224 lines
6.0 KiB
Fortran
224 lines
6.0 KiB
Fortran
*> \brief \b SGTTRS
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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 SGTTRS + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgttrs.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/sgttrs.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/sgttrs.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 SGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
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* INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
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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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*> SGTTRS solves one of the systems of equations
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*> A*X = B or A**T*X = B,
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*> with a tridiagonal matrix A using the LU factorization computed
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*> by SGTTRF.
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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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the form of the system of equations.
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*> = 'N': A * X = B (No transpose)
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*> = 'T': A**T* X = B (Transpose)
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*> = 'C': A**T* X = B (Conjugate transpose = Transpose)
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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 order of the matrix A.
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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] DL
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*> \verbatim
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*> DL is REAL array, dimension (N-1)
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*> The (n-1) multipliers that define the matrix L from the
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*> LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is REAL array, dimension (N)
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*> The n diagonal elements of the upper triangular matrix U from
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*> the LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in] DU
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*> \verbatim
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*> DU is REAL array, dimension (N-1)
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*> The (n-1) elements of the first super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[in] DU2
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*> \verbatim
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*> DU2 is REAL array, dimension (N-2)
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*> The (n-2) elements of the second super-diagonal of U.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices; for 1 <= i <= n, row i of the matrix was
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*> interchanged with row IPIV(i). IPIV(i) will always be either
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*> i or i+1; IPIV(i) = i indicates a row interchange was not
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*> required.
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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 matrix of right hand side vectors B.
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*> On exit, B is overwritten by the solution vectors 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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*> \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 realGTcomputational
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*
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* =====================================================================
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SUBROUTINE SGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
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$ INFO )
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*
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* -- LAPACK computational 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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CHARACTER TRANS
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INTEGER INFO, LDB, N, NRHS
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL NOTRAN
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INTEGER ITRANS, J, JB, NB
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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* ..
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* .. External Subroutines ..
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EXTERNAL SGTTS2, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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NOTRAN = ( TRANS.EQ.'N' .OR. TRANS.EQ.'n' )
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IF( .NOT.NOTRAN .AND. .NOT.( TRANS.EQ.'T' .OR. TRANS.EQ.
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$ 't' ) .AND. .NOT.( TRANS.EQ.'C' .OR. TRANS.EQ.'c' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) 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( LDB.LT.MAX( N, 1 ) ) 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( 'SGTTRS', -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 )
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$ RETURN
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*
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* Decode TRANS
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*
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IF( NOTRAN ) THEN
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ITRANS = 0
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ELSE
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ITRANS = 1
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END IF
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*
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* Determine the number of right-hand sides to solve at a time.
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*
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IF( NRHS.EQ.1 ) THEN
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NB = 1
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ELSE
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NB = MAX( 1, ILAENV( 1, 'SGTTRS', TRANS, N, NRHS, -1, -1 ) )
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END IF
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*
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IF( NB.GE.NRHS ) THEN
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CALL SGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
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ELSE
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DO 10 J = 1, NRHS, NB
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JB = MIN( NRHS-J+1, NB )
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CALL SGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1, J ),
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$ LDB )
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10 CONTINUE
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END IF
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*
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* End of SGTTRS
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*
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END
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