numpy.polynomial.polynomial.polyvander2d

numpy.polynomial.polynomial.polyvander2d(x, y, deg) [source]

Псевдо-Вандермондова матрица заданных степеней.

Возвращает псевдо-Вандермондову матрицу степеней deg и точек выборки (x, y). Псевдо-Вандермондова матрица определяется как

<img alt="V[..., (deg[1] + 1)*i + j] = x^i * y^j," src="data:image/svg+xml;base64,<?xml version='1.0' encoding='UTF-8'?>
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где 0 <= i <= deg[0] и 0 <= j <= deg[1]. Ведущие индексы V индексируют точки (x, y), а последний индекс кодирует степени x и y.

Если V = polyvander2d(x, y, [xdeg, ydeg]), то столбцы V соответствуют элементам двумерного массива коэффициентов c формы (xdeg + 1, ydeg + 1) в порядке

$c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...$

и np.dot(V, c.flat) и polyval2d(x, y, c) будут совпадать до округления. Это равенство полезно как для аппроксимации методом наименьших квадратов, так и для вычисления большого числа двумерных многочленов одинаковых степеней и точек выборки.

Параметры

x, yarray_like: Массивы координат точек, все одной формы. Типы данных будут преобразованы к float64 или complex128 в зависимости от того, являются ли какие-либо элементы комплексными. Скаляры преобразуются в одномерные массивы.
deglist of ints: Список максимальных степеней вида [x_deg, y_deg].

Возвращает

vander2dndarray: Форма возвращаемой матрицы — x.shape + (order,), где

<img alt="порядок = (deg[0]+1)*(deg([1]+1)" class="math" src="data:image/svg+xml;base64,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

Тип dtype будет таким же, как у преобразованных x и y.

См. также

polyvander, polyvander3d, polyval2d, polyval3d

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Licensed under the 3-clause BSD License.
https://numpy.org/doc/1.19/reference/generated/numpy.polynomial.polynomial.polyvander2d.html