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    1: *> \brief <b> DPTSV computes the solution to system of linear equations A * X = B for PT matrices</b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DPTSV + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptsv.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dptsv.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dptsv.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, 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: *> DPTSV computes the solution to a real system of linear equations
   37: *> A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
   38: *> matrix, and X and B are N-by-NRHS matrices.
   39: *>
   40: *> A is factored as A = L*D*L**T, and the factored form of A is then
   41: *> used to solve the system of equations.
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] N
   48: *> \verbatim
   49: *>          N is INTEGER
   50: *>          The order of the 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,out] D
   61: *> \verbatim
   62: *>          D is DOUBLE PRECISION array, dimension (N)
   63: *>          On entry, the n diagonal elements of the tridiagonal matrix
   64: *>          A.  On exit, the n diagonal elements of the diagonal matrix
   65: *>          D from the factorization A = L*D*L**T.
   66: *> \endverbatim
   67: *>
   68: *> \param[in,out] E
   69: *> \verbatim
   70: *>          E is DOUBLE PRECISION array, dimension (N-1)
   71: *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
   72: *>          matrix A.  On exit, the (n-1) subdiagonal elements of the
   73: *>          unit bidiagonal factor L from the L*D*L**T factorization of
   74: *>          A.  (E can also be regarded as the superdiagonal of the unit
   75: *>          bidiagonal factor U from the U**T*D*U factorization of A.)
   76: *> \endverbatim
   77: *>
   78: *> \param[in,out] B
   79: *> \verbatim
   80: *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   81: *>          On entry, the N-by-NRHS right hand side matrix B.
   82: *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   83: *> \endverbatim
   84: *>
   85: *> \param[in] LDB
   86: *> \verbatim
   87: *>          LDB is INTEGER
   88: *>          The leading dimension of the array B.  LDB >= max(1,N).
   89: *> \endverbatim
   90: *>
   91: *> \param[out] INFO
   92: *> \verbatim
   93: *>          INFO is INTEGER
   94: *>          = 0:  successful exit
   95: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   96: *>          > 0:  if INFO = i, the leading minor of order i is not
   97: *>                positive definite, and the solution has not been
   98: *>                computed.  The factorization has not been completed
   99: *>                unless i = N.
  100: *> \endverbatim
  101: *
  102: *  Authors:
  103: *  ========
  104: *
  105: *> \author Univ. of Tennessee
  106: *> \author Univ. of California Berkeley
  107: *> \author Univ. of Colorado Denver
  108: *> \author NAG Ltd.
  109: *
  110: *> \date December 2016
  111: *
  112: *> \ingroup doublePTsolve
  113: *
  114: *  =====================================================================
  115:       SUBROUTINE DPTSV( N, NRHS, D, E, B, LDB, INFO )
  116: *
  117: *  -- LAPACK driver routine (version 3.7.0) --
  118: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  119: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  120: *     December 2016
  121: *
  122: *     .. Scalar Arguments ..
  123:       INTEGER            INFO, LDB, N, NRHS
  124: *     ..
  125: *     .. Array Arguments ..
  126:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
  127: *     ..
  128: *
  129: *  =====================================================================
  130: *
  131: *     .. External Subroutines ..
  132:       EXTERNAL           DPTTRF, DPTTRS, XERBLA
  133: *     ..
  134: *     .. Intrinsic Functions ..
  135:       INTRINSIC          MAX
  136: *     ..
  137: *     .. Executable Statements ..
  138: *
  139: *     Test the input parameters.
  140: *
  141:       INFO = 0
  142:       IF( N.LT.0 ) THEN
  143:          INFO = -1
  144:       ELSE IF( NRHS.LT.0 ) THEN
  145:          INFO = -2
  146:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  147:          INFO = -6
  148:       END IF
  149:       IF( INFO.NE.0 ) THEN
  150:          CALL XERBLA( 'DPTSV ', -INFO )
  151:          RETURN
  152:       END IF
  153: *
  154: *     Compute the L*D*L**T (or U**T*D*U) factorization of A.
  155: *
  156:       CALL DPTTRF( N, D, E, INFO )
  157:       IF( INFO.EQ.0 ) THEN
  158: *
  159: *        Solve the system A*X = B, overwriting B with X.
  160: *
  161:          CALL DPTTRS( N, NRHS, D, E, B, LDB, INFO )
  162:       END IF
  163:       RETURN
  164: *
  165: *     End of DPTSV
  166: *
  167:       END