Developer Reference for Intel® oneAPI Math Kernel Library for Fortran
?trsm
Solves a triangular matrix equation.
Syntax
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)call trsm(a, b [, side] [, uplo] [, transa] [, diag] [, alpha])Include Files
mkl.fi, mkl_blas.f90
Description
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, and
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 .
Input Parameters
- Layout
-
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
side
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 .
uplo
CHARACTER*1 . Specifies whether the matrix A is upper or lower triangular.
if uplo = 'L' or ‘l’ , then the matrix is low triangular.
transa
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' ;
if transa= 'C' or 'c' , then op(A) = conjg(A') .
diag
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.
m
INTEGER . Specifies the number of rows of B . The value of m must be at least zero.
n
INTEGER . Specifies the number of columns of B . The value of n must be at least zero.
- alpha
-
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.
- a
-
REAL for strsm DOUBLE PRECISION for dtrsm COMPLEX for ctrsm DOUBLE COMPLEX for ztrsm
Array, size (lda, k)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’ uplo = CblasUpper , 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’ 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.
lda
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) .
- b
-
REAL for strsm DOUBLE PRECISION for dtrsm COMPLEX for ctrsm DOUBLE COMPLEX for ztrsm Array, size ldb by n . Before entry, the leading m -by- n part of the array b must contain the matrix B . For Layout = CblasColMajor : array, size ldb*n . Before entry, the leading m -by- n part of the array b must contain the matrix B . For Layout = CblasRowMajor : array, size ldb*m . Before entry, the leading n -by- m part of the array b must contain the matrix B .
ldb
INTEGER . Specifies the leading dimension of b as declared in the calling (sub)program. ldb must be at least max(1, m) .
Output Parameters
- b
-
Overwritten by the solution matrix X .
BLAS 95 Interface Notes
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 BLAS 95 Interface Conventions .
Specific details for the routine trsm interface are the following:
- a
-
Holds the matrix A of size ( k , k ) where k = m if side = 'L' , k = n otherwise.
- b
-
Holds the matrix B of size ( m , n ).
- side
-
Must be ‘L’ or ‘R’ . The default value is ‘L’ .
- uplo
-
Must be ‘U’ or ‘L’ . The default value is ‘U’ .
- transa
-
Must be ‘N’ , ‘C’ , or ‘T’ . The default value is ‘N’ .
- diag
-
Must be ‘N’ or ‘U’ . The default value is ‘N’ .
- alpha
-
The default value is 1.