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pstrf(3) Library Functions Manual pstrf(3)

NAME

pstrf - pstrf: triangular factor, with pivoting

SYNOPSIS

Functions


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. subroutine DPSTRF (uplo, n, a, lda, piv, rank, tol, work, info)
DPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. subroutine SPSTRF (uplo, n, a, lda, piv, rank, tol, work, info)
SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix. subroutine ZPSTRF (uplo, n, a, lda, piv, rank, tol, work, info)
ZPSTRF computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

Detailed Description

Function Documentation

subroutine CPSTRF (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)

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 

!>          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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 141 of file cpstrf.f.

subroutine DPSTRF (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, double precision tol, double precision, dimension( 2*n ) work, integer info)

DPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Purpose:

!>
!> DPSTRF computes the Cholesky factorization with complete
!> pivoting of a real symmetric positive semidefinite matrix A.
!>
!> The factorization has the form
!>    P**T * A * P = U**T * U ,  if UPLO = 'U',
!>    P**T * A * P = L  * L**T,  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 

!>          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 DOUBLE PRECISION 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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 141 of file dpstrf.f.

subroutine SPSTRF (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, real tol, real, dimension( 2*n ) work, integer info)

SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Purpose:

!>
!> SPSTRF computes the Cholesky factorization with complete
!> pivoting of a real symmetric positive semidefinite matrix A.
!>
!> The factorization has the form
!>    P**T * A * P = U**T * U ,  if UPLO = 'U',
!>    P**T * A * P = L  * L**T,  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 

!>          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 REAL 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 140 of file spstrf.f.

subroutine ZPSTRF (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( n ) piv, integer rank, double precision tol, double precision, dimension( 2*n ) work, integer info)

ZPSTRF computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

Purpose:

!>
!> ZPSTRF 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 

!>          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*16 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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION 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 Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 141 of file zpstrf.f.

Author

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