コード例 #1
0
ファイル: basic.py プロジェクト: 101man/sympy
    def find(self, query, group=False):
        """Find all subexpressions matching a query. """
        if not callable(query):
            query = sympify(query)
        if isinstance(query, type):
            _query = lambda expr: isinstance(expr, query)
        elif isinstance(query, Basic):
            _query = lambda expr: expr.match(query)
        else:
            _query = query

        results = []

        def rec_find(expr):
            q = _query(expr)
            if q or q == {}:
                results.append(expr)

            for arg in expr.args:
                rec_find(arg)

        rec_find(self)

        if not group:
            return set(results)
        else:
            groups = {}

            for result in results:
                if result in groups:
                    groups[result] += 1
                else:
                    groups[result] = 1

            return groups
コード例 #2
0
ファイル: basic.py プロジェクト: BDGLunde/sympy
    def find(self, query, group=False):
        """Find all subexpressions matching a query. """
        if not callable(query):
            query = sympify(query)
        if isinstance(query, type):
            _query = lambda expr: isinstance(expr, query)
        elif isinstance(query, Basic):
            _query = lambda expr: expr.match(query)
        else:
            _query = query

        results = []

        def rec_find(expr):
            q = _query(expr)
            if q or q == {}:
                results.append(expr)

            for arg in expr.args:
                rec_find(arg)

        rec_find(self)

        if not group:
            return set(results)
        else:
            groups = {}

            for result in results:
                if result in groups:
                    groups[result] += 1
                else:
                    groups[result] = 1

            return groups
コード例 #3
0
ファイル: basic.py プロジェクト: 101man/sympy
    def replace(self, query, value, map=False):
        """
        Replace matching subexpressions of ``self`` with ``value``.

        If ``map = True`` then also return the mapping {old: new} where ``old``
        was a sub-expression found with query and ``new`` is the replacement
        value for it.

        Traverses an expression tree and performs replacement of matching
        subexpressions from the bottom to the top of the tree. The list of
        possible combinations of queries and replacement values is listed
        below:

        1.1. type -> type
             obj.replace(sin, tan)
        1.2. type -> func
             obj.replace(sin, lambda expr, arg: ...)

        2.1. expr -> expr
             obj.replace(sin(a), tan(a))
        2.2. expr -> func
             obj.replace(sin(a), lambda a: ...)

        3.1. func -> func
             obj.replace(lambda expr: ..., lambda expr: ...)

        Examples:

        >>> from sympy import log, sin, cos, tan, Wild
        >>> from sympy.abc import x

        >>> f = log(sin(x)) + tan(sin(x**2))

        >>> f.replace(sin, cos)
        log(cos(x)) + tan(cos(x**2))
        >>> f.replace(sin, lambda arg: sin(2*arg))
        log(sin(2*x)) + tan(sin(2*x**2))

        >>> sin(x).replace(sin, cos, map=True)
        (cos(x), {sin(x): cos(x)})

        >>> a = Wild('a')

        >>> f.replace(sin(a), cos(a))
        log(cos(x)) + tan(cos(x**2))
        >>> f.replace(sin(a), lambda a: sin(2*a))
        log(sin(2*x)) + tan(sin(2*x**2))

        >>> g = 2*sin(x**3)

        >>> g.replace(lambda expr: expr.is_Number, lambda expr: expr**2)
        4*sin(x**9)

        """
        if isinstance(query, type):
            _query = lambda expr: isinstance(expr, query)

            if isinstance(value, type):
                _value = lambda expr, result: value(*expr.args)
            elif callable(value):
                _value = lambda expr, result: value(*expr.args)
            else:
                raise TypeError("given a type, replace() expects another type or a callable")
        elif isinstance(query, Basic):
            _query = lambda expr: expr.match(query)

            if isinstance(value, Basic):
                _value = lambda expr, result: value.subs(result)
            elif callable(value):
                _value = lambda expr, result: value(**dict([ (str(key)[:-1], val) for key, val in result.iteritems() ]))
            else:
                raise TypeError("given an expression, replace() expects another expression or a callable")
        elif callable(query):
            _query = query

