#include "ESMF_LapackBlas.inc" !> \brief \b DORM2R ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORM2R + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorm2r.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorm2r.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorm2r.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORM2R( 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 .. ! DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DORM2R 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(1) H(2) . . . H(k) !> !> as returned by DGEQRF. 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 DOUBLE PRECISION 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 !> DGEQRF in the first 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 DOUBLE PRECISION array, dimension (K) !> TAU(i) must contain the scalar factor of the elementary !> reflector H(i), as returned by DGEQRF. !> \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 ! ! ===================================================================== SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, 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, LDA, LDC, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) ! .. ! .. Local Scalars .. LOGICAL LEFT, NOTRAN INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ DOUBLE PRECISION AII ! .. ! .. External Functions .. LOGICAL LSAME EXTERNAL LSAME ! .. ! .. External Subroutines .. EXTERNAL DLARF, 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( LDA.LT.MAX( 1, NQ ) ) THEN INFO = -7 ELSE IF( LDC.LT.MAX( 1, M ) ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORM2R', -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 JC = 1 ELSE MI = M IC = 1 END IF ! DO 10 I = I1, I2, I3 IF( LEFT ) THEN ! ! H(i) is applied to C(i:m,1:n) ! MI = M - I + 1 IC = I ELSE ! ! H(i) is applied to C(1:m,i:n) ! NI = N - I + 1 JC = I END IF ! ! Apply H(i) ! AII = A( I, I ) A( I, I ) = ONE CALL DLARF( SIDE, MI, NI, A( I, I ), 1, TAU( I ), C( IC, JC ), & & LDC, WORK ) A( I, I ) = AII 10 CONTINUE RETURN ! ! End of DORM2R ! END