# scipy.integrate.romberg¶

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

Romberg integration of a callable function or method.

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.

Parameters : function : callable Function to be integrated. a : float Lower limit of integration. b : float Upper limit of integration. results : float Result of the integration.

cumtrapz
Cumulative integration for sampled data.

References

 [R1] ‘Romberg’s method’ http://en.wikipedia.org/wiki/Romberg%27s_method

Examples

Integrate a gaussian from 0,1 and compare to the error function.

```>>> from scipy.special import erf
>>> gaussian = lambda x: 1/np.sqrt(np.pi) * np.exp(-x**2)
>>> result = romberg(gaussian, 0, 1, show=True)
Romberg integration of <function vfunc at 0x101eceaa0> from [0, 1]
```
```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 2*result,erf(1)
0.84270079295 0.84270079295
```