hermvander(x, deg)

Returns the pseudo-Vandermonde matrix of degree :None:None:`deg` and sample points x. The pseudo-Vandermonde matrix is defined by

$$V[..., i] = H_i(x),$$

where :None:None:`0 <= i <= deg`. The leading indices of :None:None:`V` index the elements of x and the last index is the degree of the Hermite polynomial.

If :None:None:`c` is a 1-D array of coefficients of length :None:None:`n + 1` and :None:None:`V` is the array V = hermvander(x, n) , then np.dot(V, c) and hermval(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 is x.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.

Pseudo-Vandermonde matrix of given degree.

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.]])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.polynomial.hermite.hermvander2d numpy.polynomial.hermite.hermfit numpy.polynomial.hermite.hermvander3d

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