dormql.f

          SUBROUTINE DORMQL( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
         $                   WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley 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
    *  =======
    *
    *  DORMQL 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 DGEQLF. 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,K)
    *          The i-th column must contain the vector which defines the
    *          elementary reflector H(i), for i = 1,2,...,k, as returned by
    *          DGEQLF in the last k columns 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.
    *          If SIDE = 'L', LDA >= max(1,M);
    *          if SIDE = 'R', LDA >= max(1,N).
    *
    *  TAU     (input) DOUBLE PRECISION array, dimension (K)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by DGEQLF.
    *
    *  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
          INTEGER            I, I1, I2, I3, IB, IINFO, IWS, 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, DORM2L, 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( LDA.LT.MAX( 1, NQ ) ) THEN
             INFO = -7
          ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
             INFO = -10
          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, 'DORMQL', SIDE // TRANS, M, N,
         $                               K, -1 ) )
                LWKOPT = NW*NB
             END IF
             WORK( 1 ) = LWKOPT
    *
             IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN
                INFO = -12
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DORMQL', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 ) THEN
             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, 'DORMQL', 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 DORM2L( 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
             ELSE
                MI = M
             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 DLARFT( 'Backward', 'Columnwise', NQ-K+I+IB-1, IB,
         $                   A( 1, I ), LDA, TAU( I ), T, LDT )
                IF( LEFT ) THEN
    *
    *              H or H' is applied to C(1:m-k+i+ib-1,1:n)
    *
                   MI = M - K + I + IB - 1
                ELSE
    *
    *              H or H' is applied to C(1:m,1:n-k+i+ib-1)
    *
                   NI = N - K + I + IB - 1
                END IF
    *
    *           Apply H or H'
    *
                CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
         $                   IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
         $                   LDWORK )
       10    CONTINUE
          END IF
          WORK( 1 ) = LWKOPT
          RETURN
    *
    *     End of DORMQL
    *
          END