simpson(y, x=None, dx=1.0, axis=-1, even='avg')

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.

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.

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.

even : str {'avg', 'first', 'last'}, optional

'avg'

'avg'

'first'

'first'

'last'

'last'

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

See Also

cumulative_trapezoid

cumulative integration for sampled data

dblquad

double integrals

fixed_quad

fixed-order Gaussian quadrature

ode

ODE integrators

odeint

ODE integrators

quad

adaptive quadrature using QUADPACK

quadrature

adaptive Gaussian quadrature

romb

integrators for sampled data

romberg

adaptive Romberg quadrature

tplquad

triple integrals

Examples

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

>>> integrate.simpson(y, x)
40.5

>>> y = np.power(x, 3)
... integrate.simpson(y, x)
1642.5

>>> integrate.quad(lambda x: x**3, 0, 9)[0]
1640.25

>>> integrate.simpson(y, x, even='first')
1644.5

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.integrate._quadrature.simpson scipy.integrate._quadpack_py.dblquad scipy.integrate._quadrature.simps scipy.integrate._quadrature.quadrature scipy.integrate._quadrature.romb scipy.integrate._quadrature.fixed_quad scipy.integrate._quadpack_py.quad scipy.integrate._quadrature.romberg scipy.integrate._quadpack_py.tplquad

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