dormr3.f

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*> \brief \b DORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
*                          WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE, TRANS
*       INTEGER            INFO, K, L, LDA, LDC, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DORMR3 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 = 'C', or
*>
*>       C * Q  if SIDE = 'R' and TRANS = 'N', or
*>
*>       C * Q**T if SIDE = 'R' and TRANS = 'C',
*>
*> where Q is a real orthogonal matrix defined as the product of k
*> elementary reflectors
*>
*>       Q = H(1) H(2) . . . H(k)
*>
*> as returned by DTZRZF. 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] L
*> \verbatim
*>          L is INTEGER
*>          The number of columns of the matrix A containing
*>          the meaningful part of the Householder reflectors.
*>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION 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
*>          DTZRZF in the last k rows 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. LDA >= max(1,K).
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (K)
*>          TAU(i) must contain the scalar factor of the elementary
*>          reflector H(i), as returned by DTZRZF.
*> \endverbatim
*>
*> \param[in,out] C
*> \verbatim
*>          C is 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.
*> \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 DOUBLE PRECISION 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 unmr3
*
*> \par Contributors:
*  ==================
*>
*>    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
*> \par Further Details:
*  =====================
*>
*> \verbatim
*> \endverbatim
*>
*  =====================================================================
      SUBROUTINE dormr3( SIDE, TRANS, M, N, K, L, 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, L, LDA, LDC, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, NOTRAN
      INTEGER            I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarz, 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
      ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
         info = -2
      ELSE IF( m.LT.0 ) THEN
         info = -3
      ELSE IF( n.LT.0 ) THEN
         info = -4
      ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
         info = -5
      ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
     $         ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
         info = -6
      ELSE IF( lda.LT.max( 1, k ) ) THEN
         info = -8
      ELSE IF( ldc.LT.max( 1, m ) ) THEN
         info = -11
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORMR3', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
     $   RETURN
*
      IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
         i1 = 1
         i2 = k
         i3 = 1
      ELSE
         i1 = k
         i2 = 1
         i3 = -1
      END IF
*
      IF( left ) THEN
         ni = n
         ja = m - l + 1
         jc = 1
      ELSE
         mi = m
         ja = n - l + 1
         ic = 1
      END IF
*
      DO 10 i = i1, i2, i3
         IF( left ) THEN
*
*           H(i) or H(i)**T is applied to C(i:m,1:n)
*
            mi = m - i + 1
            ic = i
         ELSE
*
*           H(i) or H(i)**T is applied to C(1:m,i:n)
*
            ni = n - i + 1
            jc = i
         END IF
*
*        Apply H(i) or H(i)**T
*
         CALL dlarz( side, mi, ni, l, a( i, ja ), lda, tau( i ),
     $               c( ic, jc ), ldc, work )
*
   10 CONTINUE
*
      RETURN
*
*     End of DORMR3
*
      END