simpson — SciPy v1.15.3 Manual (original) (raw)

scipy.integrate.

scipy.integrate.simpson(y, x=None, *, dx=1.0, axis=-1)[source]#

Integrate y(x) using samples along the given axis and the composite Simpson’s rule. If x is None, spacing of dx is assumed.

Parameters:

yarray_like

Array to be integrated.

xarray_like, optional

If given, the points at which y is sampled.

dxfloat, optional

Spacing of integration points along axis of x. Only used when_x_ is None. Default is 1.

axisint, optional

Axis along which to integrate. Default is the last axis.

Returns:

float

The estimated integral computed with the composite Simpson’s rule.

Notes

For an odd number of samples that are equally spaced the result is exact if the function is a polynomial of order 3 or less. If the samples are not equally spaced, then the result is exact only if the function is a polynomial of order 2 or less.

References

[1]

Cartwright, Kenneth V. Simpson’s Rule Cumulative Integration with MS Excel and Irregularly-spaced Data. Journal of Mathematical Sciences and Mathematics Education. 12 (2): 1-9

Examples

from scipy import integrate import numpy as np x = np.arange(0, 10) y = np.arange(0, 10)

integrate.simpson(y, x=x) 40.5

y = np.power(x, 3) integrate.simpson(y, x=x) 1640.5 integrate.quad(lambda x: x**3, 0, 9)[0] 1640.25