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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine cpstf2 | ( | character | UPLO, |
integer | N, | ||
complex, dimension( lda, * ) | A, | ||
integer | LDA, | ||
integer, dimension( n ) | PIV, | ||
integer | RANK, | ||
real | TOL, | ||
real, dimension( 2*n ) | WORK, | ||
integer | INFO | ||
) |
CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
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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.
[in] | UPLO | 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 |
[in] | N | N is INTEGER The order of the matrix A. N >= 0. |
[in,out] | 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. |
[out] | PIV | PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. |
[out] | RANK | RANK is INTEGER The rank of A given by the number of steps the algorithm completed. |
[in] | 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. |
[in] | LDA | LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). |
[out] | WORK | WORK is REAL array, dimension (2*N) Work space. |
[out] | 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. |
Definition at line 144 of file cpstf2.f.