`scipy.integrate._rules._base:Rule.estimate_error`

source: /scipy/integrate/_rules/_base.py :102

Signature

def estimate_error ( self , f , a , b , args = () )

Summary

Estimate the error of the approximation for the integral of f in rectangular region described by corners a and b.

Extended Summary

If a subclass does not override this method, then a default error estimator is used. This estimates the error as |est - refined_est| where est is estimate(f, a, b) and refined_est is the sum of estimate(f, a_k, b_k) where a_k, b_k are the coordinates of each subregion of the region described by a and b. In the 1D case, this is equivalent to comparing the integral over an entire interval [a, b] to the sum of the integrals over the left and right subintervals, [a, (a+b)/2] and [(a+b)/2, b].

Parameters

f : callable

Function to estimate error for. f must have the signature::: f(xndarray, *args) -> ndarray
f should accept arrays x of shape::: (npoints, ndim)
and output arrays of shape::: (npoints, output_dim_1, ..., output_dim_n)
In this case, estimate will return arrays of shape::: (output_dim_1, ..., output_dim_n)

a, b : ndarray

Lower and upper limits of integration as rank-1 arrays specifying the left and right endpoints of the intervals being integrated over. Infinite limits are currently not supported.

args : tuple, optional

Additional positional args passed to f, if any.

Returns

err_est : ndarray: Result of error estimation. If f returns arrays of shape (npoints, output_dim_1, ..., output_dim_n), then est will be of shape (output_dim_1, ..., output_dim_n).

Aliases

scipy.integrate._rules.Rule.estimate_error