numpy.polynomial.hermite.hermvander — NumPy v1.11 Manual (original) (raw)
numpy.polynomial.hermite.hermvander(x, deg)[source]¶
Pseudo-Vandermonde matrix of given degree.
Returns the pseudo-Vandermonde matrix of degree deg and sample points_x_. The pseudo-Vandermonde matrix is defined by
![V[..., i] = H_i(x),](http://docs.scipy.org/doc/numpy-1.11.0/_images/math/faca8896a4770863f653aa77b99c1f16ce4c84eb.png)
where 0 <= i <= deg. The leading indices of V index the elements of_x_ and the last index is the degree of the Hermite polynomial.
If c is a 1-D array of coefficients of length n + 1 and V is the array V = hermvander(x, n), then np.dot(V, c) andhermval(x, c) are the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of Hermite series of the same degree and sample points.
| Parameters: | x : array_like Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array. deg : int Degree of the resulting matrix. |
|---|---|
| Returns: | vander : ndarray The pseudo-Vandermonde matrix. The shape of the returned matrix isx.shape + (deg + 1,), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x. |
Examples
from numpy.polynomial.hermite import hermvander x = np.array([-1, 0, 1]) hermvander(x, 3) array([[ 1., -2., 2., 4.], [ 1., 0., -2., -0.], [ 1., 2., 2., -4.]])