Function trapz

site-packages/numpy/lib/function_base.py:3983–4070

Integrate along the given axis using the composite trapezoidal rule. Integrate `y` (`x`) along given axis. Parameters ---------- y : array_like Input array to integrate. x : array_like, optional The sample points corresponding to the `y` values. If `x` is N

(y, x=None, dx=1.0, axis=-1)

@array_function_dispatch(_trapz_dispatcher)
def trapz(y, x=None, dx=1.0, axis=-1):
    """
    Integrate along the given axis using the composite trapezoidal rule.

    Integrate `y` (`x`) along given axis.

    Parameters
    ----------
    y : array_like
        Input array to integrate.
    x : array_like, optional
        The sample points corresponding to the `y` values. If `x` is None,
        the sample points are assumed to be evenly spaced `dx` apart. The
        default is None.
    dx : scalar, optional
        The spacing between sample points when `x` is None. The default is 1.
    axis : int, optional
        The axis along which to integrate.

    Returns
    -------
    trapz : float
        Definite integral as approximated by trapezoidal rule.

    See Also
    --------
    sum, cumsum

    Notes
    -----
    Image [2]_ illustrates trapezoidal rule -- y-axis locations of points
    will be taken from `y` array, by default x-axis distances between
    points will be 1.0, alternatively they can be provided with `x` array
    or with `dx` scalar.  Return value will be equal to combined area under
    the red lines.


    References
    ----------
    .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule

    .. [2] Illustration image:
           https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png

    Examples
    --------
    >>> np.trapz([1,2,3])
    4.0
    >>> np.trapz([1,2,3], x=[4,6,8])
    8.0
    >>> np.trapz([1,2,3], dx=2)
    8.0
    >>> a = np.arange(6).reshape(2, 3)
    >>> a
    array([[0, 1, 2],
           [3, 4, 5]])
    >>> np.trapz(a, axis=0)
    array([ 1.5,  2.5,  3.5])