Module « scipy.integrate »

Fonction tplquad - module scipy.integrate

Signature de la fonction tplquad

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

Description

tplquad.__doc__

    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 : 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 `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 `qfun`.)
    args : tuple, optional
        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
    simpson: Integrators for sampled data
    ode: ODE integrators
    odeint: ODE integrators
    scipy.special: For coefficients and roots of orthogonal polynomials

    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)