Solves a matrix equation (one matrix operand is triangular).
FORTRAN 77:
call strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
call dtrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
call ctrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
call ztrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
Fortran 95:
call trsm(a, b [,side] [, uplo] [,transa][,diag] [,alpha])
The FORTRAN 77 interfaces are specified in the mkl_blas.fi include file, the Fortran 95 interfaces are specified in the blas.f90 include file, and the C interfaces are specified in the mkl_blas.h include file.
The ?trsm routines solve one of the following matrix equations: op(A)*X = alpha*B,
or X*op(A) = alpha*B,
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
op(A) is one of op(A) = A, or op(A) = A', or op(A) = conjg(A').
The matrix B is overwritten by the solution matrix X.
CHARACTER*1. Specifies whether op(A) appears on the left or right of X in the equation:
if side = 'L' or 'l', then op(A)*X = alpha*B;
if side = 'R' or 'r', then X*op(A) = alpha*B.
CHARACTER*1. Specifies whether the matrix A is upper or lower triangular:
if uplo = 'U' or 'u', then the matrix is upper triangular;
if uplo = 'L' or 'l', then the matrix is low triangular.
CHARACTER*1. Specifies the form of op(A) used in the matrix multiplication:
if transa = 'N' or 'n', then op(A) = A;
if transa = 'T' or 't', then op(A) = A';
if transa = 'C' or 'c', then op(A) = conjg(A').
CHARACTER*1. Specifies whether the matrix A is unit triangular:
if diag = 'U' or 'u' then the matrix is unit triangular;
if diag = 'N' or 'n', then the matrix is not unit triangular.
INTEGER. Specifies the number of rows of B. The value of m must be at least zero.
INTEGER. Specifies the number of columns of B. The value of n must be at least zero.
REAL for strsm
DOUBLE PRECISION for dtrsm
COMPLEX for ctrsm
DOUBLE COMPLEX for ztrsm
Specifies the scalar alpha.
When alpha is zero, then a is not referenced and b need not be set before entry.
REAL for strsm
DOUBLE PRECISION for dtrsm
COMPLEX for ctrsm
DOUBLE COMPLEX for ztrsm
Array, 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.
When diag = 'U' or 'u', the diagonal elements of a are not referenced either, but are assumed to be unity.
INTEGER. Specifies the leading 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).
REAL for strsm
DOUBLE PRECISION for dtrsm
COMPLEX for ctrsm
DOUBLE COMPLEX for ztrsm
Array, DIMENSION (ldb,n). Before entry, the leading m-by-n part of the array b must contain the right-hand side matrix B.
INTEGER. Specifies the leading dimension of b as declared in the calling (sub)program. The value of ldb must be at least max(1, +m).
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.
Specific details for the routine trsm interface are the following:
Holds the matrix A of size (k,k) where k = m if side = 'L', k = n otherwise.
Holds the matrix B of size (m,n).
Must be 'L' or 'R'. The default value is 'L'.
Must be 'U' or 'L'. The default value is 'U'.
Must be 'N', 'C', or 'T'.
The default value is 'N'.
Must be 'N' or 'U'. The default value is 'N'.
The default value is 1.
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