+++ /dev/null
-import ast
-import functools
-import numbers
-import re
-
-from collections import OrderedDict
-from fractions import Fraction, gcd
-
-
-__all__ = [
- 'Expression',
- 'Symbol', 'symbols', 'symbolname', 'symbolnames',
- 'Constant',
-]
-
-
-def _polymorphic(func):
- @functools.wraps(func)
- def wrapper(left, right):
- if isinstance(right, Expression):
- return func(left, right)
- elif isinstance(right, numbers.Rational):
- right = Constant(right)
- return func(left, right)
- return NotImplemented
- return wrapper
-
-
-class Expression:
- """
- This class implements linear expressions.
- """
-
- __slots__ = (
- '_coefficients',
- '_constant',
- '_symbols',
- '_dimension',
- '_hash',
- )
-
- def __new__(cls, coefficients=None, constant=0):
- if isinstance(coefficients, str):
- if constant:
- raise TypeError('too many arguments')
- return cls.fromstring(coefficients)
- if isinstance(coefficients, dict):
- coefficients = coefficients.items()
- if coefficients is None:
- return Constant(constant)
- coefficients = [(symbol, coefficient)
- for symbol, coefficient in coefficients if coefficient != 0]
- if len(coefficients) == 0:
- return Constant(constant)
- elif len(coefficients) == 1 and constant == 0:
- symbol, coefficient = coefficients[0]
- if coefficient == 1:
- return Symbol(symbol)
- 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._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
-
- __getitem__ = coefficient
-
- def coefficients(self):
- yield from self._coefficients.items()
-
- @property
- def constant(self):
- return self._constant
-
- @property
- def symbols(self):
- return self._symbols
-
- @property
- def dimension(self):
- return self._dimension
-
- def __hash__(self):
- return self._hash
-
- def isconstant(self):
- return False
-
- def issymbol(self):
- return False
-
- def values(self):
- for symbol in self.symbols:
- yield self.coefficient(symbol)
- yield self.constant
-
- def __bool__(self):
- return True
-
- def __pos__(self):
- return self
-
- def __neg__(self):
- return self * -1
-
- @_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
- 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
- return Expression(coefficients, constant)
-
- def __rsub__(self, other):
- return -(self - other)
-
- @_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
- 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)
- 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
- # 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
-
- @_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):
- lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
- [value.denominator for value in self.values()])
- return self * lcm
-
- @classmethod
- def _fromast(cls, node):
- if isinstance(node, ast.Module) and len(node.body) == 1:
- return cls._fromast(node.body[0])
- elif isinstance(node, ast.Expr):
- return cls._fromast(node.value)
- elif isinstance(node, ast.Name):
- return Symbol(node.id)
- elif isinstance(node, ast.Num):
- return Constant(node.n)
- elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
- return -cls._fromast(node.operand)
- elif isinstance(node, ast.BinOp):
- left = cls._fromast(node.left)
- right = cls._fromast(node.right)
- if isinstance(node.op, ast.Add):
- return left + right
- elif isinstance(node.op, ast.Sub):
- return left - right
- elif isinstance(node.op, ast.Mult):
- return left * right
- elif isinstance(node.op, ast.Div):
- return left / right
- raise SyntaxError('invalid syntax')
-
- _RE_NUM_VAR = re.compile(r'(\d+|\))\s*([^\W\d_]\w*|\()')
-
- @classmethod
- def fromstring(cls, string):
- # add implicit multiplication operators, e.g. '5x' -> '5*x'
- string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
- tree = ast.parse(string, 'eval')
- return cls._fromast(tree)
-
- def __str__(self):
- string = ''
- i = 0
- for symbol in self.symbols:
- coefficient = self.coefficient(symbol)
- if coefficient == 1:
- if i == 0:
- string += symbol
- else:
- string += ' + {}'.format(symbol)
- elif coefficient == -1:
- if i == 0:
- string += '-{}'.format(symbol)
- else:
- string += ' - {}'.format(symbol)
- 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
- constant = self.constant
- if constant != 0 and i == 0:
- string += '{}'.format(constant)
- elif constant > 0:
- string += ' + {}'.format(constant)
- elif constant < 0:
- constant *= -1
- string += ' - {}'.format(constant)
- if string == '':
- string = '0'
- return string
-
- def _parenstr(self, always=False):
- string = str(self)
- if not always and (self.isconstant() or self.issymbol()):
- return string
- else:
- return '({})'.format(string)
-
- def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, str(self))
-
- @classmethod
- def fromsympy(cls, expr):
- import sympy
- 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
- else:
- raise ValueError('non-linear expression: {!r}'.format(expr))
- return cls(coefficients, constant)
-
- def tosympy(self):
- import sympy
- expr = 0
- for symbol, coefficient in self.coefficients():
- term = coefficient * sympy.Symbol(symbol)
- expr += term
- expr += self.constant
- return expr
-
-
-class Symbol(Expression):
-
- __slots__ = (
- '_name',
- '_hash',
- )
-
- def __new__(cls, name):
- name = symbolname(name)
- self = object().__new__(cls)
- self._name = name
- self._hash = hash(self._name)
- return self
-
- @property
- def name(self):
- 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
-
- @property
- def symbols(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
-
- @classmethod
- def _fromast(cls, node):
- if isinstance(node, ast.Module) and len(node.body) == 1:
- return cls._fromast(node.body[0])
- elif isinstance(node, ast.Expr):
- return cls._fromast(node.value)
- elif isinstance(node, ast.Name):
- return Symbol(node.id)
- raise SyntaxError('invalid syntax')
-
- def __repr__(self):
- return '{}({!r})'.format(self.__class__.__name__, self._name)
-
- @classmethod
- def fromsympy(cls, expr):
- import sympy
- if isinstance(expr, sympy.Symbol):
- return cls(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)
-
-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 symbolnames(symbols):
- if isinstance(symbols, str):
- return symbols.replace(',', ' ').split()
- return (symbolname(symbol) for symbol in symbols)
-
-
-class Constant(Expression):
-
- __slots__ = (
- '_constant',
- '_hash',
- )
-
- 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)
- 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 ()
-
- @property
- def dimension(self):
- return 0
-
- 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')
-
- def __repr__(self):
- if self.constant.denominator == 1:
- return '{}({!r})'.format(self.__class__.__name__,
- self.constant.numerator)
- else:
- return '{}({!r}, {!r})'.format(self.__class__.__name__,
- self.constant.numerator, self.constant.denominator)
-
- @classmethod
- def fromsympy(cls, expr):
- import sympy
- if isinstance(expr, sympy.Rational):
- return cls(expr.p, expr.q)
- elif isinstance(expr, numbers.Rational):
- return cls(expr)
- else:
- raise TypeError('expr must be a sympy.Rational instance')
projects / linpy.git / blobdiff