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stwind/col_piv_householder_qr_solve.ipynb

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col_piv_householder_qr_solve.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyOWL3Sg5nuledBqrh0mmjn2",
"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/stwind/7cd34c64176139e22fd4882a82927cb2/col_piv_householder_qr_solve.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "LyAcdrd-mPWf"
},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.linalg import qr\n",
"\n",
"def col_piv_householder_qr_solve(A, rhs):\n",
" \"\"\"A.colPivHouseholderQr().solve(rhs)\"\"\"\n",
" Q, R, P = qr(A, pivoting=True)\n",
"\n",
" # Solve Q @ R @ x_p = rhs => R @ x_p = Q^T @ rhs\n",
" Qt_rhs = Q.T @ rhs\n",
" x_p = np.linalg.solve(R, Qt_rhs)\n",
"\n",
" # x = P x_p => need to un-permute the solution\n",
" x = np.zeros_like(x_p)\n",
" x[P] = x_p\n",
" return x"
]
},
{
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"\n",
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"])\n",
"\n",
"result = np.array([\n",
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"[0.418833184265,-0.176422171788,-0.242411012477],\n",
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"[-0.149720107915,0.412886246268,-0.263166138353],\n",
"[0.474251884345,-0.510765240692,0.036513356347],\n",
"[-0.483021149525,0.101023708413,0.381997441112],\n",
"[-1.054276448462,-0.000001179523,1.054277627985],\n",
"[-0.101058275672,0.483188468876,-0.382130193204],\n",
"[0.145182477499,-0.328630982720,0.183448505221],\n",
"[0.250238863900,-0.110550435406,-0.139688428494],\n",
"])"
],
"metadata": {
"id": "plxT4ionmUTa"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"for a, t, r in zip(mats, rhs, result):\n",
" A = np.array([\n",
" 0.,a[0],a[1],\n",
" 0.,0.,a[2],\n",
" 1.,1.,1.\n",
" ]).reshape(3,3)\n",
"\n",
" np.testing.assert_allclose(\n",
" col_piv_householder_qr_solve(A,np.array([t[0],t[1],0])),\n",
" r\n",
" )"
],
"metadata": {
"id": "e7ac6xfamoUd"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "4vmWuQmqmsVO"
},
"execution_count": null,
"outputs": []
}
]
}
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