Merge pull request #583 from CUQI-DTU/add_576_variable_class

Add support for algebra

Author: nabriis

cuqi/experimental/__init__.py

@@ -1,2 +1,3 @@
 """ Experimental module for testing new features and ideas. """
 from . import mcmc
+from . import algebra

cuqi/experimental/algebra/__init__.py

@@ -0,0 +1 @@
+from ._ast import VariableNode

cuqi/experimental/algebra/_ast.py

@@ -0,0 +1,325 @@
+"""
+CUQIpy specific implementation of an abstract syntax tree (AST) for algebra on variables.
+
+The AST is used to record the operations applied to variables allowing a delayed evaluation
+of said operations when needed by traversing the tree with the __call__ method.
+
+For example, the following code
+
+    x = VariableNode('x')
+    y = VariableNode('y')
+    z = 2*x + 3*y
+
+will create the following AST:
+
+z = AddNode(
+        MultiplyNode(
+            ValueNode(2),
+            VariableNode('x')
+        ),
+        MultiplyNode(
+            ValueNode(3),
+            VariableNode('y')
+        )
+    )
+
+which can be evaluated by calling the __call__ method:
+
+    z(x=1, y=2) # returns 8
+
+"""
+
+from abc import ABC, abstractmethod
+
+convert_to_node = lambda x: x if isinstance(x, Node) else ValueNode(x)
+""" Converts any non-Node object to a ValueNode object. """
+
+# ====== Base classes for the nodes ======
+
+
+class Node(ABC):
+    """Base class for all nodes in the abstract syntax tree.
+
+    Responsible for building the AST by creating nodes that represent the operations applied to variables.
+
+    Each subclass must implement the __call__ method that will evaluate the node given the input parameters.
+
+    """
+
+    @abstractmethod
+    def __call__(self, **kwargs):
+        """Evaluate node at a given parameter value. This will traverse the sub-tree originated at this node and evaluate it given the recorded operations."""
+        pass
+
+    @abstractmethod
+    def __repr__(self):
+        """String representation of the node. Used for printing the AST."""
+        pass
+
+    def __add__(self, other):
+        return AddNode(self, convert_to_node(other))
+
+    def __radd__(self, other):
+        return AddNode(convert_to_node(other), self)
+
+    def __sub__(self, other):
+        return SubtractNode(self, convert_to_node(other))
+
+    def __rsub__(self, other):
+        return SubtractNode(convert_to_node(other), self)
+
+    def __mul__(self, other):
+        return MultiplyNode(self, convert_to_node(other))
+
+    def __rmul__(self, other):
+        return MultiplyNode(convert_to_node(other), self)
+
+    def __truediv__(self, other):
+        return DivideNode(self, convert_to_node(other))
+
+    def __rtruediv__(self, other):
+        return DivideNode(convert_to_node(other), self)
+
+    def __pow__(self, other):
+        return PowerNode(self, convert_to_node(other))
+
+    def __rpow__(self, other):
+        return PowerNode(convert_to_node(other), self)
+
+    def __neg__(self):
+        return NegateNode(self)
+
+    def __abs__(self):
+        return AbsNode(self)
+
+    def __getitem__(self, i):
+        return GetItemNode(self, convert_to_node(i))
+
+    def __matmul__(self, other):
+        return MatMulNode(self, convert_to_node(other))
+
+    def __rmatmul__(self, other):
+        return MatMulNode(convert_to_node(other), self)
+
+
+class UnaryNode(Node, ABC):
+    """Base class for all unary nodes in the abstract syntax tree.
+
+    Parameters
+    ----------
+    child : Node
+        The direct child node on which the unary operation is performed.
+
+    """
+
+    def __init__(self, child: Node):
+        self.child = child
+
+
+class BinaryNode(Node, ABC):
+    """Base class for all binary nodes in the abstract syntax tree.
+
+    The op_symbol attribute is used for printing the operation in the __repr__ method.
+
+    Parameters
+    ----------
+    left : Node
+        Left child node to the binary operation.
+
+    right : Node
+        Right child node to the binary operation.
+
+    """
+
+    @property
+    @abstractmethod
+    def op_symbol(self):
+        """Symbol used to represent the operation in the __repr__ method."""
+        pass
+
+    def __init__(self, left: Node, right: Node):
+        self.left = left
+        self.right = right
+
+    def __repr__(self):
+        return f"{self.left} {self.op_symbol} {self.right}"
+
+
+class BinaryNodeWithParenthesis(BinaryNode, ABC):
+    """Base class for all binary nodes in the abstract syntax tree that should be printed with parenthesis."""
+
+    def __repr__(self):
+        left = f"({self.left})" if isinstance(self.left, BinaryNode) else str(self.left)
+        right = (
+            f"({self.right})" if isinstance(self.right, BinaryNode) else str(self.right)
+        )
+        return f"{left} {self.op_symbol} {right}"
+
+class BinaryNodeWithParenthesisNoSpace(BinaryNode, ABC):
+    """Base class for all binary nodes in the abstract syntax tree that should be printed with parenthesis but no space."""
+
+    def __repr__(self):
+        left = f"({self.left})" if isinstance(self.left, BinaryNode) else str(self.left)
+        right = (
+            f"({self.right})" if isinstance(self.right, BinaryNode) else str(self.right)
+        )
+        return f"{left}{self.op_symbol}{right}"
+
+
+# ====== Specific implementations of the "leaf" nodes ======
+
+
+class VariableNode(Node):
+    """Node that represents a generic variable, e.g. "x" or "y".
+
+    Parameters
+    ----------
+    name : str
+        Name of the variable. Used for printing and to retrieve the given input value
+        of the variable in the kwargs dictionary when evaluating the tree.
+
+    """
+
+    def __init__(self, name):
+        self.name = name
+
+    def __call__(self, **kwargs):
+        """Retrieves the value of the variable from the passed kwargs. If no value is found, it raises a KeyError."""
+        if not self.name in kwargs:
+            raise KeyError(
+                f"Variable '{self.name}' not found in the given input parameters. Unable to evaluate the expression."
+            )
+        return kwargs[self.name]
+
+    def __repr__(self):
+        return self.name
+
+
+class ValueNode(Node):
+    """Node that represents a constant value. The value can be any python object that is not a Node.
+
+    Parameters
+    ----------
+    value : object
+        The python object that represents the value of the node.
+
+    """
+
+    def __init__(self, value):
+        self.value = value
+
+    def __call__(self, **kwargs):
+        """Returns the value of the node."""
+        return self.value
+
+    def __repr__(self):
+        return str(self.value)
+
+
+# ====== Specific implementations of the "internal" nodes ======
+
+
+class AddNode(BinaryNode):
+    """Node that represents the addition operation."""
+
+    @property
+    def op_symbol(self):
+        return "+"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) + self.right(**kwargs)
+
+
+class SubtractNode(BinaryNode):
+    """Node that represents the subtraction operation."""
+
+    @property
+    def op_symbol(self):
+        return "-"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) - self.right(**kwargs)
+
+
+class MultiplyNode(BinaryNodeWithParenthesis):
+    """Node that represents the multiplication operation."""
+
+    @property
+    def op_symbol(self):
+        return "*"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) * self.right(**kwargs)
+
+
+class DivideNode(BinaryNodeWithParenthesis):
+    """Node that represents the division operation."""
+
+    @property
+    def op_symbol(self):
+        return "/"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) / self.right(**kwargs)
+
+
+class PowerNode(BinaryNodeWithParenthesisNoSpace):
+    """Node that represents the power operation."""
+
+    @property
+    def op_symbol(self):
+        return "^"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) ** self.right(**kwargs)
+
+
+class GetItemNode(BinaryNode):
+    """Node that represents the get item operation. Here the left node is the object and the right node is the index."""
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs)[self.right(**kwargs)]
+
+    def __repr__(self):
+        left = f"({self.left})" if isinstance(self.left, BinaryNode) else str(self.left)
+        return f"{left}[{self.right}]"
+    
+    @property
+    def op_symbol(self):
+        pass
+
+
+class NegateNode(UnaryNode):
+    """Node that represents the arithmetic negation operation."""
+
+    def __call__(self, **kwargs):
+        return -self.child(**kwargs)
+
+    def __repr__(self):
+        child = (
+            f"({self.child})"
+            if isinstance(self.child, (BinaryNode, UnaryNode))
+            else str(self.child)
+        )
+        return f"-{child}"
+
+
+class AbsNode(UnaryNode):
+    """Node that represents the absolute value operation."""
+
+    def __call__(self, **kwargs):
+        return abs(self.child(**kwargs))
+
+    def __repr__(self):
+        return f"abs({self.child})"
+
+
+class MatMulNode(BinaryNodeWithParenthesis):
+    """Node that represents the matrix multiplication operation."""
+
+    @property
+    def op_symbol(self):
+        return "@"
+
+    def __call__(self, **kwargs):
+        return self.left(**kwargs) @ self.right(**kwargs)

