dormr3.F90 Source File


Source Code

#include "ESMF_LapackBlas.inc"
!> \brief \b DORMR3
!
!  =========== DOCUMENTATION ===========
!
! Online html documentation available at
!            http://www.netlib.org/lapack/explore-html/
!
!> \htmlonly
!> Download DORMR3 + dependencies
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!> [TGZ]</a>
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!> [ZIP]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormr3.f">
!> [TXT]</a>
!> \endhtmlonly
!
!  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.
!
!> \date November 2011
!
!> \ingroup doubleOTHERcomputational
!
!> \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 (version 3.4.0) --
!  -- LAPACK is a software package provided by Univ. of Tennessee,    --
!  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!     November 2011
!
!     .. 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