numpy.polynomial.hermite.hermgauss — NumPy v1.15 Manual (original) (raw)
numpy.polynomial.hermite. hermgauss(deg)[source]¶
Gauss-Hermite quadrature.
Computes the sample points and weights for Gauss-Hermite quadrature. These sample points and weights will correctly integrate polynomials of degree 2*deg - 1 or less over the interval [-\inf, \inf]with the weight function f(x) = \exp(-x^2).
| Parameters: | deg : int Number of sample points and weights. It must be >= 1. |
|---|---|
| Returns: | x : ndarray 1-D ndarray containing the sample points. y : ndarray 1-D ndarray containing the weights. |
Notes
New in version 1.7.0.
The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that
w_k = c / (H'_n(x_k) * H_{n-1}(x_k))
where c is a constant independent of k and x_kis the k’th root of H_n, and then scaling the results to get the right value when integrating 1.