simpson#
- 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.
If there are an even number of samples, N, then there are an odd number of intervals (N-1), but Simpson’s rule requires an even number of intervals. The parameter ‘even’ controls how this is handled.
- 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.
See also
quad
adaptive quadrature using QUADPACK
fixed_quad
fixed-order Gaussian quadrature
dblquad
double integrals
tplquad
triple integrals
romb
integrators for sampled data
cumulative_trapezoid
cumulative integration for sampled data
cumulative_simpson
cumulative integration using Simpson’s 1/3 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