Provided by: liblapack-doc_3.8.0-2_all bug

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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