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Module « numpy.matlib »

Fonction allclose - module numpy.matlib

Signature de la fonction allclose

def allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False) 

Description

help(numpy.matlib.allclose)

Returns True if 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).

NaNs are treated as equal if they are in the same place and if
``equal_nan=True``.  Infs are treated as equal if they are in the same
place and of the same sign in both arrays.

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
-------
allclose : bool
    Returns True if the two arrays are equal within the given
    tolerance; False otherwise.

See Also
--------
isclose, all, any, equal

Notes
-----
If the following equation is element-wise True, then allclose returns
True.::

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

The above equation is not symmetric in `a` and `b`, so that
``allclose(a, b)`` might be different from ``allclose(b, a)`` in
some rare cases.

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
``allclose(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`.

The comparison of `a` and `b` uses standard broadcasting, which
means that `a` and `b` need not have the same shape in order for
``allclose(a, b)`` to evaluate to True.  The same is true for
`equal` but not `array_equal`.

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

Examples
--------
>>> import numpy as np
>>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])
False

>>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])
True

>>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])
False

>>> np.allclose([1.0, np.nan], [1.0, np.nan])
False

>>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
True

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