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

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 : float

The limits of integration in x: a < b

gfun : function or float

The lower boundary curve in y which is a function taking a single floating point argument (x) and returning a floating point result or a float indicating a constant boundary curve.

hfun : function or float

The upper boundary curve in y (same requirements as :None:None:`gfun`).

qfun : function or float

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

rfun : function or float

The upper boundary surface in z. (Same requirements as :None:None:`qfun`.)

args : tuple, optional

Extra arguments to pass to :None:None:`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.

Compute a triple (definite) integral.

See Also

dblquad

Double integrals

fixed_quad

Fixed-order Gaussian quadrature

nquad

N-dimensional integrals

ode

ODE integrators

odeint

ODE integrators

quad

Adaptive quadrature using QUADPACK

quadrature

Adaptive Gaussian quadrature

romb

Integrators for sampled data

scipy.special

For coefficients and roots of orthogonal polynomials

simpson

Integrators for sampled data

Examples

Compute the triple integral of x * y * z , over x ranging from 1 to 2, y ranging from 2 to 3, z ranging from 0 to 1.

>>> from scipy import integrate
... f = lambda z, y, x: x*y*z
... integrate.tplquad(f, 1, 2, lambda x: 2, lambda x: 3,
...                   lambda x, y: 0, lambda x, y: 1)
(1.8750000000000002, 3.324644794257407e-14)

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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