximations in separate columns for convenience."
]
},
{
"cell_type": "code",
"metadata": {
"id": "O_l3Ei0U6tKA",
"colab_type": "code",
"colab": {}
},
"source": [
"d = pd.read_csv('durand_kerner.log.csv')\n",
"root_columns = [c for c in d.columns if c not in ['iter#', 'avg. correction']]"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "rK7KGwRg7ct8",
"colab_type": "code",
"outputId": "672956b8-54bf-4eec-d319-42645e0fac71",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 598
}
},
"source": [
"to_complex = lambda s: complex(s.replace(' ', ''))\n",
"\n",
"for col in root_columns:\n",
" d.loc[:,col] = d.loc[:,col].apply(to_complex)\n",
" d.loc[:,col + '_r'] = d.loc[:,col].apply(np.real).astype(float)\n",
" d.loc[:,col + '_i'] = d.loc[:,col].apply(np.imag).astype(float)\n",
" \n",
"display(d.head())\n",
"display(d.tail())"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
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" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>iter#</th>\n",
" <th>root_0</th>\n",
" <th>root_1</th>\n",
" <th>root_2</th>\n",
" <th>root_3</th>\n",
" <th>root_4</th>\n",
" <th>root_5</th>\n",
" <th>root_6</th>\n",
" <th>root_7</th>\n",
" <th>root_8</th>\n",
" <th>avg. correction</th>\n",
" <th>root_0_r</th>\n",
" <th>root_0_i</th>\n",
" <th>root_1_r</th>\n",
" <th>root_1_i</th>\n",
" <th>root_2_r</th>\n",
" <th>root_2_i</th>\n",
" <th>root_3_r</th>\n",
" <th>root_3_i</th>\n",
" <th>root_4_r</th>\n",
" <th>root_4_i</th>\n",
" <th>root_5_r</th>\n",
" <th>root_5_i</th>\n",
" <th>root_6_r</th>\n",
" <th>root_6_i</th>\n",
" <th>root_7_r</th>\n",
" <th>root_7_i</th>\n",
" <th>root_8_r</th>\n",
" <th>root_8_i</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0</td>\n",
" <td>1.270000e+09+1.814000e+09j</td>\n",
" <td>9.655000e+08+1.588000e+09j</td>\n",
" <td>8.856000e+08+1.458000e+09j</td>\n",
" <td>1.163000e+09+1.927000e+08j</td>\n",
" <td>1.318000e+09+1.574000e+09j</td>\n",
" <td>1.793000e+09+2.053000e+09j</td>\n",
" <td>9.696000e+08+7.220000e+08j</td>\n",
" <td>1.593000e+09+1.745000e+09j</td>\n",
" <td>1.651000e+09+6.870000e+08j</td>\n",
" <td>NaN</td>\n",
" <td>1.270000e+09</td>\n",
" <td>1.814000e+09</td>\n",
" <td>9.655000e+08</td>\n",
" <td>1.588000e+09</td>\n",
" <td>8.856000e+08</td>\n",
" <td>1.458000e+09</td>\n",
" <td>1.163000e+09</td>\n",
" <td>192700000.0</td>\n",
" <td>1.318000e+09</td>\n",
" <td>1.574000e+09</td>\n",
" <td>1.793000e+09</td>\n",
" <td>2.053000e+09</td>\n",
" <td>969600000.0</td>\n",
" <td>722000000.0</td>\n",
" <td>1.593000e+09</td>\n",
" <td>1.745000e+09</td>\n",
" <td>1.651000e+09</td>\n",
" <td>687000000.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1</td>\n",
" <td>-5.346000e+13-3.378000e+13j</td>\n",
" <td>9.796000e+08+1.679000e+09j</td>\n",
