Constants
=========

DPNP includes several constants:

.. currentmodule:: dpnp

.. autodata:: DLDeviceType

.. data:: e

    Euler's constant, base of natural logarithms, Napier's constant.

    ``e = 2.71828182845904523536028747135266249775724709369995...``

    .. rubric:: See Also

    :func:`exp` : Exponential function

    :func:`log` : Natural logarithm

    .. rubric:: References

    https://en.wikipedia.org/wiki/E_%28mathematical_constant%29


.. data:: euler_gamma

    ``γ = 0.5772156649015328606065120900824024310421...``

    .. rubric:: References

    https://en.wikipedia.org/wiki/Euler%27s_constant


.. data:: inf

    IEEE 754 floating point representation of (positive) infinity.

    .. rubric:: Returns

    y : float
        A floating point representation of positive infinity.

    .. rubric:: See Also

    :func:`isinf` : Shows which elements are positive or negative infinity

    :func:`isposinf` : Shows which elements are positive infinity

    :func:`isneginf` : Shows which elements are negative infinity

    :func:`isnan` : Shows which elements are Not a Number

    :func:`isfinite` : Shows which elements are finite (not one of Not a Number,
    positive infinity and negative infinity)

    .. rubric:: Notes

    DPNP uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.
    Also that positive infinity is not equivalent to negative infinity. But
    infinity is equivalent to positive infinity.

    .. rubric:: Examples

    .. code-block:: python

        >>> import dpnp as np
        >>> np.inf
        inf
        >>> np.array([1]) / 0.0
        array([inf])


.. data:: nan

    IEEE 754 floating point representation of Not a Number (NaN).

    .. rubric:: Returns

    y : A floating point representation of Not a Number.

    .. rubric:: See Also

    :func:`isnan` : Shows which elements are Not a Number

    :func:`isfinite` : Shows which elements are finite (not one of Not a Number,
    positive infinity and negative infinity)

    .. rubric:: Notes

    DPNP uses the IEEE Standard for Binary Floating-Point for Arithmetic
    (IEEE 754). This means that Not a Number is not equivalent to infinity.

    .. rubric:: Examples

    .. code-block:: python

        >>> import dpnp as np
        >>> np.nan
        nan
        >>> np.log(np.array(-1))
        array(nan)
        >>> np.log(np.array([-1, 1, 2]))
        array([       nan, 0.        , 0.69314718])


.. data:: newaxis

    A convenient alias for *None*, useful for indexing arrays.

    .. rubric:: Examples

    .. code-block:: python

        >>> import dpnp as np
        >>> np.newaxis is None
        True
        >>> x = np.arange(3)
        >>> x
        array([0, 1, 2])
        >>> x[:, np.newaxis]
        array([[0],
               [1],
               [2]])
        >>> x[:, np.newaxis, np.newaxis]
        array([[[0]],
               [[1]],
               [[2]]])
        >>> x[:, np.newaxis] * x
        array([[0, 0, 0],
               [0, 1, 2],
               [0, 2, 4]])

        Outer product, same as ``outer(x, y)``:

        >>> y = np.arange(3, 6)
        >>> x[:, np.newaxis] * y
        array([[ 0,  0,  0],
            [ 3,  4,  5],
            [ 6,  8, 10]])

        ``x[np.newaxis, :]`` is equivalent to ``x[np.newaxis]`` and ``x[None]``:

        >>> x[np.newaxis, :].shape
        (1, 3)
        >>> x[np.newaxis].shape
        (1, 3)
        >>> x[None].shape
        (1, 3)
        >>> x[:, np.newaxis].shape
        (3, 1)


.. data:: pi

    ``pi = 3.1415926535897932384626433...``

    .. rubric:: References

    https://en.wikipedia.org/wiki/Pi