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Annotation of rpl/lapack/lapack/dptts2.f, revision 1.9

1.9     ! bertrand    1: *> \brief \b DPTTS2
        !             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: *> \date November 2011
        !            99: *
        !           100: *> \ingroup doubleOTHERcomputational
        !           101: *
        !           102: *  =====================================================================
1.1       bertrand  103:       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
                    104: *
1.9     ! bertrand  105: *  -- LAPACK computational routine (version 3.4.0) --
1.1       bertrand  106: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    107: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9     ! bertrand  108: *     November 2011
1.1       bertrand  109: *
                    110: *     .. Scalar Arguments ..
                    111:       INTEGER            LDB, N, NRHS
                    112: *     ..
                    113: *     .. Array Arguments ..
                    114:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
                    115: *     ..
                    116: *
                    117: *  =====================================================================
                    118: *
                    119: *     .. Local Scalars ..
                    120:       INTEGER            I, J
                    121: *     ..
                    122: *     .. External Subroutines ..
                    123:       EXTERNAL           DSCAL
                    124: *     ..
                    125: *     .. Executable Statements ..
                    126: *
                    127: *     Quick return if possible
                    128: *
                    129:       IF( N.LE.1 ) THEN
                    130:          IF( N.EQ.1 )
                    131:      $      CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
                    132:          RETURN
                    133:       END IF
                    134: *
1.8       bertrand  135: *     Solve A * X = B using the factorization A = L*D*L**T,
1.1       bertrand  136: *     overwriting each right hand side vector with its solution.
                    137: *
                    138:       DO 30 J = 1, NRHS
                    139: *
                    140: *           Solve L * x = b.
                    141: *
                    142:          DO 10 I = 2, N
                    143:             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
                    144:    10    CONTINUE
                    145: *
1.8       bertrand  146: *           Solve D * L**T * x = b.
1.1       bertrand  147: *
                    148:          B( N, J ) = B( N, J ) / D( N )
                    149:          DO 20 I = N - 1, 1, -1
                    150:             B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
                    151:    20    CONTINUE
                    152:    30 CONTINUE
                    153: *
                    154:       RETURN
                    155: *
                    156: *     End of DPTTS2
                    157: *
                    158:       END