#include "ESMF_LapackBlas.inc" !> \brief \b DORMRZ ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DORMRZ + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dormrz.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dormrz.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dormrz.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, ! WORK, LWORK, INFO ) ! ! .. Scalar Arguments .. ! CHARACTER SIDE, TRANS ! INTEGER INFO, K, L, LDA, LDC, LWORK, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DORMRZ 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 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': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !> \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**H*C or C*Q**H 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 (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> \endverbatim !> !> \param[in] LWORK !> \verbatim !> LWORK is 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. !> \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 DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, & & WORK, LWORK, 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, LWORK, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. INTEGER NBMAX, LDT PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) ! .. ! .. Local Scalars .. LOGICAL LEFT, LQUERY, NOTRAN CHARACTER TRANST INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JA, JC, & & LDWORK, LWKOPT, MI, NB, NBMIN, NI, NQ, NW ! .. ! .. Local Arrays .. DOUBLE PRECISION T( LDT, NBMAX ) ! .. ! .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV ! .. ! .. External Subroutines .. EXTERNAL DLARZB, DLARZT, DORMR3, XERBLA ! .. ! .. Intrinsic Functions .. INTRINSIC MAX, MIN ! .. ! .. Executable Statements .. ! ! Test the input arguments ! INFO = 0 LEFT = LSAME( SIDE, 'L' ) NOTRAN = LSAME( TRANS, 'N' ) LQUERY = ( LWORK.EQ.-1 ) ! ! NQ is the order of Q and NW is the minimum dimension of WORK ! IF( LEFT ) THEN NQ = M NW = MAX( 1, N ) ELSE NQ = N NW = MAX( 1, M ) 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.EQ.0 ) THEN IF( M.EQ.0 .OR. N.EQ.0 ) THEN LWKOPT = 1 ELSE ! ! Determine the block size. NB may be at most NBMAX, where ! NBMAX is used to define the local array T. ! NB = MIN( NBMAX, ILAENV( 1, 'DORMRQ', SIDE // TRANS, M, N, & & K, -1 ) ) LWKOPT = NW*NB END IF WORK( 1 ) = LWKOPT ! IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN INFO = -13 END IF END IF ! IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORMRZ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF ! ! Quick return if possible ! IF( M.EQ.0 .OR. N.EQ.0 ) THEN WORK( 1 ) = 1 RETURN END IF ! NBMIN = 2 LDWORK = NW IF( NB.GT.1 .AND. NB.LT.K ) THEN IWS = NW*NB IF( LWORK.LT.IWS ) THEN NB = LWORK / LDWORK NBMIN = MAX( 2, ILAENV( 2, 'DORMRQ', SIDE // TRANS, M, N, K, & & -1 ) ) END IF ELSE IWS = NW END IF ! IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN ! ! Use unblocked code ! CALL DORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, & & WORK, IINFO ) ELSE ! ! Use blocked code ! IF( ( LEFT .AND. .NOT.NOTRAN ) .OR. & & ( .NOT.LEFT .AND. NOTRAN ) ) THEN I1 = 1 I2 = K I3 = NB ELSE I1 = ( ( K-1 ) / NB )*NB + 1 I2 = 1 I3 = -NB END IF ! IF( LEFT ) THEN NI = N JC = 1 JA = M - L + 1 ELSE MI = M IC = 1 JA = N - L + 1 END IF ! IF( NOTRAN ) THEN TRANST = 'T' ELSE TRANST = 'N' END IF ! DO 10 I = I1, I2, I3 IB = MIN( NB, K-I+1 ) ! ! Form the triangular factor of the block reflector ! H = H(i+ib-1) . . . H(i+1) H(i) ! CALL DLARZT( 'Backward', 'Rowwise', L, IB, A( I, JA ), LDA, & & TAU( I ), T, LDT ) ! IF( LEFT ) THEN ! ! H or H**T is applied to C(i:m,1:n) ! MI = M - I + 1 IC = I ELSE ! ! H or H**T is applied to C(1:m,i:n) ! NI = N - I + 1 JC = I END IF ! ! Apply H or H**T ! CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI, & & IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ), & & LDC, WORK, LDWORK ) 10 CONTINUE ! END IF ! WORK( 1 ) = LWKOPT ! RETURN ! ! End of DORMRZ ! END