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


SYNOPSIS

       SUBROUTINE SORMHR( 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

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


PURPOSE

       SORMHR overwrites the general real M-by-N  matrix  C  with
       SIDE  =  'L'  SIDE  = 'R' TRANS = 'N': Q * C C * Q 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 SGEHRD:

       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  SGEHRD.  Q
               is  equal  to the unit matrix except in the subma­
               trix 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.

               (LDA,M) if SIDE = 'L' (LDA,N) if SIDE  =  'R'  The
               vectors which define the elementary reflectors, as
               returned by SGEHRD.

       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) REAL 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 SGEHRD.

       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.

               If  LWORK = -1, then a workspace query is assumed;
               the routine only calculates the  optimal  size  of
               the  WORK  array,  returns this value as the first
               entry of the WORK  array,  and  no  error  message
               related to LWORK is issued by XERBLA.

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


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