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    1: *> \brief \b DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DPTTS2 + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptts2.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dptts2.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dptts2.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            LDB, N, NRHS
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
   28: *       ..
   29: *
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> DPTTS2 solves a tridiagonal system of the form
   37: *>    A * X = B
   38: *> using the L*D*L**T factorization of A computed by DPTTRF.  D is a
   39: *> diagonal matrix specified in the vector D, L is a unit bidiagonal
   40: *> matrix whose subdiagonal is specified in the vector E, and X and B
   41: *> are N by NRHS matrices.
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] N
   48: *> \verbatim
   49: *>          N is INTEGER
   50: *>          The order of the tridiagonal matrix A.  N >= 0.
   51: *> \endverbatim
   52: *>
   53: *> \param[in] NRHS
   54: *> \verbatim
   55: *>          NRHS is INTEGER
   56: *>          The number of right hand sides, i.e., the number of columns
   57: *>          of the matrix B.  NRHS >= 0.
   58: *> \endverbatim
   59: *>
   60: *> \param[in] D
   61: *> \verbatim
   62: *>          D is DOUBLE PRECISION array, dimension (N)
   63: *>          The n diagonal elements of the diagonal matrix D from the
   64: *>          L*D*L**T factorization of A.
   65: *> \endverbatim
   66: *>
   67: *> \param[in] E
   68: *> \verbatim
   69: *>          E is DOUBLE PRECISION array, dimension (N-1)
   70: *>          The (n-1) subdiagonal elements of the unit bidiagonal factor
   71: *>          L from the L*D*L**T factorization of A.  E can also be regarded
   72: *>          as the superdiagonal of the unit bidiagonal factor U from the
   73: *>          factorization A = U**T*D*U.
   74: *> \endverbatim
   75: *>
   76: *> \param[in,out] B
   77: *> \verbatim
   78: *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   79: *>          On entry, the right hand side vectors B for the system of
   80: *>          linear equations.
   81: *>          On exit, the solution vectors, X.
   82: *> \endverbatim
   83: *>
   84: *> \param[in] LDB
   85: *> \verbatim
   86: *>          LDB is INTEGER
   87: *>          The leading dimension of the array B.  LDB >= max(1,N).
   88: *> \endverbatim
   89: *
   90: *  Authors:
   91: *  ========
   92: *
   93: *> \author Univ. of Tennessee
   94: *> \author Univ. of California Berkeley
   95: *> \author Univ. of Colorado Denver
   96: *> \author NAG Ltd.
   97: *
   98: *> \ingroup doublePTcomputational
   99: *
  100: *  =====================================================================
  101:       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
  102: *
  103: *  -- LAPACK computational routine --
  104: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  105: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  106: *
  107: *     .. Scalar Arguments ..
  108:       INTEGER            LDB, N, NRHS
  109: *     ..
  110: *     .. Array Arguments ..
  111:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
  112: *     ..
  113: *
  114: *  =====================================================================
  115: *
  116: *     .. Local Scalars ..
  117:       INTEGER            I, J
  118: *     ..
  119: *     .. External Subroutines ..
  120:       EXTERNAL           DSCAL
  121: *     ..
  122: *     .. Executable Statements ..
  123: *
  124: *     Quick return if possible
  125: *
  126:       IF( N.LE.1 ) THEN
  127:          IF( N.EQ.1 )
  128:      $      CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
  129:          RETURN
  130:       END IF
  131: *
  132: *     Solve A * X = B using the factorization A = L*D*L**T,
  133: *     overwriting each right hand side vector with its solution.
  134: *
  135:       DO 30 J = 1, NRHS
  136: *
  137: *           Solve L * x = b.
  138: *
  139:          DO 10 I = 2, N
  140:             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
  141:    10    CONTINUE
  142: *
  143: *           Solve D * L**T * x = b.
  144: *
  145:          B( N, J ) = B( N, J ) / D( N )
  146:          DO 20 I = N - 1, 1, -1
  147:             B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
  148:    20    CONTINUE
  149:    30 CONTINUE
  150: *
  151:       RETURN
  152: *
  153: *     End of DPTTS2
  154: *
  155:       END