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    1: *> \brief \b DPTTRS
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DPTTRS + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpttrs.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpttrs.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpttrs.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPTTRS( 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: *> DPTTRS 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: *> \param[out] INFO
   91: *> \verbatim
   92: *>          INFO is INTEGER
   93: *>          = 0: successful exit
   94: *>          < 0: if INFO = -k, the k-th argument had an illegal value
   95: *> \endverbatim
   96: *
   97: *  Authors:
   98: *  ========
   99: *
  100: *> \author Univ. of Tennessee
  101: *> \author Univ. of California Berkeley
  102: *> \author Univ. of Colorado Denver
  103: *> \author NAG Ltd.
  104: *
  105: *> \ingroup doublePTcomputational
  106: *
  107: *  =====================================================================
  108:       SUBROUTINE DPTTRS( N, NRHS, D, E, B, LDB, INFO )
  109: *
  110: *  -- LAPACK computational routine --
  111: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  112: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  113: *
  114: *     .. Scalar Arguments ..
  115:       INTEGER            INFO, LDB, N, NRHS
  116: *     ..
  117: *     .. Array Arguments ..
  118:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
  119: *     ..
  120: *
  121: *  =====================================================================
  122: *
  123: *     .. Local Scalars ..
  124:       INTEGER            J, JB, NB
  125: *     ..
  126: *     .. External Functions ..
  127:       INTEGER            ILAENV
  128:       EXTERNAL           ILAENV
  129: *     ..
  130: *     .. External Subroutines ..
  131:       EXTERNAL           DPTTS2, XERBLA
  132: *     ..
  133: *     .. Intrinsic Functions ..
  134:       INTRINSIC          MAX, MIN
  135: *     ..
  136: *     .. Executable Statements ..
  137: *
  138: *     Test the input arguments.
  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( 'DPTTRS', -INFO )
  150:          RETURN
  151:       END IF
  152: *
  153: *     Quick return if possible
  154: *
  155:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  156:      $   RETURN
  157: *
  158: *     Determine the number of right-hand sides to solve at a time.
  159: *
  160:       IF( NRHS.EQ.1 ) THEN
  161:          NB = 1
  162:       ELSE
  163:          NB = MAX( 1, ILAENV( 1, 'DPTTRS', ' ', N, NRHS, -1, -1 ) )
  164:       END IF
  165: *
  166:       IF( NB.GE.NRHS ) THEN
  167:          CALL DPTTS2( N, NRHS, D, E, B, LDB )
  168:       ELSE
  169:          DO 10 J = 1, NRHS, NB
  170:             JB = MIN( NRHS-J+1, NB )
  171:             CALL DPTTS2( N, JB, D, E, B( 1, J ), LDB )
  172:    10    CONTINUE
  173:       END IF
  174: *
  175:       RETURN
  176: *
  177: *     End of DPTTRS
  178: *
  179:       END