KPG1_MDETx

Computes the determinant of a matrix

Description:

This routine calculates the determinant of an arbitrary n-by-n matrix. It LU decomposes the matrix and then forms the product of the diagonals by summing their logarithms to base 10. Logarithmic calculations are used to prevent overflows. A bad status is returned when the matrix is singular or the determinant is too large to store in the chosen data type’ s number representation.

Invocation

CALL KPG1_MDETX( N, EL, ARRAY, WORK1, WORK2, DET, STATUS )

Arguments

N = INTEGER (Given)
The number of rows and columns in the matrix whose determinant is to be derived.
EL = INTEGER (Given)
The size of the first dimension of the array as declared in the calling routine. This should be at least equal to N.
ARRAY( EL, N ) = ? (Given and Returned)
On input this is the matrix whose determinant is to be found. Since the LU decomposition is performed in situ, the input values are lost. (On exit it is the LU decomposed form of the rowwise-permuted input ARRAY, with the diagonals being part of the upper triangular matrix.)
WORK1( N ) = INTEGER (Returned)
Workspace for the LU decomposition.
WORK2( N ) = ? (Returned)
Workspace for the LU decomposition.
DET = ? (Returned)
The determinant of matrix ARRAY. It is set to 1.0 when the matrix is singular.
STATUS = INTEGER (Given and Returned)
The global status.

Notes: