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Module « scipy.integrate »

Fonction simpson - module scipy.integrate

Signature de la fonction simpson

def simpson(y, x=None, *, dx=1.0, axis=-1) 

Description

help(scipy.integrate.simpson)

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
----------
y : array_like
    Array to be integrated.
x : array_like, optional
    If given, the points at which `y` is sampled.
dx : float, optional
    Spacing of integration points along axis of `x`. Only used when
    `x` is None. Default is 1.
axis : int, 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

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