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Divide one Hermite series by another.

Returns the quotient-with-remainder of two Hermite series
`c1` / `c2`.  The arguments are sequences of coefficients from lowest
order "term" to highest, e.g., [1,2,3] represents the series
``P_0 + 2*P_1 + 3*P_2``.

Parameters
----------
c1, c2 : array_like(more...)

        def hermdiv(c1, c2):
    """
    Divide one Hermite series by another.

    Returns the quotient-with-remainder of two Hermite series
    `c1` / `c2`.  The arguments are sequences of coefficients from lowest
    order "term" to highest, e.g., [1,2,3] represents the series
    ``P_0 + 2*P_1 + 3*P_2``.

    Parameters
    ----------
    c1, c2 : array_like
        1-D arrays of Hermite series coefficients ordered from low to
        high.

    Returns
    -------
    [quo, rem] : ndarrays
        Of Hermite series coefficients representing the quotient and
        remainder.

    See Also
    --------
    hermadd, hermsub, hermmul, hermpow

    Notes
    -----
    In general, the (polynomial) division of one Hermite series by another
    results in quotient and remainder terms that are not in the Hermite
    polynomial basis set.  Thus, to express these results as a Hermite
    series, it is necessary to "reproject" the results onto the Hermite
    basis set, which may produce "unintuitive" (but correct) results; see
    Examples section below.

    Examples
    --------
    >>> from numpy.polynomial.hermite import hermdiv
    >>> hermdiv([ 52.,  29.,  52.,   7.,   6.], [0, 1, 2])
    (array([ 1.,  2.,  3.]), array([ 0.]))
    >>> hermdiv([ 54.,  31.,  52.,   7.,   6.], [0, 1, 2])
    (array([ 1.,  2.,  3.]), array([ 2.,  2.]))
    >>> hermdiv([ 53.,  30.,  52.,   7.,   6.], [0, 1, 2])
    (array([ 1.,  2.,  3.]), array([ 1.,  1.]))

    """
    # c1, c2 are trimmed copies
    [c1, c2] = pu.as_series([c1, c2])
    if c2[-1] == 0 :
        raise ZeroDivisionError()

    lc1 = len(c1)
    lc2 = len(c2)
    if lc1 < lc2 :
        return c1[:1]*0, c1
    elif lc2 == 1 :
        return c1/c2[-1], c1[:1]*0
    else :
        quo = np.empty(lc1 - lc2 + 1, dtype=c1.dtype)
        rem = c1
        for i in range(lc1 - lc2, - 1, -1):
            p = hermmul([0]*i + [1], c2)
            q = rem[-1]/p[-1]
            rem = rem[:-1] - q*p[:-1]
            quo[i] = q
        return quo, pu.trimseq(rem)
        


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_hermite.py   nupic-linux64(Download)
                cj = [0]*j + [1]
                tgt = herm.hermadd(ci, cj)
                quo, rem = herm.hermdiv(tgt, ci)
                res = herm.hermadd(herm.hermmul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite.py   numpy(Download)
                cj = [0]*j + [1]
                tgt = herm.hermadd(ci, cj)
                quo, rem = herm.hermdiv(tgt, ci)
                res = herm.hermadd(herm.hermmul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)