# -*- coding: utf-8 -*-
"""
=================================================================
Math helper functions (:mod:`sknano.core.math.extras`)
=================================================================
.. currentmodule:: sknano.core.math.extras
"""
from __future__ import absolute_import, division, print_function
from __future__ import unicode_literals
__docformat__ = 'restructuredtext en'
from fractions import gcd
import operator
import numpy as np
__all__ = ['abs_cap', 'math_functions', 'function_map',
'comparison_symbol_operator_mappings',
'math_symbol_operator_mappings',
'symbol_operator_mappings', 'operator_map',
'math_operators', 'convert_condition_str',
'totient_func']
math_functions = function_map = {}
function_map.update(dict(
abs=np.abs,
sqrt=np.sqrt,
floor=np.floor,
ceil=np.ceil,
sin=np.sin,
cos=np.cos,
tan=np.tan,
atan=np.arctan,
asin=np.arcsin,
acos=np.arccos,
sinh=np.sinh,
cosh=np.cosh,
tanh=np.tanh,
exp=np.exp,
log=np.log,
log10=np.log10))
math_operators = symbol_operator_mappings = operator_map = {}
comparison_symbol_operator_mappings = \
{'==': operator.eq,
'!=': operator.ne,
'<': operator.lt,
'<=': operator.le,
'>': operator.gt,
'>=': operator.ge,
'is': operator.is_,
'is not': operator.is_not}
operator_map.update(comparison_symbol_operator_mappings)
math_symbol_operator_mappings = \
{'+': operator.add,
'-': operator.sub,
'*': operator.mul,
'/': operator.truediv,
'//': operator.floordiv}
operator_map.update(math_symbol_operator_mappings)
[docs]def abs_cap(val, max_abs_val=1):
"""Returns the value with its absolute value capped at max_abs_val.
Modified implementation of
:func:`pymatgen:pymatgen.util.num_utils.abs_cap`.
Particularly useful in passing values to trignometric functions where
numerical errors may result in an argument > 1 being passed in.
Parameters
----------
val : :class:`~python:float`
max_abs_val : :class:`~python:float`
The maximum absolute value for val. Default=1.
Returns
-------
val if abs(val) < `max_abs_val` else sign of val * max_abs_val.
"""
return max(min(val, max_abs_val), -max_abs_val)
[docs]def convert_condition_str(obj, condition):
"""Evaluates a boolean condtion of an object attribute.
Parameters
----------
obj : :class:`~python:object`
condtion : :class:`~python:str`
Returns
-------
:class:`~python:bool`
Raises
------
:class:`~python:ValueError`
"""
try:
attr, comparison, value = condition.split()
except ValueError:
print('the condition string must be of the form:\n'
'ATTRIBUTE COMPARISON_OPERATOR VALUE')
condition = \
math_operators[comparison](getattr(obj, attr), float(value))
return condition
[docs]def totient_func(n=int):
"""Compute the totatives of :math:`n`.
Parameters
----------
n : int
Returns
-------
int : the number of totatives of :math:`n`
"""
if not isinstance(n, int) and int(n) != n:
raise ValueError('n must be an integer')
n = int(n)
tots = 0
for k in range(1, n + 1):
if gcd(n, k) == 1:
tots += 1
return tots
