p?trsm

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?trsm

Solves a distributed matrix equation (one matrix operand is triangular).

Syntax

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

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

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

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

Include Files

mkl_pblas.h

Description

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

op(sub(A))*X = alpha*sub(B),

X*op(sub(A)) = alpha*sub(B),

where:

alpha is a scalar,

X and sub(B) are m-by-n distributed matrices, 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)').

The distributed matrix sub(B) is overwritten by the solution matrix X.

Input Parameters

side

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

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

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

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 equation:

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 pstrsm

DOUBLE PRECISION for pdtrsm

COMPLEX for pctrsm

DOUBLE COMPLEX for pztrsm

Specifies the scalar alpha.

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

a

(local)REAL for pstrsm

DOUBLE PRECISION for pdtrsm

COMPLEX for pctrsm

DOUBLE COMPLEX for pztrsm

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 pstrsm

DOUBLE PRECISION for pdtrsm

COMPLEX for pctrsm

DOUBLE COMPLEX for pztrsm

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 solution distributed matrix X.

Parent topic: PBLAS Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?trsm