scipy.integrate.

romb#

scipy.integrate.romb(y, dx=1.0, axis=-1, show=False)[source]#

Romberg integration using samples of a function.

Parameters:

yarray_like: A vector of 2**k + 1 equally-spaced samples of a function.
dxfloat, optional: The sample spacing. Default is 1.
axisint, optional: The axis along which to integrate. Default is -1 (last axis).
showbool, optional: When y is a single 1-D array, then if this argument is True print the table showing Richardson extrapolation from the samples. Default is False.

Returns:

rombndarray: The integrated result for axis.

See also

quad: adaptive quadrature using QUADPACK
fixed_quad: fixed-order Gaussian quadrature
dblquad: double integrals
tplquad: triple integrals
simpson: integrators for sampled data
cumulative_trapezoid: cumulative integration for sampled data

Examples

>>> from scipy import integrate
>>> import numpy as np
>>> x = np.arange(10, 14.25, 0.25)
>>> y = np.arange(3, 12)

>>> integrate.romb(y)
56.0

>>> y = np.sin(np.power(x, 2.5))
>>> integrate.romb(y)
-0.742561336672229

>>> integrate.romb(y, show=True)
Richardson Extrapolation Table for Romberg Integration
======================================================
-0.81576
 4.63862  6.45674
-1.10581 -3.02062 -3.65245
-2.57379 -3.06311 -3.06595 -3.05664
-1.34093 -0.92997 -0.78776 -0.75160 -0.74256
======================================================
-0.742561336672229  # may vary