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=========
Constants
=========
.. currentmodule:: numpy
NumPy includes several constants:
%(constant_list)s
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add_newdocr
s � �
���d�C�[�!�!�!�!�!� �numpy�pizv
``pi = 3.1415926535897932384626433...``
References
----------
https://en.wikipedia.org/wiki/Pi
�eaE
Euler's constant, base of natural logarithms, Napier's constant.
``e = 2.71828182845904523536028747135266249775724709369995...``
See Also
--------
exp : Exponential function
log : Natural logarithm
References
----------
https://en.wikipedia.org/wiki/E_%28mathematical_constant%29
� euler_gammau�
``γ = 0.5772156649015328606065120900824024310421...``
References
----------
https://en.wikipedia.org/wiki/Euler-Mascheroni_constant
�infa�
IEEE 754 floating point representation of (positive) infinity.
Returns
-------
y : float
A floating point representation of positive infinity.
See Also
--------
isinf : Shows which elements are positive or negative infinity
isposinf : Shows which elements are positive infinity
isneginf : Shows which elements are negative infinity
isnan : Shows which elements are Not a Number
isfinite : Shows which elements are finite (not one of Not a Number,
positive infinity and negative infinity)
Notes
-----
NumPy 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.
`Inf`, `Infinity`, `PINF` and `infty` are aliases for `inf`.
Examples
--------
>>> np.inf
inf
>>> np.array([1]) / 0.
array([ Inf])
�nana�
IEEE 754 floating point representation of Not a Number (NaN).
Returns
-------
y : A floating point representation of Not a Number.
See Also
--------
isnan : Shows which elements are Not a Number.
isfinite : Shows which elements are finite (not one of
Not a Number, positive infinity and negative infinity)
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). This means that Not a Number is not equivalent to infinity.
`NaN` and `NAN` are aliases of `nan`.
Examples
--------
>>> np.nan
nan
>>> np.log(-1)
nan
>>> np.log([-1, 1, 2])
array([ NaN, 0. , 0.69314718])
�newaxisa
A convenient alias for None, useful for indexing arrays.
Examples
--------
>>> newaxis is None
True
>>> x = np.arange(3)
>>> x
array([0, 1, 2])
>>> x[:, newaxis]
array([[0],
[1],
[2]])
>>> x[:, newaxis, newaxis]
array([[[0]],
[[1]],
[[2]]])
>>> x[:, 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[:, newaxis] * y
array([[ 0, 0, 0],
[ 3, 4, 5],
[ 6, 8, 10]])
``x[newaxis, :]`` is equivalent to ``x[newaxis]`` and ``x[None]``:
>>> x[newaxis, :].shape
(1, 3)
>>> x[newaxis].shape
(1, 3)
>>> x[None].shape
(1, 3)
>>> x[:, newaxis].shape
(3, 1)
�NZEROa�
IEEE 754 floating point representation of negative zero.
Returns
-------
y : float
A floating point representation of negative zero.
See Also
--------
PZERO : Defines positive zero.
isinf : Shows which elements are positive or negative infinity.
isposinf : Shows which elements are positive infinity.
isneginf : Shows which elements are negative infinity.
isnan : Shows which elements are Not a Number.
isfinite : Shows which elements are finite - not one of
Not a Number, positive infinity and negative infinity.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). Negative zero is considered to be a finite number.
Examples
--------
>>> np.NZERO
-0.0
>>> np.PZERO
0.0
>>> np.isfinite([np.NZERO])
array([ True])
>>> np.isnan([np.NZERO])
array([False])
>>> np.isinf([np.NZERO])
array([False])
�PZEROa�
IEEE 754 floating point representation of positive zero.
Returns
-------
y : float
A floating point representation of positive zero.
See Also
--------
NZERO : Defines negative zero.
isinf : Shows which elements are positive or negative infinity.
isposinf : Shows which elements are positive infinity.
isneginf : Shows which elements are negative infinity.
isnan : Shows which elements are Not a Number.
isfinite : Shows which elements are finite - not one of
Not a Number, positive infinity and negative infinity.
Notes
-----
NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic
(IEEE 754). Positive zero is considered to be a finite number.
Examples
--------
>>> np.PZERO
0.0
>>> np.NZERO
-0.0
>>> np.isfinite([np.PZERO])
array([ True])
>>> np.isnan([np.PZERO])
array([False])
>>> np.isinf([np.PZERO])
array([False])
�NANz�
IEEE 754 floating point representation of Not a Number (NaN).
`NaN` and `NAN` are equivalent definitions of `nan`. Please use
`nan` instead of `NAN`.
See Also
--------
nan
�NaNz�
IEEE 754 floating point representation of Not a Number (NaN).
`NaN` and `NAN` are equivalent definitions of `nan`. Please use
`nan` instead of `NaN`.
See Also
--------
nan
�NINFa�
IEEE 754 floating point representation of negative infinity.
Returns
-------
y : float
A floating point representation of negative infinity.
See Also
--------
isinf : Shows which elements are positive or negative infinity
isposinf : Shows which elements are positive infinity
isneginf : Shows which elements are negative infinity
isnan : Shows which elements are Not a Number
isfinite : Shows which elements are finite (not one of Not a Number,
positive infinity and negative infinity)
Notes
-----
NumPy 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.
Examples
--------
>>> np.NINF
-inf
>>> np.log(0)
-inf
�PINFz�
IEEE 754 floating point representation of (positive) infinity.
Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
`inf`. For more details, see `inf`.
See Also
--------
inf
�infty�Inf�Infinity�
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