SORML2 (3lapack)

overwrite the general real m by n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L' and TRANS = 'T', or C * Q if SIDE = 'R' and TRANS = 'N', or C * Q' if SIDE = 'R' and TRANS = 'T',

SYNOPSIS

  SUBROUTINE SORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO )

      CHARACTER      SIDE, TRANS

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

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

PURPOSE

  SORML2 overwrites the general real m by n matrix C with

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

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

  as returned by SGELQF. 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' from the Left
          = 'R': apply Q or Q' from the Right

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

  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 SGELQF in the first 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 SGELQF.

  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'*C or C*Q' or C*Q.

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

  WORK    (workspace) REAL array, dimension
          (N) if SIDE = 'L', (M) if SIDE = 'R'

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