" <td>8.667000e+08+1.449000e+09j</td>\n",
" <td>1.163000e+09+1.926000e+08j</td>\n",
" <td>1.281000e+09+1.343000e+09j</td>\n",
" <td>1.705000e+09+2.012000e+09j</td>\n",
" <td>9.699000e+08+7.220000e+08j</td>\n",
" <td>1.824000e+09+1.839000e+09j</td>\n",
" <td>1.653000e+09+6.835000e+08j</td>\n",
" <td>6.324000e+13</td>\n",
" <td>-5.346000e+13</td>\n",
" <td>-3.378000e+13</td>\n",
" <td>9.796000e+08</td>\n",
" <td>1.679000e+09</td>\n",
" <td>8.667000e+08</td>\n",
" <td>1.449000e+09</td>\n",
" <td>1.163000e+09</td>\n",
" <td>192600000.0</td>\n",
" <td>1.281000e+09</td>\n",
" <td>1.343000e+09</td>\n",
" <td>1.705000e+09</td>\n",
" <td>2.012000e+09</td>\n",
" <td>969900000.0</td>\n",
" <td>722000000.0</td>\n",
" <td>1.824000e+09</td>\n",
" <td>1.839000e+09</td>\n",
" <td>1.653000e+09</td>\n",
" <td>683500000.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2</td>\n",
" <td>-1.044000e+10-9.918000e+09j</td>\n",
" <td>-1.149000e+11+1.375000e+11j</td>\n",
" <td>7.891000e+08+1.481000e+09j</td>\n",
" <td>1.163000e+09+1.931000e+08j</td>\n",
" <td>1.124000e+09+8.713000e+08j</td>\n",
" <td>-1.465000e+08+1.580000e+09j</td>\n",
" <td>9.640000e+08+7.077000e+08j</td>\n",
" <td>1.967000e+09+1.665000e+09j</td>\n",
" <td>1.554000e+09+6.766000e+08j</td>\n",
" <td>6.322000e+13</td>\n",
" <td>-1.044000e+10</td>\n",
" <td>-9.918000e+09</td>\n",
" <td>-1.149000e+11</td>\n",
" <td>1.375000e+11</td>\n",
" <td>7.891000e+08</td>\n",
" <td>1.481000e+09</td>\n",
" <td>1.163000e+09</td>\n",
" <td>193100000.0</td>\n",
" <td>1.124000e+09</td>\n",
" <td>8.713000e+08</td>\n",
" <td>-1.465000e+08</td>\n",
" <td>1.580000e+09</td>\n",
" <td>964000000.0</td>\n",
" <td>707700000.0</td>\n",
" <td>1.967000e+09</td>\n",
" <td>1.665000e+09</td>\n",
" <td>1.554000e+09</td>\n",
" <td>676600000.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>3</td>\n",
" <td>-9.990000e+09-1.028000e+10j</td>\n",
" <td>2.037000e+09+3.472000e+09j</td>\n",
" <td>-2.201000e+09+2.112000e+09j</td>\n",
" <td>1.164000e+09+2.223000e+08j</td>\n",
" <td>5.561000e+08+2.046000e+09j</td>\n",
" <td>-9.227000e+07+1.530000e+09j</td>\n",
" <td>9.263000e+08+6.980000e+08j</td>\n",
" <td>3.237000e+09+6.670000e+09j</td>\n",
" <td>1.523000e+09+5.961000e+08j</td>\n",
" <td>1.779000e+11</td>\n",
" <td>-9.990000e+09</td>\n",
" <td>-1.028000e+10</td>\n",
" <td>2.037000e+09</td>\n",
" <td>3.472000e+09</td>\n",
" <td>-2.201000e+09</td>\n",
" <td>2.112000e+09</td>\n",
" <td>1.164000e+09</td>\n",
" <td>222300000.0</td>\n",
" <td>5.561000e+08</td>\n",
" <td>2.046000e+09</td>\n",
" <td>-9.227000e+07</td>\n",
" <td>1.530000e+09</td>\n",
" <td>926300000.0</td>\n",
" <td>698000000.0</td>\n",
" <td>3.237000e+09</td>\n",
" <td>6.670000e+09</td>\n",
" <td>1.523000e+09</td>\n",
" <td>596100000.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>4</td>\n",
