numpy.polynomial.hermite_e.hermevander

numpy.polynomial.hermite_e.hermevander(x, deg) [source]

Псевдо-Вандермондова матрица заданной степени.

Возвращает псевдо-Вандермондову матрицу степени deg и точек выборки x. Псевдо-Вандермондова матрица определяется следующим образом

<img alt="V[..., i] = He_i(x)," 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

где 0 <= i <= deg. Ведущие индексы V индексируют элементы x, а последний индекс — степень полинома HermiteE.

Если c — одномерный массив коэффициентов длиной n + 1, а V — массив V = hermevander(x, n), то np.dot(V, c) и hermeval(x, c) совпадают с точностью до округления. Это эквивалентность полезна как для подгонки методом наименьших квадратов, так и для вычисления большого количества рядов HermiteE той же степени и точек выборки.

Параметры:	x : array_like Массив точек. Тип данных преобразуется к float64 или complex128 в зависимости от того, являются ли какие-либо элементы комплексными. Если x — скаляр, он преобразуется в одномерный массив. deg : int Степень получаемой матрицы.
Возвращает:	vander : ndarray Псевдо-Вандермондова матрица. Форма возвращаемой матрицы — x.shape + (deg + 1,), где последний индекс — степень соответствующего полинома HermiteE. Тип данных будет таким же, как преобразованный x.

Примеры

>>> from numpy.polynomial.hermite_e import hermevander
>>> x = np.array([-1, 0, 1])
>>> hermevander(x, 3)
array([[ 1., -1.,  0.,  2.],
       [ 1.,  0., -1., -0.],
       [ 1.,  1.,  0., -2.]])