NAME
DTRSM - solve one of the matrix equations op( A )*X = alpha*B, or
X*op( A ) = alpha*B,
SYNOPSIS
SUBROUTINE DTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B,
LDB )
CHARACTER*1 SIDE, UPLO, TRANSA, DIAG
INTEGER M, N, LDA, LDB
DOUBLE PRECISION ALPHA
DOUBLE PRECISION A( LDA, * ), B( LDB, * )
PURPOSE
DTRSM solves one of the matrix equations
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’.
The matrix X is overwritten on B.
PARAMETERS
SIDE - 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.
Unchanged on exit.
UPLO - 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.
Unchanged on exit.
TRANSA - 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’.
TRANSA = ’C’ or ’c’ op( A ) = A’.
Unchanged on exit.
DIAG - 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.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero. Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be at
least zero. Unchanged on exit.
ALPHA - 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. Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = ’L’ or ’l’ and 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. Unchanged on exit.
LDA - 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 ). Unchanged on exit.
B - 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.
LDB - 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 ). Unchanged on exit.
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.