Module « scipy.integrate »

Fonction dblquad - module scipy.integrate

Signature de la fonction dblquad

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

Description

dblquad.__doc__

    Compute a double integral.

    Return the double (definite) integral of ``func(y, x)`` from ``x = a..b``
    and ``y = gfun(x)..hfun(x)``.

    Parameters
    ----------
    func : callable
        A Python function or method of at least two variables: y must be the
        first argument and x the second argument.
    a, b : float
        The limits of integration in x: `a` < `b`
    gfun : callable 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 : callable or float
        The upper boundary curve in y (same requirements as `gfun`).
    args : sequence, optional
        Extra arguments to pass to `func`.
    epsabs : float, optional
        Absolute tolerance passed directly to the inner 1-D quadrature
        integration. Default is 1.49e-8. `dblquad`` tries to obtain
        an accuracy of ``abs(i-result) <= max(epsabs, epsrel*abs(i))``
        where ``i`` = inner integral of ``func(y, x)`` from ``gfun(x)``
        to ``hfun(x)``, and ``result`` is the numerical approximation.
        See `epsrel` below.
    epsrel : float, optional
        Relative tolerance of the inner 1-D integrals. Default is 1.49e-8.
        If ``epsabs <= 0``, `epsrel` must be greater than both 5e-29
        and ``50 * (machine epsilon)``. See `epsabs` above.

    Returns
    -------
    y : float
        The resultant integral.
    abserr : float
        An estimate of the error.

    See also
    --------
    quad : single integral
    tplquad : triple integral
    nquad : N-dimensional integrals
    fixed_quad : fixed-order Gaussian quadrature
    quadrature : adaptive Gaussian quadrature
    odeint : ODE integrator
    ode : ODE integrator
    simpson : integrator for sampled data
    romb : integrator for sampled data
    scipy.special : for coefficients and roots of orthogonal polynomials

    Examples
    --------

    Compute the double integral of ``x * y**2`` over the box
    ``x`` ranging from 0 to 2 and ``y`` ranging from 0 to 1.

    >>> from scipy import integrate
    >>> f = lambda y, x: x*y**2
    >>> integrate.dblquad(f, 0, 2, lambda x: 0, lambda x: 1)
        (0.6666666666666667, 7.401486830834377e-15)