" <td>-5.612000e+09-8.478000e+09j</td>\n",
" <td>3.001000e+09+1.080000e+10j</td>\n",
" <td>-2.167000e+09+2.194000e+09j</td>\n",
" <td>1.165000e+09+2.236000e+08j</td>\n",
" <td>5.949000e+08+1.913000e+09j</td>\n",
" <td>-9.958000e+07+1.525000e+09j</td>\n",
" <td>9.236000e+08+6.988000e+08j</td>\n",
" <td>1.237000e+10+1.801000e+10j</td>\n",
" <td>1.520000e+09+5.875000e+08j</td>\n",
" <td>1.456000e+10</td>\n",
" <td>-5.612000e+09</td>\n",
" <td>-8.478000e+09</td>\n",
" <td>3.001000e+09</td>\n",
" <td>1.080000e+10</td>\n",
" <td>-2.167000e+09</td>\n",
" <td>2.194000e+09</td>\n",
" <td>1.165000e+09</td>\n",
" <td>223600000.0</td>\n",
" <td>5.949000e+08</td>\n",
" <td>1.913000e+09</td>\n",
" <td>-9.958000e+07</td>\n",
" <td>1.525000e+09</td>\n",
" <td>923600000.0</td>\n",
" <td>698800000.0</td>\n",
" <td>1.237000e+10</td>\n",
" <td>1.801000e+10</td>\n",
" <td>1.520000e+09</td>\n",
" <td>587500000.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" iter# root_0 ... root_8_r root_8_i\n",
"0 0 1.270000e+09+1.814000e+09j ... 1.651000e+09 687000000.0\n",
"1 1 -5.346000e+13-3.378000e+13j ... 1.653000e+09 683500000.0\n",
"2 2 -1.044000e+10-9.918000e+09j ... 1.554000e+09 676600000.0\n",
"3 3 -9.990000e+09-1.028000e+10j ... 1.523000e+09 596100000.0\n",
"4 4 -5.612000e+09-8.478000e+09j ... 1.520000e+09 587500000.0\n",
"\n",
"[5 rows x 29 columns]"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"text/html": [
"<div>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>iter#</th>\n",
" <th>root_0</th>\n",
" <th>root_1</th>\n",
" <th>root_2</th>\n",
" <th>root_3</th>\n",
" <th>root_4</th>\n",
" <th>root_5</th>\n",
" <th>root_6</th>\n",
" <th>root_7</th>\n",
" <th>root_8</th>\n",
" <th>avg. correction</th>\n",
" <th>root_0_r</th>\n",
" <th>root_0_i</th>\n",
" <th>root_1_r</th>\n",
" <th>root_1_i</th>\n",
" <th>root_2_r</th>\n",
" <th>root_2_i</th>\n",
" <th>root_3_r</th>\n",
" <th>root_3_i</th>\n",
" <th>root_4_r</th>\n",
" <th>root_4_i</th>\n",
" <th>root_5_r</th>\n",
" <th>root_5_i</th>\n",
" <th>root_6_r</th>\n",
" <th>root_6_i</th>\n",
" <th>root_7_r</th>\n",
" <th>root_7_i</th>\n",
" <th>root_8_r</th>\n",
" <th>root_8_i</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>145</th>\n",
" <td>145</td>\n",
" <td>0.919300+0.458100j</td>\n",
" <td>0.897400-0.462900j</td>\n",
" <td>0.352400-0.784900j</td>\n",
" <td>-0.534100+1.444000j</td>\n",
" <td>-0.976800-0.525100j</td>\n",
" <td>-0.532800-1.443000j</td>\n",
" <td>-0.955400+0.524600j</td>\n",
" <td>0.366100+0.777600j</td>\n",
" <td>-0.493200-0.006509j</td>\n",
" <td>2.847000e-01</td>\n",
" <td>0.9193</td>\n",
" <td>0.4581</td>\n",
" <td>0.8974</td>\n",
" <td>-0.4629</td>\n",
" <td>0.3524</td>\n",
" <td>-0.7849</td>\n",
" <td>-0.5341</td>\n",
