290 lines
9.8 KiB
Python
290 lines
9.8 KiB
Python
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"""
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The objects in this module allow the usage of the MatchPy pattern matching
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library on SymPy expressions.
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"""
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import re
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from typing import List, Callable
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from sympy.core.sympify import _sympify
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from sympy.external import import_module
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from sympy.functions import (log, sin, cos, tan, cot, csc, sec, erf, gamma, uppergamma)
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from sympy.functions.elementary.hyperbolic import acosh, asinh, atanh, acoth, acsch, asech, cosh, sinh, tanh, coth, sech, csch
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from sympy.functions.elementary.trigonometric import atan, acsc, asin, acot, acos, asec
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from sympy.functions.special.error_functions import fresnelc, fresnels, erfc, erfi, Ei
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from sympy.core.add import Add
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from sympy.core.basic import Basic
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from sympy.core.expr import Expr
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from sympy.core.mul import Mul
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from sympy.core.power import Pow
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from sympy.core.relational import (Equality, Unequality)
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from sympy.core.symbol import Symbol
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from sympy.functions.elementary.exponential import exp
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from sympy.integrals.integrals import Integral
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from sympy.printing.repr import srepr
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from sympy.utilities.decorator import doctest_depends_on
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matchpy = import_module("matchpy")
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if matchpy:
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from matchpy import Operation, CommutativeOperation, AssociativeOperation, OneIdentityOperation
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from matchpy.expressions.functions import op_iter, create_operation_expression, op_len
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Operation.register(Integral)
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Operation.register(Pow)
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OneIdentityOperation.register(Pow)
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Operation.register(Add)
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OneIdentityOperation.register(Add)
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CommutativeOperation.register(Add)
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AssociativeOperation.register(Add)
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Operation.register(Mul)
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OneIdentityOperation.register(Mul)
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CommutativeOperation.register(Mul)
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AssociativeOperation.register(Mul)
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Operation.register(Equality)
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CommutativeOperation.register(Equality)
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Operation.register(Unequality)
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CommutativeOperation.register(Unequality)
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Operation.register(exp)
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Operation.register(log)
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Operation.register(gamma)
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Operation.register(uppergamma)
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Operation.register(fresnels)
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Operation.register(fresnelc)
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Operation.register(erf)
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Operation.register(Ei)
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Operation.register(erfc)
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Operation.register(erfi)
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Operation.register(sin)
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Operation.register(cos)
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Operation.register(tan)
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Operation.register(cot)
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Operation.register(csc)
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Operation.register(sec)
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Operation.register(sinh)
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Operation.register(cosh)
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Operation.register(tanh)
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Operation.register(coth)
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Operation.register(csch)
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Operation.register(sech)
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Operation.register(asin)
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Operation.register(acos)
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Operation.register(atan)
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Operation.register(acot)
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Operation.register(acsc)
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Operation.register(asec)
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Operation.register(asinh)
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Operation.register(acosh)
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Operation.register(atanh)
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Operation.register(acoth)
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Operation.register(acsch)
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Operation.register(asech)
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@op_iter.register(Integral) # type: ignore
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def _(operation):
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return iter((operation._args[0],) + operation._args[1])
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@op_iter.register(Basic) # type: ignore
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def _(operation):
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return iter(operation._args)
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@op_len.register(Integral) # type: ignore
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def _(operation):
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return 1 + len(operation._args[1])
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@op_len.register(Basic) # type: ignore
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def _(operation):
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return len(operation._args)
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@create_operation_expression.register(Basic)
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def sympy_op_factory(old_operation, new_operands, variable_name=True):
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return type(old_operation)(*new_operands)
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if matchpy:
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from matchpy import Wildcard
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else:
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class Wildcard: # type: ignore
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def __init__(self, min_length, fixed_size, variable_name, optional):
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self.min_count = min_length
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self.fixed_size = fixed_size
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self.variable_name = variable_name
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self.optional = optional
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@doctest_depends_on(modules=('matchpy',))
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class _WildAbstract(Wildcard, Symbol):
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min_length: int # abstract field required in subclasses
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fixed_size: bool # abstract field required in subclasses
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def __init__(self, variable_name=None, optional=None, **assumptions):
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min_length = self.min_length
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fixed_size = self.fixed_size
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if optional is not None:
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optional = _sympify(optional)
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Wildcard.__init__(self, min_length, fixed_size, str(variable_name), optional)
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def __getstate__(self):
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return {
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"min_length": self.min_length,
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"fixed_size": self.fixed_size,
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"min_count": self.min_count,
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"variable_name": self.variable_name,
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"optional": self.optional,
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}
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def __new__(cls, variable_name=None, optional=None, **assumptions):
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cls._sanitize(assumptions, cls)
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return _WildAbstract.__xnew__(cls, variable_name, optional, **assumptions)
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def __getnewargs__(self):
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return self.variable_name, self.optional
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@staticmethod
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def __xnew__(cls, variable_name=None, optional=None, **assumptions):
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obj = Symbol.__xnew__(cls, variable_name, **assumptions)
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return obj
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def _hashable_content(self):
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if self.optional:
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return super()._hashable_content() + (self.min_count, self.fixed_size, self.variable_name, self.optional)
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else:
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return super()._hashable_content() + (self.min_count, self.fixed_size, self.variable_name)
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def __copy__(self) -> '_WildAbstract':
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return type(self)(variable_name=self.variable_name, optional=self.optional)
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def __repr__(self):
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return str(self)
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def __str__(self):
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return self.name
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@doctest_depends_on(modules=('matchpy',))
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class WildDot(_WildAbstract):
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min_length = 1
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fixed_size = True
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@doctest_depends_on(modules=('matchpy',))
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class WildPlus(_WildAbstract):
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min_length = 1
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fixed_size = False
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@doctest_depends_on(modules=('matchpy',))
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class WildStar(_WildAbstract):
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min_length = 0
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fixed_size = False
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def _get_srepr(expr):
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s = srepr(expr)
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s = re.sub(r"WildDot\('(\w+)'\)", r"\1", s)
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s = re.sub(r"WildPlus\('(\w+)'\)", r"*\1", s)
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s = re.sub(r"WildStar\('(\w+)'\)", r"*\1", s)
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return s
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@doctest_depends_on(modules=('matchpy',))
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class Replacer:
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"""
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Replacer object to perform multiple pattern matching and subexpression
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replacements in SymPy expressions.
