Skip to content

Instantly share code, notes, and snippets.

@sachinruk

sachinruk/Python Cholesky Decomposition.ipynb

Created March 31, 2017 02:20
Show Gist options
  • Save sachinruk/bed215437a9f572d407975225d2ba018 to your computer and use it in GitHub Desktop.
Save sachinruk/bed215437a9f572d407975225d2ba018 to your computer and use it in GitHub Desktop.
Download ZIP

Revisions

  1. sachinruk created this gist Mar 31, 2017.
    189 changes: 189 additions & 0 deletions Python Cholesky Decomposition.ipynb
    View file
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,189 @@
    {
    "cells": [
    {
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
    "collapsed": true
    },
    "outputs": [],
    "source": [
    "import numpy as np"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "Create a positive definite matrix"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {
    "collapsed": false
    },
    "outputs": [
    {
    "data": {
    "text/plain": [
    "(100, 100)"
    ]
    },
    "execution_count": 4,
    "metadata": {},
    "output_type": "execute_result"
    }
    ],
    "source": [
    "A = np.random.randn(100,120)\n",
    "A = A.dot(A.T)\n",
    "A.shape"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "Implementation of cholesky algorithm from:\n",
    "\n",
    "https://en.wikipedia.org/wiki/Cholesky_decomposition#The_Cholesky.E2.80.93Banachiewicz_and_Cholesky.E2.80.93Crout_algorithms"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 9,
    "metadata": {
    "collapsed": true
    },
    "outputs": [],
    "source": [
    "def cholesky_d(A):\n",
    " L = np.zeros_like(A)\n",
    " n = len(L)\n",
    " for i in range(n):\n",
    " for j in range(i+1):\n",
    " if i==j:\n",
    " val = A[i,i] - np.sum(np.square(L[i,:i]))\n",
    " # if diagonal values are negative return zero - not throw exception\n",
    " if val<0:\n",
    " return 0.0\n",
    " L[i,i] = np.sqrt(val)\n",
    " else:\n",
    " L[i,j] = (A[i,j] - np.sum(L[i,:j]*L[j,:j]))/L[j,j]\n",
    " \n",
    " return L"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 7,
    "metadata": {
    "collapsed": false
    },
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "CPU times: user 2 µs, sys: 1 µs, total: 3 µs\n",
    "Wall time: 5.01 µs\n"
    ]
    }
    ],
    "source": [
    "%time\n",
    "L1 = cholesky_d(A)"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 8,
    "metadata": {
    "collapsed": false
    },
    "outputs": [
    {
    "name": "stdout",
    "output_type": "stream",
    "text": [
    "CPU times: user 2 µs, sys: 1e+03 ns, total: 3 µs\n",
    "Wall time: 6.2 µs\n"
    ]
    }
    ],
    "source": [
    "%time\n",
    "L2 = np.linalg.cholesky(A)"
    ]
    },
    {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
    "Are the values similar?"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {
    "collapsed": false
    },
    "outputs": [
    {
    "data": {
    "text/plain": [
    "True"
    ]
    },
    "execution_count": 10,
    "metadata": {},
    "output_type": "execute_result"
    }
    ],
    "source": [
    "np.allclose(L1,L2)"
    ]
    },
    {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
    "collapsed": true
    },
    "outputs": [],
    "source": []
    }
    ],
    "metadata": {
    "anaconda-cloud": {},
    "kernelspec": {
    "display_name": "Python [default]",
    "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": "3.5.2"
    },
    "latex_envs": {
    "bibliofile": "biblio.bib",
    "cite_by": "apalike",
    "current_citInitial": 1,
    "eqLabelWithNumbers": true,
    "eqNumInitial": 0
    }
    },
    "nbformat": 4,
    "nbformat_minor": 2
    }