import numbers
import re
-from collections import OrderedDict
+from collections import OrderedDict, defaultdict, Mapping
from fractions import Fraction, gcd
__all__ = [
'Expression',
- 'Symbol', 'symbols', 'symbolname', 'symbolnames',
- 'Constant',
+ 'Symbol', 'Dummy', 'symbols',
+ 'Rational',
]
if isinstance(right, Expression):
return func(left, right)
elif isinstance(right, numbers.Rational):
- right = Constant(right)
+ right = Rational(right)
return func(left, right)
return NotImplemented
return wrapper
This class implements linear expressions.
"""
- __slots__ = (
- '_coefficients',
- '_constant',
- '_symbols',
- '_dimension',
- '_hash',
- )
-
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
- if constant:
+ if constant != 0:
raise TypeError('too many arguments')
- return cls.fromstring(coefficients)
- if isinstance(coefficients, dict):
- coefficients = coefficients.items()
+ return Expression.fromstring(coefficients)
if coefficients is None:
- return Constant(constant)
- coefficients = [(symbol, coefficient)
- for symbol, coefficient in coefficients if coefficient != 0]
+ return Rational(constant)
+ if isinstance(coefficients, Mapping):
+ coefficients = coefficients.items()
+ coefficients = list(coefficients)
+ for symbol, coefficient in coefficients:
+ if not isinstance(symbol, Symbol):
+ raise TypeError('symbols must be Symbol instances')
+ if not isinstance(coefficient, numbers.Rational):
+ raise TypeError('coefficients must be rational numbers')
+ if not isinstance(constant, numbers.Rational):
+ raise TypeError('constant must be a rational number')
if len(coefficients) == 0:
- return Constant(constant)
- elif len(coefficients) == 1 and constant == 0:
+ return Rational(constant)
+ if len(coefficients) == 1 and constant == 0:
symbol, coefficient = coefficients[0]
if coefficient == 1:
- return Symbol(symbol)
+ return symbol
+ coefficients = [(symbol, Fraction(coefficient))
+ for symbol, coefficient in coefficients if coefficient != 0]
+ coefficients.sort(key=lambda item: item[0].sortkey())
self = object().__new__(cls)
- self._coefficients = {}
- for symbol, coefficient in coefficients:
- symbol = symbolname(symbol)
- if isinstance(coefficient, Constant):
- coefficient = coefficient.constant
- if not isinstance(coefficient, numbers.Rational):
- raise TypeError('coefficients must be rational numbers '
- 'or Constant instances')
- self._coefficients[symbol] = coefficient
- self._coefficients = OrderedDict(sorted(self._coefficients.items()))
- if isinstance(constant, Constant):
- constant = constant.constant
- if not isinstance(constant, numbers.Rational):
- raise TypeError('constant must be a rational number '
- 'or a Constant instance')
- self._constant = constant
+ self._coefficients = OrderedDict(coefficients)
+ self._constant = Fraction(constant)
self._symbols = tuple(self._coefficients)
self._dimension = len(self._symbols)
- self._hash = hash((tuple(self._coefficients.items()), self._constant))
return self
def coefficient(self, symbol):
- symbol = symbolname(symbol)
- try:
- return self._coefficients[symbol]
- except KeyError:
- return 0
+ if not isinstance(symbol, Symbol):
+ raise TypeError('symbol must be a Symbol instance')
+ return Rational(self._coefficients.get(symbol, 0))
__getitem__ = coefficient
def coefficients(self):
- yield from self._coefficients.items()
+ for symbol, coefficient in self._coefficients.items():
+ yield symbol, Rational(coefficient)
@property
def constant(self):
- return self._constant
+ return Rational(self._constant)
@property
def symbols(self):
return self._dimension
def __hash__(self):
- return self._hash
+ return hash((tuple(self._coefficients.items()), self._constant))
def isconstant(self):
return False
return False
def values(self):
- for symbol in self.symbols:
- yield self.coefficient(symbol)
- yield self.constant
+ for coefficient in self._coefficients.values():
+ yield Rational(coefficient)
+ yield Rational(self._constant)
def __bool__(self):
return True
@_polymorphic
def __add__(self, other):
- coefficients = dict(self.coefficients())
- for symbol, coefficient in other.coefficients():
- if symbol in coefficients:
- coefficients[symbol] += coefficient
- else:
- coefficients[symbol] = coefficient
- constant = self.constant + other.constant
+ coefficients = defaultdict(Fraction, self._coefficients)
