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variantsPOcomputational(3) LAPACK variantsPOcomputational(3)

NAME

variantsPOcomputational

SYNOPSIS

Functions


subroutine cpotrf (UPLO, N, A, LDA, INFO)
CPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. subroutine dpotrf (UPLO, N, A, LDA, INFO)
DPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. subroutine spotrf (UPLO, N, A, LDA, INFO)
SPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. subroutine zpotrf (UPLO, N, A, LDA, INFO)
ZPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS.

Detailed Description

This is the group of Variants Computational routines

Function Documentation

subroutine cpotrf (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, integer INFO)

CPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. CPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

Purpose:


CPOTRF computes the Cholesky factorization of a real Hermitian
positive definite matrix A.
The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the right looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N


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

A


A is COMPLEX array, dimension (LDA,N)
On entry, the Hermitian 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 A = U**H*U or A = L*L**H.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Purpose:


CPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the top-looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**H*U or A = L*L**H.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

subroutine dpotrf (character UPLO, integer N, double precision, dimension( lda, * ) A, integer LDA, integer INFO)

DPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. DPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

Purpose:


DPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the right looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**T*U or A = L*L**T.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Purpose:


DPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the top-looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**T*U or A = L*L**T.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

subroutine spotrf (character UPLO, integer N, real, dimension( lda, * ) A, integer LDA, integer INFO)

SPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. SPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

Purpose:


SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the right looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**T*U or A = L*L**T.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Purpose:


SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the top-looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**T*U or A = L*L**T.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

subroutine zpotrf (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, integer INFO)

ZPOTRF VARIANT: right looking block version of the algorithm, calling Level 3 BLAS. ZPOTRF VARIANT: top-looking block version of the algorithm, calling Level 3 BLAS.

Purpose:


ZPOTRF computes the Cholesky factorization of a real Hermitian
positive definite matrix A.
The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the right looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N


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

A


A is COMPLEX*16 array, dimension (LDA,N)
On entry, the Hermitian 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 A = U**H*U or A = L*L**H.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Purpose:


ZPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the top-looking block version of the algorithm, calling Level 3 BLAS.

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

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 A = U**H*U or A = L*L**H.

LDA


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

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Author

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