p?orgrq

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?orgrq

Generates the orthogonal matrix Q of the RQ factorization formed by p?gerqf.

Syntax

call psorgrq(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

call pdorgrq(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

Include Files

Description

The p?orgrqroutine generates the whole or part of m-by-n real distributed matrix Q denoting A(ia:ia+m-1,ja:ja+n-1) with orthonormal rows that is defined as the last m rows of a product of k elementary reflectors of order n

Q= H(1)*H(2)*...*H(k)

as returned by p?gerqf.

Input Parameters

m

(global) INTEGER. The number of rows in the matrix sub(Q), (m≥0).

n

(global) INTEGER. The number of columns in the matrix sub(Q), (n≥m≥0).

k

(global) INTEGER. The number of elementary reflectors whose product defines the matrix Q(m≥k≥0).

a

(local)

REAL for psorgrq

DOUBLE PRECISION for pdorgrq

Pointer into the local memory to an array of local size (lld_a,LOCc(ja+n-1)). The i-th row must contain the vector that defines the elementary reflector H(i), ia≤i≤ia+m-1, as returned by p?gerqf in the k rows of its distributed matrix argument A(ia+m-k:ia+m-1, ja:*).

ia, ja

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

desca

(global and local) INTEGER array of size dlen_. The array descriptor for the distributed matrix A.

tau

(local)

REAL for psorgrq

DOUBLE PRECISION for pdorgrq

Array of size LOCc(ja+k-1).

Contains the scalar factor tau(i) of elementary reflectors H(i) as returned by p?gerqf. tau is tied to the distributed matrix A.

work

(local)

REAL for psorgrq

DOUBLE PRECISION for pdorgrq

Workspace array of size of lwork.

lwork

(local or global) INTEGER, size of work, must be at least lwork≥mb_a*(mpa0 + nqa0 + mb_a), where

iroffa = mod(ia-1, mb_a),

icoffa = mod(ja-1, nb_a),

iarow = indxg2p(ia, mb_a, MYROW, rsrc_a, NPROW),

iacol = indxg2p(ja, nb_a, MYCOL, csrc_a, NPCOL),

mpa0 = numroc(m+iroffa, mb_a, MYROW, iarow, NPROW),

nqa0 = numroc(n+icoffa, nb_a, MYCOL, iacol, NPCOL)

indxg2p and numroc are ScaLAPACK tool functions; MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine blacs_gridinfo.

NOTE:

mod(x,y) is the integer remainder of x/y.

If lwork = -1, then lwork is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by pxerbla.

Output Parameters

a

Contains the local pieces of the m-by-n distributed matrix Q.

work(1)

On exit, work(1) contains the minimum value of lwork required for optimum performance.

info

(global) INTEGER.

= 0: the execution is successful.

< 0: if the i-th argument is an array and the j-th entry had an illegal value, then info = -(i*100+j); if the i-th argument is a scalar and had an illegal value, then info = -i.

Parent topic: Orthogonal Factorizations: ScaLAPACK Computational Routines

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