SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 1,6
!
! -- 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 ..
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! ..
!
! 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 (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 ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
! ..
! .. Local Scalars ..
LOGICAL LQUERY
INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK, &
LWKOPT, 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
NB = ILAENV
( 1, 'DORGQR', ' ', M, N, K, -1 )
LWKOPT = MAX( 1, N )*NB
WORK( 1 ) = LWKOPT
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
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORGQR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
!
! Quick return if possible
!
IF( N.LE.0 ) THEN
WORK( 1 ) = 1
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, '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 SUBROUTINE DORGQR