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scipy.integrate.simps

scipy.integrate.simps(y, x=None, dx=1, axis=-1, even='avg')

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 as follows:

even=’avg’: Average two results: 1) use the first N-2 intervals with

a trapezoidal rule on the last interval and 2) use the last N-2 intervals with a trapezoidal rule on the first interval

even=’first’: Use Simpson’s rule for the first N-2 intervals with

a trapezoidal rule on the last interval.

even=’last’: Use Simpson’s rule for the last N-2 intervals with a

trapezoidal rule on the first interval.

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.

See also:

quad - adaptive quadrature using QUADPACK romberg - adaptive Romberg quadrature quadrature - adaptive Gaussian quadrature fixed_quad - fixed-order Gaussian quadrature dblquad, tplquad - double and triple integrals romb, trapz - integrators for sampled data cumtrapz - cumulative integration for sampled data ode, odeint - ODE integrators