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Calculate the linear least squares solution of a matrix using QR factorisation


Lapack::leastSquaresByFactorisation

(PECL lapack >= 0.1.0)

Lapack::leastSquaresByFactorisationCalculate the linear least squares solution of a matrix using QR factorisation

Description

public static array Lapack::leastSquaresByFactorisation ( array $a , array $b )

Solve the linear least squares problem, find min x in || B - Ax || Returns an array representing x. Expects arrays of arrays, and will return an array of arrays in the dimension B num cols x A num cols. Uses QR or LQ factorisation on matrix A.

Parameters

a

Matrix A

b

Matrix B

Return Values

Array of the solution matrix

Examples

Example #1 Using Lapack::leastSquaresByFactorisation():

<?php

 $a 
= array(
     array( 
1.44,  -7.84,  -4.39,   4.53),
     array(-
9.96,  -0.28,  -3.24,   3.83),
     array(-
7.55,   3.24,   6.27,  -6.64),
     array( 
8.34,   8.09,   5.28,   2.06),
     array( 
7.08,   2.52,   0.74,  -2.47),
     array(-
5.45,  -5.70,  -1.19,   4.70),
 );

 
$b = array(
     array( 
8.58,   9.35),
     array( 
8.26,  -4.43),
     array( 
8.48,  -0.70),
     array(-
5.28,  -0.26),
     array( 
5.72,  -7.36),
     array( 
8.93,  -2.52),           
 );

 
$result Lapack::leastSquaresByFactorisation($a$b);
 
?>



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