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Evaluate an Hermite series at points x.

If `c` is of length `n + 1`, this function returns the value:

.. math:: p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x)

The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.(more...)

        def hermval(x, c, tensor=True):
    """
    Evaluate an Hermite series at points x.

    If `c` is of length `n + 1`, this function returns the value:

    .. math:: p(x) = c_0 * H_0(x) + c_1 * H_1(x) + ... + c_n * H_n(x)

    The parameter `x` is converted to an array only if it is a tuple or a
    list, otherwise it is treated as a scalar. In either case, either `x`
    or its elements must support multiplication and addition both with
    themselves and with the elements of `c`.

    If `c` is a 1-D array, then `p(x)` will have the same shape as `x`.  If
    `c` is multidimensional, then the shape of the result depends on the
    value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
    x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
    scalars have shape (,).

    Trailing zeros in the coefficients will be used in the evaluation, so
    they should be avoided if efficiency is a concern.

    Parameters
    ----------
    x : array_like, compatible object
        If `x` is a list or tuple, it is converted to an ndarray, otherwise
        it is left unchanged and treated as a scalar. In either case, `x`
        or its elements must support addition and multiplication with
        with themselves and with the elements of `c`.
    c : array_like
        Array of coefficients ordered so that the coefficients for terms of
        degree n are contained in c[n]. If `c` is multidimensional the
        remaining indices enumerate multiple polynomials. In the two
        dimensional case the coefficients may be thought of as stored in
        the columns of `c`.
    tensor : boolean, optional
        If True, the shape of the coefficient array is extended with ones
        on the right, one for each dimension of `x`. Scalars have dimension 0
        for this action. The result is that every column of coefficients in
        `c` is evaluated for every element of `x`. If False, `x` is broadcast
        over the columns of `c` for the evaluation.  This keyword is useful
        when `c` is multidimensional. The default value is True.

        .. versionadded:: 1.7.0

    Returns
    -------
    values : ndarray, algebra_like
        The shape of the return value is described above.

    See Also
    --------
    hermval2d, hermgrid2d, hermval3d, hermgrid3d

    Notes
    -----
    The evaluation uses Clenshaw recursion, aka synthetic division.

    Examples
    --------
    >>> from numpy.polynomial.hermite import hermval
    >>> coef = [1,2,3]
    >>> hermval(1, coef)
    11.0
    >>> hermval([[1,2],[3,4]], coef)
    array([[  11.,   51.],
           [ 115.,  203.]])

    """
    c = np.array(c, ndmin=1, copy=0)
    if c.dtype.char in '?bBhHiIlLqQpP':
        c = c.astype(np.double)
    if isinstance(x, (tuple, list)):
        x = np.asarray(x)
    if isinstance(x, np.ndarray) and tensor:
       c = c.reshape(c.shape + (1,)*x.ndim)

    x2 = x*2
    if len(c) == 1 :
        c0 = c[0]
        c1 = 0
    elif len(c) == 2 :
        c0 = c[0]
        c1 = c[1]
    else :
        nd = len(c)
        c0 = c[-2]
        c1 = c[-1]
        for i in range(3, len(c) + 1) :
            tmp = c0
            nd =  nd - 1
            c0 = c[-i] - c1*(2*(nd - 1))
            c1 = tmp + c1*x2
    return c0 + c1*x2
        


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_hermite.py   nupic-linux64(Download)
    def test_hermmul(self) :
        # check values of result
        for i in range(5) :
            pol1 = [0]*i + [1]
            val1 = herm.hermval(self.x, pol1)
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i,j)
                pol2 = [0]*j + [1]
                val2 = herm.hermval(self.x, pol2)
                val2 = herm.hermval(self.x, pol2)
                pol3 = herm.hermmul(pol1, pol2)
                val3 = herm.hermval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                assert_almost_equal(val3, val1*val2, err_msg=msg)
            ser = np.zeros
            tgt = y[i]
            res = herm.hermval(x, [0]*i + [1])
            assert_almost_equal(res, tgt, err_msg=msg)
 
            hermpol = herm.poly2herm(pol)
            hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(herm.hermval(-1, hermint), i)
 
        # check single integration with integration constant and scaling

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite.py   numpy(Download)
    def test_hermmul(self) :
        # check values of result
        for i in range(5) :
            pol1 = [0]*i + [1]
            val1 = herm.hermval(self.x, pol1)
            for j in range(5) :
                msg = "At i=%d, j=%d" % (i, j)
                pol2 = [0]*j + [1]
                val2 = herm.hermval(self.x, pol2)
                val2 = herm.hermval(self.x, pol2)
                pol3 = herm.hermmul(pol1, pol2)
                val3 = herm.hermval(self.x, pol3)
                assert_(len(pol3) == i + j + 1, msg)
                assert_almost_equal(val3, val1*val2, err_msg=msg)
            ser = np.zeros
            tgt = y[i]
            res = herm.hermval(x, [0]*i + [1])
            assert_almost_equal(res, tgt, err_msg=msg)
 
            hermpol = herm.poly2herm(pol)
            hermint = herm.hermint(hermpol, m=1, k=[i], lbnd=-1)
            assert_almost_equal(herm.hermval(-1, hermint), i)
 
        # check single integration with integration constant and scaling