127 lines
3.5 KiB
FortranFixed
127 lines
3.5 KiB
FortranFixed
SUBROUTINE ZGERQS( M, N, NRHS, A, LDA, TAU, B, LDB, WORK, LWORK,
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$ INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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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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* Purpose
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* =======
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*
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* Compute a minimum-norm solution
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* min || A*X - B ||
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* using the RQ factorization
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* A = R*Q
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* computed by ZGERQF.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= M >= 0.
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*
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* NRHS (input) INTEGER
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* The number of columns of B. NRHS >= 0.
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*
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* A (input) COMPLEX*16 array, dimension (LDA,N)
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* Details of the RQ factorization of the original matrix A as
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* returned by ZGERQF.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= M.
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*
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* TAU (input) COMPLEX*16 array, dimension (M)
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* Details of the orthogonal matrix Q.
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*
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* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
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* On entry, the right hand side vectors for the linear system.
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* On exit, the solution vectors X. Each solution vector
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* is contained in rows 1:N of a column of B.
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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= max(1,N).
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*
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* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
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*
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* LWORK (input) 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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*
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* INFO (output) 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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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZLASET, ZTRSM, ZUNMRQ
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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 parameters.
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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. M.GT.N ) 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, N ) ) 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( 'ZGERQS', -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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* Solve R*X = B(n-m+1:n,:)
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*
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CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', M, NRHS,
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$ CONE, A( 1, N-M+1 ), LDA, B( N-M+1, 1 ), LDB )
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*
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* Set B(1:n-m,:) to zero
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*
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CALL ZLASET( 'Full', N-M, NRHS, CZERO, CZERO, B, LDB )
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*
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* B := Q' * B
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*
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CALL ZUNMRQ( 'Left', 'Conjugate transpose', N, NRHS, M, A, LDA,
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$ TAU, B, LDB, WORK, LWORK, INFO )
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*
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RETURN
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*
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* End of ZGERQS
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*
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END
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