# p?orgqr

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

## Syntax

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

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

## Description

The routine generates the whole or part of m-by-n real 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)

  REAL for psorgqr

  DOUBLE PRECISION for pdorgqr

  Pointer into the local memory to an array of local 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(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)

  REAL for psorgqr

  DOUBLE PRECISION for pdorgqr

  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)

  REAL for psorgqr

  DOUBLE PRECISION for pdorgqr

  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