SUBROUTINE ZUNGLQ( 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 ..
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* ZUNGLQ generates an M-by-N complex 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 ZGELQF.
*
* 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) COMPLEX*16 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 ZGELQF 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) COMPLEX*16 array, dimension (K)
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by ZGELQF.
*
* WORK (workspace/output) COMPLEX*16 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,M).
* For optimum performance LWORK >= M*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 ..
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
$ LWKOPT, NB, NBMIN, NX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLARFB, ZLARFT, ZUNGL2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
NB = ILAENV( 1, 'ZUNGLQ', ' ', M, N, K, -1 )
LWKOPT = MAX( 1, M )*NB
WORK( 1 ) = LWKOPT
LQUERY = ( LWORK.EQ.-1 )
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
ELSE IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZUNGLQ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.LE.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
NBMIN = 2
NX = 0
IWS = M
IF( NB.GT.1 .AND. NB.LT.K ) THEN
*
* Determine when to cross over from blocked to unblocked code.
*
NX = MAX( 0, ILAENV( 3, 'ZUNGLQ', ' ', M, N, K, -1 ) )
IF( NX.LT.K ) THEN
*
* Determine if workspace is large enough for blocked code.
*
LDWORK = M
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, 'ZUNGLQ', ' ', 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 rows are handled by the block method.
*
KI = ( ( K-NX-1 ) / NB )*NB
KK = MIN( K, KI+NB )
*
* Set A(kk+1:m,1:kk) to zero.
*
DO 20 J = 1, KK
DO 10 I = KK + 1, M
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.M )
$ CALL ZUNGL2( 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.M ) THEN
*
* Form the triangular factor of the block reflector
* H = H(i) H(i+1) . . . H(i+ib-1)
*
CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
$ LDA, TAU( I ), WORK, LDWORK )
*
* Apply H' to A(i+ib:m,i:n) from the right
*
CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward',
$ 'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
$ LDA, WORK, LDWORK, A( I+IB, I ), LDA,
$ WORK( IB+1 ), LDWORK )
END IF
*
* Apply H' to columns i:n of current block
*
CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
$ IINFO )
*
* Set columns 1:i-1 of current block to zero
*
DO 40 J = 1, I - 1
DO 30 L = I, I + IB - 1
A( L, J ) = ZERO
30 CONTINUE
40 CONTINUE
50 CONTINUE
END IF
*
WORK( 1 ) = IWS
RETURN
*
* End of ZUNGLQ
*
END