Cleaner and faster linear expressions
[linpy.git] / pypol / linexprs.py
index ed68493..ccd1564 100644 (file)
@@ -3,13 +3,13 @@ import functools
 import numbers
 import re
 
-from collections import OrderedDict
+from collections import OrderedDict, defaultdict
 from fractions import Fraction, gcd
 
 
 __all__ = [
     'Expression',
-    'Symbol', 'symbols', 'symbolname', 'symbolnames',
+    'Symbol', 'symbols',
     'Constant',
 ]
 
@@ -36,37 +36,38 @@ class Expression:
         '_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()
+            return Expression.fromstring(coefficients)
         if coefficients is None:
             return Constant(constant)
+        if isinstance(coefficients, dict):
+            coefficients = coefficients.items()
+        for symbol, coefficient in coefficients:
+            if not isinstance(symbol, Symbol):
+                raise TypeError('symbols must be Symbol instances')
         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:
+        if len(coefficients) == 1 and constant == 0:
             symbol, coefficient = coefficients[0]
             if coefficient == 1:
-                return Symbol(symbol)
+                return symbol
         self = object().__new__(cls)
-        self._coefficients = {}
-        for symbol, coefficient in coefficients:
-            symbol = symbolname(symbol)
+        self._coefficients = OrderedDict()
+        for symbol, coefficient in sorted(coefficients,
+                key=lambda item: item[0].name):
             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):
@@ -75,11 +76,11 @@ class Expression:
         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)
+        if not isinstance(symbol, Symbol):
+            raise TypeError('symbol must be a Symbol instance')
         try:
             return self._coefficients[symbol]
         except KeyError:
@@ -103,7 +104,7 @@ class Expression:
         return self._dimension
 
     def __hash__(self):
-        return self._hash
+        return hash((tuple(self._coefficients.items()), self._constant))
 
     def isconstant(self):
         return False
@@ -112,8 +113,7 @@ class Expression:
         return False
 
     def values(self):
-        for symbol in self.symbols:
-            yield self.coefficient(symbol)
+        yield from self._coefficients.values()
         yield self.constant
 
     def __bool__(self):
@@ -127,12 +127,9 @@ class Expression:
 
     @_polymorphic
     def __add__(self, other):
-        coefficients = dict(self.coefficients())
+        coefficients = defaultdict(Constant, self.coefficients())
         for symbol, coefficient in other.coefficients():
-            if symbol in coefficients:
-                coefficients[symbol] += coefficient
-            else:
-                coefficients[symbol] = coefficient
+            coefficients[symbol] += coefficient
         constant = self.constant + other.constant
         return Expression(coefficients, constant)
 
@@ -140,12 +137,9 @@ class Expression:
 
     @_polymorphic
     def __sub__(self, other):
-        coefficients = dict(self.coefficients())
+        coefficients = defaultdict(Constant, self.coefficients())
         for symbol, coefficient in other.coefficients():
-            if symbol in coefficients:
-                coefficients[symbol] -= coefficient
-            else:
-                coefficients[symbol] = -coefficient
+            coefficients[symbol] -= coefficient
         constant = self.constant - other.constant
         return Expression(coefficients, constant)
 
@@ -172,9 +166,8 @@ class Expression:
         if other.isconstant():
             coefficients = dict(self.coefficients())
             for symbol in coefficients:
-                coefficients[symbol] = \
-                        Fraction(coefficients[symbol], other.constant)
-            constant = Fraction(self.constant, other.constant)
+                coefficients[symbol] = Constant(coefficients[symbol], other.constant)
+            constant = Constant(self.constant, other.constant)
             return Expression(coefficients, constant)
         if isinstance(other, Expression):
             raise ValueError('non-linear expression: '
@@ -184,8 +177,7 @@ class Expression:
     def __rtruediv__(self, other):
         if isinstance(other, self):
             if self.isconstant():
-                constant = Fraction(other, self.constant)
-                return Expression(constant=constant)
+                return Constant(other, self.constant)
             else:
                 raise ValueError('non-linear expression: '
                         '{} / {}'.format(other._parenstr(), self._parenstr()))
@@ -196,8 +188,8 @@ class Expression:
         # "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
+            self._coefficients == other._coefficients and \
+            self.constant == other.constant
 
