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romberg(function, a, b, args=(), tol=1.48e-08, rtol=1.48e-08, show=False, divmax=10, vec_func=False)

Returns the integral of function (a function of one variable) over the interval (a, b).

If show is 1, the triangular array of the intermediate results will be printed. If vec_func is True (default is False), then function is assumed to support vector arguments.

Other Parameters

args : tuple, optional

Extra arguments to pass to function. Each element of args will be passed as a single argument to func. Default is to pass no extra arguments.

tol, rtol : float, optional

The desired absolute and relative tolerances. Defaults are 1.48e-8.

show : bool, optional

Whether to print the results. Default is False.

divmax : int, optional

Maximum order of extrapolation. Default is 10.

vec_func : bool, optional

Whether func handles arrays as arguments (i.e., whether it is a "vector" function). Default is False.

Parameters

function : callable

Function to be integrated.

a : float

Lower limit of integration.

b : float

Upper limit of integration.

Returns

results : float

Result of the integration.

Romberg integration of a callable function or method.

See Also

cumulative_trapezoid

Cumulative integration for sampled data.

dblquad

Double integrals.

fixed_quad

Fixed-order Gaussian quadrature.

ode

ODE integrator.

odeint

ODE integrator.

quad

Adaptive quadrature using QUADPACK.

romb

Integrators for sampled data.

simpson

Integrators for sampled data.

tplquad

Triple integrals.

Examples

Integrate a gaussian from 0 to 1 and compare to the error function.
from scipy import integrate
from scipy.special import erf
import numpy as np
gaussian = lambda x: 1/np.sqrt(np.pi) * np.exp(-x**2)
result = integrate.romberg(gaussian, 0, 1, show=True)
::
Steps StepSize Results 1 1.000000 0.385872 2 0.500000 0.412631 0.421551 4 0.250000 0.419184 0.421368 0.421356 8 0.125000 0.420810 0.421352 0.421350 0.421350 16 0.062500 0.421215 0.421350 0.421350 0.421350 0.421350 32 0.031250 0.421317 0.421350 0.421350 0.421350 0.421350 0.421350
The final result is 0.421350396475 after 33 function evaluations.
print("%g %g" % (2*result, erf(1)))
See :

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quadquadodeodescipy.integrate._quadpack_py:tplquad_quadpack_py:tplquadscipy.integrate._quadpack_py:dblquad_quadpack_py:dblquadscipy.integrate._quadrature:cumulative_trapezoid_quadrature:cumulative_trapezoidrombrombsimpsonsimpsonscipy.integrate._quadrature:fixed_quad_quadrature:fixed_quadodeintodeint

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GitHub : /scipy/integrate/_quadrature.py#848
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