SORGRQ (3lapack)

generate an M-by-N real matrix Q with orthonormal rows,

SYNOPSIS

  SUBROUTINE SORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

      INTEGER        INFO, K, LDA, LWORK, M, N

      REAL           A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE

  SORGRQ generates an M-by-N real matrix Q 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)

  as returned by SGERQF.

ARGUMENTS

  M       (input) INTEGER
          The number of rows of the matrix Q. M >= 0.

  N       (input) INTEGER
          The number of columns of the matrix Q. N >= M.

  K       (input) INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

  A       (input/output) REAL array, dimension (LDA,N)
          On entry, the (m-k+i)-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned by
          SGERQF in the last k rows of its array argument A.  On exit, the
          M-by-N matrix Q.

  LDA     (input) INTEGER
          The first dimension of the array A. LDA >= max(1,M).

  TAU     (input) REAL array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary reflector
          H(i), as returned by SGERQF.

  WORK    (workspace/output) REAL array, dimension (LWORK)
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

  LWORK   (input) INTEGER
          The dimension of the array WORK. LWORK >= max(1,M).  For optimum
          performance LWORK >= M*NB, where NB is the optimal blocksize.

  INFO    (output) INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument has an illegal value