334 lines
9.5 KiB
Fortran
334 lines
9.5 KiB
Fortran
*> \brief <b> SGTSV computes the solution to system of linear equations A * X = B for GT matrices <b>
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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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*> \htmlonly
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*> Download SGTSV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgtsv.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgtsv.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgtsv.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* REAL B( LDB, * ), D( * ), DL( * ), DU( * )
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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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*> SGTSV solves the equation
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*>
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*> A*X = B,
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*>
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*> where A is an n by n tridiagonal matrix, by Gaussian elimination with
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*> partial pivoting.
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*>
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*> Note that the equation A**T*X = B may be solved by interchanging the
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*> order of the arguments DU and DL.
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. 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 right hand sides, i.e., the number of columns
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*> of the matrix B. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] DL
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*> \verbatim
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*> DL is REAL array, dimension (N-1)
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*> On entry, DL must contain the (n-1) sub-diagonal elements of
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*> A.
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*>
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*> On exit, DL is overwritten by the (n-2) elements of the
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*> second super-diagonal of the upper triangular matrix U from
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*> the LU factorization of A, in DL(1), ..., DL(n-2).
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*> \endverbatim
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*>
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*> \param[in,out] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> On entry, D must contain the diagonal elements of A.
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*>
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*> On exit, D is overwritten by the n diagonal elements of U.
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*> \endverbatim
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*>
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*> \param[in,out] DU
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*> \verbatim
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*> DU is REAL array, dimension (N-1)
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*> On entry, DU must contain the (n-1) super-diagonal elements
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*> of A.
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*>
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*> On exit, DU is overwritten by the (n-1) elements of the first
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*> super-diagonal of U.
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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 REAL array, dimension (LDB,NRHS)
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*> On entry, the N by NRHS matrix of right hand side matrix B.
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*> On exit, if INFO = 0, the N by NRHS solution matrix X.
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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 >= max(1,N).
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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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*> > 0: if INFO = i, U(i,i) is exactly zero, and the solution
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*> has not been computed. The factorization has not been
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*> completed unless i = N.
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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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*> \date September 2012
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*
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*> \ingroup realGTsolve
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*
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* =====================================================================
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SUBROUTINE SGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
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*
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* -- LAPACK driver routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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REAL B( LDB, * ), D( * ), DL( * ), DU( * )
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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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REAL ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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REAL FACT, TEMP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -1
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGTSV ', -INFO )
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RETURN
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END IF
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*
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IF( N.EQ.0 )
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$ RETURN
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*
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IF( NRHS.EQ.1 ) THEN
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DO 10 I = 1, N - 2
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IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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*
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* No row interchange required
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*
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IF( D( I ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
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ELSE
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INFO = I
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RETURN
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END IF
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DL( I ) = ZERO
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ELSE
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*
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* Interchange rows I and I+1
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*
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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TEMP = D( I+1 )
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D( I+1 ) = DU( I ) - FACT*TEMP
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DL( I ) = DU( I+1 )
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DU( I+1 ) = -FACT*DL( I )
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DU( I ) = TEMP
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TEMP = B( I, 1 )
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B( I, 1 ) = B( I+1, 1 )
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B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
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END IF
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10 CONTINUE
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IF( N.GT.1 ) THEN
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I = N - 1
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IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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IF( D( I ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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B( I+1, 1 ) = B( I+1, 1 ) - FACT*B( I, 1 )
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ELSE
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INFO = I
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RETURN
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END IF
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ELSE
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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TEMP = D( I+1 )
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D( I+1 ) = DU( I ) - FACT*TEMP
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DU( I ) = TEMP
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TEMP = B( I, 1 )
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B( I, 1 ) = B( I+1, 1 )
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B( I+1, 1 ) = TEMP - FACT*B( I+1, 1 )
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END IF
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END IF
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IF( D( N ).EQ.ZERO ) THEN
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INFO = N
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RETURN
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END IF
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ELSE
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DO 40 I = 1, N - 2
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IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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*
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* No row interchange required
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*
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IF( D( I ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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DO 20 J = 1, NRHS
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B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
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20 CONTINUE
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ELSE
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INFO = I
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RETURN
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END IF
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DL( I ) = ZERO
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ELSE
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*
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* Interchange rows I and I+1
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*
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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TEMP = D( I+1 )
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D( I+1 ) = DU( I ) - FACT*TEMP
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DL( I ) = DU( I+1 )
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DU( I+1 ) = -FACT*DL( I )
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DU( I ) = TEMP
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DO 30 J = 1, NRHS
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TEMP = B( I, J )
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B( I, J ) = B( I+1, J )
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B( I+1, J ) = TEMP - FACT*B( I+1, J )
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30 CONTINUE
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END IF
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40 CONTINUE
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IF( N.GT.1 ) THEN
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I = N - 1
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IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN
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IF( D( I ).NE.ZERO ) THEN
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FACT = DL( I ) / D( I )
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D( I+1 ) = D( I+1 ) - FACT*DU( I )
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DO 50 J = 1, NRHS
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B( I+1, J ) = B( I+1, J ) - FACT*B( I, J )
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50 CONTINUE
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ELSE
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INFO = I
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RETURN
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END IF
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ELSE
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FACT = D( I ) / DL( I )
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D( I ) = DL( I )
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TEMP = D( I+1 )
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D( I+1 ) = DU( I ) - FACT*TEMP
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DU( I ) = TEMP
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DO 60 J = 1, NRHS
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TEMP = B( I, J )
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B( I, J ) = B( I+1, J )
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B( I+1, J ) = TEMP - FACT*B( I+1, J )
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60 CONTINUE
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END IF
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END IF
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IF( D( N ).EQ.ZERO ) THEN
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INFO = N
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RETURN
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END IF
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END IF
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*
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* Back solve with the matrix U from the factorization.
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*
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IF( NRHS.LE.2 ) THEN
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J = 1
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70 CONTINUE
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B( N, J ) = B( N, J ) / D( N )
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IF( N.GT.1 )
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$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
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DO 80 I = N - 2, 1, -1
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B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
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$ B( I+2, J ) ) / D( I )
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80 CONTINUE
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IF( J.LT.NRHS ) THEN
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J = J + 1
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GO TO 70
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END IF
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ELSE
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DO 100 J = 1, NRHS
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B( N, J ) = B( N, J ) / D( N )
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IF( N.GT.1 )
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$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
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$ D( N-1 )
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DO 90 I = N - 2, 1, -1
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B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DL( I )*
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$ B( I+2, J ) ) / D( I )
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90 CONTINUE
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100 CONTINUE
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END IF
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*
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RETURN
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*
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* End of SGTSV
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*
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END
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