"""
Types used to represent a full function/module as an Abstract Syntax Tree.
Most types are small, and are merely used as tokens in the AST. A tree diagram
has been included below to illustrate the relationships between the AST types.
AST Type Tree

*Basic*
>Assignment
 >AugmentedAssignment
 >AddAugmentedAssignment
 >SubAugmentedAssignment
 >MulAugmentedAssignment
 >DivAugmentedAssignment
 >ModAugmentedAssignment

>CodeBlock

>For
"""
from __future__ import print_function, division
from sympy.core import Symbol, Tuple
from sympy.core.basic import Basic
from sympy.core.sympify import _sympify
from sympy.core.relational import Relational
from sympy.utilities.iterables import iterable
[docs]class Assignment(Relational):
"""
Represents variable assignment for code generation.
Parameters

lhs : Expr
Sympy object representing the lhs of the expression. These should be
singular objects, such as one would use in writing code. Notable types
include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
subclass these types are also supported.
rhs : Expr
Sympy object representing the rhs of the expression. This can be any
type, provided its shape corresponds to that of the lhs. For example,
a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
the dimensions will not align.
Examples
========
>>> from sympy import symbols, MatrixSymbol, Matrix
>>> from sympy.codegen.ast import Assignment
>>> x, y, z = symbols('x, y, z')
>>> Assignment(x, y)
Assignment(x, y)
>>> Assignment(x, 0)
Assignment(x, 0)
>>> A = MatrixSymbol('A', 1, 3)
>>> mat = Matrix([x, y, z]).T
>>> Assignment(A, mat)
Assignment(A, Matrix([[x, y, z]]))
>>> Assignment(A[0, 1], x)
Assignment(A[0, 1], x)
"""
rel_op = ':='
__slots__ = []
def __new__(cls, lhs, rhs=0, **assumptions):
from sympy.matrices.expressions.matexpr import (
MatrixElement, MatrixSymbol)
from sympy.tensor.indexed import Indexed
lhs = _sympify(lhs)
rhs = _sympify(rhs)
# Tuple of things that can be on the lhs of an assignment
assignable = (Symbol, MatrixSymbol, MatrixElement, Indexed)
if not isinstance(lhs, assignable):
raise TypeError("Cannot assign to lhs of type %s." % type(lhs))
# Indexed types implement shape, but don't define it until later. This
# causes issues in assignment validation. For now, matrices are defined
# as anything with a shape that is not an Indexed
lhs_is_mat = hasattr(lhs, 'shape') and not isinstance(lhs, Indexed)
rhs_is_mat = hasattr(rhs, 'shape') and not isinstance(rhs, Indexed)
# If lhs and rhs have same structure, then this assignment is ok
if lhs_is_mat:
if not rhs_is_mat:
raise ValueError("Cannot assign a scalar to a matrix.")
elif lhs.shape != rhs.shape:
raise ValueError("Dimensions of lhs and rhs don't align.")
elif rhs_is_mat and not lhs_is_mat:
raise ValueError("Cannot assign a matrix to a scalar.")
return Relational.__new__(cls, lhs, rhs, **assumptions)
# XXX: This should be handled better
Relational.ValidRelationOperator[':='] = Assignment
class AugmentedAssignment(Assignment):
"""
Base class for augmented assignments
"""
@property
def rel_op(self):
return self._symbol + '='
class AddAugmentedAssignment(AugmentedAssignment):
_symbol = '+'
class SubAugmentedAssignment(AugmentedAssignment):
_symbol = ''
class MulAugmentedAssignment(AugmentedAssignment):
_symbol = '*'
class DivAugmentedAssignment(AugmentedAssignment):
_symbol = '/'
class ModAugmentedAssignment(AugmentedAssignment):
_symbol = '%'
Relational.ValidRelationOperator['+='] = AddAugmentedAssignment
Relational.ValidRelationOperator['='] = SubAugmentedAssignment
Relational.ValidRelationOperator['*='] = MulAugmentedAssignment
Relational.ValidRelationOperator['/='] = DivAugmentedAssignment
Relational.ValidRelationOperator['%='] = ModAugmentedAssignment
def aug_assign(lhs, op, rhs):
"""
Create 'lhs op= rhs'.
Represents augmented variable assignment for code generation. This is a
convenience function. You can also use the AugmentedAssignment classes
directly, like AddAugmentedAssignment(x, y).
Parameters

lhs : Expr
Sympy object representing the lhs of the expression. These should be
singular objects, such as one would use in writing code. Notable types
include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that
subclass these types are also supported.
op : str
Operator (+, , /, *, %).
rhs : Expr
Sympy object representing the rhs of the expression. This can be any
type, provided its shape corresponds to that of the lhs. For example,
a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as
the dimensions will not align.
Examples

