p?atrmv

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?atrmv

Computes a distributed matrix-vector product using absolute values for a triangular matrix.

Syntax

call psatrmv(uplo, trans, diag, n, alpha, a, ia, ja, desca, x, ix, jx, descx, incx, beta, y, iy, jy, descy, incy)

call pdatrmv(uplo, trans, diag, n, alpha, a, ia, ja, desca, x, ix, jx, descx, incx, beta, y, iy, jy, descy, incy)

call pcatrmv(uplo, trans, diag, n, alpha, a, ia, ja, desca, x, ix, jx, descx, incx, beta, y, iy, jy, descy, incy)

call pzatrmv(uplo, trans, diag, n, alpha, a, ia, ja, desca, x, ix, jx, descx, incx, beta, y, iy, jy, descy, incy)

Include Files

mkl_pblas.h

Description

The p?atrmv routines perform one of the following distributed matrix-vector operations defined as

sub(y) := abs(alpha)*abs(sub(A))*abs(sub(x))+ abs(beta*sub(y)), or

sub(y) := abs(alpha)*abs(sub( A)')*abs(sub(x))+ abs(beta*sub(y)), or

sub(y) := abs(alpha)*abs(conjg(sub(A)'))*abs(sub(x))+ abs(beta*sub(y)),

where:

alpha and beta are scalars,

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),

sub(x) is an n-element distributed vector.

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

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 op(sub(A)) used in the matrix equation:

if trans = 'N' or 'n', then sub(y) := |alpha|*|sub(A)|*|sub(x)|+|beta*sub(y)|;

if trans = 'T' or 't', then sub(y) := |alpha|*|sub(A)'|*|sub(x)|+|beta*sub(y)|;

if trans = 'C' or 'c', then sub(y) := |alpha|*|conjg(sub(A)')|*|sub(x)|+|beta*sub(y)|.

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.

alpha

(global)REAL for psatrmv

DOUBLE PRECISION for pdatrmv

COMPLEX for pcatrmv

DOUBLE COMPLEX for pzatrmv

Specifies the scalar alpha.

a

(local)REAL for psatrmv

DOUBLE PRECISION for pdatrmv

COMPLEX for pcatrmv

DOUBLE COMPLEX for pzatrmv

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 psatrmv

DOUBLE PRECISION for pdatrmv

COMPLEX for pcatrmv

DOUBLE COMPLEX for pzatrmv

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

This array contains the entries of the distributed vector sub(x).

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.

beta

(global)REAL for psatrmv

DOUBLE PRECISION for pdatrmv

COMPLEX for pcatrmv

DOUBLE COMPLEX for pzatrmv

Specifies the scalar beta. When beta is set to zero, then sub(y) need not be set on input.

y

(local)REAL for psatrmv

DOUBLE PRECISION for pdatrmv

COMPLEX for pcatrmv

DOUBLE COMPLEX for pzatrmv

Array, size (jy-1)*m_y + iy+(m-1)*abs(incy)) when trans = 'N' or 'n', and (jy-1)*m_y + iy+(n-1)*abs(incy)) otherwise.

This array contains the entries of the distributed vector sub(y).

iy, jy

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

descy

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

incy

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

Output Parameters

y: Overwritten by the transformed distributed vector sub(y).

Parent topic: PBLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?atrmv