DORMHR (3lapack)

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

SYNOPSIS

  SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, WORK,
                     LWORK, INFO )

      CHARACTER      SIDE, TRANS

      INTEGER        IHI, ILO, INFO, LDA, LDC, LWORK, M, N

      DOUBLE         PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
                     LWORK )

PURPOSE

  DORMHR 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 of order nq, with nq = m if SIDE = 'L'
  and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO elementary
  reflectors, as returned by DGEHRD:

  Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

  ILO     (input) INTEGER
          IHI     (input) INTEGER ILO and IHI must have the same values as in
          the previous call of DGEHRD. Q is equal to the unit matrix except
          in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE = 'L', then 1 <=
          ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if
          SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and ILO = 1 and
          IHI = 0, if N = 0.

  A       (input) DOUBLE PRECISION array, dimension
          (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
          define the elementary reflectors, as returned by DGEHRD.

  LDA     (input) INTEGER
          The leading dimension of the array A.  LDA >= max(1,M) if SIDE =
          'L'; LDA >= max(1,N) if SIDE = 'R'.

  TAU     (input) DOUBLE PRECISION array, dimension
          (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
          scalar factor of the elementary reflector H(i), as returned by
          DGEHRD.

  C       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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