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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

   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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