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murraybj committed Oct 15, 2024
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: b0447c1d44c8bed488ca48d70a7cce9f
tags: 645f666f9bcd5a90fca523b33c5a78b7
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# Dynamic Exercises
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Collocation Matrix"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[\n",
"[np.float64(-9.000001008080126), np.float64(-4.139388773624379), np.float64(1.7393879671602779), np.float64(-3.0000002520200333)],\n",
"[np.float64(10.048810106494384), np.float64(3.2247461916839306), np.float64(-3.567840077120941), np.float64(5.531972415060627)],\n",
"[np.float64(-1.382142403745367), np.float64(1.1678398419022438), np.float64(0.7752546483828548), np.float64(-7.53197233105394)],\n",
"[np.float64(0.33333330533110994), np.float64(-0.25319725996179565), np.float64(1.0531974615778044), np.float64(5.000000168013341)],\n",
"]\n"
]
}
],
"source": [
"import numpy\n",
"\n",
"cp = [0, 0.155051, 0.644949, 1]\n",
"\n",
"a = []\n",
"\n",
"print('[')\n",
"for i in range(len(cp)):\n",
" ptmp = []\n",
" tmp = 0\n",
" for j in range(len(cp)):\n",
" if j != i:\n",
" row = []\n",
" row.insert(0,1/(cp[i]-cp[j]))\n",
" row.insert(1,-cp[j]/(cp[i]-cp[j]))\n",
" ptmp.insert(tmp,row)\n",
" tmp += 1\n",
" p=[1]\n",
" for j in range(len(cp)-1):\n",
" p = numpy.convolve(p,ptmp[j])\n",
" pder = numpy.polyder(p,1)\n",
" arow = []\n",
" for j in range(len(cp)):\n",
" arow.append(numpy.polyval(pder,cp[j]))\n",
" a.append(arow)\n",
" print(str(arow)+',')\n",
"print(']')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": ".venv",
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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