" <td>1.444</td>\n",
" <td>-0.9768</td>\n",
" <td>-0.5251</td>\n",
" <td>-0.5328</td>\n",
" <td>-1.443</td>\n",
" <td>-0.9554</td>\n",
" <td>0.5246</td>\n",
" <td>0.3661</td>\n",
" <td>0.7776</td>\n",
" <td>-0.4932</td>\n",
" <td>-6.509000e-03</td>\n",
" </tr>\n",
" <tr>\n",
" <th>146</th>\n",
" <td>146</td>\n",
" <td>0.901200+0.463400j</td>\n",
" <td>0.902100-0.462700j</td>\n",
" <td>0.360400-0.804100j</td>\n",
" <td>-0.532900+1.444000j</td>\n",
" <td>-0.973200-0.523800j</td>\n",
" <td>-0.532900-1.444000j</td>\n",
" <td>-0.973000+0.523600j</td>\n",
" <td>0.360200+0.803700j</td>\n",
" <td>-0.496900+0.000004j</td>\n",
" <td>2.677000e-02</td>\n",
" <td>0.9012</td>\n",
" <td>0.4634</td>\n",
" <td>0.9021</td>\n",
" <td>-0.4627</td>\n",
" <td>0.3604</td>\n",
" <td>-0.8041</td>\n",
" <td>-0.5329</td>\n",
" <td>1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>-0.5238</td>\n",
" <td>-0.5329</td>\n",
" <td>-1.444</td>\n",
" <td>-0.9730</td>\n",
" <td>0.5236</td>\n",
" <td>0.3602</td>\n",
" <td>0.8037</td>\n",
" <td>-0.4969</td>\n",
" <td>4.303000e-06</td>\n",
" </tr>\n",
" <tr>\n",
" <th>147</th>\n",
" <td>147</td>\n",
" <td>0.902000+0.462800j</td>\n",
" <td>0.902000-0.462800j</td>\n",
" <td>0.360000-0.803600j</td>\n",
" <td>-0.532900+1.444000j</td>\n",
" <td>-0.973200-0.524000j</td>\n",
" <td>-0.532900-1.444000j</td>\n",
" <td>-0.973200+0.524000j</td>\n",
" <td>0.360000+0.803600j</td>\n",
" <td>-0.496900-0.000000j</td>\n",
" <td>9.285000e-04</td>\n",
" <td>0.9020</td>\n",
" <td>0.4628</td>\n",
" <td>0.9020</td>\n",
" <td>-0.4628</td>\n",
" <td>0.3600</td>\n",
" <td>-0.8036</td>\n",
" <td>-0.5329</td>\n",
" <td>1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>-0.5240</td>\n",
" <td>-0.5329</td>\n",
" <td>-1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>0.5240</td>\n",
" <td>0.3600</td>\n",
" <td>0.8036</td>\n",
" <td>-0.4969</td>\n",
" <td>-2.211000e-12</td>\n",
" </tr>\n",
" <tr>\n",
" <th>148</th>\n",
" <td>148</td>\n",
" <td>0.902000+0.462800j</td>\n",
" <td>0.902000-0.462800j</td>\n",
" <td>0.360000-0.803600j</td>\n",
" <td>-0.532900+1.444000j</td>\n",
" <td>-0.973200-0.524000j</td>\n",
" <td>-0.532900-1.444000j</td>\n",
" <td>-0.973200+0.524000j</td>\n",
" <td>0.360000+0.803600j</td>\n",
" <td>-0.496900+0.000000j</td>\n",
" <td>4.987000e-07</td>\n",
" <td>0.9020</td>\n",
" <td>0.4628</td>\n",
" <td>0.9020</td>\n",
" <td>-0.4628</td>\n",
" <td>0.3600</td>\n",
" <td>-0.8036</td>\n",
" <td>-0.5329</td>\n",
" <td>1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>-0.5240</td>\n",
" <td>-0.5329</td>\n",
" <td>-1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>0.5240</td>\n",
" <td>0.3600</td>\n",
" <td>0.8036</td>\n",
" <td>-0.4969</td>\n",
" <td>8.900000e-17</td>\n",
" </tr>\n",
" <tr>\n",
" <th>149</th>\n",
