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"""
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=========
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Constants
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=========
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.. currentmodule:: numpy
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NumPy includes several constants:
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%(constant_list)s
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"""
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#
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# Note: the docstring is autogenerated.
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#
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import re
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import textwrap
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# Maintain same format as in numpy.add_newdocs
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constants = []
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def add_newdoc(module, name, doc):
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|
constants.append((name, doc))
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add_newdoc('numpy', 'pi',
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|
"""
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|
``pi = 3.1415926535897932384626433...``
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References
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----------
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https://en.wikipedia.org/wiki/Pi
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""")
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add_newdoc('numpy', 'e',
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"""
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|
Euler's constant, base of natural logarithms, Napier's constant.
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``e = 2.71828182845904523536028747135266249775724709369995...``
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See Also
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|
--------
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exp : Exponential function
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log : Natural logarithm
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References
|
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|
----------
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|
https://en.wikipedia.org/wiki/E_%28mathematical_constant%29
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""")
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add_newdoc('numpy', 'euler_gamma',
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"""
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|
``γ = 0.5772156649015328606065120900824024310421...``
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References
|
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|
----------
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|
https://en.wikipedia.org/wiki/Euler-Mascheroni_constant
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|
""")
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|
add_newdoc('numpy', 'inf',
|
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|
|
"""
|
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|
|
IEEE 754 floating point representation of (positive) infinity.
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|
Returns
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|
-------
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|
|
y : float
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|
|
|
|
A floating point representation of positive infinity.
|
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|
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|
|
See Also
|
|
|
|
|
|
--------
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|
|
isinf : Shows which elements are positive or negative infinity
|
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|
isposinf : Shows which elements are positive infinity
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|
|
isneginf : Shows which elements are negative infinity
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|
|
isnan : Shows which elements are Not a Number
|
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|
isfinite : Shows which elements are finite (not one of Not a Number,
|
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|
|
positive infinity and negative infinity)
|
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|
|
|
|
|
|
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.
|
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|
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|
|
Also that positive infinity is not equivalent to negative infinity. But
|
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|
|
infinity is equivalent to positive infinity.
|
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|
|
`Inf`, `Infinity`, `PINF` and `infty` are aliases for `inf`.
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|
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|
|
Examples
|
|
|
|
|
|
--------
|
|
|
|
|
|
>>> np.inf
|
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|
|
inf
|
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|
|
|
>>> np.array([1]) / 0.
|
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|
|
array([ Inf])
|
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|
|
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|
|
""")
|
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|
|
|
|
|
|
add_newdoc('numpy', 'nan',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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])
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'newaxis',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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)
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'NZERO',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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])
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'PZERO',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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])
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'NAN',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'NaN',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'NINF',
|
|
|
|
|
|
"""
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|
|
|
|
""")
|
|
|
|
|
|
|
|
|
|
|
|
add_newdoc('numpy', 'PINF',
|
|
|
|
|
|
"""
|
|
|
|
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IEEE 754 floating point representation of (positive) infinity.
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Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
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`inf`. For more details, see `inf`.
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See Also
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--------
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inf
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""")
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add_newdoc('numpy', 'infty',
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"""
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IEEE 754 floating point representation of (positive) infinity.
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Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
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`inf`. For more details, see `inf`.
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See Also
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--------
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inf
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""")
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add_newdoc('numpy', 'Inf',
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"""
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IEEE 754 floating point representation of (positive) infinity.
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Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
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`inf`. For more details, see `inf`.
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See Also
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--------
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inf
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""")
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add_newdoc('numpy', 'Infinity',
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"""
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IEEE 754 floating point representation of (positive) infinity.
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Use `inf` because `Inf`, `Infinity`, `PINF` and `infty` are aliases for
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`inf`. For more details, see `inf`.
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See Also
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--------
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inf
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""")
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if __doc__:
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constants_str = []
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constants.sort()
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for name, doc in constants:
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s = textwrap.dedent(doc).replace("\n", "\n ")
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# Replace sections by rubrics
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lines = s.split("\n")
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new_lines = []
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for line in lines:
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m = re.match(r'^(\s+)[-=]+\s*$', line)
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if m and new_lines:
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prev = textwrap.dedent(new_lines.pop())
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new_lines.append('%s.. rubric:: %s' % (m.group(1), prev))
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new_lines.append('')
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else:
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new_lines.append(line)
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s = "\n".join(new_lines)
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# Done.
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constants_str.append(""".. data:: %s\n %s""" % (name, s))
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constants_str = "\n".join(constants_str)
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__doc__ = __doc__ % dict(constant_list=constants_str)
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del constants_str, name, doc
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del line, lines, new_lines, m, s, prev
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del constants, add_newdoc
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