variantsPOcomputational(3)

NAME
variantsPOcomputational - Variants Computational routines

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

Definition at line 101 of file VARIANTS/cholesky/RL/cpotrf.f.

  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

Definition at line 101 of file VARIANTS/cholesky/RL/dpotrf.f.

  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

Definition at line 101 of file VARIANTS/cholesky/RL/spotrf.f.

  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

Definition at line 101 of file VARIANTS/cholesky/RL/zpotrf.f.

Author

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