CPST01
Craig Lucas, University of Manchester / NAG Ltd.
October, 2008
October, 2008
Purpose
CPST01 reconstructs an Hermitian positive semidefinite matrix A
from its L or U factors and the permutation matrix P and computes
the residual
norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of L,
and U' is the conjugate transpose of U.
from its L or U factors and the permutation matrix P and computes
the residual
norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
norm( P*U'*U*P' - A ) / ( N * norm(A) * EPS ),
where EPS is the machine epsilon, L' is the conjugate transpose of L,
and U' is the conjugate transpose of U.
Arguments
| UPLO |
(input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
Hermitian matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular |
| N |
(input) INTEGER
The number of rows and columns of the matrix A. N >= 0.
|
| A |
(input) COMPLEX array, dimension (LDA,N)
The original Hermitian matrix A.
|
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N)
|
| AFAC |
(input) COMPLEX array, dimension (LDAFAC,N)
The factor L or U from the L*L' or U'*U
factorization of A. |
| LDAFAC |
(input) INTEGER
The leading dimension of the array AFAC. LDAFAC >= max(1,N).
|
| PERM |
(output) COMPLEX array, dimension (LDPERM,N)
Overwritten with the reconstructed matrix, and then with the
difference P*L*L'*P' - A (or P*U'*U*P' - A) |
| LDPERM |
(input) INTEGER
The leading dimension of the array PERM.
LDAPERM >= max(1,N). |
| PIV |
(input) INTEGER array, dimension (N)
PIV is such that the nonzero entries are
P( PIV( K ), K ) = 1. |
| RWORK |
(workspace) REAL array, dimension (N)
|
| RESID |
(output) REAL
If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ) |