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Multiply one Hermite series by another.

Returns the product 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(more...)

        def hermemul(c1, c2):
    """
    Multiply one Hermite series by another.

    Returns the product 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
    -------
    out : ndarray
        Of Hermite series coefficients representing their product.

    See Also
    --------
    hermeadd, hermesub, hermediv, hermepow

    Notes
    -----
    In general, the (polynomial) product of two C-series results in terms
    that are not in the Hermite polynomial basis set.  Thus, to express
    the product as a Hermite series, it is necessary to "reproject" the
    product onto said basis set, which may produce "unintuitive" (but
    correct) results; see Examples section below.

    Examples
    --------
    >>> from numpy.polynomial.hermite_e import hermemul
    >>> hermemul([1, 2, 3], [0, 1, 2])
    array([ 14.,  15.,  28.,   7.,   6.])

    """
    # s1, s2 are trimmed copies
    [c1, c2] = pu.as_series([c1, c2])

    if len(c1) > len(c2):
        c = c2
        xs = c1
    else:
        c = c1
        xs = c2

    if len(c) == 1:
        c0 = c[0]*xs
        c1 = 0
    elif len(c) == 2:
        c0 = c[0]*xs
        c1 = c[1]*xs
    else :
        nd = len(c)
        c0 = c[-2]*xs
        c1 = c[-1]*xs
        for i in range(3, len(c) + 1) :
            tmp = c0
            nd =  nd - 1
            c0 = hermesub(c[-i]*xs, c1*(nd - 1))
            c1 = hermeadd(tmp, hermemulx(c1))
    return hermeadd(c0, hermemulx(c1))
        


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_hermite_e.py   nupic-linux64(Download)
                pol2 = [0]*j + [1]
                val2 = herme.hermeval(self.x, pol2)
                pol3 = herme.hermemul(pol1, pol2)
                val3 = herme.hermeval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                tgt = herme.hermeadd(ci, cj)
                quo, rem = herme.hermediv(tgt, ci)
                res = herme.hermeadd(herme.hermemul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)
 

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite_e.py   numpy(Download)
                pol2 = [0]*j + [1]
                val2 = herme.hermeval(self.x, pol2)
                pol3 = herme.hermemul(pol1, pol2)
                val3 = herme.hermeval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                tgt = herme.hermeadd(ci, cj)
                quo, rem = herme.hermediv(tgt, ci)
                res = herme.hermeadd(herme.hermemul(quo, ci), rem)
                assert_equal(trim(res), trim(tgt), err_msg=msg)