Function isclose

numpy/_core/numeric.py:2320–2448

Returns a boolean array where two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolut

(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False)

@array_function_dispatch(_isclose_dispatcher)
def isclose(a, b, rtol=1.e-5, atol=1.e-8, equal_nan=False):
    """
    Returns a boolean array where two arrays are element-wise equal within a
    tolerance.

    The tolerance values are positive, typically very small numbers.  The
    relative difference (`rtol` * abs(`b`)) and the absolute difference
    `atol` are added together to compare against the absolute difference
    between `a` and `b`.

    .. warning:: The default `atol` is not appropriate for comparing numbers
                 with magnitudes much smaller than one (see Notes).

    Parameters
    ----------
    a, b : array_like
        Input arrays to compare.
    rtol : array_like
        The relative tolerance parameter (see Notes).
    atol : array_like
        The absolute tolerance parameter (see Notes).
    equal_nan : bool
        Whether to compare NaN's as equal.  If True, NaN's in `a` will be
        considered equal to NaN's in `b` in the output array.

    Returns
    -------
    y : array_like
        Returns a boolean array of where `a` and `b` are equal within the
        given tolerance. If both `a` and `b` are scalars, returns a single
        boolean value.

    See Also
    --------
    allclose
    math.isclose

    Notes
    -----
    For finite values, isclose uses the following equation to test whether
    two floating point values are equivalent.::

     absolute(a - b) <= (atol + rtol * absolute(b))

    Unlike the built-in `math.isclose`, the above equation is not symmetric
    in `a` and `b` -- it assumes `b` is the reference value -- so that
    `isclose(a, b)` might be different from `isclose(b, a)`.

    The default value of `atol` is not appropriate when the reference value
    `b` has magnitude smaller than one. For example, it is unlikely that
    ``a = 1e-9`` and ``b = 2e-9`` should be considered "close", yet
    ``isclose(1e-9, 2e-9)`` is ``True`` with default settings. Be sure
    to select `atol` for the use case at hand, especially for defining the
    threshold below which a non-zero value in `a` will be considered "close"
    to a very small or zero value in `b`.

    `isclose` is not defined for non-numeric data types.
    :class:`bool` is considered a numeric data-type for this purpose.