# pstrf - Man Page

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**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***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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