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
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
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
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
