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    1: *> \brief <b> ZPTSV 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 ZPTSV + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zptsv.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zptsv.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zptsv.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZPTSV( N, NRHS, D, E, B, LDB, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, LDB, N, NRHS
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   D( * )
   28: *       COMPLEX*16         B( LDB, * ), E( * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> ZPTSV computes the solution to a complex system of linear equations
   38: *> A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal
   39: *> matrix, and X and B are N-by-NRHS matrices.
   40: *>
   41: *> A is factored as A = L*D*L**H, and the factored form of A is then
   42: *> used to solve the system of equations.
   43: *> \endverbatim
   44: *
   45: *  Arguments:
   46: *  ==========
   47: *
   48: *> \param[in] N
   49: *> \verbatim
   50: *>          N is INTEGER
   51: *>          The order of the matrix A.  N >= 0.
   52: *> \endverbatim
   53: *>
   54: *> \param[in] NRHS
   55: *> \verbatim
   56: *>          NRHS is INTEGER
   57: *>          The number of right hand sides, i.e., the number of columns
   58: *>          of the matrix B.  NRHS >= 0.
   59: *> \endverbatim
   60: *>
   61: *> \param[in,out] D
   62: *> \verbatim
   63: *>          D is DOUBLE PRECISION array, dimension (N)
   64: *>          On entry, the n diagonal elements of the tridiagonal matrix
   65: *>          A.  On exit, the n diagonal elements of the diagonal matrix
   66: *>          D from the factorization A = L*D*L**H.
   67: *> \endverbatim
   68: *>
   69: *> \param[in,out] E
   70: *> \verbatim
   71: *>          E is COMPLEX*16 array, dimension (N-1)
   72: *>          On entry, the (n-1) subdiagonal elements of the tridiagonal
   73: *>          matrix A.  On exit, the (n-1) subdiagonal elements of the
   74: *>          unit bidiagonal factor L from the L*D*L**H factorization of
   75: *>          A.  E can also be regarded as the superdiagonal of the unit
   76: *>          bidiagonal factor U from the U**H*D*U factorization of A.
   77: *> \endverbatim
   78: *>
   79: *> \param[in,out] B
   80: *> \verbatim
   81: *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
   82: *>          On entry, the N-by-NRHS right hand side matrix B.
   83: *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   84: *> \endverbatim
   85: *>
   86: *> \param[in] LDB
   87: *> \verbatim
   88: *>          LDB is INTEGER
   89: *>          The leading dimension of the array B.  LDB >= max(1,N).
   90: *> \endverbatim
   91: *>
   92: *> \param[out] INFO
   93: *> \verbatim
   94: *>          INFO is INTEGER
   95: *>          = 0:  successful exit
   96: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   97: *>          > 0:  if INFO = i, the leading minor of order i is not
   98: *>                positive definite, and the solution has not been
   99: *>                computed.  The factorization has not been completed
  100: *>                unless i = N.
  101: *> \endverbatim
  102: *
  103: *  Authors:
  104: *  ========
  105: *
  106: *> \author Univ. of Tennessee
  107: *> \author Univ. of California Berkeley
  108: *> \author Univ. of Colorado Denver
  109: *> \author NAG Ltd.
  110: *
  111: *> \ingroup complex16PTsolve
  112: *
  113: *  =====================================================================
  114:       SUBROUTINE ZPTSV( N, NRHS, D, E, B, LDB, INFO )
  115: *
  116: *  -- LAPACK driver routine --
  117: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  118: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  119: *
  120: *     .. Scalar Arguments ..
  121:       INTEGER            INFO, LDB, N, NRHS
  122: *     ..
  123: *     .. Array Arguments ..
  124:       DOUBLE PRECISION   D( * )
  125:       COMPLEX*16         B( LDB, * ), E( * )
  126: *     ..
  127: *
  128: *  =====================================================================
  129: *
  130: *     .. External Subroutines ..
  131:       EXTERNAL           XERBLA, ZPTTRF, ZPTTRS
  132: *     ..
  133: *     .. Intrinsic Functions ..
  134:       INTRINSIC          MAX
  135: *     ..
  136: *     .. Executable Statements ..
  137: *
  138: *     Test the input parameters.
  139: *
  140:       INFO = 0
  141:       IF( N.LT.0 ) THEN
  142:          INFO = -1
  143:       ELSE IF( NRHS.LT.0 ) THEN
  144:          INFO = -2
  145:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  146:          INFO = -6
  147:       END IF
  148:       IF( INFO.NE.0 ) THEN
  149:          CALL XERBLA( 'ZPTSV ', -INFO )
  150:          RETURN
  151:       END IF
  152: *
  153: *     Compute the L*D*L**H (or U**H*D*U) factorization of A.
  154: *
  155:       CALL ZPTTRF( N, D, E, INFO )
  156:       IF( INFO.EQ.0 ) THEN
  157: *
  158: *        Solve the system A*X = B, overwriting B with X.
  159: *
  160:          CALL ZPTTRS( 'Lower', N, NRHS, D, E, B, LDB, INFO )
  161:       END IF
  162:       RETURN
  163: *
  164: *     End of ZPTSV
  165: *
  166:       END