            if callable(value):
                _value = lambda expr, result: value(expr)
            else:
                raise TypeError("given a callable, replace() expects another callable")
        else:
            raise TypeError("first argument to replace() must be a type, an expression or a callable")

        mapping = {}

        def rec_replace(expr):
            args, construct = [], False

            for arg in expr.args:
                result = rec_replace(arg)

                if result is not None:
                    construct = True
                else:
                    result = arg

                args.append(result)

            if construct:
                return expr.__class__(*args)
            else:
                result = _query(expr)

                if result:
                    value = _value(expr, result)

                    if map:
                        mapping[expr] = value

                    return value
                else:
                    return None

        result = rec_replace(self)

        if result is None:
            result = self

        if not map:
            return result
        else:
            return result, mapping
コード例 #4
0
    def replace(self, query, value, map=False):
        """
        Replace matching subexpressions of ``self`` with ``value``.

        If ``map = True`` then also return the mapping {old: new} where ``old``
        was a sub-expression found with query and ``new`` is the replacement
        value for it.

        Traverses an expression tree and performs replacement of matching
        subexpressions from the bottom to the top of the tree. The list of
        possible combinations of queries and replacement values is listed
        below:

        1.1. type -> type
             obj.replace(sin, tan)
        1.2. type -> func
             obj.replace(sin, lambda expr, arg: ...)

        2.1. expr -> expr
             obj.replace(sin(a), tan(a))
        2.2. expr -> func
             obj.replace(sin(a), lambda a: ...)

        3.1. func -> func
             obj.replace(lambda expr: ..., lambda expr: ...)

        Examples:

        >>> from sympy import log, sin, cos, tan, Wild
        >>> from sympy.abc import x

        >>> f = log(sin(x)) + tan(sin(x**2))

        >>> f.replace(sin, cos)
        log(cos(x)) + tan(cos(x**2))
        >>> f.replace(sin, lambda arg: sin(2*arg))
        log(sin(2*x)) + tan(sin(2*x**2))

        >>> sin(x).replace(sin, cos, map=True)
        (cos(x), {sin(x): cos(x)})

        >>> a = Wild('a')

        >>> f.replace(sin(a), cos(a))
        log(cos(x)) + tan(cos(x**2))
        >>> f.replace(sin(a), lambda a: sin(2*a))
        log(sin(2*x)) + tan(sin(2*x**2))

        >>> g = 2*sin(x**3)

        >>> g.replace(lambda expr: expr.is_Number, lambda expr: expr**2)
        4*sin(x**9)

        """
        if isinstance(query, type):
            _query = lambda expr: isinstance(expr, query)

            if isinstance(value, type):
                _value = lambda expr, result: value(*expr.args)
            elif callable(value):
                _value = lambda expr, result: value(*expr.args)
            else:
                raise TypeError(
                    "given a type, replace() expects another type or a callable"
                )
        elif isinstance(query, Basic):
            _query = lambda expr: expr.match(query)

            if isinstance(value, Basic):
                _value = lambda expr, result: value.subs(result)
            elif callable(value):
                _value = lambda expr, result: value(**dict(
                    [(str(key)[:-1], val) for key, val in result.iteritems()]))
            else:
                raise TypeError(
                    "given an expression, replace() expects another expression or a callable"
                )
        elif callable(query):
            _query = query

            if callable(value):
                _value = lambda expr, result: value(expr)
            else:
                raise TypeError(
                    "given a callable, replace() expects another callable")
        else:
            raise TypeError(
                "first argument to replace() must be a type, an expression or a callable"
            )

        mapping = {}

        def rec_replace(expr):
            args, construct = [], False

            for arg in expr.args:
                result = rec_replace(arg)

                if result is not None:
                    construct = True
                else:
                    result = arg

                args.append(result)

            if construct:
                return expr.__class__(*args)
            else:
                result = _query(expr)

                if result:
                    value = _value(expr, result)

                    if map:
                        mapping[expr] = value

                    return value
                else:
                    return None

        result = rec_replace(self)

        if result is None:
            result = self

        if not map:
            return result
        else:
            return result, mapping