stwind · May 7, 2025 07:20
diff --git a/col_piv_householder_qr_solve.ipynb b/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",
        "rhs = np.array([\n",
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        "[-0.333974019442,-0.942582279877],\n",
        "[0.904095618957,0.427330213982],\n",
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        "[-0.457610080728,0.889152975599],\n",
        "[0.150703327059,0.988579034379],\n",
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        "[0.865310532040,-0.501236155062],\n",
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        "[0.954791660805,0.297275771730],\n",
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        "[0.861424473341,0.507885692582],\n",
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        "[-0.286761914388,-0.958001881238],\n",
        "[0.446458099598,-0.894804540279],\n",
        "[-0.403017441581,-0.915192297707],\n",
        "[-0.974267426981,0.225395165708],\n",
        "[0.547724196635,-0.836658953469],\n",
        "[0.813948389114,-0.580937190976],\n",
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        "[-0.951217839590,-0.308520050637],\n",
        "[-0.398473271392,0.917179945259],\n",
        "[0.675968877593,0.736930170726],\n",
        "[0.951223579675,0.308502352455],\n",
        "[-0.946496195780,-0.322714969245],\n",
        "[-0.270236053271,0.962794098192],\n",
        "[0.744638817839,0.667467625408],\n",
        "[-0.436671305670,0.899621126255],\n",
        "[-0.965324970316,-0.261051147639],\n",
        "[-0.688533255969,-0.725204767928],\n",
        "[0.356488404531,-0.934299747102],\n",
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        "[-0.840736532008,-0.541444441976],\n",
        "[0.786455034838,0.617647535555],\n",
        "[0.370669379380,-0.928764884774],\n",
        "[-0.877712324228,-0.479187933799],\n",
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        "[0.953809209502,-0.300413035452],\n",
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        "[-0.444126441515,0.895964119788],\n",
        "[0.192646162765,0.981268289497],\n",
        "[-0.346083837730,0.938203590519],\n",
        "[0.352539195959,0.935797048143],\n",
        "[-0.087661411671,0.996150328466],\n",
        "[-0.408625441128,0.912702168762],\n",
        "[0.772460301142,-0.635063054475],\n",
        "[-0.996274841848,0.086234792869],\n",
        "[0.387316742337,0.921946712726],\n",
        "[0.064501125244,0.997917634298],\n",
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        "[-0.925425522866,0.378929547052],\n",
        "[-0.266393169007,-0.963864450795],\n",
        "])\n",
        "\n",
        "result = np.array([\n",
        "    [0.136841011935,0.099590312620,-0.236431324555],\n",
        "[0.418833184265,-0.176422171788,-0.242411012477],\n",
        "[-0.556499444562,0.399622485111,0.156876959451],\n",
        "[-0.347031395626,0.032887469750,0.314143925876],\n",
        "[-0.254346765055,0.341489633857,-0.087142868803],\n",
        "[-0.275377713801,0.125072161205,0.150305552596],\n",
        "[-0.200800457043,-0.167089949105,0.367890406148],\n",
        "[-0.363432040182,0.161845155835,0.201586884348],\n",
        "[-0.169485855371,-0.139269433074,0.308755288445],\n",
        "[0.285518523871,-0.662883929421,0.377365405550],\n",
        "[-0.241059279862,-0.318604312159,0.559663592021],\n",
        "[0.244059661359,-0.198380921417,-0.045678739942],\n",
        "[0.112414995673,-0.287917173330,0.175502177657],\n",
        "[-0.159108611740,-0.248400203880,0.407508815619],\n",
        "[0.000888728366,-0.451057849396,0.450169121030],\n",
        "[0.330384125744,0.174928905044,-0.505313030788],\n",
        "[-0.163635986231,0.250276540866,-0.086640554635],\n",
        "[-0.200054834273,0.280748006085,-0.080693171812],\n",
        "[0.072680383838,0.181860501527,-0.254540885365],\n",
        "[0.374282716398,-0.267411824310,-0.106870892087],\n",
        "[0.169989037480,0.107257170502,-0.277246207982],\n",
        "[0.307797424379,-0.095620510361,-0.212176914019],\n",
        "[0.065738187218,0.059825928240,-0.125564115458],\n",
        "[0.189263493598,0.011924662273,-0.201188155871],\n",
        "[-0.183680777211,0.218017716505,-0.034336939295],\n",
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        "[-0.109599575724,0.038384814070,0.071214761654],\n",
        "[0.013715970059,0.315687487801,-0.329403457859],\n",
        "[0.087207550093,-0.082082567850,-0.005124982244],\n",
        "[-0.335077429691,0.123822536827,0.211254892865],\n",
        "[-0.110094249600,0.297927171621,-0.187832922022],\n",
        "[0.107641110034,0.362329661780,-0.469970771814],\n",
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        "[-0.077371460041,0.154253788144,-0.076882328103],\n",
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        "[-0.082352127102,0.156227021743,-0.073874894642],\n",
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        "[-0.176412508608,0.106363031321,0.070049477287],\n",
        "[-0.130950208766,0.416567264593,-0.285617055827],\n",
        "[-0.200558351692,0.112484613196,0.088073738497],\n",
        "[-0.284402360072,-0.087875262463,0.372277622535],\n",
        "[-0.075590029700,0.251604546928,-0.176014517227],\n",
        "[0.112795012883,-0.281843360838,0.169048347955],\n",
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        "[0.184187298421,-0.110217215786,-0.073970082635],\n",
        "[0.198473603756,0.024619514221,-0.223093117977],\n",
        "[-0.215076089793,0.241755047353,-0.026678957559],\n",
        "[-0.136940558852,0.028766776487,0.108173782365],\n",
        "[0.047026185258,0.167649437217,-0.214675622474],\n",
        "[0.232810818472,-0.234177890299,0.001367071827],\n",
        "[-0.167777280224,-0.048323588321,0.216100868545],\n",
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        "[0.212256135444,-0.239015643956,0.026759508512],\n",
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        "[-0.487685523794,0.679525299259,-0.191839775465],\n",
        "[0.159909185708,0.275432235648,-0.435341421356],\n",
        "[-0.589862275063,0.352929741490,0.236932533574],\n",
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        "[0.171185059592,0.053262290719,-0.224447350311],\n",
        "[0.232536008945,0.146816846291,-0.379352855236],\n",
        "[-0.111484785561,0.181873215721,-0.070388430161],\n",
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        "[0.092492065308,0.054301481387,-0.146793546696],\n",
        "[0.151380871165,-0.248046611449,0.096665740285],\n",
        "[-0.118355121310,-0.075576823742,0.193931945052],\n",
        "[0.062537811180,-0.147009261953,0.084471450773],\n",
        "[-0.103412857944,-0.055969270528,0.159382128472],\n",
        "[-0.441774386560,0.029031577042,0.412742809519],\n",
        "[-0.900882933625,-0.063366463788,0.964249397413],\n",
        "[-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": []
    }
  ]
 }
No results found