" <td>149</td>\n",
" <td>0.902000+0.462800j</td>\n",
" <td>0.902000-0.462800j</td>\n",
" <td>0.360000-0.803600j</td>\n",
" <td>-0.532900+1.444000j</td>\n",
" <td>-0.973200-0.524000j</td>\n",
" <td>-0.532900-1.444000j</td>\n",
" <td>-0.973200+0.524000j</td>\n",
" <td>0.360000+0.803600j</td>\n",
" <td>-0.496900+0.000000j</td>\n",
" <td>1.065000e-13</td>\n",
" <td>0.9020</td>\n",
" <td>0.4628</td>\n",
" <td>0.9020</td>\n",
" <td>-0.4628</td>\n",
" <td>0.3600</td>\n",
" <td>-0.8036</td>\n",
" <td>-0.5329</td>\n",
" <td>1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>-0.5240</td>\n",
" <td>-0.5329</td>\n",
" <td>-1.444</td>\n",
" <td>-0.9732</td>\n",
" <td>0.5240</td>\n",
" <td>0.3600</td>\n",
" <td>0.8036</td>\n",
" <td>-0.4969</td>\n",
" <td>2.816000e-17</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" iter# root_0 ... root_8_r root_8_i\n",
"145 145 0.919300+0.458100j ... -0.4932 -6.509000e-03\n",
"146 146 0.901200+0.463400j ... -0.4969 4.303000e-06\n",
"147 147 0.902000+0.462800j ... -0.4969 -2.211000e-12\n",
"148 148 0.902000+0.462800j ... -0.4969 8.900000e-17\n",
"149 149 0.902000+0.462800j ... -0.4969 2.816000e-17\n",
"\n",
"[5 rows x 29 columns]"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "-FRyeuTU4GyG",
"colab_type": "text"
},
"source": [
"## Plotting\n",
"### Plot convergence of error per iteration"
]
},
{
"cell_type": "code",
"metadata": {
"id": "uT70NXGL9Fbq",
"colab_type": "code",
"outputId": "e6733bea-792b-47d5-e082-d360ffb47e00",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 296
}
},
"source": [
"fig, ax = plt.subplots(figsize=(8,4))\n",
"ax = d.plot(x='iter#', y='avg. correction', ax=ax)\n",
"ax.grid(True)\n",
"ax.set_yscale('log')\n",
"ax.set_ylabel('Avg. error in roots')\n",
"ax.set_xlabel('Iter #')"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 0, 'Iter #')"
]
},
"metadata": {
"tags": []
},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MfPUDkmC4RR1",
"colab_type": "text"
},
"source": [
"### Obtain limits for X (real components) and Y (imaginary components)"
]
},
{
"cell_type": "code",
"metadata": {
"id": "kgQUxPdgC8Sj",
"colab_type": "code",
"colab": {}
},
"source": [
"xmin, xmax = d.iloc[-1][root_columns].apply(np.real).min(), d.iloc[-1][root_columns].apply(np.real).max()\n",
"ymin, ymax = d.iloc[-1][root_columns].apply(np.imag).min(), d.iloc[-1][root_columns].apply(np.imag).max()"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "5DfEcnyf4YJy",
"colab_type": "text"
},
"source": [
"### Plot complex plane\n",
"The root approximations are color-coded. The lines show the convergence path of the roots. The initial approximations are indicated by '`o`' and the final root approximations are represented by '`x`'. The first plot is a static plot using Matplotlib."
