Module « scipy.integrate »

Fonction quadrature - module scipy.integrate

Signature de la fonction quadrature

def quadrature(func, a, b, args=(), tol=1.49e-08, rtol=1.49e-08, maxiter=50, vec_func=True, miniter=1) 

Description

quadrature.__doc__

    Compute a definite integral using fixed-tolerance Gaussian quadrature.

    Integrate `func` from `a` to `b` using Gaussian quadrature
    with absolute tolerance `tol`.

    Parameters
    ----------
    func : function
        A Python function or method to integrate.
    a : float
        Lower limit of integration.
    b : float
        Upper limit of integration.
    args : tuple, optional
        Extra arguments to pass to function.
    tol, rtol : float, optional
        Iteration stops when error between last two iterates is less than
        `tol` OR the relative change is less than `rtol`.
    maxiter : int, optional
        Maximum order of Gaussian quadrature.
    vec_func : bool, optional
        True or False if func handles arrays as arguments (is
        a "vector" function). Default is True.
    miniter : int, optional
        Minimum order of Gaussian quadrature.

    Returns
    -------
    val : float
        Gaussian quadrature approximation (within tolerance) to integral.
    err : float
        Difference between last two estimates of the integral.

    See also
    --------
    romberg: adaptive Romberg quadrature
    fixed_quad: fixed-order Gaussian quadrature
    quad: adaptive quadrature using QUADPACK
    dblquad: double integrals
    tplquad: triple integrals
    romb: integrator for sampled data
    simpson: integrator for sampled data
    cumulative_trapezoid: cumulative integration for sampled data
    ode: ODE integrator
    odeint: ODE integrator

    Examples
    --------
    >>> from scipy import integrate
    >>> f = lambda x: x**8
    >>> integrate.quadrature(f, 0.0, 1.0)
    (0.11111111111111106, 4.163336342344337e-17)
    >>> print(1/9.0)  # analytical result
    0.1111111111111111

    >>> integrate.quadrature(np.cos, 0.0, np.pi/2)
    (0.9999999999999536, 3.9611425250996035e-11)
    >>> np.sin(np.pi/2)-np.sin(0)  # analytical result
    1.0