p?ungql

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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p?ungql

Generates the unitary matrix Q of the QL factorization formed by p?geqlf.

Syntax

void pcungql (const MKL_INT *m , const MKL_INT *n , const MKL_INT *k , MKL_Complex8 *a , const MKL_INT *ia , const MKL_INT *ja , const MKL_INT *desca , const MKL_Complex8 *tau , MKL_Complex8 *work , const MKL_INT *lwork , MKL_INT *info );

void pzungql (const MKL_INT *m , const MKL_INT *n , const MKL_INT *k , MKL_Complex16 *a , const MKL_INT *ia , const MKL_INT *ja , const MKL_INT *desca , const MKL_Complex16 *tau , MKL_Complex16 *work , const MKL_INT *lwork , MKL_INT *info );

Include Files

mkl_scalapack.h

Description

This function generates the whole or part of m-by-n complex distributed matrix Q denoting A(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first n columns of a product of k elementary reflectors of order m

Q = (H(k))^H...*(H(2))^H*(H(1))^H as returned by p?geqlf.

Input Parameters

m

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

n

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

k

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

a

(local)

Pointer into the local memory to an array of local size lld_a*LOCc(ja+n-1). On entry, the j-th columnof the matrix stored in a must contain the vector that defines the elementary reflector H(j), ja+n-k≤ j≤ ja+n-1, as returned by p?geqlf in the k columns of its distributed matrix argument A(ia:*, ja+n-k: ja+n-1).

ia, ja

(global) The row and column indices in the global matrix A indicating the first row and the first column of the submatrix A(ia:ia+m-1,ja:ja+n-1), respectively.

desca

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

tau

(local)

Array of size LOCr(ia+n-1).

Contains the scalar factors tau[j] of elementary reflectors H(j+1), 0 ≤ j < LOCr(ia+n-1). tau is tied to the distributed matrix A.

work

(local)

Workspace array of size of lwork.

lwork

(local or global) size of work, must be at least lwork≥nb_a*(nqa0 + mpa0 + nb_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 function blacs_gridinfo.

If lwork = -1, then lwork is global input and a workspace query is assumed; the function 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 to be factored.

work[0]

On exit, work[0] contains the minimum value of lwork required for optimum performance.

info

(global)

= 0: the execution is successful.

< 0: if the i-th argument is an array and the j-th entry, indexed j - 1, 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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p?ungql

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