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SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
*
* -- LAPACK routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INFO, K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( LWORK )
* ..
*
* Purpose
* =======
*
* DORGQR generates an M-by-N real matrix Q with orthonormal columns,
* which is defined as the first N columns of a product of K elementary
* reflectors of order M
*
* Q = H(1) H(2) . . . H(k)
*
* as returned by DGEQRF.
*
* 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) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the i-th column must contain the vector which
* defines the elementary reflector H(i), for i = 1,2,...,k, as
* returned by DGEQRF in the first 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) DOUBLE PRECISION array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DGEQRF.
*
* 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. LWORK >= max(1,N).
* For optimum performance LWORK >= N*NB, where NB is the
* optimal blocksize.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument has an illegal value
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, NB,
$ NBMIN, NX
* ..
* .. External Subroutines ..
EXTERNAL DLARFB, DLARFT, DORG2R, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
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
ELSE IF( LWORK.LT.MAX( 1, N ) ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORGQR', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
* Determine the block size.
*
NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
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, 'DORGQR', ' ', 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, 'DORGQR', ' ', 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 last block.
* The first kk columns are handled by the block method.
*
KI = ( ( K-NX-1 ) / NB )*NB
KK = MIN( K, KI+NB )
*
* Set A(1:kk,kk+1:n) to zero.
*
DO 20 J = KK + 1, N
DO 10 I = 1, KK
A( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE
KK = 0
END IF
*
* Use unblocked code for the last or only block.
*
IF( KK.LT.N )
$ CALL DORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
$ TAU( KK+1 ), WORK, IINFO )
*
IF( KK.GT.0 ) THEN
*
* Use blocked code
*
DO 50 I = KI + 1, 1, -NB
IB = MIN( NB, K-I+1 )
IF( I+IB.LE.N ) THEN
*
* Form the triangular factor of the block reflector
* H = H(i) H(i+1) . . . H(i+ib-1)
*
CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
$ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
*
* Apply H to A(i:m,i+ib:n) from the left
*
CALL DLARFB( 'Left', 'No transpose', 'Forward',
$ 'Columnwise', M-I+1, N-I-IB+1, IB,
$ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
$ LDA, WORK( IB+1 ), LDWORK )
END IF
*
* Apply H to rows i:m of current block
*
CALL DORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
$ IINFO )
*
* Set rows 1:i-1 of current block to zero
*
DO 40 J = I, I + IB - 1
DO 30 L = 1, I - 1
A( L, J ) = ZERO
30 CONTINUE
40 CONTINUE
50 CONTINUE
END IF
*
WORK( 1 ) = IWS
RETURN
*
* End of DORGQR
*
END
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