matrix.ludcmp

Syntax

m := matrix.ludcmp(v,a)

Get the LU decomposition.

The LU decomposition is a factorization of v as the product of lower-triangular and upper-triangular matrices. Gaussian elimination with pivoting is used. v is converted to a matrix and must be square. a, the pivot vector, must be a one-dimensional array with the number of rows equal to the number of rows/columns in v. The pivot vector shows the row interchanges. The lower-triangular matrix is the lower-triangular portion of m with ones along the diagonal. The upper-diagonal matrix is the upper-diagonal portion of m.

Returns:

m - Composite LU factorization matrix. The lower-triangular matrix is the lower-triangular portion of m with ones along the diagonal. The upper-diagonal matrix is the upper-diagonal portion of m.

Arguments:

v - array, matrix, or tensor pointer corresponding to a square matrix a - The pivot vector, to be used later with matrix.lubksb.