version 1.7, 2011/07/22 07:38:02
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version 1.8, 2011/11/21 20:37:08
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*> \brief \b DTRMM |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) |
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* |
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* .. Scalar Arguments .. |
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* DOUBLE PRECISION ALPHA |
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* INTEGER LDA,LDB,M,N |
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* CHARACTER DIAG,SIDE,TRANSA,UPLO |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A(LDA,*),B(LDB,*) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DTRMM performs one of the matrix-matrix operations |
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*> |
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*> B := alpha*op( A )*B, or B := alpha*B*op( A ), |
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*> |
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*> where alpha is a scalar, B is an m by n matrix, A is a unit, or |
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*> non-unit, upper or lower triangular matrix and op( A ) is one of |
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*> |
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*> op( A ) = A or op( A ) = A**T. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] SIDE |
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*> \verbatim |
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*> SIDE is CHARACTER*1 |
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*> On entry, SIDE specifies whether op( A ) multiplies B from |
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*> the left or right as follows: |
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*> |
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*> SIDE = 'L' or 'l' B := alpha*op( A )*B. |
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*> |
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*> SIDE = 'R' or 'r' B := alpha*B*op( A ). |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> On entry, UPLO specifies whether the matrix A is an upper or |
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*> lower triangular matrix as follows: |
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*> |
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*> UPLO = 'U' or 'u' A is an upper triangular matrix. |
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*> |
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*> UPLO = 'L' or 'l' A is a lower triangular matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] TRANSA |
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*> \verbatim |
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*> TRANSA is CHARACTER*1 |
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*> On entry, TRANSA specifies the form of op( A ) to be used in |
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*> the matrix multiplication as follows: |
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*> |
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*> TRANSA = 'N' or 'n' op( A ) = A. |
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*> |
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*> TRANSA = 'T' or 't' op( A ) = A**T. |
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*> |
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*> TRANSA = 'C' or 'c' op( A ) = A**T. |
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*> \endverbatim |
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*> |
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*> \param[in] DIAG |
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*> \verbatim |
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*> DIAG is CHARACTER*1 |
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*> On entry, DIAG specifies whether or not A is unit triangular |
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*> as follows: |
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*> |
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*> DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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*> |
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*> DIAG = 'N' or 'n' A is not assumed to be unit |
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*> triangular. |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> On entry, M specifies the number of rows of B. M must be at |
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*> least zero. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> On entry, N specifies the number of columns of B. N must be |
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*> at least zero. |
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*> \endverbatim |
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*> |
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*> \param[in] ALPHA |
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*> \verbatim |
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*> ALPHA is DOUBLE PRECISION. |
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*> On entry, ALPHA specifies the scalar alpha. When alpha is |
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*> zero then A is not referenced and B need not be set before |
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*> entry. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m |
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*> when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. |
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*> Before entry with UPLO = 'U' or 'u', the leading k by k |
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*> upper triangular part of the array A must contain the upper |
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*> triangular matrix and the strictly lower triangular part of |
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*> A is not referenced. |
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*> Before entry with UPLO = 'L' or 'l', the leading k by k |
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*> lower triangular part of the array A must contain the lower |
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*> triangular matrix and the strictly upper triangular part of |
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*> A is not referenced. |
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*> Note that when DIAG = 'U' or 'u', the diagonal elements of |
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*> A are not referenced either, but are assumed to be unity. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> On entry, LDA specifies the first dimension of A as declared |
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*> in the calling (sub) program. When SIDE = 'L' or 'l' then |
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*> LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' |
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*> then LDA must be at least max( 1, n ). |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). |
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*> Before entry, the leading m by n part of the array B must |
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*> contain the matrix B, and on exit is overwritten by the |
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*> transformed matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> On entry, LDB specifies the first dimension of B as declared |
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*> in the calling (sub) program. LDB must be at least |
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*> max( 1, m ). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup double_blas_level3 |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Level 3 Blas routine. |
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*> |
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*> -- Written on 8-February-1989. |
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*> Jack Dongarra, Argonne National Laboratory. |
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*> Iain Duff, AERE Harwell. |
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*> Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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*> Sven Hammarling, Numerical Algorithms Group Ltd. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) |
SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) |
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* |
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* -- Reference BLAS level3 routine (version 3.4.0) -- |
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* November 2011 |
