dormlq.f

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      SUBROUTINE dormlq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
     $                   WORK, LWORK, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     June 30, 1999
*
*     .. 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 (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