# p?ungrq

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

## Syntax

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

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

## Description

The routine 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) INTEGER. The number of rows in the submatrix sub(Q); `(m≥0)`.

n

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

k

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

a

  (local)

  COMPLEX for pcungrq

  DOUBLE COMPLEX for pzungrqc

  Pointer into the local memory to an array of dimension `(lld_a, LOCc(ja+n-1))`. The i-th row must contain the vector which 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) INTEGER. The row and column indices in the global array a indicating the first row and the first column of the submatrix A, respectively.

desca

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

tau

  (local)

  COMPLEX for pcungrq

  DOUBLE COMPLEX for pzungrq

  Array, DIMENSION `LOCr(ia+m-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)

  COMPLEX for pcungrq

  DOUBLE COMPLEX for pzungrq

  Workspace array of dimension of lwork.

lwork

  (local or global) INTEGER, dimension 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.

  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-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