p?trsv

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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p?trsv

Solves a system of linear equations whose coefficients are in a distributed triangular matrix.

Syntax

call pstrsv(uplo, trans, diag, n, a, ia, ja, desca, x, ix, jx, descx, incx)

call pdtrsv(uplo, trans, diag, n, a, ia, ja, desca, x, ix, jx, descx, incx)

call pctrsv(uplo, trans, diag, n, a, ia, ja, desca, x, ix, jx, descx, incx)

call pztrsv(uplo, trans, diag, n, a, ia, ja, desca, x, ix, jx, descx, incx)

Include Files

mkl_pblas.h

Description

The p?trsv routines solve one of the systems of equations:

sub(A)*sub(x) = b, or sub(A)'*sub(x) = b, or conjg(sub(A)')*sub(x) = b,

where:

sub(A) is a n-by-n unit, or non-unit, upper or lower triangular distributed matrix, sub(A) = A(ia:ia+n-1, ja:ja+n-1),

b and sub(x) are n-element distributed vectors,

sub(x) denotes X(ix, jx:jx+n-1) if incx = m_x, and X(ix: ix+n-1, jx) if incx = 1,.

The routine does not test for singularity or near-singularity. Such tests must be performed before calling this routine.

Input Parameters

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.

trans

(global) CHARACTER*1. Specifies the form of the system of equations:

if transa = 'N' or 'n', then sub(A)*sub(x) = b;

if transa = 'T' or 't', then sub(A)'*sub(x) = b;

if transa = 'C' or 'c', then conjg(sub(A)')*sub(x) = b.

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.

n

(global) INTEGER. Specifies the order of the distributed matrix sub(A), n≥ 0.

a

(local)REAL for pstrsv

DOUBLE PRECISION for pdtrsv

COMPLEX for pctrsv

DOUBLE COMPLEX for pztrsv

Array, size at least (lld_a, LOCq(1, ja+n-1)).

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.

x

(local)REAL for pstrsv

DOUBLE PRECISION for pdtrsv

COMPLEX for pctrsv

DOUBLE COMPLEX for pztrsv

Array, size at least (jx-1)*m_x + ix+(n-1)*abs(incx)).

This array contains the entries of the distributed vector sub(x). Before entry, sub(x) must contain the n-element right-hand side distributed vector b.

ix, jx

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

descx

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

incx

(global) INTEGER. Specifies the increment for the elements of sub(x). Only two values are supported, namely 1 and m_x. incx must not be zero.

Output Parameters

x: Overwritten with the solution vector.

Parent topic: PBLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?trsv