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sorml2

 NAME
      SORML2 - 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 elemen-
              tary 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