p?ungrq

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 6/24/2024

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p?ungrq

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

Syntax

void pcungrq (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 pzungrq (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 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 last m rows of a product of k elementary reflectors of order n

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

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 size lld_a*LOCc(ja+n-1). The i-th row of the matrix stored in amust contain the vector that defines the elementary reflector H(i), ia+m-k≤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) 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) array of size dlen_. The array descriptor for the distributed matrix A.

tau

(local)

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

Contains the scalar factor tau[i] of elementary reflectors H(i+1) as returned by p?gerqf, 0 ≤ i < LOCr(ia+m-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)

NOTE:

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

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.

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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Developer Reference for Intel® oneAPI Math Kernel Library for C

p?ungrq

Syntax

Include Files

Description

Input Parameters

Output Parameters

See Also