p?her2

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?her2

Performs a rank-2 update of a distributed Hermitian matrix.

Syntax

call pcher2(uplo, n, alpha, x, ix, jx, descx, incx, y, iy, jy, descy, incy, a, ia, ja, desca)

call pzher2(uplo, n, alpha, x, ix, jx, descx, incx, y, iy, jy, descy, incy, a, ia, ja, desca)

Include Files

mkl_pblas.h

Description

The p?her2 routines perform a distributed matrix-vector operation defined as

sub(A) := alpha*sub(x)*conj(sub(y)')+ conj(alpha)*sub(y)*conj(sub(x)') + sub(A),

where:

alpha is a scalar,

sub(A) is a n-by-n distributed Hermitian matrix, sub(A)=A(ia:ia+n-1, ja:ja+n-1),

sub(x) and sub(y) are 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,

sub(y) denotes Y(iy, jy:jy+n-1) if incy = m_y, and Y(iy: iy+n-1, jy) if incy = 1.

Input Parameters

uplo

(global) CHARACTER*1. Specifies whether the upper or lower triangular part of the distributed Hermitian matrix sub(A) is used:

If uplo = 'U' or 'u', then the upper triangular part of the sub(A) is used.

If uplo = 'L' or 'l', then the low triangular part of the sub(A) is used.

n

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

alpha

(global)COMPLEX for pcher2

DOUBLE COMPLEX for pzher2

Specifies the scalar alpha.

x

(local)COMPLEX for pcher2

DOUBLE COMPLEX for pzher2

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.

y

(local)COMPLEX for pcher2

DOUBLE COMPLEX for pzher2

Array, size at least (jy-1)*m_y + iy+(n-1)*abs(incy)).

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.

a

(local)COMPLEX for pcher2

DOUBLE COMPLEX for pzher2

Array, size (lld_a, LOCq(ja+n-1)). This array contains the local pieces of the distributed matrix sub(A).

Before entry with uplo = 'U' or 'u', the n-by-n upper triangular part of the distributed matrix sub(A) must contain the upper triangular part of the Hermitian distributed matrix and the strictly lower triangular part of sub(A) is not referenced, and with uplo = 'L' or 'l', the n-by-n lower triangular part of the distributed matrix sub(A) must contain the lower triangular part of the Hermitian distributed matrix and the strictly upper triangular part of sub(A) is not referenced.

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.

Output Parameters

a

With uplo = 'U' or 'u', the upper triangular part of the array a is overwritten by the upper triangular part of the updated distributed matrix sub(A).

With uplo = 'L' or 'l', the lower triangular part of the array a is overwritten by the lower triangular part of the updated distributed matrix sub(A).

Parent topic: PBLAS Level 2 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?her2