cpstf2-f(3)

cpstf2.f –

Synopsis

Functions/Subroutines

subroutine cpstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
CPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

Function/Subroutine Documentation

subroutine cpstf2 (characterUPLO, integerN, complex, dimension( lda, * )A, integerLDA, integer, dimension( n )PIV, integerRANK, realTOL, real, dimension( 2*n )WORK, integerINFO)

CPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

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.

Parameters:

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

 N is INTEGER
 The order of the matrix A. N >= 0.

 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.

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.

LDA

 LDA is INTEGER
 The leading dimension of the array A. LDA >= max(1,N).

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 indefinite. See Section 7 of
 LAPACK Working Note #161 for further information.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 142 of file cpstf2.f.

Author

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