SORMRQ (3lapack)

overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

  SUBROUTINE SORMRQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK,
                     INFO )

      CHARACTER      SIDE, TRANS

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

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

PURPOSE

  SORMRQ overwrites the general real M-by-N matrix C with TRANS = 'T':
  Q**T * C       C * Q**T

  where Q is a real orthogonal matrix defined as the product of k elementary
  reflectors

        Q = H(1) H(2) . . . H(k)

  as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N if SIDE
  = 'R'.

ARGUMENTS

  SIDE    (input) CHARACTER*1
          = 'L': apply Q or Q**T from the Left;
          = 'R': apply Q or Q**T from the Right.

  TRANS   (input) CHARACTER*1
          = 'N':  No transpose, apply Q;
          = 'T':  Transpose, apply Q**T.

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

  N       (input) INTEGER
          The number of columns of the matrix C. N >= 0.

  K       (input) INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.

  A       (input) REAL array, dimension
          (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The 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.  A is modified by the routine but restored on
          exit.

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

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

  C       (input/output) REAL array, dimension (LDC,N)
          On entry, the M-by-N matrix C.  On exit, C is overwritten by Q*C or
          Q**T*C or C*Q**T or C*Q.

  LDC     (input) INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

  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.  If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).  For optimum performance LWORK >=
          N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE = 'R', where NB is
          the optimal blocksize.

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