p?trmm

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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p?trmm

Computes a scalar-matrix-matrix product (one matrix operand is triangular) for distributed matrices.

Syntax

call pstrmm(side, uplo, transa, diag, m, n, alpha, a, ia, ja, desca, b, ib, jb, descb)

call pdtrmm(side, uplo, transa, diag, m, n, alpha, a, ia, ja, desca, b, ib, jb, descb)

call pctrmm(side, uplo, transa, diag, m, n, alpha, a, ia, ja, desca, b, ib, jb, descb)

call pztrmm(side, uplo, transa, diag, m, n, alpha, a, ia, ja, desca, b, ib, jb, descb)

Include Files

mkl_pblas.h

Description

The p?trmm routines perform a matrix-matrix operation using triangular matrices. The operation is defined as

sub(B) := alpha*op(sub(A))*sub(B)

sub(B) := alpha*sub(B)*op(sub(A))

where:

alpha is a scalar,

sub(B) is an m-by-n distributed matrix, sub(B)=B(ib:ib+m-1, jb:jb+n-1).

A is a unit, or non-unit, upper or lower triangular distributed matrix, sub(A)=A(ia:ia+m-1, ja:ja+m-1), if side = 'L' or 'l', and sub(A)=A(ia:ia+n-1, ja:ja+n-1), if side = 'R' or 'r'.

op(sub(A)) is one of op(sub(A)) = sub(A), or op(sub(A)) = sub(A)', or op(sub(A)) = conjg(sub(A)').

Input Parameters

side

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

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

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

uplo

(global) CHARACTER*1. Specifies whether the distributed matrix sub(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.

transa

(global) CHARACTER*1. Specifies the form of op(sub(A)) used in the matrix multiplication:

if transa = 'N' or 'n', then op(sub(A)) = sub(A);

if transa = 'T' or 't', then op(sub(A)) = sub(A)' ;

if transa = 'C' or 'c', then op(sub(A)) = conjg(sub(A)').

diag

(global) CHARACTER*1. Specifies whether the matrix sub(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

(global) INTEGER. Specifies the number of rows of the distributed matrix sub(B), m≥ 0.

n

(global) INTEGER. Specifies the number of columns of the distributed matrix sub(B), n≥ 0.

alpha

(global)REAL for pstrmm

DOUBLE PRECISION for pdtrmm

COMPLEX for pctrmm

DOUBLE COMPLEX for pztrmm

Specifies the scalar alpha.

When alpha is zero, then the arrayb need not be set before entry.

a

(local)REAL for pstrmm

DOUBLE PRECISION for pdtrmm

COMPLEX for pctrmm

DOUBLE COMPLEX for pztrmm

Array, size lld_a by ka, where ka is at least LOCq(1, ja+m-1) when side = 'L' or 'l' and is at least LOCq(1, ja+n-1) when side = 'R' or 'r'.

Before entry with uplo = 'U' or 'u', this array contains the local entries corresponding to the entries of the upper triangular distributed matrix sub(A), and the local entries corresponding to the entries of the strictly lower triangular part of the distributed matrix sub(A) is not referenced.

Before entry with uplo = 'L' or 'l', this array contains the local entries corresponding to the entries of the lower triangular distributed matrix sub(A), and the local entries corresponding to the entries of the strictly upper triangular part of the distributed matrix sub(A) is not referenced .

When diag = 'U' or 'u', the local entries corresponding to the diagonal elements of the submatrix sub(A) are not referenced either, but are assumed to be unity.

ia, ja

(global) INTEGER. The row and column indices in the distributed matrix A indicating the first row and the first column of the submatrix sub(A), respectively.

desca

(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix A.

b

(local)REAL for pstrmm

DOUBLE PRECISION for pdtrmm

COMPLEX for pctrmm

DOUBLE COMPLEX for pztrmm

Array, size (lld_b, LOCq(1, jb+n-1)).

Before entry, this array contains the local pieces of the distributed matrix sub(B).

ib, jb

(global) INTEGER. The row and column indices in the distributed matrix B indicating the first row and the first column of the submatrix sub(B), respectively.

descb

(global and local) INTEGER array of dimension 9. The array descriptor of the distributed matrix B.

Output Parameters

b: Overwritten by the transformed distributed matrix.

Parent topic: PBLAS Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?trmm