]
},
{
"cell_type": "code",
"metadata": {
"id": "YZHR6YXrDt2e",
"colab_type": "code",
"outputId": "6de069a2-57c1-4e90-8fc3-e6cf3cf20341",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 497
}
},
"source": [
"window = 1\n",
"fig, ax = plt.subplots(figsize=(8,8))\n",
"for col in root_columns:\n",
" l = ax.plot(d.loc[:,col + '_r'], d.loc[:,col + '_i'], label=col)\n",
" ax.plot(d.loc[:,col + '_r'].iloc[-1], d.loc[:,col + '_i'].iloc[-1], 'x', c=l[0].get_color(), markersize=10)\n",
" ax.plot(d.loc[0,col + '_r'], d.loc[0,col + '_i'], 'o', c=l[0].get_color(), markersize=10)\n",
"ax.set_xlim(xmin - window, xmax + window)\n",
"ax.set_ylim(ymin - window, ymax + window)\n",
"ax.set_xlabel(r'Real(x)')\n",
"ax.set_ylabel(r'Imag(x)')\n",
"ax.legend()\n",
"ax.grid()\n",
"plt.show(fig)"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Vh9X5FNcQy3g",
"colab_type": "text"
},
"source": [
"### Plot Interactive graph using Plotly"
]
},
{
"cell_type": "code",
"metadata": {
"id": "nwml4DKM6GQu",
"colab_type": "code",
"outputId": "6d0fb518-e96f-4d2a-e8a1-e420d3a9d4f2",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 617
}
},
"source": [
"window = 1\n",
"fig = go.Figure()\n",
"for col in root_columns:\n",
" fig.add_trace(\n",
" go.Scatter(x=d.loc[:,col + '_r'], y=d.loc[:,col + '_i'], name=col, \n",
" mode='lines+markers'),\n",
" )\n",
" # fig.add_trace(\n",
" # go.Scatter(x=d.loc[0,col + '_r'], y=d.loc[0,col + '_i'], name=col, \n",
" # mode='markers')\n",
" # )\n",
" # ax.plot(d.loc[:,col + '_r'].iloc[-1], d.loc[:,col + '_i'].iloc[-1], 'x', c=l[0].get_color(), markersize=10)\n",
" # ax.plot(d.loc[0,col + '_r'], d.loc[0,col + '_i'], 'o', c=l[0].get_color(), markersize=10)\n",
"fig.update_xaxes(range=[xmin - window, xmax + window])\n",
"fig.update_yaxes(range=[ymin - window, ymax + window])\n",
"fig.update_layout(xaxis_title=\"Real\", yaxis_title=\"Imag\", \n",
" autosize=False, width=600, height=600)\n",
"fig.show()"
],
"execution_count": 0,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/html": [
"<html>\n",
"<head><meta charset=\"utf-8\" /></head>\n",
"<body>\n",
" <div>\n",
" <script src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_SVG\"></script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script>\n",
" <script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script>\n",
" <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script> \n",
" <div id=\"02e4c8c6-1ff8-4fd3-a42c-967c8117de2c\" class=\"plotly-graph-div\" style=\"height:600px; width:600px;\"></div>\n",
" <script type=\"text/javascript\">\n",
" \n",
" window.PLOTLYENV=window.PLOTLYENV || {};\n",
" \n",
" if (document.getElementById(\"02e4c8c6-1ff8-4fd3-a42c-967c8117de2c\")) {\n",
" Plotly.newPlot(\n",
" '02e4c8c6-1ff8-4fd3-a42c-967c8117de2c',\n",
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\"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 600, \"xaxis\": {\"range\": [-1.9731999999999998, 1.9020000000000001], \"title\": {\"text\": \"Real\"}}, \"yaxis\": {\"range\": [-2.444, 2.444], \"title\": {\"text\": \"Imag\"}}},\n",
" {\"responsive\": true}\n",
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" observer.disconnect();\n",
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"</body>\n",
"</html>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "lnio6-9Z9e52",
"colab_type": "code",
"outputId": "2030cc9b-bda0-4dd0-be32-4f4704828e98",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
}
},
"source": [
"window = 2\n",
"fig, ax = plt.subplots(figsize=(8,8))\n",
"lines = []\n",
"line, = ax.plot([],[])\n",
"\n",
"for i, col in enumerate(root_columns):\n",
" l, = ax.plot([], [], label=col)\n",
" ax.plot(d.loc[:,col + '_r'].iloc[-1], d.loc[:,col + '_i'].iloc[-1], 'x', c=l.get_color(), markersize=10)\n",
" ax.plot(d.loc[0,col + '_r'], d.loc[0,col + '_i'], 'o', c=l.get_color(), markersize=10)\n",
" lines.append(l)\n",
" \n",
"ax.set_xlim(xmin - window, xmax + window)\n",
"ax.set_ylim(ymin - window, ymax + window)\n",
"ax.set_xlabel(r'Real(x)')\n",
"ax.set_ylabel(r'Imag(x)')\n",
"ax.legend()\n",
"ax.grid()\n",
"\n",
"def init_plot():\n",
" for i, col in enumerate(root_columns):\n",
" # l = ax.plot(d.loc[0,col + '_r'], d.loc[0,col + '_i'], label=col)\n",
" lines[i].set_data([], [])\n",
" # ax.plot(d.loc[:,col + '_r'].iloc[-1], d.loc[:,col + '_i'].iloc[-1], 'x', c=l[0].get_color(), markersize=10)\n",
" # ax.plot(d.loc[0,col + '_r'], d.loc[0,col + '_i'], 'o', c=l[0].get_color(), markersize=10)\n",
" # lines.append(l)\n",
" return lines\n",
"\n",
"def update_frame(frame):\n",
" for i, col in enumerate(root_columns):\n",
" lines[i].set_data(d.loc[0:frame,col + '_r'], d.loc[0:frame,col + '_i'])\n",
" return lines\n",
"\n",
"anim = FuncAnimation(fig, update_frame, frames=d.shape[0],\n",
" init_func=init_plot, blit=True, interval=50)\n",
"plt.rc('animation', html='jshtml')\n",
"anim"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img3207d75a5a2a4651b14169d0c1a2bb16\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider3207d75a5a2a4651b14169d0c1a2bb16\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim3207d75a5a2a4651b14169d0c1a2bb16.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim3207d75a5a2a4651b14169d0c1a2bb16.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select3207d75a5a2a4651b14169d0c1a2bb16\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_3207d75a5a2a4651b14169d0c1a2bb16\"\n",
" >\n",
" <label for=\"_anim_radio1_3207d75a5a2a4651b14169d0c1a2bb16\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_3207d75a5a2a4651b14169d0c1a2bb16\"\n",
" checked>\n",
" <label for=\"_anim_radio2_3207d75a5a2a4651b14169d0c1a2bb16\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_3207d75a5a2a4651b14169d0c1a2bb16\"\n",
" >\n",
" <label for=\"_anim_radio3_3207d75a5a2a4651b14169d0c1a2bb16\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img3207d75a5a2a4651b14169d0c1a2bb16\";\n",
" var slider_id = \"_anim_slider3207d75a5a2a4651b14169d0c1a2bb16\";\n",
" var loop_select_id = \"_anim_loop_select3207d75a5a2a4651b14169d0c1a2bb16\";\n",
" var frames = new Array(150);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAJACAYAAABlmtk2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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notebook.ipynb
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@kvedala
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kvedala commented Jun 3, 2020

A support notebook to compile and run C algorithms online - https://github.com/kvedala/C
Sample implementations to generate images and animations from the algorithm outputs.

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