ESMF_DTRSM Subroutine

subroutine ESMF_DTRSM(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)

\brief \b ESMF_DTRSM \par Purpose:

\verbatim

ESMF_DTRSM solves one of the matrix equations

op( A )X = alphaB, or Xop( A ) = alphaB,

where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

op( A ) = A or op( A ) = A**T.

The matrix X is overwritten on B. \endverbatim \param[in] SIDE \verbatim SIDE is CHARACTER*1 On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows:

         SIDE = 'L' or 'l'   op( A )*X = alpha*B.

         SIDE = 'R' or 'r'   X*op( A ) = alpha*B.

\endverbatim

\param[in] UPLO \verbatim UPLO is CHARACTER*1 On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows:

         UPLO = 'U' or 'u'   A is an upper triangular matrix.

         UPLO = 'L' or 'l'   A is a lower triangular matrix.

\endverbatim

\param[in] TRANSA \verbatim TRANSA is CHARACTER*1 On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows:

         TRANSA = 'N' or 'n'   op( A ) = A.

         TRANSA = 'T' or 't'   op( A ) = A**T.

         TRANSA = 'C' or 'c'   op( A ) = A**T.

\endverbatim

\param[in] DIAG \verbatim DIAG is CHARACTER*1 On entry, DIAG specifies whether or not A is unit triangular as follows:

         DIAG = 'U' or 'u'   A is assumed to be unit triangular.

         DIAG = 'N' or 'n'   A is not assumed to be unit
                             triangular.

\endverbatim

\param[in] M \verbatim M is INTEGER On entry, M specifies the number of rows of B. M must be at least zero. \endverbatim

\param[in] N \verbatim N is INTEGER On entry, N specifies the number of columns of B. N must be at least zero. \endverbatim

\param[in] ALPHA \verbatim ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry. \endverbatim

\param[in] A \verbatim A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = ‘L’ or ‘l’ and k is n when SIDE = ‘R’ or ‘r’. Before entry with UPLO = ‘U’ or ‘u’, the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = ‘L’ or ‘l’, the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = ‘U’ or ‘u’, the diagonal elements of A are not referenced either, but are assumed to be unity. \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 SIDE = ‘L’ or ‘l’ then LDA must be at least max( 1, m ), when SIDE = ‘R’ or ‘r’ then LDA must be at least max( 1, n ). \endverbatim

\param[in,out] B \verbatim B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X. \endverbatim

\param[in] LDB \verbatim LDB is INTEGER On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \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