scipy.integrate.romb

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

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

romberg

adaptive Romberg quadrature

quadrature

adaptive Gaussian quadrature

fixed_quad

fixed-order Gaussian quadrature

dblquad

double integrals

tplquad

triple integrals

simpson

integrators for sampled data

cumulative_trapezoid

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