Generated condensed version of https://github.com/mattjj/autodidact

autodidact.py

"""
The MIT License (MIT)

Copyright (c) 2014 by the President and Fellows of Harvard University
Condensed version Copyright (c) 2024 by Gavia Gray

This condensed version is based on the original mattjj/autodidact implementation,
with assistance from Claude 3.5 Sonnet.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""

import numpy as _np
from collections import defaultdict
from contextlib import contextmanager
from itertools import count

# Core tracer functionality
class Box:
    type_mappings = {}
    types = set()
    
    def __init__(self, value, trace_id, node):
        self._value = value
        self._node = node
        self._trace_id = trace_id
    
    @classmethod
    def register(cls, value_type):
        Box.types.add(cls)
        Box.type_mappings[value_type] = cls
        Box.type_mappings[cls] = cls

def new_box(value, trace_id, node):
    try:
        return Box.type_mappings[type(value)](value, trace_id, node)
    except KeyError:
        raise TypeError(f"Can't differentiate w.r.t. type {type(value)}")

class Node:
    def __init__(self, value, fun, args, kwargs, parent_argnums, parents):
        self.parents = parents
        self.recipe = (fun, value, args, kwargs, parent_argnums)

    def initialize_root(self):
        self.parents = []
        self.recipe = (lambda x: x, None, (), {}, [])

    @classmethod
    def new_root(cls):
        root = cls.__new__(cls)
        root.initialize_root()
        return root

class TraceStack:
    def __init__(self):
        self.top = -1

    @contextmanager
    def new_trace(self):
        self.top += 1
        yield self.top
        self.top -= 1

_trace_stack = TraceStack()

def trace(start_node, fun, x):
    with _trace_stack.new_trace() as trace_id:
        start_box = new_box(x, trace_id, start_node)
        end_box = fun(start_box)
        if isbox(end_box) and end_box._trace_id == start_box._trace_id:
            return end_box._value, end_box._node
        else:
            return end_box, None

# Core VJP functionality
primitive_vjps = defaultdict(dict)

def backward_pass(g, end_node):
    outgrads = {end_node: g}
    for node in toposort(end_node):
        outgrad = outgrads.pop(node)
        fun, value, args, kwargs, argnums = node.recipe
        for argnum, parent in zip(argnums, node.parents):
            vjp = primitive_vjps[fun][argnum]
            parent_grad = vjp(outgrad, value, *args, **kwargs)
            outgrads[parent] = add_outgrads(outgrads.get(parent), parent_grad)
    return outgrad

def add_outgrads(prev_g, g):
    return g if prev_g is None else prev_g + g

def make_vjp(fun, x):
    start_node = Node.new_root()
    end_value, end_node = trace(start_node, fun, x)
    if end_node is None:
        def vjp(g): return _np.zeros_like(x)
    else:
        def vjp(g): return backward_pass(g, end_node)
    return vjp, end_value

def grad(fun, argnum=0):
    def gradfun(*args, **kwargs):
        unary_fun = lambda x: fun(*subval(args, argnum, x), **kwargs)
        vjp, ans = make_vjp(unary_fun, args[argnum])
        return vjp(_np.ones_like(ans))
    return gradfun

# Utilities
def subval(x, i, v):
    x_ = list(x)
    x_[i] = v
    return tuple(x_)

def toposort(end_node):
    child_counts = {}
    stack = [end_node]
    while stack:
        node = stack.pop()
        if node in child_counts:
            child_counts[node] += 1
        else:
            child_counts[node] = 1
            stack.extend(node.parents)
    
    childless_nodes = [end_node]
    while childless_nodes:
        node = childless_nodes.pop()
        yield node
        for parent in node.parents:
            if child_counts[parent] == 1:
                childless_nodes.append(parent)
            else:
                child_counts[parent] -= 1

# NumPy wrapping functionality
def primitive(f_raw):
    def f_wrapped(*args, **kwargs):
        boxed_args, trace_id = find_top_boxed_args(args)
        if boxed_args:
            argvals = list(args)
            for argnum, box in boxed_args:
                argvals[argnum] = box._value
            argvals = tuple(argvals)
            parents = tuple(box._node for _, box in boxed_args)
            argnums = tuple(argnum for argnum, _ in boxed_args)
            ans = f_raw(*argvals, **kwargs)
            node = Node(ans, f_wrapped, argvals, kwargs, argnums, parents)
            return new_box(ans, trace_id, node)
        else:
            return f_raw(*args, **kwargs)
    return f_wrapped

def find_top_boxed_args(args):
    top_trace_id = -1
    top_boxes = []
    for argnum, arg in enumerate(args):
        if isbox(arg):
            if arg._trace_id > top_trace_id:
                top_boxes = [(argnum, arg)]
                top_trace_id = arg._trace_id
            elif arg._trace_id == top_trace_id:
                top_boxes.append((argnum, arg))
    return top_boxes, top_trace_id

isbox = lambda x: type(x) in Box.types
getval = lambda x: getval(x._value) if isbox(x) else x

