# p?org2r/p?ung2r

Generates all or part of the orthogonal/unitary matrix Q from a QR factorization determined by p?geqrf (unblocked algorithm).

## Syntax

call psorg2r(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pdorg2r(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pcung2r(m, n, k, a, ia, ja, desca, tau, work, l work, info)

call pzung2r(m, n, k, a, ia, ja, desca, tau, work, l work, info)

## Description

The routine p?org2r/p?ung2r generates an m-by-n real/complex matrix Q denoting `A(ia:ia+m-1, ja:ja+n-1)` with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m:
`Q = H(1)*H(2)*...*H(k)`

as returned by p?geqrf.

## 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. `m ≥ n ≥ 0`.

k

  (global) INTEGER.

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

a

  REAL for psorg2r

  DOUBLE PRECISION for pdorg2r

  COMPLEX for pcung2r

  COMPLEX*16 for pzung2r.

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

  On entry, the j-th column must contain the vector that defines the elementary reflector `H(j), ja ≤ j ≤ ja+k-1`, as returned by p?geqrf in the k columns of its distributed matrix argument `A(ia:*,ja:ja+k-1)`.

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 psorg2r

  DOUBLE PRECISION for pdorg2r

  COMPLEX for pcung2r

  COMPLEX*16 for pzung2r.

  Array, DIMENSION LOCc(ja+k-1).

  This array contains the scalar factor tau(j) of the elementary reflector H(j), as returned by p?geqrf. This array is tied to the distributed matrix A.

work

  (local)

  REAL for psorg2r

  DOUBLE PRECISION for pdorg2r

  COMPLEX for pcung2r

  COMPLEX*16 for pzung2r.

  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 ≥ mpa0 + max(1, nqa0)`,

  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