# p?ungql

Generates the unitary matrix Q of the QL factorization formed by p?geqlf.

## Syntax

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

call pzungql( 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 rows, which is defined as the first n columns of a product of k elementary reflectors of order m

``Q = (H(k))H...*(H(2))H*(H(1))H`` as returned by p?geqlf.

## 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 pcungql

  DOUBLE COMPLEX for pzungql Pointer into the local memory to an array of local dimension `(lld_a, LOCc(ja+n-1))`. On entry, the j-th column must contain the vector which defines the elementary reflector H(j), ja+n-k≤ j≤ ja+n-1, as returned by p?geqlf in the k columns of its distributed matrix argument A(ia:*, ja+n-k: ja+n-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(ia:ia+m-1,ja:ja+n-1), respectively.

desca

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

tau

  (local)

  COMPLEX for pcungql

  DOUBLE COMPLEX for pzungql

  Array, DIMENSION LOCr(ia+n-1)).

  Contains the scalar factors tau (j) of elementary reflectors H(j). tau is tied to the distributed matrix A.

work

  (local)

  COMPLEX for pcungql

  DOUBLE COMPLEX for pzungql

  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 to be factored.

`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