Man page - pstf2(3)

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Manual

pstf2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
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)
subroutine dpstf2 (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, integerinfo)
subroutine spstf2 (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)
subroutine zpstf2 (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( n ) piv, integer rank, doubleprecision tol, double precision, dimension( 2*n ) work, integer info)
Author

NAME

pstf2 - pstf2: triangular factor, with pivoting panel, level 2

SYNOPSIS

Functions

subroutine cpstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
CPSTF2 computes the Cholesky factorization with complete pivoting of complex Hermitian positive semidefinite matrix.
subroutine dpstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.
subroutine spstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.
subroutine zpstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

Detailed Description

Function Documentation

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.

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 = ā€™Uā€™,
P**T * A * P = L * L**H, if UPLO = ā€™Lā€™,
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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 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.

subroutine dpstf2 (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, integerinfo)

DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Purpose:

DPSTF2 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 = ā€™Uā€™,
P**T * A * P = L * L**T, if UPLO = ā€™Lā€™,
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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 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.

LDA

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

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.

subroutine spstf2 (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)

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix.

Purpose:

SPSTF2 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 = ā€™Uā€™,
P**T * A * P = L * L**T, if UPLO = ā€™Lā€™,
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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 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.

subroutine zpstf2 (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( n ) piv, integer rank, doubleprecision tol, double precision, dimension( 2*n ) work, integer info)

ZPSTF2 computes the Cholesky factorization with complete pivoting of a complex Hermitian positive semidefinite matrix.

Purpose:

ZPSTF2 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 = ā€™Uā€™,
P**T * A * P = L * L**H, if UPLO = ā€™Lā€™,
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.
= ā€™Uā€™: Upper triangular
= ā€™Lā€™: 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 = ā€™Uā€™, 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 = ā€™Lā€™, 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 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.

LDA

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

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.

Author

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