DecomposeLU (FUN)

FUNCTION DecomposeLU : ResultCode

This function computes the LU-decomposition of a quadratic matrix A,

which is updated in-place.

The lower triangular matrix L and the upper triangular matrix R are stored

in A’, the updated A. The column permutation Q is stored in padiPCol^.

After successful completion the condition

A * Q = L * R

holds.

See http://de.wikipedia.org/wiki/Gau%C3%9Fsches_Eliminationsverfahren#LR-Zerlegung

Note 1: this function is used for solving systems of linear equations A*x = b,

for inverting matrices, and for the computation of the determinant.

Note 2: the pivot strategy is to select the column that has the element with the

greatest absolute value for the given row.

InOut:

Scope	Name	Type	Comment
Return	DecomposeLU	ResultCode
Inout	A	Matrix	The input matrix, must be quadratic. The input is updated in-place.
Input	padiPCol	POINTER TO ARRAY [0..0] OF DINT	The permutation of the columns, pointer to an array of at least A.nRows elements.
Output	diSign	DINT	The sign of the permutation, equal to (-1)^np where np is the number of columns swaps