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190 lines
4.7 KiB
190 lines
4.7 KiB
*> \brief \b ZGEQLS
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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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* Definition:
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* ===========
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*
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* SUBROUTINE ZGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
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* $ WORK( LWORK )
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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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*> Solve the least squares problem
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*> min || A*X - B ||
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*> using the QL factorization
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*> A = Q*L
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*> computed by ZGEQLF.
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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 A. 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 A. M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of columns of B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> Details of the QL factorization of the original matrix A as
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*> returned by ZGEQLF.
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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 leading dimension of the array A. LDA >= 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 COMPLEX*16 array, dimension (N)
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*> Details of the orthogonal matrix Q.
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the m-by-nrhs right hand side matrix B.
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*> On exit, the n-by-nrhs solution matrix X, stored in rows
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*> m-n+1:m.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= M.
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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 COMPLEX*16 array, dimension (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 length of the array WORK. LWORK must be at least NRHS,
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*> and should be at least NRHS*NB, where NB is the block size
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*> for this environment.
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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 had 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 complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZGEQLS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
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$ INFO )
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*
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* -- LAPACK test 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, LDA, LDB, LWORK, M, N, NRHS
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), B( LDB, * ), TAU( * ),
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$ WORK( LWORK )
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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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COMPLEX*16 ONE
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PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZTRSM, ZUNMQL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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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( NRHS.LT.0 ) 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( LDB.LT.MAX( 1, M ) ) THEN
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INFO = -8
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ELSE IF( LWORK.LT.1 .OR. LWORK.LT.NRHS .AND. M.GT.0 .AND. N.GT.0 )
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$ THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZGEQLS', -INFO )
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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.EQ.0 .OR. NRHS.EQ.0 .OR. M.EQ.0 )
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$ RETURN
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*
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* B := Q' * B
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*
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CALL ZUNMQL( 'Left', 'Conjugate transpose', M, NRHS, N, A, LDA,
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$ TAU, B, LDB, WORK, LWORK, INFO )
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*
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* Solve L*X = B(m-n+1:m,:)
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*
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CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N, NRHS,
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$ ONE, A( M-N+1, 1 ), LDA, B( M-N+1, 1 ), LDB )
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*
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RETURN
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*
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* End of ZGEQLS
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*
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END
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