demos/howtos/algebra.py

@@ -0,0 +1,66 @@
+"""
+Algebra in CUQIpy
+=================
+
+CUQIpy provides a simple algebraic framework for defining and manipulating
+variables.
+
+In this example, we will demonstrate how to define a simple algebraic structure
+and perform some basic algebraic operations.
+
+"""
+
+#%%
+# Defining Variables
+# ------------------
+# To utilize the algebraic framework in CUQIpy, we first need to define some
+# variables to apply the algebraic operations on. In this example, we will
+# define variables `x` and `y`.
+
+from cuqi.experimental.algebra import VariableNode
+
+x = VariableNode('x')
+y = VariableNode('y')
+
+#%%
+# Recording Algebraic Operations
+# --------------------
+# We can now perform some algebraic operations on the variables `x` and `y`.
+# The algebraic operations are recorded in a computational graph (abstract syntax tree).
+# The operations are recoding the correct ordering and adhering to the rules of
+# algebra.
+
+print("Basic operations:")
+print(x + 1)
+print(x + y)
+print(x * y)
+print(x / y)
+
+print("\nComplex operations:")
+print(x**2 + 2*x*y + y**2)
+print((x + y)**2)
+
+print("\nProgrammatric operations:")
+print(x[2]+y[3])
+
+# %%
+# Utilizing the Computational Graph
+# ---------------------------------
+# The computational graph can be utilized to evaluate the algebraic expressions
+# when desired. This means we can define mathematical expressions without
+# needing to evaluate them immediately.
+
+# Define a mathematical expression
+expr1 = (x + y)**2
+
+# Evaluate the expression (using the __call__ method)
+print(f"Expression {expr1} evaluated at x=2, y=3 yields {expr1(x=2, y=3)}")
+
+# Another example
+expr2 = x**2 + 2*x*y + y**2 + 16
+print(f"Expression {expr2} evaluated at x=2, y=3 yields {expr2(x=2, y=3)}")
+
+# Another example utilizing array indexing
+expr3 = x[1] + y[2]
+print(f"Expression {expr3} evaluated at x=[1,2,3], y=[4,5,6] yields {expr3(x=[1,2,3], y=[4,5,6])}")
+# %%