scipy.integrate.tplquad

scipy.integrate.tplquad(func, a, b, gfun, hfun, qfun, rfun, args=(), epsabs=1.49e-08, epsrel=1.49e-08)

Compute a triple (definite) integral.

Return the triple integral of func(z, y, x) from x = a..b, y = gfun(x)..hfun(x), and z = qfun(x,y)..rfun(x,y).

Parameters :

func : function

A Python function or method of at least three variables in the order (z, y, x).

(a,b) : tuple

The limits of integration in x: a < b

gfun : function

The lower boundary curve in y which is a function taking a single floating point argument (x) and returning a floating point result: a lambda function can be useful here.

hfun : function

The upper boundary curve in y (same requirements as gfun).

qfun : function

The lower boundary surface in z. It must be a function that takes two floats in the order (x, y) and returns a float.

rfun : function

The upper boundary surface in z. (Same requirements as qfun.)

args : Arguments

Extra arguments to pass to func.

epsabs : float, optional

Absolute tolerance passed directly to the innermost 1-D quadrature integration. Default is 1.49e-8.

epsrel : float, optional

Relative tolerance of the innermost 1-D integrals. Default is 1.49e-8.

Returns :

y : float

The resultant integral.

abserr : float

An estimate of the error.

See also

quad

Adaptive quadrature using QUADPACK

quadrature

Adaptive Gaussian quadrature

fixed_quad

Fixed-order Gaussian quadrature

dblquad

Double integrals

nquad

N-dimensional integrals

romb

Integrators for sampled data

simps

Integrators for sampled data

ode

ODE integrators

odeint

ODE integrators

scipy.special

For coefficients and roots of orthogonal polynomials