122 lines
3.2 KiB
FortranFixed
122 lines
3.2 KiB
FortranFixed
SUBROUTINE SGEQLS( 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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REAL 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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* 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 SGEQLF.
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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. M >= N >= 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) REAL 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 SGEQLF.
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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) REAL array, dimension (N)
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* Details of the orthogonal matrix Q.
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*
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* B (input/output) REAL 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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*
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* LDB (input) INTEGER
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* The leading dimension of the array B. LDB >= M.
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*
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* WORK (workspace) REAL 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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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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* ..
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* .. External Subroutines ..
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EXTERNAL SORMQL, STRSM, XERBLA
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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( 'SGEQLS', -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 SORMQL( 'Left', 'Transpose', M, NRHS, N, A, LDA, TAU, B, LDB,
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$ 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 STRSM( '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 SGEQLS
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*
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END
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