289 lines
7.9 KiB
Fortran
289 lines
7.9 KiB
Fortran
*> \brief \b SORGQR
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SORGQR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorgqr.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorgqr.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorgqr.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SORGQR generates an M-by-N real matrix Q with orthonormal columns,
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*> which is defined as the first N columns of a product of K elementary
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*> reflectors of order M
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*>
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*> Q = H(1) H(2) . . . H(k)
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*>
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*> as returned by SGEQRF.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix Q. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix Q. M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines the
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*> matrix Q. N >= K >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> On entry, the i-th column must contain the vector which
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*> defines the elementary reflector H(i), for i = 1,2,...,k, as
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*> returned by SGEQRF in the first k columns of its array
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*> argument A.
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*> On exit, the M-by-N matrix Q.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The first dimension of the array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is REAL array, dimension (K)
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*> TAU(i) must contain the scalar factor of the elementary
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*> reflector H(i), as returned by SGEQRF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK. LWORK >= max(1,N).
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*> For optimum performance LWORK >= N*NB, where NB is the
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*> optimal blocksize.
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*>
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*> If LWORK = -1, then a workspace query is assumed; the routine
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*> only calculates the optimal size of the WORK array, returns
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*> this value as the first entry of the WORK array, and no error
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*> message related to LWORK is issued by XERBLA.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument has an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup ungqr
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*
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* =====================================================================
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SUBROUTINE SORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER INFO, K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY
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INTEGER I, IB, IINFO, IWS, J, KI, KK, L, LDWORK,
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$ LWKOPT, NB, NBMIN, NX
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* ..
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* .. External Subroutines ..
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EXTERNAL SLARFB, SLARFT, SORG2R, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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REAL SROUNDUP_LWORK
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EXTERNAL ILAENV, SROUNDUP_LWORK
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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NB = ILAENV( 1, 'SORGQR', ' ', M, N, K, -1 )
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LWKOPT = MAX( 1, N )*NB
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WORK( 1 ) = SROUNDUP_LWORK(LWKOPT)
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LQUERY = ( LWORK.EQ.-1 )
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
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INFO = -2
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ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -5
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ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SORGQR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.LE.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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NBMIN = 2
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NX = 0
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IWS = N
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IF( NB.GT.1 .AND. NB.LT.K ) THEN
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*
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* Determine when to cross over from blocked to unblocked code.
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*
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NX = MAX( 0, ILAENV( 3, 'SORGQR', ' ', M, N, K, -1 ) )
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IF( NX.LT.K ) THEN
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*
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* Determine if workspace is large enough for blocked code.
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*
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LDWORK = N
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IWS = LDWORK*NB
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IF( LWORK.LT.IWS ) THEN
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*
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* Not enough workspace to use optimal NB: reduce NB and
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* determine the minimum value of NB.
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*
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NB = LWORK / LDWORK
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NBMIN = MAX( 2, ILAENV( 2, 'SORGQR', ' ', M, N, K, -1 ) )
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END IF
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END IF
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END IF
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*
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IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
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*
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* Use blocked code after the last block.
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* The first kk columns are handled by the block method.
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*
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KI = ( ( K-NX-1 ) / NB )*NB
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KK = MIN( K, KI+NB )
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*
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* Set A(1:kk,kk+1:n) to zero.
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*
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DO 20 J = KK + 1, N
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DO 10 I = 1, KK
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A( I, J ) = ZERO
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10 CONTINUE
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20 CONTINUE
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ELSE
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KK = 0
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END IF
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*
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* Use unblocked code for the last or only block.
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*
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IF( KK.LT.N )
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$ CALL SORG2R( M-KK, N-KK, K-KK, A( KK+1, KK+1 ), LDA,
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$ TAU( KK+1 ), WORK, IINFO )
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*
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IF( KK.GT.0 ) THEN
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*
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* Use blocked code
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*
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DO 50 I = KI + 1, 1, -NB
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IB = MIN( NB, K-I+1 )
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IF( I+IB.LE.N ) THEN
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*
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* Form the triangular factor of the block reflector
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* H = H(i) H(i+1) . . . H(i+ib-1)
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*
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CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB,
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$ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
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*
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* Apply H to A(i:m,i+ib:n) from the left
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*
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CALL SLARFB( 'Left', 'No transpose', 'Forward',
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$ 'Columnwise', M-I+1, N-I-IB+1, IB,
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$ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
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$ LDA, WORK( IB+1 ), LDWORK )
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END IF
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*
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* Apply H to rows i:m of current block
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*
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CALL SORG2R( M-I+1, IB, IB, A( I, I ), LDA, TAU( I ), WORK,
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$ IINFO )
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*
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* Set rows 1:i-1 of current block to zero
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*
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DO 40 J = I, I + IB - 1
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DO 30 L = 1, I - 1
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A( L, J ) = ZERO
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30 CONTINUE
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40 CONTINUE
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50 CONTINUE
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END IF
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*
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WORK( 1 ) = SROUNDUP_LWORK(IWS)
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RETURN
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*
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* End of SORGQR
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*
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END
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