p?org2r/p?ung2r

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?org2r/p?ung2r

Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by p?geqrf (unblocked algorithm).

Syntax

call psorg2r(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

call pdorg2r(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

call pcung2r(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

call pzung2r(m, n, k, a, ia, ja, desca, tau, work, lwork, info)

Description

The p?org2r/p?ung2rroutine generates an m-by-n real/complex matrix Q denoting A(ia:ia+m-1, ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m:

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

as returned by p?geqrf.

Input Parameters

m

(global) INTEGER.

The number of rows in the distributed submatrix Q.m ≥ 0.

n

(global) INTEGER.

The number of columns in the distributed submatrix Q. m ≥ n ≥ 0.

k

(global) INTEGER.

The number of elementary reflectors whose product defines the matrix Q. n ≥ k ≥ 0.

a

REAL for psorg2r

DOUBLE PRECISION for pdorg2r

COMPLEX for pcung2r

COMPLEX*16 for pzung2r.

Pointer into the local memory to an array of size(lld_a, LOCc(ja+n-1))

On entry, the j-th column must contain the vector that defines the elementary reflector H(j), ja ≤ j ≤ ja+k-1, as returned by p?geqrf in the k columns of its distributed matrix argument A(ia:*,ja:ja+k-1).

ia

(global) INTEGER.

The row index in the global matrix A indicating the first row of sub(A).

ja

(global) INTEGER.

The column index in the global matrix A indicating the first column of sub(A).

desca

(global and local) INTEGER array of size dlen_.

The array descriptor for the distributed matrix A.

tau

(local)

REAL for psorg2r

DOUBLE PRECISION for pdorg2r

COMPLEX for pcung2r

COMPLEX*16 for pzung2r.

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

tau(j) contains the scalar factor of the elementary reflector H(j), as returned by p?geqrf. This array is tied to the distributed matrix A.

work

(local)

REAL for psorg2r

DOUBLE PRECISION for pdorg2r

COMPLEX for pcung2r

COMPLEX*16 for pzung2r.

Workspace array of size lwork.

lwork

(local or global) INTEGER.

The size of the array work.

lwork is local input and must be at least lwork ≥ mpa0 + max(1, nqa0),

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.

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

On exit, this array contains the local pieces of the m-by-n distributed matrix Q.

work

On exit, work(1) returns the minimal and optimal lwork.

info

(local)INTEGER.

= 0: successful exit

< 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: ScaLAPACK Auxiliary Routines

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