?trsm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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?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, blas.f90

Description

The ?trsm routines solve one of the following matrix equations:

op(A)*X = alpha*B,

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

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.

uplo = 'U' or 'u'

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) , 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' 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.

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.

Parent topic: BLAS Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?trsm

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes