sorm2l.f

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*> \brief \b SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE SORM2L( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
*                          WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS
*       INTEGER            INFO, K, LDA, LDC, M, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SORM2L overwrites the general real m by n matrix C with
*>
*>       Q * C  if SIDE = 'L' and TRANS = 'N', or
*>
*>       Q**T * C  if SIDE = 'L' and TRANS = 'T', or
*>
*>       C * Q  if SIDE = 'R' and TRANS = 'N', or
*>
*>       C * Q**T if SIDE = 'R' and TRANS = 'T',
*>
*> 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 SGEQLF. Q is of order m if SIDE = 'L' and of order n
*> if SIDE = 'R'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>          = 'L': apply Q or Q**T from the Left
*>          = 'R': apply Q or Q**T from the Right
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          = 'N': apply Q  (No transpose)
*>          = 'T': apply Q**T (Transpose)
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix C. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix C. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines
*>          the matrix Q.
*>          If SIDE = 'L', M >= K >= 0;
*>          if SIDE = 'R', N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL array, dimension (LDA,K)
*>          The i-th column must contain the vector which defines the
*>          elementary reflector H(i), for i = 1,2,...,k, as returned by
*>          SGEQLF in the last k columns of its array argument A.
*>          A is modified by the routine but restored on exit.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.
*>          If SIDE = 'L', LDA >= max(1,M);
*>          if SIDE = 'R', LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is REAL array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by SGEQLF.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is 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.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>          The leading dimension of the array C. LDC >= max(1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension
*>                                   (N) if SIDE = 'L',
*>                                   (M) if SIDE = 'R'
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup realOTHERcomputational
*
*  =====================================================================
      SUBROUTINE sorm2l( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            INFO, K, LDA, LDC, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE
      parameter( one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, MI, NI, NQ
      REAL               AII
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           slarf, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      left = lsame( side, 'L' )
      notran = lsame( trans, 'N' )
*
*     NQ is the order of Q
*
      IF( left ) THEN
         nq = m
      ELSE
         nq = n
      END IF
      IF( .NOT.left .AND. .NOT.lsame( side, 'r' ) ) THEN
         INFO = -1
.NOT..AND..NOT.      ELSE IF( NOTRAN  LSAME( TRANS, 't' ) ) THEN
         INFO = -2
.LT.      ELSE IF( M0 ) THEN
         INFO = -3
.LT.      ELSE IF( N0 ) THEN
         INFO = -4
.LT..OR..GT.      ELSE IF( K0  KNQ ) THEN
         INFO = -5
.LT.      ELSE IF( LDAMAX( 1, NQ ) ) THEN
         INFO = -7
.LT.      ELSE IF( LDCMAX( 1, M ) ) THEN
         INFO = -10
      END IF
.NE.      IF( INFO0 ) THEN
         CALL XERBLA( 'sorm2l', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
.EQ..OR..EQ..OR..EQ.      IF( M0  N0  K0 )
     $   RETURN
*
.AND..OR..NOT..AND..NOT.      IF( ( LEFT  NOTRAN )  ( LEFT  NOTRAN ) )
     $     THEN
         I1 = 1
         I2 = K
         I3 = 1
      ELSE
         I1 = K
         I2 = 1
         I3 = -1
      END IF
*
      IF( LEFT ) THEN
         NI = N
      ELSE
         MI = M
      END IF
*
      DO 10 I = I1, I2, I3
         IF( LEFT ) THEN
*
*           H(i) is applied to C(1:m-k+i,1:n)
*
            MI = M - K + I
         ELSE
*
*           H(i) is applied to C(1:m,1:n-k+i)
*
            NI = N - K + I
         END IF
*
*        Apply H(i)
*
         AII = A( NQ-K+I, I )
         A( NQ-K+I, I ) = ONE
         CALL SLARF( SIDE, MI, NI, A( 1, I ), 1, TAU( I ), C, LDC,
     $               WORK )
         A( NQ-K+I, I ) = AII
   10 CONTINUE
      RETURN
*
*     End of SORM2L
*
      END