fixed_quad(func, a, b, args=(), n=5)

Integrate :None:None:`func` from a to b using Gaussian quadrature of order n.

Parameters

func : callable

A Python function or method to integrate (must accept vector inputs). If integrating a vector-valued function, the returned array must have shape (..., len(x)) .

a : float

Lower limit of integration.

b : float

Upper limit of integration.

args : tuple, optional

Extra arguments to pass to function, if any.

n : int, optional

Order of quadrature integration. Default is 5.

Returns

val : float

Gaussian quadrature approximation to the integral

none : None

Statically returned value of None

Compute a definite integral using fixed-order Gaussian quadrature.

See Also

cumulative_trapezoid

cumulative integration for sampled data

dblquad

double integrals

ode

ODE integrator

odeint

ODE integrator

quad

adaptive quadrature using QUADPACK

quadrature

adaptive Gaussian quadrature

romb

integrators for sampled data

romberg

adaptive Romberg quadrature

simpson

integrators for sampled data

tplquad

triple integrals

Examples

>>> from scipy import integrate
... f = lambda x: x**8
... integrate.fixed_quad(f, 0.0, 1.0, n=4)
(0.1110884353741496, None)

>>> integrate.fixed_quad(f, 0.0, 1.0, n=5)
(0.11111111111111102, None)

>>> print(1/9.0)  # analytical result
0.1111111111111111

>>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=4)
(0.9999999771971152, None)

>>> integrate.fixed_quad(np.cos, 0.0, np.pi/2, n=5)
(1.000000000039565, None)

>>> np.sin(np.pi/2)-np.sin(0)  # analytical result
1.0

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.integrate._quadrature.simpson scipy.integrate._quadpack_py.dblquad scipy.integrate._quadrature.quadrature scipy.integrate._quadrature.romb scipy.integrate._quadrature.fixed_quad scipy.integrate._quadrature.cumulative_trapezoid scipy.integrate._quadpack_py.quad scipy.integrate._quadpack_py.nquad scipy.integrate._quadrature.romberg scipy.integrate._quadpack_py.tplquad

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