ESMF_DSYR2K Subroutine

subroutine ESMF_DSYR2K(UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)

\brief \b ESMF_DSYR2K \par Purpose:

\verbatim

ESMF_DSYR2K performs one of the symmetric rank 2k operations

C := alphaABT + alphaBAT + beta*C,

or

C := alphaATB + alphaBTA + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case. \endverbatim \param[in] UPLO \verbatim UPLO is CHARACTER*1 On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows:

         UPLO = 'U' or 'u'   Only the  upper triangular part of  C
                             is to be referenced.

         UPLO = 'L' or 'l'   Only the  lower triangular part of  C
                             is to be referenced.

\endverbatim

\param[in] TRANS \verbatim TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows:

         TRANS = 'N' or 'n'   C := alpha*A*B**T + alpha*B*A**T +
                                   beta*C.

         TRANS = 'T' or 't'   C := alpha*A**T*B + alpha*B**T*A +
                                   beta*C.

         TRANS = 'C' or 'c'   C := alpha*A**T*B + alpha*B**T*A +
                                   beta*C.

\endverbatim

\param[in] N \verbatim N is INTEGER On entry, N specifies the order of the matrix C. N must be at least zero. \endverbatim

\param[in] K \verbatim K is INTEGER On entry with TRANS = ‘N’ or ‘n’, K specifies the number of columns of the matrices A and B, and on entry with TRANS = ‘T’ or ‘t’ or ‘C’ or ‘c’, K specifies the number of rows of the matrices A and B. K must be at least zero. \endverbatim

\param[in] ALPHA \verbatim ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. \endverbatim

\param[in] A \verbatim A is DOUBLE PRECISION array, dimension ( LDA, ka ), where ka is k when TRANS = ‘N’ or ‘n’, and is n otherwise. Before entry with TRANS = ‘N’ or ‘n’, the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A. \endverbatim

\param[in] LDA \verbatim LDA is INTEGER On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = ‘N’ or ‘n’ then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ). \endverbatim

\param[in] B \verbatim B is DOUBLE PRECISION array, dimension ( LDB, kb ), where kb is k when TRANS = ‘N’ or ‘n’, and is n otherwise. Before entry with TRANS = ‘N’ or ‘n’, the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B. \endverbatim

\param[in] LDB \verbatim LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = ‘N’ or ‘n’ then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ). \endverbatim

\param[in] BETA \verbatim BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. \endverbatim

\param[in,out] C \verbatim C is DOUBLE PRECISION array, dimension ( LDC, N ) Before entry with UPLO = ‘U’ or ‘u’, the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = ‘L’ or ‘l’, the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix. \endverbatim

\param[in] LDC \verbatim LDC is INTEGER On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date December 2016 \ingroup double_blas_level3 \par Further Details:

\verbatim

Level 3 Blas routine.

– Written on 8-February-1989. Jack Dongarra, Argonne National Laboratory. Iain Duff, AERE Harwell. Jeremy Du Croz, Numerical Algorithms Group Ltd. Sven Hammarling, Numerical Algorithms Group Ltd. \endverbatim

Arguments