scijs/ndarray-gram-schmidt-qr-complex

Name: ndarray-gram-schmidt-qr-complex

Owner: scijs

Description: Modified Gram-Schmidt Algorithm for QR Factorization of complex matrices

Created: 2015-05-03 14:36:02.0

Updated: 2017-04-16 02:43:46.0

Pushed: 2015-05-16 06:24:46.0

Homepage: null

Size: 136

Language: JavaScript

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README

ndarray-gram-schmidt-qr-complex

A module for calculating the in-place QR decomposition of a complex matrix

Introduction

The algorithm is the numerically stable variant of the Gram-Schmidt QR decomposition as found on p. 58 of Trefethen and Bau's Numerical Linear Algebra. In pseudocode, the algorithm is:

i = 1 to n
i = a_i

i = 1 to n
ii = ||v_i||
i = v_i / r_ii

r j = i+1 to n
r_ij = q_i' * v_j
v_j = v_j - r_ij * q_i

For real numbers, see ndarray-gram-schmidt-qr.

Usage

The algorithm currently only calculates the in-place QR decomposition and returns true on successful completion.

qr = require('ndarray-gram-schmidt-qr-complex'),
pool = require('ndarray-scratch');

A_r = ndarray( new Float64Array([1,2,7,4,5,1,7,4,9]), [3,3] ),
A_i = ndarray( new Float64Array([9,3,2,4,4,0,4,1,1]), [3,3] ),
R_r = pool.zeros( A_r.shape, A_r.dtype );
R_i = pool.zeros( A_r.shape, A_r.dtype );

A_r, A_i, R_r, R_i );

Then the product A * R is approximately equal to the original matrix.

Credits

(c) 2015 Ricky Reusser. MIT License