CPSTF2
Craig Lucas, University of Manchester / NAG Ltd.
October, 2008
October, 2008
Purpose
CPSTF2 computes the Cholesky factorization with complete
pivoting of a complex Hermitian positive semidefinite matrix A.
The factorization has the form
P**T * A * P = U**H * U , if UPLO = 'U',
P**T * A * P = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular, and
P is stored as vector PIV.
This algorithm does not attempt to check that A is positive
semidefinite. This version of the algorithm calls level 2 BLAS.
pivoting of a complex Hermitian positive semidefinite matrix A.
The factorization has the form
P**T * A * P = U**H * U , if UPLO = 'U',
P**T * A * P = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular, and
P is stored as vector PIV.
This algorithm does not attempt to check that A is positive
semidefinite. This version of the algorithm calls level 2 BLAS.
Arguments
| UPLO |
(input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| A |
(input/output) COMPLEX array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = 'U', the leading
n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization as above. |
| PIV |
(output) INTEGER array, dimension (N)
PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
|
| RANK |
(output) INTEGER
The rank of A given by the number of steps the algorithm
completed. |
| TOL |
(input) REAL
User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) )
will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. |
| LDA |
(input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
|
| WORK |
(workspace) REAL array, dimension (2*N)
Work space.
|
| INFO |
(output) INTEGER
< 0: If INFO = -K, the K-th argument had an illegal value,
= 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is indefinite. See Section 7 of LAPACK Working Note #161 for further information. |