constants.py

"""
=========
Constants
=========

.. currentmodule:: numpy

NumPy includes several constants:

%(constant_list)s
"""
#
# Note: the docstring is autogenerated.
#
import re
import textwrap

# Maintain same format as in numpy.add_newdocs
constants = []
def add_newdoc(module, name, doc):
    constants.append((name, doc))

add_newdoc('numpy', 'pi',
    """
    ``pi = 3.1415926535897932384626433...``

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

    """)

add_newdoc('numpy', 'e',
    """
    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

    """)

add_newdoc('numpy', 'euler_gamma',
    """
    ``γ = 0.5772156649015328606065120900824024310421...``

    References
    ----------
    https://en.wikipedia.org/wiki/Euler-Mascheroni_constant

    """)

add_newdoc('numpy', 'inf',
    """
    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])

    """)

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',
    """
    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

    """)

add_newdoc('numpy', 'infty',
    """
    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

    """)

add_newdoc('numpy', 'Inf',
    """
    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

    """)

add_newdoc('numpy', 'Infinity',
    """
    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

    """)


if __doc__:
    constants_str = []
    constants.sort()
    for name, doc in constants:
        s = textwrap.dedent(doc).replace("\n", "\n    ")

        # Replace sections by rubrics
        lines = s.split("\n")
        new_lines = []
        for line in lines:
            m = re.match(r'^(\s+)[-=]+\s*$', line)
            if m and new_lines:
                prev = textwrap.dedent(new_lines.pop())
                new_lines.append('%s.. rubric:: %s' % (m.group(1), prev))
                new_lines.append('')
            else:
                new_lines.append(line)
        s = "\n".join(new_lines)

        # Done.
        constants_str.append(""".. data:: %s\n    %s""" % (name, s))
    constants_str = "\n".join(constants_str)

    __doc__ = __doc__ % dict(constant_list=constants_str)
    del constants_str, name, doc
    del line, lines, new_lines, m, s, prev

del constants, add_newdoc