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(PECL lapack >= 0.1.0)
Lapack::leastSquaresByFactorisation — Calculate the linear least squares solution of a matrix using QR factorisation
$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.
a
Matrix A
b
Matrix B
Array of the solution matrix
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 );
?>