297 lines
8.0 KiB
Fortran
297 lines
8.0 KiB
Fortran
*> \brief \b SORGQL
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download SORGQL + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorgql.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgql.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgql.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE SORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, K, LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> 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.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] M
|
|
*> \verbatim
|
|
*> M is INTEGER
|
|
*> The number of rows of the matrix Q. M >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The number of columns of the matrix Q. M >= N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] K
|
|
*> \verbatim
|
|
*> K is INTEGER
|
|
*> The number of elementary reflectors whose product defines the
|
|
*> matrix Q. N >= K >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] A
|
|
*> \verbatim
|
|
*> A is 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.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The first dimension of the array A. LDA >= max(1,M).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TAU
|
|
*> \verbatim
|
|
*> TAU is REAL array, dimension (K)
|
|
*> TAU(i) must contain the scalar factor of the elementary
|
|
*> reflector H(i), as returned by SGEQLF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is REAL array, dimension (MAX(1,LWORK))
|
|
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LWORK
|
|
*> \verbatim
|
|
*> LWORK is 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.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] INFO
|
|
*> \verbatim
|
|
*> INFO is INTEGER
|
|
*> = 0: successful exit
|
|
*> < 0: if INFO = -i, the i-th argument has an illegal value
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \ingroup realOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE SORGQL( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.7.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* December 2016
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, K, LDA, LWORK, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. 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
|