+ for symbol, coefficient in other._coefficients.items():
+ coefficients[symbol] += coefficient
+ constant = self._constant + other._constant
return Expression(coefficients, constant)
__radd__ = __add__
@_polymorphic
def __sub__(self, other):
- coefficients = dict(self.coefficients())
- for symbol, coefficient in other.coefficients():
- if symbol in coefficients:
- coefficients[symbol] -= coefficient
- else:
- coefficients[symbol] = -coefficient
- constant = self.constant - other.constant
+ coefficients = defaultdict(Fraction, self._coefficients)
+ for symbol, coefficient in other._coefficients.items():
+ coefficients[symbol] -= coefficient
+ constant = self._constant - other._constant
return Expression(coefficients, constant)
+ @_polymorphic
def __rsub__(self, other):
- return -(self - other)
+ return other - self
- @_polymorphic
def __mul__(self, other):
- if other.isconstant():
- coefficients = dict(self.coefficients())
- for symbol in coefficients:
- coefficients[symbol] *= other.constant
- constant = self.constant * other.constant
+ if isinstance(other, numbers.Rational):
+ coefficients = ((symbol, coefficient * other)
+ for symbol, coefficient in self._coefficients.items())
+ constant = self._constant * other
return Expression(coefficients, constant)
- if isinstance(other, Expression) and not self.isconstant():
- raise ValueError('non-linear expression: '
- '{} * {}'.format(self._parenstr(), other._parenstr()))
return NotImplemented
__rmul__ = __mul__
- @_polymorphic
def __truediv__(self, other):
- if other.isconstant():
- coefficients = dict(self.coefficients())
- for symbol in coefficients:
- coefficients[symbol] = \
- Fraction(coefficients[symbol], other.constant)
- constant = Fraction(self.constant, other.constant)
+ if isinstance(other, numbers.Rational):
+ coefficients = ((symbol, coefficient / other)
+ for symbol, coefficient in self._coefficients.items())
+ constant = self._constant / other
return Expression(coefficients, constant)
- if isinstance(other, Expression):
- raise ValueError('non-linear expression: '
- '{} / {}'.format(self._parenstr(), other._parenstr()))
- return NotImplemented
-
- def __rtruediv__(self, other):
- if isinstance(other, self):
- if self.isconstant():
- constant = Fraction(other, self.constant)
- return Expression(constant=constant)
- else:
- raise ValueError('non-linear expression: '
- '{} / {}'.format(other._parenstr(), self._parenstr()))
return NotImplemented
@_polymorphic
def __eq__(self, other):
- # "normal" equality
+ # returns a boolean, not a constraint
# see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
return isinstance(other, Expression) and \
- self._coefficients == other._coefficients and \
- self.constant == other.constant
+ self._coefficients == other._coefficients and \
+ self._constant == other._constant
- @_polymorphic
def __le__(self, other):
from .polyhedra import Le
return Le(self, other)
- @_polymorphic
def __lt__(self, other):
from .polyhedra import Lt
return Lt(self, other)
- @_polymorphic
def __ge__(self, other):
from .polyhedra import Ge
return Ge(self, other)
- @_polymorphic
def __gt__(self, other):
from .polyhedra import Gt
return Gt(self, other)
- def _toint(self):
+ def scaleint(self):
lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
[value.denominator for value in self.values()])
return self * lcm
+ def subs(self, symbol, expression=None):
+ if expression is None:
+ if isinstance(symbol, Mapping):
+ symbol = symbol.items()
+ substitutions = symbol
+ else:
+ substitutions = [(symbol, expression)]
+ result = self
+ for symbol, expression in substitutions:
+ if not isinstance(symbol, Symbol):
+ raise TypeError('symbols must be Symbol instances')
+ coefficients = [(othersymbol, coefficient)
+ for othersymbol, coefficient in result._coefficients.items()
+ if othersymbol != symbol]
+ coefficient = result._coefficients.get(symbol, 0)
+ constant = result._constant
+ result = Expression(coefficients, constant) + coefficient*expression
+ return result
+
@classmethod
def _fromast(cls, node):
if isinstance(node, ast.Module) and len(node.body) == 1:
elif isinstance(node, ast.Name):
return Symbol(node.id)
elif isinstance(node, ast.Num):
- return Constant(node.n)
+ return Rational(node.n)
elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
return -cls._fromast(node.operand)
elif isinstance(node, ast.BinOp):
@classmethod
