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. - 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