scipy.integrate.quad

scipy.integrate.quad(func, a, b, args=(), full_output=0, epsabs=1.4899999999999999e-08, epsrel=1.4899999999999999e-08, limit=50, points=None, weight=None, wvar=None, wopts=None, maxp1=50, limlst=50)

Compute a definite integral.

Integrate func from a to b (possibly infinite interval) using a technique from the Fortran library QUADPACK.

If func takes many arguments, it is integrated along the axis corresponding to the first argument. Use the keyword argument args to pass the other arguments.

Run scipy.integrate.quad_explain() for more information on the more esoteric inputs and outputs.

Parameters :

func : function

A Python function or method to integrate.

a : float

Lower limit of integration (use -scipy.integrate.Inf for -infinity).

b : float

Upper limit of integration (use scipy.integrate.Inf for +infinity).

args : tuple, optional

extra arguments to pass to func

full_output : int

Non-zero to return a dictionary of integration information. If non-zero, warning messages are also suppressed and the message is appended to the output tuple.

Returns :

y : float

The integral of func from a to b.

abserr : float

an estimate of the absolute error in the result.

infodict : dict

a dictionary containing additional information. Run scipy.integrate.quad_explain() for more information.

message : :

a convergence message.

explain : :

appended only with ‘cos’ or ‘sin’ weighting and infinite integration limits, it contains an explanation of the codes in infodict[‘ierlst’]

Examples

Calculate and compare with an analytic result

>>> from scipy import integrate
>>> x2 = lambda x: x**2
>>> integrate.quad(x,0.,4.)
(21.333333333333332, 2.3684757858670003e-13)
>> print 4.**3/3
21.3333333333

Calculate

>>> invexp = lambda x: exp(-x)
>>> integrate.quad(invexp,0,inf)
(0.99999999999999989, 5.8426061711142159e-11)

>>> f = lambda x,a : a*x
>>> y, err = integrate.quad(f, 0, 1, args=(1,))
>>> y
0.5
>>> y, err = integrate.quad(f, 0, 1, args=(3,))
>>> y
1.5