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*> \brief \b DGTTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition
* ==========
*
* SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* Purpose
* =======
*
*>\details \b Purpose:
*>\verbatim
*>
*> DGTTRS solves one of the systems of equations
*> A*X = B or A**T*X = B,
*> with a tridiagonal matrix A using the LU factorization computed
*> by DGTTRF.
*>
*>\endverbatim
*
* Arguments
* =========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations.
*> = 'N': A * X = B (No transpose)
*> = 'T': A**T* X = B (Transpose)
*> = 'C': A**T* X = B (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) multipliers that define the matrix L from the
*> LU factorization of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> The n diagonal elements of the upper triangular matrix U from
*> the LU factorization of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) elements of the first super-diagonal of U.
*> \endverbatim
*>
*> \param[in] DU2
*> \verbatim
*> DU2 is DOUBLE PRECISION array, dimension (N-2)
*> The (n-2) elements of the second super-diagonal of U.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices; for 1 <= i <= n, row i of the matrix was
*> interchanged with row IPIV(i). IPIV(i) will always be either
*> i or i+1; IPIV(i) = i indicates a row interchange was not
*> required.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the matrix of right hand side vectors B.
*> On exit, B is overwritten by the solution vectors X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*>
*
* Authors
* =======
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup doubleOTHERcomputational
*
* =====================================================================
SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB,
$ INFO )
*
* -- LAPACK computational routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL NOTRAN
INTEGER ITRANS, J, JB, NB
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DGTTS2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
INFO = 0
NOTRAN = ( TRANS.EQ.'N' .OR. TRANS.EQ.'n' )
IF( .NOT.NOTRAN .AND. .NOT.( TRANS.EQ.'T' .OR. TRANS.EQ.
$ 't' ) .AND. .NOT.( TRANS.EQ.'C' .OR. TRANS.EQ.'c' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( NRHS.LT.0 ) THEN
INFO = -3
ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DGTTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Decode TRANS
*
IF( NOTRAN ) THEN
ITRANS = 0
ELSE
ITRANS = 1
END IF
*
* Determine the number of right-hand sides to solve at a time.
*
IF( NRHS.EQ.1 ) THEN
NB = 1
ELSE
NB = MAX( 1, ILAENV( 1, 'DGTTRS', TRANS, N, NRHS, -1, -1 ) )
END IF
*
IF( NB.GE.NRHS ) THEN
CALL DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
ELSE
DO 10 J = 1, NRHS, NB
JB = MIN( NRHS-J+1, NB )
CALL DGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1, J ),
$ LDB )
10 CONTINUE
END IF
*
* End of DGTTRS
*
END
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