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import math
class Scalar:
def __init__(self, data, _children=(), _op='', label='') -> None:
self.label = label
self.data = float(data)
self.grad = 0.0
self._prev = set(_children)
self._op = _op
self._backward = lambda: None
def __add__(self, y):
y = y if isinstance(y, Scalar) else Scalar(y)
result = Scalar(self.data + y.data, (self, y), _op='+')
def _backward():
self.grad += result.grad
y.grad += result.grad
result._backward = _backward
return result
def __mul__(self, y):
y = y if isinstance(y, Scalar) else Scalar(y)
result = Scalar(self.data * y.data, (self, y), _op='*')
def _backward():
self.grad += y.data * result.grad
y.grad += self.data * result.grad
result._backward = _backward
return result
def __pow__(self, y):
assert isinstance(y, (int, float))
result = Scalar(self.data ** y, (self, ), _op=f'** {y}')
def _backward():
self.grad += (y * self.data ** (y - 1)) * result.grad
result._backward = _backward
return result
def exp(self):
x = self.data
e = math.exp(x)
result = Scalar(e, (self, ), 'exp')
def _backward():
self.grad += result.data * result.grad
result._backward = _backward
return result
def tanh(self):
x = self.data
t = (math.exp(2 * x) - 1) / (math.exp(2 * x) + 1)
result = Scalar(t, (self, ), 'tanh')
def _backward():
self.grad += (1 - t ** 2) * result.grad
result._backward = _backward
return result
def build_children(self):
result = []
visited = set()
def build(v):
if v not in visited:
visited.add(v)
for child in v._prev:
build(child)
result.append(v)
build(self)
return result
def backward(self):
self.grad = 1.0
children = self.build_children()
for child in reversed(children):
child._backward()
def zero_grad(self):
self.grad = 0.0
children = self.build_children()
for child in children:
child.grad = 0.0
def __truediv__(self, y):
return self * y ** -1
def __rtruediv__(self, y):
return self * y ** -1
def __neg__(self):
return self * -1
def __sub__(self, y):
return self + (-y)
def __rsub__(self, y):
return self + (-y)
def __radd__(self, y):
return self + y
def __rmul__(self, y):
return self * y
def __repr__(self) -> str:
return f'Scalar({self.data})'
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