# p?orgr2/p?ungr2

Generates all or part of the orthogonal/unitary matrix Q from an RQ factorization determined by p?gerqf (unblocked algorithm).

## Syntax

call psorgr2(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pdorgr2(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pcungr2(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pzungr2(m, n, k, a, ia, ja, desca, tau, work, l work, info)

## Description

The routine p?orgr2/p?ungr2 generates an m-by-n real/complex 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(2)*...*H(k)` (for real flavors);

`Q = (H(1))H*(H(2))H...*(H(k))H` (for complex flavors) as returned by p?gerqf.

## Input Parameters

m

  (global) INTEGER.

  The number of rows to be operated on, that is, the number of rows of the distributed submatrix Q. `m ≥ 0`.

n

  (global) INTEGER.

  The number of columns to be operated on, that is, the number of columns of the distributed submatrix Q.`n ≥ m ≥ 0`.

k

  (global) INTEGER.

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

a

  REAL for psorgr2

  DOUBLE PRECISION for pdorgr2

  COMPLEX for pcungr2

  COMPLEX*16 for pzungr2.

  Pointer into the local memory to an array, DIMENSION`(lld_a, LOCc(ja+n-1)`.

  On entry, the i-th row must 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

  (global) INTEGER.

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

ja

  (global) INTEGER.

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

desca

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

tau

  (local)

  REAL for psorgr2

  DOUBLE PRECISION for pdorgr2

  COMPLEX for pcungr2

  COMPLEX*16 for pzungr2.

  Array, DIMENSION `LOCr(ja+m-1)`. This array contains the scalar factors tau(i) of the elementary reflectors H(i), as returned by p?gerqf. This array is tied to the distributed matrix A.

work

  (local)

  REAL for psorgr2

  DOUBLE PRECISION for pdorgr2

  COMPLEX for pcungr2

  COMPLEX*16 for pzungr2.

  Workspace array, DIMENSION (lwork).

lwork

  (local or global) INTEGER.

  The dimension of the array work.

  lwork is local input and must be at least `lwork ≥ nqa0 + max(1, mpa0 )`, 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-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: Auxiliary Routines