def fromstring(cls, string):
# add implicit multiplication operators, e.g. '5x' -> '5*x'
- string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
+ string = Expression._RE_NUM_VAR.sub(r'\1*\2', string)
tree = ast.parse(string, 'eval')
return cls._fromast(tree)
- def __str__(self):
+ def __repr__(self):
string = ''
- i = 0
- for symbol in self.symbols:
- coefficient = self.coefficient(symbol)
+ for i, (symbol, coefficient) in enumerate(self.coefficients()):
if coefficient == 1:
- if i == 0:
- string += symbol
- else:
- string += ' + {}'.format(symbol)
+ if i != 0:
+ string += ' + '
elif coefficient == -1:
- if i == 0:
- string += '-{}'.format(symbol)
- else:
- string += ' - {}'.format(symbol)
+ string += '-' if i == 0 else ' - '
+ elif i == 0:
+ string += '{}*'.format(coefficient)
+ elif coefficient > 0:
+ string += ' + {}*'.format(coefficient)
else:
- if i == 0:
- string += '{}*{}'.format(coefficient, symbol)
- elif coefficient > 0:
- string += ' + {}*{}'.format(coefficient, symbol)
- else:
- assert coefficient < 0
- coefficient *= -1
- string += ' - {}*{}'.format(coefficient, symbol)
- i += 1
+ string += ' - {}*'.format(-coefficient)
+ string += '{}'.format(symbol)
constant = self.constant
- if constant != 0 and i == 0:
+ if len(string) == 0:
string += '{}'.format(constant)
elif constant > 0:
string += ' + {}'.format(constant)
elif constant < 0:
- constant *= -1
- string += ' - {}'.format(constant)
- if string == '':
- string = '0'
+ string += ' - {}'.format(-constant)
return string
+ def _repr_latex_(self):
+ string = ''
+ for i, (symbol, coefficient) in enumerate(self.coefficients()):
+ if coefficient == 1:
+ if i != 0:
+ string += ' + '
+ elif coefficient == -1:
+ string += '-' if i == 0 else ' - '
+ elif i == 0:
+ string += '{}'.format(coefficient._repr_latex_().strip('$'))
+ elif coefficient > 0:
+ string += ' + {}'.format(coefficient._repr_latex_().strip('$'))
+ elif coefficient < 0:
+ string += ' - {}'.format((-coefficient)._repr_latex_().strip('$'))
+ string += '{}'.format(symbol._repr_latex_().strip('$'))
+ constant = self.constant
+ if len(string) == 0:
+ string += '{}'.format(constant._repr_latex_().strip('$'))
+ elif constant > 0:
+ string += ' + {}'.format(constant._repr_latex_().strip('$'))
+ elif constant < 0:
+ string += ' - {}'.format((-constant)._repr_latex_().strip('$'))
+ return '$${}$$'.format(string)
+
def _parenstr(self, always=False):
string = str(self)
if not always and (self.isconstant() or self.issymbol()):
else:
return '({})'.format(string)
- def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, str(self))
-
@classmethod
def fromsympy(cls, expr):
import sympy
- coefficients = {}
+ coefficients = []
constant = 0
for symbol, coefficient in expr.as_coefficients_dict().items():
coefficient = Fraction(coefficient.p, coefficient.q)
if symbol == sympy.S.One:
constant = coefficient
elif isinstance(symbol, sympy.Symbol):
- symbol = symbol.name
- coefficients[symbol] = coefficient
+ symbol = Symbol(symbol.name)
+ coefficients.append((symbol, coefficient))
else:
raise ValueError('non-linear expression: {!r}'.format(expr))
- return cls(coefficients, constant)
+ return Expression(coefficients, constant)
def tosympy(self):
import sympy
expr = 0
for symbol, coefficient in self.coefficients():
- term = coefficient * sympy.Symbol(symbol)
+ term = coefficient * sympy.Symbol(symbol.name)
expr += term
expr += self.constant
return expr
class Symbol(Expression):
- __slots__ = (
- '_name',
- '_hash',
- )
-
def __new__(cls, name):
- name = symbolname(name)
+ if not isinstance(name, str):
+ raise TypeError('name must be a string')
self = object().__new__(cls)
- self._name = name
- self._hash = hash(self._name)
+ self._name = name.strip()
+ self._coefficients = {self: Fraction(1)}
+ self._constant = Fraction(0)
+ self._symbols = (self,)
+ self._dimension = 1
return self
@property
return self._name
def __hash__(self):
- return self._hash
-
- def coefficient(self, symbol):
- symbol = symbolname(symbol)
- if symbol == self.name:
- return 1
- else:
- return 0
-
- def coefficients(self):
- yield self.name, 1
-
- @property
- def constant(self):
- return 0
+ return hash(self.sortkey())
- @property
- def symbols(self):
+ def sortkey(self):
return self.name,
- @property
- def dimension(self):
- return 1
-
def issymbol(self):
return True
def __eq__(self, other):
