p?her2k

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?her2k

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

Syntax

call pcher2k(uplo, trans, n, k, alpha, a, ia, ja, desca, b, ib, jb, descb, beta, c, ic, jc, descc)

call pzher2k(uplo, trans, n, k, alpha, a, ia, ja, desca, b, ib, jb, descb, beta, c, ic, jc, descc)

Include Files

mkl_pblas.h

Description

The p?her2k routines perform a distributed matrix-matrix operation defined as

sub(C):=alpha*sub(A)*conjg(sub(B)')+ conjg(alpha)*sub(B)*conjg(sub(A)')+beta*sub(C),

sub(C):=alpha*conjg(sub(A)')*sub(A)+ conjg(alpha)*conjg(sub(B)')*sub(A) + beta*sub(C),

where:

alpha and beta are scalars,

sub(C) is an n-by-n Hermitian distributed matrix, sub(C) = C(ic:ic+n-1, jc:jc+n-1).

sub(A) is a distributed matrix, sub(A)=A(ia:ia+n-1, ja:ja+k-1), if trans = 'N' or 'n', and sub(A) = A(ia:ia+k-1, ja:ja+n-1) otherwise.

sub(B) is a distributed matrix, sub(B) = B(ib:ib+n-1, jb:jb+k-1), if trans = 'N' or 'n', and sub(B)=B(ib:ib+k-1, jb:jb+n-1) otherwise.

Input Parameters

uplo

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

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

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

trans

(global) CHARACTER*1. Specifies the operation:

if trans = 'N' or 'n', then sub(C) := alpha*sub(A)*conjg(sub(B)')+ conjg(alpha)*sub(B)*conjg(sub(A)') + beta*sub(C);

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

n

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

k

(global) INTEGER. On entry with trans = 'N' or 'n', k specifies the number of columns of the distributed matrices sub(A) and sub(B), and on entry with trans = 'C' or 'c' , k specifies the number of rows of the distributed matrices sub(A) and sub(B), k≥ 0.

alpha

(global)COMPLEX for pcher2k

DOUBLE COMPLEX for pzher2k

Specifies the scalar alpha.

a

(local)COMPLEX for pcher2k

DOUBLE COMPLEX for pzher2k

Array, size (lld_a, kla), where kla is LOCq(ja+k-1) when trans = 'N' or 'n', and is LOCq(ja+n-1) otherwise. Before entry with trans = 'N' or 'n', this array contains the local pieces of the distributed matrix sub(A).

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)COMPLEX for pcher2k

DOUBLE COMPLEX for pzher2k

Array, size (lld_b, klb), where klb is LOCq(jb+k-1) when trans = 'N' or 'n', and is LOCq(jb+n-1) otherwise. Before entry with trans = 'N' or 'n', 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.

beta

(global)REAL for pcher2k

DOUBLE PRECISION for pzher2k

Specifies the scalar beta.

c

(local)COMPLEX for pcher2k

DOUBLE COMPLEX for pzher2k

Array, size (lld_c, LOCq(jc+n-1)).

Before entry with uplo = 'U' or 'u', this array contains n-by-n upper triangular part of the symmetric distributed matrix sub(C) and its strictly lower triangular part is not referenced.

Before entry with uplo = 'L' or 'l', this array contains n-by-n lower triangular part of the symmetric distributed matrix sub(C) and its strictly upper triangular part is not referenced.

ic, jc

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

descc

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

Output Parameters

c

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

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

Parent topic: PBLAS Level 3 Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

p?her2k