>>> from sympy import symbols
>>> from sympy.codegen.ast import aug_assign
>>> x, y = symbols('x, y')
>>> aug_assign(x, '+', y)
AddAugmentedAssignment(x, y)
"""
if op + '=' not in Relational.ValidRelationOperator:
raise ValueError("Unrecognized operator %s" % op)
return Relational.ValidRelationOperator[op + '='](lhs, rhs)
class CodeBlock(Basic):
"""
Represents a block of code
For now only assignments are supported. This restriction will be lifted in
the future.
Useful methods on this object are
``left_hand_sides``: Tuple of lefthand sides of assignments, in order.
``left_hand_sides``: Tuple of righthand sides of assignments, in order.
``topological_sort``: Class method. Return a CodeBlock with assignments
sorted so that variables are assigned before they
are used.
``cse``: Return a new CodeBlock with common subexpressions eliminated and
pulled out as assignments.
Example
=======
>>> from sympy import symbols, ccode
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y = symbols('x y')
>>> c = CodeBlock(Assignment(x, 1), Assignment(y, x + 1))
>>> print(ccode(c))
x = 1;
y = x + 1;
"""
def __new__(cls, *args):
left_hand_sides = []
right_hand_sides = []
for i in args:
if isinstance(i, Assignment):
lhs, rhs = i.args
left_hand_sides.append(lhs)
right_hand_sides.append(rhs)
obj = Basic.__new__(cls, *args)
obj.left_hand_sides = Tuple(*left_hand_sides)
obj.right_hand_sides = Tuple(*right_hand_sides)
return obj
@classmethod
def topological_sort(cls, assignments):
"""
Return a CodeBlock with topologically sorted assignments so that
variables are assigned before they are used.
The existing order of assignments is preserved as much as possible.
This function assumes that variables are assigned to only once.
This is a class constructor so that the default constructor for
CodeBlock can error when variables are used before they are assigned.
Example
=======
>>> from sympy import symbols
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> assignments = [
... Assignment(x, y + z),
... Assignment(y, z + 1),
... Assignment(z, 2),
... ]
>>> CodeBlock.topological_sort(assignments)
CodeBlock(Assignment(z, 2), Assignment(y, z + 1), Assignment(x, y + z))
"""
from sympy.utilities.iterables import topological_sort
# Create a graph where the nodes are assignments and there is a directed edge
# between nodes that use a variable and nodes that assign that
# variable, like
# [(x := 1, y := x + 1), (x := 1, z := y + z), (y := x + 1, z := y + z)]
# If we then topologically sort these nodes, they will be in
# assignment order, like
# x := 1
# y := x + 1
# z := y + z
# A = The nodes
#
# enumerate keeps nodes in the same order they are already in if
# possible. It will also allow us to handle duplicate assignments to
# the same variable when those are implemented.
A = list(enumerate(assignments))
# var_map = {variable: [assignments using variable]}
# like {x: [y := x + 1, z := y + x], ...}
var_map = {}
# E = Edges in the graph
E = []
for i in A:
if i[1].lhs in var_map:
E.append((var_map[i[1].lhs], i))
var_map[i[1].lhs] = i
for i in A:
for x in i[1].rhs.free_symbols:
if x not in var_map:
# XXX: Allow this case?
raise ValueError("Undefined variable %s" % x)
E.append((var_map[x], i))
ordered_assignments = topological_sort([A, E])
# Deenumerate the result
return cls(*list(zip(*ordered_assignments))[1])
def cse(self, symbols=None, optimizations=None, postprocess=None,
order='canonical'):
"""
Return a new code block with common subexpressions eliminated
See the docstring of :func:`sympy.simplify.cse_main.cse` for more
information.
Examples
========
>>> from sympy import symbols, sin
>>> from sympy.codegen.ast import CodeBlock, Assignment
>>> x, y, z = symbols('x y z')
>>> c = CodeBlock(
... Assignment(x, 1),
... Assignment(y, sin(x) + 1),
... Assignment(z, sin(x)  1),
... )
...
>>> c.cse()
CodeBlock(Assignment(x, 1), Assignment(x0, sin(x)), Assignment(y, x0 +
1), Assignment(z, x0  1))
"""
# TODO: Check that the symbols are new
from sympy.simplify.cse_main import cse
if not all(isinstance(i, Assignment) for i in self.args):
# Will support more things later
raise NotImplementedError("CodeBlock.cse only supports Assignments")
if any(isinstance(i, AugmentedAssignment) for i in self.args):
raise NotImplementedError("CodeBlock.cse doesn't yet work with AugmentedAssignments")
for i, lhs in enumerate(self.left_hand_sides):
if lhs in self.left_hand_sides[:i]:
raise NotImplementedError("Duplicate assignments to the same "
"variable are not yet supported (%s)" % lhs)
replacements, reduced_exprs = cse(self.right_hand_sides, symbols=symbols,
optimizations=optimizations, postprocess=postprocess, order=order)
assert len(reduced_exprs) == 1
new_block = tuple(Assignment(var, expr) for var, expr in
zip(self.left_hand_sides, reduced_exprs[0]))
new_assignments = tuple(Assignment(*i) for i in replacements)
return self.topological_sort(new_assignments + new_block)
class For(Basic):
"""Represents a 'forloop' in the code.
Expressions are of the form:
"for target in iter:
body..."
Parameters

target : symbol
iter : iterable
body : sympy expr
Examples

>>> from sympy import symbols, Range
>>> from sympy.codegen.ast import aug_assign, For
>>> x, n = symbols('x n')
>>> For(n, Range(10), [aug_assign(x, '+', n)])
For(n, Range(0, 10, 1), CodeBlock(AddAugmentedAssignment(x, n)))
"""
def __new__(cls, target, iter, body):
target = _sympify(target)
if not iterable(iter):
raise TypeError("iter must be an iterable")
if isinstance(iter, list):
# _sympify errors on lists because they are mutable
iter = tuple(iter)
iter = _sympify(iter)
if not isinstance(body, CodeBlock):
if not iterable(body):
raise TypeError("body must be an iterable or CodeBlock")
body = CodeBlock(*(_sympify(i) for i in body))
return Basic.__new__(cls, target, iter, body)
@property
def target(self):
"""
Return the symbol (target) from the forloop representation.
This object changes each iteration.
Target must be a symbol.
"""
return self._args[0]
@property
def iterable(self):
"""
Return the iterable from the forloop representation.
This is the object that target takes values from.
Must be an iterable object.
"""
return self._args[1]
@property
def body(self):
"""
Return the sympy expression (body) from the forloop representation.
This is run for each value of target.
Must be an iterable object or CodeBlock.
"""
return self._args[2]