File size: 4,543 Bytes
9c6594c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 |
from sympy.core.function import Add, ArgumentIndexError, Function
from sympy.core.power import Pow
from sympy.core.singleton import S
from sympy.core.sorting import default_sort_key
from sympy.core.sympify import sympify
from sympy.functions.elementary.exponential import exp, log
from sympy.functions.elementary.miscellaneous import Max, Min
from .ast import Token, none
def _logaddexp(x1, x2, *, evaluate=True):
return log(Add(exp(x1, evaluate=evaluate), exp(x2, evaluate=evaluate), evaluate=evaluate))
_two = S.One*2
_ln2 = log(_two)
def _lb(x, *, evaluate=True):
return log(x, evaluate=evaluate)/_ln2
def _exp2(x, *, evaluate=True):
return Pow(_two, x, evaluate=evaluate)
def _logaddexp2(x1, x2, *, evaluate=True):
return _lb(Add(_exp2(x1, evaluate=evaluate),
_exp2(x2, evaluate=evaluate), evaluate=evaluate))
class logaddexp(Function):
""" Logarithm of the sum of exponentiations of the inputs.
Helper class for use with e.g. numpy.logaddexp
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.logaddexp.html
"""
nargs = 2
def __new__(cls, *args):
return Function.__new__(cls, *sorted(args, key=default_sort_key))
def fdiff(self, argindex=1):
"""
Returns the first derivative of this function.
"""
if argindex == 1:
wrt, other = self.args
elif argindex == 2:
other, wrt = self.args
else:
raise ArgumentIndexError(self, argindex)
return S.One/(S.One + exp(other-wrt))
def _eval_rewrite_as_log(self, x1, x2, **kwargs):
return _logaddexp(x1, x2)
def _eval_evalf(self, *args, **kwargs):
return self.rewrite(log).evalf(*args, **kwargs)
def _eval_simplify(self, *args, **kwargs):
a, b = (x.simplify(**kwargs) for x in self.args)
candidate = _logaddexp(a, b)
if candidate != _logaddexp(a, b, evaluate=False):
return candidate
else:
return logaddexp(a, b)
class logaddexp2(Function):
""" Logarithm of the sum of exponentiations of the inputs in base-2.
Helper class for use with e.g. numpy.logaddexp2
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.logaddexp2.html
"""
nargs = 2
def __new__(cls, *args):
return Function.__new__(cls, *sorted(args, key=default_sort_key))
def fdiff(self, argindex=1):
"""
Returns the first derivative of this function.
"""
if argindex == 1:
wrt, other = self.args
elif argindex == 2:
other, wrt = self.args
else:
raise ArgumentIndexError(self, argindex)
return S.One/(S.One + _exp2(other-wrt))
def _eval_rewrite_as_log(self, x1, x2, **kwargs):
return _logaddexp2(x1, x2)
def _eval_evalf(self, *args, **kwargs):
return self.rewrite(log).evalf(*args, **kwargs)
def _eval_simplify(self, *args, **kwargs):
a, b = (x.simplify(**kwargs).factor() for x in self.args)
candidate = _logaddexp2(a, b)
if candidate != _logaddexp2(a, b, evaluate=False):
return candidate
else:
return logaddexp2(a, b)
class amin(Token):
""" Minimum value along an axis.
Helper class for use with e.g. numpy.amin
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.amin.html
"""
__slots__ = _fields = ('array', 'axis')
defaults = {'axis': none}
_construct_axis = staticmethod(sympify)
class amax(Token):
""" Maximum value along an axis.
Helper class for use with e.g. numpy.amax
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.amax.html
"""
__slots__ = _fields = ('array', 'axis')
defaults = {'axis': none}
_construct_axis = staticmethod(sympify)
class maximum(Function):
""" Element-wise maximum of array elements.
Helper class for use with e.g. numpy.maximum
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.maximum.html
"""
def _eval_rewrite_as_Max(self, *args):
return Max(*self.args)
class minimum(Function):
""" Element-wise minimum of array elements.
Helper class for use with e.g. numpy.minimum
See Also
========
https://numpy.org/doc/stable/reference/generated/numpy.minimum.html
"""
def _eval_rewrite_as_Min(self, *args):
return Min(*self.args)
|