Chimie Théorique » Opt'n Path

      SUBROUTINE DORMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,

     $                   WORK, LWORK, INFO )

*

*  -- LAPACK routine (version 3.2) --

*  -- LAPACK is a software package provided by Univ. of Tennessee,    --

*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--

*     November 2006

*

*     .. Scalar Arguments ..

      CHARACTER          SIDE, TRANS

      INTEGER            INFO, K, LDA, LDC, LWORK, M, N

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION   A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )

*     ..

*

*  Purpose

*  =======

*

*  DORMLQ 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(k) . . . H(2) H(1)

*

*  as returned by DGELQF. Q is of order M if SIDE = 'L' and of order N

*  if SIDE = 'R'.

*

*  Arguments

*  =========

*

*  SIDE    (input) CHARACTER*1

*          = 'L': apply Q or Q**T from the Left;

*          = 'R': apply Q or Q**T from the Right.

*

*  TRANS   (input) CHARACTER*1

*          = 'N':  No transpose, apply Q;

*          = 'T':  Transpose, apply Q**T.

*

*  M       (input) INTEGER

*          The number of rows of the matrix C. M >= 0.

*

*  N       (input) INTEGER

*          The number of columns of the matrix C. N >= 0.

*

*  K       (input) INTEGER

*          The number of elementary reflectors whose product defines

*          the matrix Q.

*          If SIDE = 'L', M >= K >= 0;

*          if SIDE = 'R', N >= K >= 0.

*

*  A       (input) 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

*          DGELQF in the first k rows of its array argument A.

*          A is modified by the routine but restored on exit.

*

*  LDA     (input) INTEGER

*          The leading dimension of the array A. LDA >= max(1,K).

*

*  TAU     (input) DOUBLE PRECISION array, dimension (K)

*          TAU(i) must contain the scalar factor of the elementary

*          reflector H(i), as returned by DGELQF.

*

*  C       (input/output) 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.

*

*  LDC     (input) INTEGER

*          The leading dimension of the array C. LDC >= max(1,M).

*

*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))

*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*

*  LWORK   (input) 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.

*

*  INFO    (output) INTEGER

*          = 0:  successful exit

*          < 0:  if INFO = -i, the i-th argument had an illegal value

*

*  =====================================================================

*

*     .. 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, 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           DLARFB, DLARFT, DORML2, 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 = N

      ELSE

         NQ = N

         NW = 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( LDA.LT.MAX( 1, K ) ) THEN

         INFO = -7

      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN

         INFO = -10

      ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN

         INFO = -12

      END IF

*

      IF( INFO.EQ.0 ) THEN

*

*        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, 'DORMLQ', SIDE // TRANS, M, N, K,

     $        -1 ) )

         LWKOPT = MAX( 1, NW )*NB

         WORK( 1 ) = LWKOPT

      END IF

*

      IF( INFO.NE.0 ) THEN

         CALL XERBLA( 'DORMLQ', -INFO )

         RETURN

      ELSE IF( LQUERY ) THEN

         RETURN

      END IF

*

*     Quick return if possible

*

      IF( M.EQ.0 .OR. N.EQ.0 .OR. K.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, 'DORMLQ', 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 DORML2( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK,

     $                IINFO )

      ELSE

*

*        Use blocked code

*

         IF( ( LEFT .AND. NOTRAN ) .OR.

     $       ( .NOT.LEFT .AND. .NOT.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

         ELSE

            MI = M

            IC = 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) H(i+1) . . . H(i+ib-1)

*

            CALL DLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ),

     $                   LDA, TAU( I ), T, LDT )

            IF( LEFT ) THEN

*

*              H or H' is applied to C(i:m,1:n)

*

               MI = M - I + 1

               IC = I

            ELSE

*

*              H or H' is applied to C(1:m,i:n)

*

               NI = N - I + 1

               JC = I

            END IF

*

*           Apply H or H'

*

            CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,

     $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,

     $                   LDWORK )

   10    CONTINUE

      END IF

      WORK( 1 ) = LWKOPT

      RETURN

*

*     End of DORMLQ

*

      END