subroutine cpstrf (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
CPSTRF computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
CPSTRF computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
Purpose:
CPSTRF 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 3 BLAS.
Parameters:
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N
N is INTEGER
The order of the matrix A. N >= 0.
A
A is 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.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
PIV
PIV is INTEGER array, dimension (N)
PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
RANK
RANK is INTEGER
The rank of A given by the number of steps the algorithm
completed.
TOL
TOL is 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.
WORK
WORK is REAL array, dimension (2*N)
Work space.
INFO
INFO is 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 not positive semidefinite. See
Section 7 of LAPACK Working Note #161 for further
information.
Author:
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 144 of file cpstrf.f.
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