numpy.polynomial.legendre.leggauss(deg)
[source]
Gauss-Legendre quadrature.
Computes the sample points and weights for Gauss-Legendre quadrature. These sample points and weights will correctly integrate polynomials of degree or less over the interval with the weight function .
Parameters: |
deg : int Number of sample points and weights. It must be >= 1. |
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Returns: |
x : ndarray 1-D ndarray containing the sample points. y : ndarray 1-D ndarray containing the weights. |
The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that
where is a constant independent of and is the k’th root of , and then scaling the results to get the right value when integrating 1.
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https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.polynomial.legendre.leggauss.html