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* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION ALPHA |
DOUBLE PRECISION ALPHA |
INTEGER LDA,LDB,M,N |
INTEGER LDA,LDB,M,N |
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DOUBLE PRECISION A(LDA,*),B(LDB,*) |
DOUBLE PRECISION A(LDA,*),B(LDB,*) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DTRMM performs one of the matrix-matrix operations |
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* |
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* B := alpha*op( A )*B, or B := alpha*B*op( A ), |
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* |
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* where alpha is a scalar, B is an m by n matrix, A is a unit, or |
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* non-unit, upper or lower triangular matrix and op( A ) is one of |
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* |
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* op( A ) = A or op( A ) = A**T. |
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* |
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* Arguments |
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* ========== |
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* |
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* SIDE - CHARACTER*1. |
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* On entry, SIDE specifies whether op( A ) multiplies B from |
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* the left or right as follows: |
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* |
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* SIDE = 'L' or 'l' B := alpha*op( A )*B. |
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* |
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* SIDE = 'R' or 'r' B := alpha*B*op( A ). |
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* |
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* Unchanged on exit. |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the matrix A is an upper or |
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* lower triangular matrix as follows: |
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* |
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* UPLO = 'U' or 'u' A is an upper triangular matrix. |
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* |
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* UPLO = 'L' or 'l' A is a lower triangular matrix. |
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* |
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* Unchanged on exit. |
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* |
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* TRANSA - CHARACTER*1. |
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* On entry, TRANSA specifies the form of op( A ) to be used in |
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* the matrix multiplication as follows: |
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* |
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* TRANSA = 'N' or 'n' op( A ) = A. |
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* |
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* TRANSA = 'T' or 't' op( A ) = A**T. |
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* |
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* TRANSA = 'C' or 'c' op( A ) = A**T. |
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* |
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* Unchanged on exit. |
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* |
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* DIAG - CHARACTER*1. |
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* On entry, DIAG specifies whether or not A is unit triangular |
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* as follows: |
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* |
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* DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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* |
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* DIAG = 'N' or 'n' A is not assumed to be unit |
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* triangular. |
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* |
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* Unchanged on exit. |
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* |
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* M - INTEGER. |
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* On entry, M specifies the number of rows of B. M must be at |
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* least zero. |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the number of columns of B. N must be |
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* at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - DOUBLE PRECISION. |
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* On entry, ALPHA specifies the scalar alpha. When alpha is |
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* zero then A is not referenced and B need not be set before |
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* entry. |
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* Unchanged on exit. |
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* |
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* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m |
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* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. |
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* Before entry with UPLO = 'U' or 'u', the leading k by k |
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* upper triangular part of the array A must contain the upper |
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* triangular matrix and the strictly lower triangular part of |
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* A is not referenced. |
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* Before entry with UPLO = 'L' or 'l', the leading k by k |
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* lower triangular part of the array A must contain the lower |
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* triangular matrix and the strictly upper triangular part of |
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* A is not referenced. |
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* Note that when DIAG = 'U' or 'u', the diagonal elements of |
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* A are not referenced either, but are assumed to be unity. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. When SIDE = 'L' or 'l' then |
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* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' |
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* then LDA must be at least max( 1, n ). |
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* Unchanged on exit. |
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* |
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* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). |
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* Before entry, the leading m by n part of the array B must |
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* contain the matrix B, and on exit is overwritten by the |
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* transformed matrix. |
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* |
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* LDB - INTEGER. |
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* On entry, LDB specifies the first dimension of B as declared |
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* in the calling (sub) program. LDB must be at least |
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* max( 1, m ). |
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* Unchanged on exit. |
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* |
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* Further Details |
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* =============== |
|
* |
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* Level 3 Blas routine. |
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* |
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* -- Written on 8-February-1989. |
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* Jack Dongarra, Argonne National Laboratory. |
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* Iain Duff, AERE Harwell. |
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* Jeremy Du Croz, Numerical Algorithms Group Ltd. |
|
* Sven Hammarling, Numerical Algorithms Group Ltd. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. External Functions .. |
* .. External Functions .. |