dorgl2.f

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      SUBROUTINE dorgl2( M, N, K, A, LDA, TAU, WORK, 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 ..
      INTEGER            INFO, K, LDA, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  DORGL2 generates an m by n real matrix Q with orthonormal rows,
*  which is defined as the first m rows of a product of k elementary
*  reflectors of order n
*
*        Q  =  H(k) . . . H(2) H(1)
*
*  as returned by DGELQF.
*
*  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. N >= M.
*
*  K       (input) INTEGER
*          The number of elementary reflectors whose product defines the
*          matrix Q. M >= K >= 0.
*
*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
*          On entry, 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.
*          On exit, the m-by-n matrix Q.
*
*  LDA     (input) INTEGER
*          The first dimension of the array A. LDA >= max(1,M).
*
*  TAU     (input) DOUBLE PRECISION array, dimension (K)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DGELQF.
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (M)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument has an illegal value
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, L
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarf, dscal, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.m ) THEN
         info = -2
      ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
         info = -3
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -5
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DORGL2', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.LE.0 )
     $   RETURN
*
      IF( k.LT.m ) THEN
*
*        Initialise rows k+1:m to rows of the unit matrix
*
         DO 20 j = 1, n
            DO 10 l = k + 1, m
               a( l, j ) = zero
   10       CONTINUE
            IF( j.GT.k .AND. j.LE.m )
     $         a( j, j ) = one
   20    CONTINUE
      END IF
*
      DO 40 i = k, 1, -1
*
*        Apply H(i) to A(i:m,i:n) from the right
*
         IF( i.LT.n ) THEN
            IF( i.LT.m ) THEN
               a( i, i ) = one
               CALL dlarf( 'Right', m-i, n-i+1, a( i, i ), lda,
     $                     tau( i ), a( i+1, i ), lda, work )
            END IF
            CALL dscal( n-i, -tau( i ), a( i, i+1 ), lda )
         END IF
         a( i, i ) = one - tau( i )
*
*        Set A(i,1:i-1) to zero
*
         DO 30 l = 1, i - 1
            a( i, l ) = zero
   30    CONTINUE
   40 CONTINUE
      RETURN
*
*     End of DORGL2
*
      END