- return isinstance(other, Symbol) and self.name == other.name
+ return self.sortkey() == other.sortkey()
+
+ def asdummy(self):
+ return Dummy(self.name)
@classmethod
def _fromast(cls, node):
raise SyntaxError('invalid syntax')
def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, self._name)
+ return self.name
+
+ def _repr_latex_(self):
+ return '$${}$$'.format(self.name)
@classmethod
def fromsympy(cls, expr):
import sympy
- if isinstance(expr, sympy.Symbol):
- return cls(expr.name)
+ if isinstance(expr, sympy.Dummy):
+ return Dummy(expr.name)
+ elif isinstance(expr, sympy.Symbol):
+ return Symbol(expr.name)
else:
raise TypeError('expr must be a sympy.Symbol instance')
-def symbols(names):
- if isinstance(names, str):
- names = names.replace(',', ' ').split()
- return (Symbol(name) for name in names)
+class Dummy(Symbol):
+
+ _count = 0
+
+ def __new__(cls, name=None):
+ if name is None:
+ name = 'Dummy_{}'.format(Dummy._count)
+ elif not isinstance(name, str):
+ raise TypeError('name must be a string')
+ self = object().__new__(cls)
+ self._index = Dummy._count
+ self._name = name.strip()
+ self._coefficients = {self: Fraction(1)}
+ self._constant = Fraction(0)
+ self._symbols = (self,)
+ self._dimension = 1
+ Dummy._count += 1
+ return self
-def symbolname(symbol):
- if isinstance(symbol, str):
- return symbol.strip()
- elif isinstance(symbol, Symbol):
- return symbol.name
- else:
- raise TypeError('symbol must be a string or a Symbol instance')
+ def __hash__(self):
+ return hash(self.sortkey())
-def symbolnames(symbols):
- if isinstance(symbols, str):
- return symbols.replace(',', ' ').split()
- return (symbolname(symbol) for symbol in symbols)
+ def sortkey(self):
+ return self._name, self._index
+ def __repr__(self):
+ return '_{}'.format(self.name)
+
+ def _repr_latex_(self):
+ return '$${}_{{{}}}$$'.format(self.name, self._index)
+
+
+def symbols(names):
+ if isinstance(names, str):
+ names = names.replace(',', ' ').split()
+ return tuple(Symbol(name) for name in names)
-class Constant(Expression):
- __slots__ = (
- '_constant',
- '_hash',
- )
+class Rational(Expression, Fraction):
def __new__(cls, numerator=0, denominator=None):
self = object().__new__(cls)
- if denominator is None and isinstance(numerator, Constant):
- self._constant = numerator.constant
- else:
- self._constant = Fraction(numerator, denominator)
- self._hash = hash(self._constant)
+ self._coefficients = {}
+ self._constant = Fraction(numerator, denominator)
+ self._symbols = ()
+ self._dimension = 0
+ self._numerator = self._constant.numerator
+ self._denominator = self._constant.denominator
return self
def __hash__(self):
- return self._hash
-
- def coefficient(self, symbol):
- symbol = symbolname(symbol)
- return 0
-
- def coefficients(self):
- yield from []
-
- @property
- def symbols(self):
- return ()
+ return Fraction.__hash__(self)
@property
- def dimension(self):
- return 0
+ def constant(self):
+ return self
def isconstant(self):
return True
- @_polymorphic
- def __eq__(self, other):
- return isinstance(other, Constant) and self.constant == other.constant
-
def __bool__(self):
- return self.constant != 0
-
- @classmethod
- def fromstring(cls, string):
- if isinstance(string, str):
- return Constant(Fraction(string))
- else:
- raise TypeError('string must be a string instance')
+ return Fraction.__bool__(self)
def __repr__(self):
- if self.constant.denominator == 1:
- return '{}({!r})'.format(self.__class__.__name__,
- self.constant.numerator)
+ if self.denominator == 1:
+ return '{!r}'.format(self.numerator)
+ else:
+ return '{!r}/{!r}'.format(self.numerator, self.denominator)
+
+ def _repr_latex_(self):
+ if self.denominator == 1:
+ return '$${}$$'.format(self.numerator)
+ elif self.numerator < 0:
+ return '$$-\\frac{{{}}}{{{}}}$$'.format(-self.numerator,
+ self.denominator)
else:
- return '{}({!r}, {!r})'.format(self.__class__.__name__,
- self.constant.numerator, self.constant.denominator)
+ return '$$\\frac{{{}}}{{{}}}$$'.format(self.numerator,
+ self.denominator)
@classmethod
def fromsympy(cls, expr):
import sympy
if isinstance(expr, sympy.Rational):
- return cls(expr.p, expr.q)
+ return Rational(expr.p, expr.q)
elif isinstance(expr, numbers.Rational):
- return cls(expr)
+ return Rational(expr)
else:
raise TypeError('expr must be a sympy.Rational instance')
projects / linpy.git / blobdiff