p?unglq

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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p?unglq

Generates the unitary matrix Q of the LQ factorization formed by p?gelqf.

Syntax

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

void pzunglq (MKL_INT *m , MKL_INT *n , MKL_INT *k , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_Complex16 *tau , MKL_Complex16 *work , 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 m rows of a product of k elementary reflectors of order n

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

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) (n≥m≥0).

k

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

a

(local)

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

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+k-1).

Contains the scalar factors tau[j] of elementary reflectors H(j+1), 0 ≤ j < LOCr(ia+k-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≥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 function 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 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?unglq

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