     @_polymorphic
     def __le__(self, other):
@@ -219,11 +211,28 @@ class Expression:
         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, dict):
+                symbol = symbol.items()
+            substitutions = symbol
+        else:
+            substitutions = [(symbol, expression)]
+        result = self
+        for symbol, expression in substitutions:
+            coefficients = [(othersymbol, coefficient)
+                for othersymbol, coefficient in result.coefficients()
+                if othersymbol != symbol]
+            coefficient = result.coefficient(symbol)
+            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:
@@ -254,18 +263,18 @@ class Expression:
     @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)
             if coefficient == 1:
                 if i == 0:
-                    string += symbol
+                    string += symbol.name
                 else:
                     string += ' + {}'.format(symbol)
             elif coefficient == -1:
@@ -302,30 +311,27 @@ class Expression:
         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
@@ -335,14 +341,13 @@ 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()
         return self
 
     @property
@@ -350,17 +355,18 @@ class Symbol(Expression):
         return self._name
 
     def __hash__(self):
-        return self._hash
+        return hash(self._name)
 
     def coefficient(self, symbol):
-        symbol = symbolname(symbol)
-        if symbol == self.name:
+        if not isinstance(symbol, Symbol):
+            raise TypeError('symbol must be a Symbol instance')
+        if symbol == self:
             return 1
         else:
             return 0
 
     def coefficients(self):
-        yield self.name, 1
+        yield self, 1
 
     @property
     def constant(self):
@@ -368,7 +374,7 @@ class Symbol(Expression):
 
     @property
     def symbols(self):
-        return self.name,
+        return self,
 
     @property
     def dimension(self):
@@ -377,6 +383,9 @@ class Symbol(Expression):
     def issymbol(self):
         return True
 
+    def values(self):
+        yield 1
+
     def __eq__(self, other):
         return isinstance(other, Symbol) and self.name == other.name
 
@@ -390,14 +399,11 @@ class Symbol(Expression):
             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)
+            return Symbol(expr.name)
         else:
             raise TypeError('expr must be a sympy.Symbol instance')
 
@@ -405,27 +411,13 @@ class Symbol(Expression):
 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)
+    return tuple(Symbol(name) for name in names)
 
 
 class Constant(Expression):
 
     __slots__ = (
         '_constant',
-        '_hash',
     )
 
     def __new__(cls, numerator=0, denominator=None):
@@ -434,18 +426,18 @@ class Constant(Expression):
             self._constant = numerator.constant
         else:
             self._constant = Fraction(numerator, denominator)
-        self._hash = hash(self._constant)
         return self
 
     def __hash__(self):
-        return self._hash
+        return hash(self.constant)
 
     def coefficient(self, symbol):
-        symbol = symbolname(symbol)
+        if not isinstance(symbol, Symbol):
+            raise TypeError('symbol must be a Symbol instance')
         return 0
 
     def coefficients(self):
-        yield from []
+        yield from ()
 
     @property
     def symbols(self):
@@ -458,6 +450,9 @@ class Constant(Expression):
     def isconstant(self):
         return True
 
+    def values(self):
+        yield self._constant
+
     @_polymorphic
     def __eq__(self, other):
         return isinstance(other, Constant) and self.constant == other.constant
@@ -467,25 +462,16 @@ class Constant(Expression):
 
     @classmethod
     def fromstring(cls, string):
-        if isinstance(string, str):
-            return Constant(Fraction(string))
-        else:
+        if not isinstance(string, str):
             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)
+        return Constant(Fraction(string))
 
     @classmethod
     def fromsympy(cls, expr):
         import sympy
         if isinstance(expr, sympy.Rational):
-            return cls(expr.p, expr.q)
+            return Constant(expr.p, expr.q)
         elif isinstance(expr, numbers.Rational):
-            return cls(expr)
+            return Constant(expr)
         else:
             raise TypeError('expr must be a sympy.Rational instance')