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Annotation of rpl/lapack/lapack/dptts2.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
        !             2: *
        !             3: *  -- LAPACK routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       INTEGER            LDB, N, NRHS
        !            10: *     ..
        !            11: *     .. Array Arguments ..
        !            12:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
        !            13: *     ..
        !            14: *
        !            15: *  Purpose
        !            16: *  =======
        !            17: *
        !            18: *  DPTTS2 solves a tridiagonal system of the form
        !            19: *     A * X = B
        !            20: *  using the L*D*L' factorization of A computed by DPTTRF.  D is a
        !            21: *  diagonal matrix specified in the vector D, L is a unit bidiagonal
        !            22: *  matrix whose subdiagonal is specified in the vector E, and X and B
        !            23: *  are N by NRHS matrices.
        !            24: *
        !            25: *  Arguments
        !            26: *  =========
        !            27: *
        !            28: *  N       (input) INTEGER
        !            29: *          The order of the tridiagonal matrix A.  N >= 0.
        !            30: *
        !            31: *  NRHS    (input) INTEGER
        !            32: *          The number of right hand sides, i.e., the number of columns
        !            33: *          of the matrix B.  NRHS >= 0.
        !            34: *
        !            35: *  D       (input) DOUBLE PRECISION array, dimension (N)
        !            36: *          The n diagonal elements of the diagonal matrix D from the
        !            37: *          L*D*L' factorization of A.
        !            38: *
        !            39: *  E       (input) DOUBLE PRECISION array, dimension (N-1)
        !            40: *          The (n-1) subdiagonal elements of the unit bidiagonal factor
        !            41: *          L from the L*D*L' factorization of A.  E can also be regarded
        !            42: *          as the superdiagonal of the unit bidiagonal factor U from the
        !            43: *          factorization A = U'*D*U.
        !            44: *
        !            45: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
        !            46: *          On entry, the right hand side vectors B for the system of
        !            47: *          linear equations.
        !            48: *          On exit, the solution vectors, X.
        !            49: *
        !            50: *  LDB     (input) INTEGER
        !            51: *          The leading dimension of the array B.  LDB >= max(1,N).
        !            52: *
        !            53: *  =====================================================================
        !            54: *
        !            55: *     .. Local Scalars ..
        !            56:       INTEGER            I, J
        !            57: *     ..
        !            58: *     .. External Subroutines ..
        !            59:       EXTERNAL           DSCAL
        !            60: *     ..
        !            61: *     .. Executable Statements ..
        !            62: *
        !            63: *     Quick return if possible
        !            64: *
        !            65:       IF( N.LE.1 ) THEN
        !            66:          IF( N.EQ.1 )
        !            67:      $      CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
        !            68:          RETURN
        !            69:       END IF
        !            70: *
        !            71: *     Solve A * X = B using the factorization A = L*D*L',
        !            72: *     overwriting each right hand side vector with its solution.
        !            73: *
        !            74:       DO 30 J = 1, NRHS
        !            75: *
        !            76: *           Solve L * x = b.
        !            77: *
        !            78:          DO 10 I = 2, N
        !            79:             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
        !            80:    10    CONTINUE
        !            81: *
        !            82: *           Solve D * L' * x = b.
        !            83: *
        !            84:          B( N, J ) = B( N, J ) / D( N )
        !            85:          DO 20 I = N - 1, 1, -1
        !            86:             B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
        !            87:    20    CONTINUE
        !            88:    30 CONTINUE
        !            89: *
        !            90:       RETURN
        !            91: *
        !            92: *     End of DPTTS2
        !            93: *
        !            94:       END