SciPy

scipy.integrate.romb

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

Romberg integration using samples of a function.

Parameters:
y : array_like

A vector of 2**k + 1 equally-spaced samples of a function.

dx : float, optional

The sample spacing. Default is 1.

axis : int, optional

The axis along which to integrate. Default is -1 (last axis).

show : bool, 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:
romb : ndarray

The integrated result for axis.

See also

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

Examples

>>> from scipy import integrate
>>> 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

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