196 lines
5.1 KiB
Fortran
196 lines
5.1 KiB
Fortran
*> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download DORG2L + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2l.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2l.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2l.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER INFO, K, LDA, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> DORG2L 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 DGEQLF.
|
|
*> \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 DOUBLE PRECISION 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 DGEQLF 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 DOUBLE PRECISION array, dimension (K)
|
|
*> TAU(i) must contain the scalar factor of the elementary
|
|
*> reflector H(i), as returned by DGEQLF.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is DOUBLE PRECISION array, dimension (N)
|
|
*> \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.
|
|
*
|
|
*> \ingroup doubleOTHERcomputational
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
|
|
*
|
|
* -- LAPACK computational routine --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
*
|
|
* .. Scalar Arguments ..
|
|
INTEGER INFO, K, LDA, M, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE, ZERO
|
|
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I, II, J, L
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL DLARF, DSCAL, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. 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
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'DORG2L', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.LE.0 )
|
|
$ RETURN
|
|
*
|
|
* Initialise columns 1:n-k to columns of the unit matrix
|
|
*
|
|
DO 20 J = 1, N - K
|
|
DO 10 L = 1, M
|
|
A( L, J ) = ZERO
|
|
10 CONTINUE
|
|
A( M-N+J, J ) = ONE
|
|
20 CONTINUE
|
|
*
|
|
DO 40 I = 1, K
|
|
II = N - K + I
|
|
*
|
|
* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
|
|
*
|
|
A( M-N+II, II ) = ONE
|
|
CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
|
|
$ LDA, WORK )
|
|
CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
|
|
A( M-N+II, II ) = ONE - TAU( I )
|
|
*
|
|
* Set A(m-k+i+1:m,n-k+i) to zero
|
|
*
|
|
DO 30 L = M - N + II + 1, M
|
|
A( L, II ) = ZERO
|
|
30 CONTINUE
|
|
40 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of DORG2L
|
|
*
|
|
END
|