You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
196 lines
4.9 KiB
196 lines
4.9 KiB
2 years ago
|
*> \brief \b ZGERQS
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
|
||
|
|
* INFO )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
|
||
|
|
* $ WORK( LWORK )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> Compute a minimum-norm solution
|
||
|
|
*> min || A*X - B ||
|
||
|
|
*> using the RQ factorization
|
||
|
|
*> A = R*Q
|
||
|
|
*> computed by ZGERQF.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] M
|
||
|
|
*> \verbatim
|
||
|
|
*> M is INTEGER
|
||
|
|
*> The number of rows of the matrix A. M >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The number of columns of the matrix A. N >= M >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] NRHS
|
||
|
|
*> \verbatim
|
||
|
|
*> NRHS is INTEGER
|
||
|
|
*> The number of columns of B. NRHS >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is COMPLEX*16 array, dimension (LDA,N)
|
||
|
|
*> Details of the RQ factorization of the original matrix A as
|
||
|
|
*> returned by ZGERQF.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER
|
||
|
|
*> The leading dimension of the array A. LDA >= M.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] TAU
|
||
|
|
*> \verbatim
|
||
|
|
*> TAU is COMPLEX*16 array, dimension (M)
|
||
|
|
*> Details of the orthogonal matrix Q.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
|
||
|
|
*> On entry, the right hand side vectors for the linear system.
|
||
|
|
*> On exit, the solution vectors X. Each solution vector
|
||
|
|
*> is contained in rows 1:N of a column of B.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDB
|
||
|
|
*> \verbatim
|
||
|
|
*> LDB is INTEGER
|
||
|
|
*> The leading dimension of the array B. LDB >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] WORK
|
||
|
|
*> \verbatim
|
||
|
|
*> WORK is COMPLEX*16 array, dimension (LWORK)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> LWORK is INTEGER
|
||
|
|
*> The length of the array WORK. LWORK must be at least NRHS,
|
||
|
|
*> and should be at least NRHS*NB, where NB is the block size
|
||
|
|
*> for this environment.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] INFO
|
||
|
|
*> \verbatim
|
||
|
|
*> INFO is INTEGER
|
||
|
|
*> = 0: successful exit
|
||
|
|
*> < 0: if INFO = -i, the i-th argument had an illegal value
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complex16_lin
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
|
||
|
|
$ INFO )
|
||
|
|
*
|
||
|
|
* -- LAPACK test 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, LDA, LDB, LWORK, M, N, NRHS
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
|
||
|
|
$ WORK( LWORK )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
COMPLEX*16 CZERO, CONE
|
||
|
|
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
|
||
|
|
$ CONE = ( 1.0D+0, 0.0D+0 ) )
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMRQ
|
||
|
|
* ..
|
||
|
|
* .. Intrinsic Functions ..
|
||
|
|
INTRINSIC MAX
|
||
|
|
* ..
|
||
|
|
* .. Executable Statements ..
|
||
|
|
*
|
||
|
|
* Test the input parameters.
|
||
|
|
*
|
||
|
|
INFO = 0
|
||
|
|
IF( M.LT.0 ) THEN
|
||
|
|
INFO = -1
|
||
|
|
ELSE IF( N.LT.0 .OR. M.GT.N ) THEN
|
||
|
|
INFO = -2
|
||
|
|
ELSE IF( NRHS.LT.0 ) THEN
|
||
|
|
INFO = -3
|
||
|
|
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
|
||
|
|
INFO = -5
|
||
|
|
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
|
||
|
|
INFO = -8
|
||
|
|
ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
|
||
|
|
$ THEN
|
||
|
|
INFO = -10
|
||
|
|
END IF
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
CALL XERBLA( 'ZGERQS', -INFO )
|
||
|
|
RETURN
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Quick return if possible
|
||
|
|
*
|
||
|
|
IF( N.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
|
||
|
|
$ RETURN
|
||
|
|
*
|
||
|
|
* Solve R*X = B(n-m+1:n,:)
|
||
|
|
*
|
||
|
|
CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
|
||
|
|
$ CONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
|
||
|
|
*
|
||
|
|
* Set B(1:n-m,:) to zero
|
||
|
|
*
|
||
|
|
CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B, LDB )
|
||
|
|
*
|
||
|
|
* B := Q' * B
|
||
|
|
*
|
||
|
|
CALL ZUNMRQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
|
||
|
|
$ TAU, B, LDB, WORK, LWORK, INFO )
|
||
|
|
*
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZGERQS
|
||
|
|
*
|
||
|
|
END
|