Source code for sympy.codegen.ast

"""
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 left-hand sides of assignments, in order. ``left_hand_sides``: Tuple of right-hand 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]) # De-enumerate 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 'for-loop' 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 for-loop representation. This object changes each iteration. Target must be a symbol. """ return self._args[0] @property def iterable(self): """ Return the iterable from the for-loop 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 for-loop representation. This is run for each value of target. Must be an iterable object or CodeBlock. """ return self._args[2]