numpy.polynomial.hermite.hermvander()

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

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

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) 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:

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`.

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.

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.]])

Links:

https://docs.scipy.org/doc/numpy-1.11.0/reference/generated/numpy.polynomial.hermite.hermvander.html

doc_NumPy

2025-01-10 15:47:30

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