sorgql.f

          SUBROUTINE SORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, K, LDA, LWORK, M, N
    *     ..
    *     .. Array Arguments ..
          REAL               A( LDA, * ), TAU( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SORGQL generates an M-by-N real matrix Q with orthonormal columns,
    *  which is defined as the last N columns of a product of K elementary
    *  reflectors of order M
    *
    *        Q  =  H(k) . . . H(2) H(1)
    *
    *  as returned by SGEQLF.
    *
    *  Arguments
    *  =========
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix Q. M >= 0.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix Q. M >= N >= 0.
    *
    *  K       (input) INTEGER
    *          The number of elementary reflectors whose product defines the
    *          matrix Q. N >= K >= 0.
    *
    *  A       (input/output) REAL array, dimension (LDA,N)
    *          On entry, the (n-k+i)-th column must contain the vector which
    *          defines the elementary reflector H(i), for i = 1,2,...,k, as
    *          returned by SGEQLF in the last k columns of its array
    *          argument A.
    *          On exit, the M-by-N matrix Q.
    *
    *  LDA     (input) INTEGER
    *          The first dimension of the array A. LDA >= max(1,M).
    *
    *  TAU     (input) REAL array, dimension (K)
    *          TAU(i) must contain the scalar factor of the elementary
    *          reflector H(i), as returned by SGEQLF.
    *
    *  WORK    (workspace/output) REAL 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. LWORK >= max(1,N).
    *          For optimum performance LWORK >= N*NB, 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 has an illegal value
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ZERO
          PARAMETER          ( ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            LQUERY
          INTEGER            I, IB, IINFO, IWS, J, KK, L, LDWORK, LWKOPT,
         $                   NB, NBMIN, NX
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SLARFB, SLARFT, SORG2L, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          EXTERNAL           ILAENV
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input arguments
    *
          INFO = 0
          LQUERY = ( LWORK.EQ.-1 )
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
             INFO = -2
          ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
             INFO = -3
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -5
          END IF
    *
          IF( INFO.EQ.0 ) THEN
             IF( N.EQ.0 ) THEN
                LWKOPT = 1
             ELSE
                NB = ILAENV( 1, 'SORGQL', ' ', M, N, K, -1 )
                LWKOPT = N*NB
             END IF
             WORK( 1 ) = LWKOPT
    *
             IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
                INFO = -8
             END IF
          END IF
    *
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SORGQL', -INFO )
             RETURN
          ELSE IF( LQUERY ) THEN
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.LE.0 ) THEN
             RETURN
          END IF
    *
          NBMIN = 2
          NX = 0
          IWS = N
          IF( NB.GT.1 .AND. NB.LT.K ) THEN
    *
    *        Determine when to cross over from blocked to unblocked code.
    *
             NX = MAX( 0, ILAENV( 3, 'SORGQL', ' ', M, N, K, -1 ) )
             IF( NX.LT.K ) THEN
    *
    *           Determine if workspace is large enough for blocked code.
    *
                LDWORK = N
                IWS = LDWORK*NB
                IF( LWORK.LT.IWS ) THEN
    *
    *              Not enough workspace to use optimal NB:  reduce NB and
    *              determine the minimum value of NB.
    *
                   NB = LWORK / LDWORK
                   NBMIN = MAX( 2, ILAENV( 2, 'SORGQL', ' ', M, N, K, -1 ) )
                END IF
             END IF
          END IF
    *
          IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
    *
    *        Use blocked code after the first block.
    *        The last kk columns are handled by the block method.
    *
             KK = MIN( K, ( ( K-NX+NB-1 ) / NB )*NB )
    *
    *        Set A(m-kk+1:m,1:n-kk) to zero.
    *
             DO 20 J = 1, N - KK
                DO 10 I = M - KK + 1, M
                   A( I, J ) = ZERO
       10       CONTINUE
       20    CONTINUE
          ELSE
             KK = 0
          END IF
    *
    *     Use unblocked code for the first or only block.
    *
          CALL SORG2L( M-KK, N-KK, K-KK, A, LDA, TAU, WORK, IINFO )
    *
          IF( KK.GT.0 ) THEN
    *
    *        Use blocked code
    *
             DO 50 I = K - KK + 1, K, NB
                IB = MIN( NB, K-I+1 )
                IF( N-K+I.GT.1 ) THEN
    *
    *              Form the triangular factor of the block reflector
    *              H = H(i+ib-1) . . . H(i+1) H(i)
    *
                   CALL SLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
         $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
    *
    *              Apply H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
    *
                   CALL SLARFB( 'Left', 'No transpose', 'Backward',
         $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
         $                      A( 1, N-K+I ), LDA, WORK, LDWORK, A, LDA,
         $                      WORK( IB+1 ), LDWORK )
                END IF
    *
    *           Apply H to rows 1:m-k+i+ib-1 of current block
    *
                CALL SORG2L( M-K+I+IB-1, IB, IB, A( 1, N-K+I ), LDA,
         $                   TAU( I ), WORK, IINFO )
    *
    *           Set rows m-k+i+ib:m of current block to zero
    *
                DO 40 J = N - K + I, N - K + I + IB - 1
                   DO 30 L = M - K + I + IB, M
                      A( L, J ) = ZERO
       30          CONTINUE
       40       CONTINUE
       50    CONTINUE
          END IF
    *
          WORK( 1 ) = IWS
          RETURN
    *
    *     End of SORGQL
    *
          END