scipy.integrate.quad¶

scipy.integrate.quad(func, a, b, args=(), full_output=0, epsabs=1.49e-08, epsrel=1.49e-08, limit=50, points=None, weight=None, wvar=None, wopts=None, maxp1=50, limlst=50)[source]¶

Compute a definite integral.

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

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

Parameters :

Parameters :	func : function A Python function or method to integrate. If func takes many arguments, it is integrated along the axis corresponding to the first argument. a : float Lower limit of integration (use -numpy.inf for -infinity). b : float Upper limit of integration (use numpy.inf for +infinity). args : tuple, optional Extra arguments to pass to func. full_output : int, optional 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’]
Other Parameters:
	epsabs : float or int, optional Absolute error tolerance. epsrel : float or int, optional Relative error tolerance. limit : float or int, optional An upper bound on the number of subintervals used in the adaptive algorithm. points : (sequence of floats,ints), optional A sequence of break points in the bounded integration interval where local difficulties of the integrand may occur (e.g., singularities, discontinuities). The sequence does not have to be sorted. weight : float or int, optional String indicating weighting function. wvar : optional Variables for use with weighting functions. wopts : optional Optional input for reusing Chebyshev moments. maxp1 : float or int, optional An upper bound on the number of Chebyshev moments. limlst : int, optional Upper bound on the number of cylces (>=3) for use with a sinusoidal weighting and an infinite end-point.

func : function

A Python function or method to integrate. If func takes many arguments, it is integrated along the axis corresponding to the first argument.

a : float

Lower limit of integration (use -numpy.inf for -infinity).

b : float

Upper limit of integration (use numpy.inf for +infinity).

args : tuple, optional

Extra arguments to pass to func.

full_output : int, optional

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’]

Other Parameters:

epsabs : float or int, optional

Absolute error tolerance.

epsrel : float or int, optional

Relative error tolerance.

limit : float or int, optional

An upper bound on the number of subintervals used in the adaptive algorithm.

points : (sequence of floats,ints), optional

A sequence of break points in the bounded integration interval where local difficulties of the integrand may occur (e.g., singularities, discontinuities). The sequence does not have to be sorted.

weight : float or int, optional

String indicating weighting function.

wvar : optional

Variables for use with weighting functions.

wopts : optional

Optional input for reusing Chebyshev moments.

maxp1 : float or int, optional

An upper bound on the number of Chebyshev moments.

limlst : int, optional

Upper bound on the number of cylces (>=3) for use with a sinusoidal weighting and an infinite end-point.

See also

dblquad: double integral
tplquad: triple integral
nquad: n-dimensional integrals (uses quad recursively)
fixed_quad: fixed-order Gaussian quadrature
quadrature: adaptive Gaussian quadrature
odeint: ODE integrator
ode: ODE integrator
simps: integrator for sampled data
romb: integrator for sampled data
scipy.special: for coefficients and roots of orthogonal polynomials

Examples

Calculate $\int^4_0 x^2 dx$ and compare with an analytic result

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

Calculate $\int^\infty_0 e^{-x} dx$

>>> invexp = lambda x: np.exp(-x)
>>> integrate.quad(invexp, 0, np.inf)
(1.0, 5.842605999138044e-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

Previous topic

scipy.integrate.complex_ode.successful

Next topic

scipy.integrate.dblquad