# NumPy box implementation
class ArrayBox(Box):
    __array_priority__ = 100.0
    
    def __init__(self, value, trace_id, node):
        super().__init__(value, trace_id, node)
        
    @property
    def shape(self): return self._value.shape
    @property
    def ndim(self): return self._value.ndim
    @property
    def size(self): return self._value.size
    @property
    def dtype(self): return self._value.dtype
    
    def __neg__(self): return np.negative(self)
    def __add__(self, other): return np.add(self, other)
    def __sub__(self, other): return np.subtract(self, other)
    def __mul__(self, other): return np.multiply(self, other)
    def __truediv__(self, other): return np.true_divide(self, other)
    def __pow__(self, other): return np.power(self, other)

# Register array box
ArrayBox.register(_np.ndarray)
for type_ in [float, _np.float64, _np.float32]:
    ArrayBox.register(type_)

# Create numpy namespace
class AutogradNumpy:
    pass

np = AutogradNumpy()

# Define some basic VJPs
def unbroadcast(target, g):
    while _np.ndim(g) > _np.ndim(target):
        g = _np.sum(g, axis=0)
    for axis, size in enumerate(_np.shape(target)):
        if size == 1:
            g = _np.sum(g, axis=axis, keepdims=True)
    return g

def defvjp(fun, *vjps):
    for argnum, vjp in zip(count(), vjps):
        if vjp is not None:
            primitive_vjps[fun][argnum] = vjp

# Define core numpy functions and their VJPs
basic_funcs = ['add', 'subtract', 'multiply', 'true_divide', 'power', 
               'negative', 'exp', 'log', 'sin', 'cos', 'tanh']

for name in basic_funcs:
    setattr(np, name, primitive(getattr(_np, name)))

defvjp(np.add,      lambda g, ans, x, y: unbroadcast(x, g),
                    lambda g, ans, x, y: unbroadcast(y, g))
defvjp(np.multiply, lambda g, ans, x, y: unbroadcast(x, y * g),
                    lambda g, ans, x, y: unbroadcast(y, x * g))
defvjp(np.subtract, lambda g, ans, x, y: unbroadcast(x, g),
                    lambda g, ans, x, y: unbroadcast(y, -g))
defvjp(np.true_divide, lambda g, ans, x, y: unbroadcast(x, g / y),
                       lambda g, ans, x, y: unbroadcast(y, -g * x / y**2))
defvjp(np.power,    lambda g, ans, x, y: unbroadcast(x, g * y * x ** (y - 1)),
                    lambda g, ans, x, y: unbroadcast(y, g * _np.log(x) * x ** y))
defvjp(np.negative, lambda g, ans, x: -g)
defvjp(np.exp,      lambda g, ans, x: ans * g)
defvjp(np.log,      lambda g, ans, x: g / x)
defvjp(np.sin,      lambda g, ans, x: g * _np.cos(x))
defvjp(np.cos,      lambda g, ans, x: -g * _np.sin(x))
defvjp(np.tanh,     lambda g, ans, x: g / _np.cosh(x) ** 2)

# Testing utilities
def finite_difference(f, x, eps=1e-8):
    """Compute gradient using finite difference."""
    return (f(x + eps) - f(x - eps)) / (2 * eps)

def check_gradient(f, x, tol=1e-4):
    """Compare autograd gradient with finite difference."""
    grad_f = grad(f)
    auto_grad = grad_f(x)
    num_grad = finite_difference(f, x)
    diff = abs(auto_grad - num_grad)
    print(f"x = {x}")
    print(f"Autograd gradient: {auto_grad}")
    print(f"Numeric gradient: {num_grad}")
    print(f"Difference: {diff}")
    assert diff < tol, f"Gradient check failed! Difference: {diff}"
    print("Gradient check passed!")

# Example usage and testing:
if __name__ == "__main__":
    def example_fun(x):
        return np.sin(x) * np.exp(x)
    
    x = 2.0
    check_gradient(example_fun, x)