?trmm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 7/13/2023

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?trmm

Computes a matrix-matrix product where one input matrix is triangular.

Syntax

call strmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)

call dtrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)

call ctrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)

call ztrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)

call trmm(a, b [,side] [, uplo] [,transa][,diag] [,alpha])

Include Files

mkl.fi, blas.f90

Description

The ?trmm routines compute a scalar-matrix-matrix product with one triangular matrix . The operation is defined as

B := alpha*op(A)*B

B := alpha*B*op(A)

where:

alpha is a scalar,

B is an m-by-n matrix,

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').

Input Parameters

side

CHARACTER*1. Specifies whether op(A) appears on the left or right of B in the operation:

if side = 'L' or 'l' , then B := alpha*op(A)*B;

if side = 'R' or 'r' , then B := alpha*B*op(A).

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' , then op(A) = A';

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 strmm

DOUBLE PRECISION for dtrmm

COMPLEX for ctrmm

DOUBLE COMPLEX for ztrmm

Specifies the scalar alpha.

When alpha is zero, then a is not referenced and b need not be set before entry.

a

REAL for strmm

DOUBLE PRECISION for dtrmm

COMPLEX for ctrmm

DOUBLE COMPLEX for ztrmm

Array, size lda by k, where k is m when side = 'L'side 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.

lda

INTEGER. Specifies the leading dimension of a as declared in the calling (sub)program. Whenside = '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 strmm

DOUBLE PRECISION for dtrmm

COMPLEX for ctrmm

DOUBLE COMPLEX for ztrmm

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 transformed matrix.

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 trmm 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

?trmm

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes