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version 1.3, 2010/08/06 15:28:38 version 1.15, 2016/08/27 15:34:24
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   *> \brief \b DGTTS2 solves a system of linear equations with a tridiagonal matrix using the LU factorization computed by sgttrf.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGTTS2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtts2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgtts2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgtts2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            ITRANS, LDB, N, NRHS
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGTTS2 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] ITRANS
   *> \verbatim
   *>          ITRANS is INTEGER
   *>          Specifies the form of the system of equations.
   *>          = 0:  A * X = B  (No transpose)
   *>          = 1:  A**T* X = B  (Transpose)
   *>          = 2:  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
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date September 2012
   *
   *> \ingroup doubleGTcomputational
   *
   *  =====================================================================
       SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )        SUBROUTINE DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.2) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     September 2012
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            ITRANS, LDB, N, NRHS        INTEGER            ITRANS, LDB, N, NRHS
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       DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )        DOUBLE PRECISION   B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGTTS2 solves one of the systems of equations  
 *     A*X = B  or  A'*X = B,  
 *  with a tridiagonal matrix A using the LU factorization computed  
 *  by DGTTRF.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  ITRANS  (input) INTEGER  
 *          Specifies the form of the system of equations.  
 *          = 0:  A * X = B  (No transpose)  
 *          = 1:  A'* X = B  (Transpose)  
 *          = 2:  A'* X = B  (Conjugate transpose = Transpose)  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix A.  
 *  
 *  NRHS    (input) INTEGER  
 *          The number of right hand sides, i.e., the number of columns  
 *          of the matrix B.  NRHS >= 0.  
 *  
 *  DL      (input) DOUBLE PRECISION array, dimension (N-1)  
 *          The (n-1) multipliers that define the matrix L from the  
 *          LU factorization of A.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          The n diagonal elements of the upper triangular matrix U from  
 *          the LU factorization of A.  
 *  
 *  DU      (input) DOUBLE PRECISION array, dimension (N-1)  
 *          The (n-1) elements of the first super-diagonal of U.  
 *  
 *  DU2     (input) DOUBLE PRECISION array, dimension (N-2)  
 *          The (n-2) elements of the second super-diagonal of U.  
 *  
 *  IPIV    (input) 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.  
 *  
 *  B       (input/output) 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.  
 *  
 *  LDB     (input) INTEGER  
 *          The leading dimension of the array B.  LDB >= max(1,N).  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
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          END IF           END IF
       ELSE        ELSE
 *  *
 *        Solve A' * X = B.  *        Solve A**T * X = B.
 *  *
          IF( NRHS.LE.1 ) THEN           IF( NRHS.LE.1 ) THEN
 *  *
 *           Solve U'*x = b.  *           Solve U**T*x = b.
 *  *
             J = 1              J = 1
    70       CONTINUE     70       CONTINUE
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      $                     B( I-2, J ) ) / D( I )       $                     B( I-2, J ) ) / D( I )
    80       CONTINUE     80       CONTINUE
 *  *
 *           Solve L'*x = b.  *           Solve L**T*x = b.
 *  *
             DO 90 I = N - 1, 1, -1              DO 90 I = N - 1, 1, -1
                IP = IPIV( I )                 IP = IPIV( I )
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          ELSE           ELSE
             DO 120 J = 1, NRHS              DO 120 J = 1, NRHS
 *  *
 *              Solve U'*x = b.  *              Solve U**T*x = b.
 *  *
                B( 1, J ) = B( 1, J ) / D( 1 )                 B( 1, J ) = B( 1, J ) / D( 1 )
                IF( N.GT.1 )                 IF( N.GT.1 )
Removed from v.1.3  
changed lines
  Added in v.1.15

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