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Examples
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========
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Example to construct a simple first degree equation solver:
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>>> from sympy.utilities.matchpy_connector import WildDot, Replacer
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>>> from sympy import Equality, Symbol
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>>> x = Symbol("x")
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>>> a_ = WildDot("a_", optional=1)
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>>> b_ = WildDot("b_", optional=0)
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The lines above have defined two wildcards, ``a_`` and ``b_``, the
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coefficients of the equation `a x + b = 0`. The optional values specified
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indicate which expression to return in case no match is found, they are
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necessary in equations like `a x = 0` and `x + b = 0`.
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Create two constraints to make sure that ``a_`` and ``b_`` will not match
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any expression containing ``x``:
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>>> from matchpy import CustomConstraint
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>>> free_x_a = CustomConstraint(lambda a_: not a_.has(x))
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>>> free_x_b = CustomConstraint(lambda b_: not b_.has(x))
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Now create the rule replacer with the constraints:
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>>> replacer = Replacer(common_constraints=[free_x_a, free_x_b])
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Add the matching rule:
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>>> replacer.add(Equality(a_*x + b_, 0), -b_/a_)
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Let's try it:
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>>> replacer.replace(Equality(3*x + 4, 0))
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-4/3
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Notice that it will not match equations expressed with other patterns:
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>>> eq = Equality(3*x, 4)
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>>> replacer.replace(eq)
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Eq(3*x, 4)
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In order to extend the matching patterns, define another one (we also need
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to clear the cache, because the previous result has already been memorized
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and the pattern matcher will not iterate again if given the same expression)
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>>> replacer.add(Equality(a_*x, b_), b_/a_)
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>>> replacer._replacer.matcher.clear()
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>>> replacer.replace(eq)
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4/3
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"""
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def __init__(self, common_constraints: list = []):
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self._replacer = matchpy.ManyToOneReplacer()
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self._common_constraint = common_constraints
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def _get_lambda(self, lambda_str: str) -> Callable[..., Expr]:
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exec("from sympy import *")
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return eval(lambda_str, locals())
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def _get_custom_constraint(self, constraint_expr: Expr, condition_template: str) -> Callable[..., Expr]:
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wilds = [x.name for x in constraint_expr.atoms(_WildAbstract)]
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lambdaargs = ', '.join(wilds)
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fullexpr = _get_srepr(constraint_expr)
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condition = condition_template.format(fullexpr)
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return matchpy.CustomConstraint(
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self._get_lambda(f"lambda {lambdaargs}: ({condition})"))
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def _get_custom_constraint_nonfalse(self, constraint_expr: Expr) -> Callable[..., Expr]:
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return self._get_custom_constraint(constraint_expr, "({}) != False")
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def _get_custom_constraint_true(self, constraint_expr: Expr) -> Callable[..., Expr]:
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return self._get_custom_constraint(constraint_expr, "({}) == True")
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def add(self, expr: Expr, result: Expr, conditions_true: List[Expr] = [], conditions_nonfalse: List[Expr] = []) -> None:
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expr = _sympify(expr)
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result = _sympify(result)
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lambda_str = f"lambda {', '.join((x.name for x in expr.atoms(_WildAbstract)))}: {_get_srepr(result)}"
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lambda_expr = self._get_lambda(lambda_str)
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constraints = self._common_constraint[:]
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constraint_conditions_true = [
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self._get_custom_constraint_true(cond) for cond in conditions_true]
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constraint_conditions_nonfalse = [
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self._get_custom_constraint_nonfalse(cond) for cond in conditions_nonfalse]
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constraints.extend(constraint_conditions_true)
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constraints.extend(constraint_conditions_nonfalse)
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self._replacer.add(
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matchpy.ReplacementRule(matchpy.Pattern(expr, *constraints), lambda_expr))
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def replace(self, expr: Expr) -> Expr:
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return self._replacer.replace(expr)
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