HP MLIB User's Guide Vol. 2 7th Ed.

1098 HP MLIB User’s Guide
LINPACK subprograms included in VECLIB LU factorization
LINPACK subprograms included in VECLIB
Name DGEFA
LU factorization
Purpose This subprogram computes the triangular factorization of a general dense
n-by-n matrix A. Specifically, given A, DGEFA determines an n-by-n
permutation matrix P, an n-by-n unit lower-triangular matrix L, and an n-by-n
upper-triangular matrix U, such that
Computational singularity of A results in one or more zero diagonal elements of
U. This condition is detected during factorization, and a status response is
returned to indicate its occurrence.
The triangular factors may be used to solve a system of linear equations,
Ax = b, by successively solving L(Ux)=Pb. This operation is performed by the
VECLIB subprogram DGESL. Refer to “DGESL” on page 1100 for more
information.
Usage VECLIB:
INTEGER*4 lda, n, ipvt(n), ier
REAL*8 a(lda, n)
CALL DGEFA(a, lda, n, ipvt, ier)
Input a Array containing the n-by-n matrix A.
lda The leading dimension of array a as declared in the
calling program unit, with lda ≥ max(n,1).
n The order of matrix A, n ≥ 0.
Output a The triangular factors replace the input matrix; the
strict lower triangle of a contains the strict lower
triangle of L and the upper triangle of a contains U. a
must be preserved between the factorization call and
any solve call.
ipvt The pivot information necessary to construct the
permutation matrix P. ipvt must be preserved between
the factorization call and any solve call.
PA LU.=