# p?ungqr

Generates the complex unitary matrix Q of the QR factorization formed by p?geqrf.

## Syntax

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

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

## Description

The routine 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 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 in the submatrix sub(Q); `(m≥0)`.

n

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

k

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

a

  (local)

  COMPLEX for pcungqr

  DOUBLE COMPLEX for pzungqr

  Pointer into the local memory to an array of dimension (lld_a, LOCc(ja+n-1)).The j-th column must contain the vector which 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, 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 pcungqr

  DOUBLE COMPLEX for pzungqr

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

  Contains the scalar factor tau (j) of elementary reflectors H(j) as returned by p?geqrf. tau is tied to the distributed matrix A.

work

  (local)

  COMPLEX for pcungqr

  DOUBLE COMPLEX for pzungqr

  Workspace array of dimension of lwork.

lwork

  (local or global) INTEGER, dimension of work, must be at least lwork ≥ nb_a*(nqa0 + mpa0 + nb_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