def add_(t1: "Tensor",
t2: "Tensor") -> Tuple[np.ndarray, bool, List[ContextGraph]]:
"""Addition of two tensors
Parameters
----------
t1 : "Tensor"
t1
t2 : 'Tensor'
t2
Returns
-------
Tuple[np.ndarray, bool, List[ContextGraph]]
"""
o = t1.data + t2.data
requires_grad = t1.requires_grad or t2.requires_grad
_ctx: List[ContextGraph] = []
if t1.requires_grad:
def grad_fn1(grad: np.ndarray) -> np.ndarray:
for _ in range(grad.ndim - t1.data.ndim):
grad = grad.sum(axis=0)
for i, dim in enumerate(t1.shape):
if dim == 1:
grad = grad.sum(axis=i, keepdims=True)
return grad
_ctx.append(ContextGraph(t1, grad_fn1))
if t2.requires_grad:
def grad_fn2(grad: np.ndarray) -> np.ndarray:
for _ in range(grad.ndim - t2.data.ndim):
grad = grad.sum(axis=0)
for i, dim in enumerate(t2.shape):
if dim == 1:
grad = grad.sum(axis=i, keepdims=True)
return grad
_ctx.append(ContextGraph(t2, grad_fn2))
return o, requires_grad, _ctx
def sum_(t: "Tensor") -> Tuple[np.ndarray, bool, List[ContextGraph]]:
"""Sum of elements of a Tensor
Parameters
----------
t : 'Tensor'
t
Returns
-------
Tuple[np.ndarray, bool, List[ContextGraph]]
"""
o = t.data.sum()
requires_grad = t.requires_grad
if requires_grad:
def grad_fn(grad: np.ndarray) -> np.ndarray:
return grad * np.ones_like(t.data)
_ctx = [ContextGraph(t, grad_fn)]
else:
_ctx = []
return o, requires_grad, _ctx
def neg_(t: "Tensor") -> Tuple[np.ndarray, bool, List[ContextGraph]]:
o = -t.data
requires_grad = t.requires_grad
if requires_grad:
_ctx = [ContextGraph(t, lambda x: -x)]
else:
_ctx = []
return o, requires_grad, _ctx
def div_(t1: "Tensor",
t2: "Tensor") -> Tuple[np.ndarray, bool, List[ContextGraph]]:
o = t1.data / t2.data
requires_grad = t1.requires_grad or t2.requires_grad
_ctx: List[ContextGraph] = []
if t1.requires_grad:
def grad_fn1(grad: np.ndarray) -> np.ndarray:
grad = grad * (1 / t2.data)
for _ in range(grad.ndim - t1.data.ndim):
grad = grad.sum(axis=0)
for i, dim in enumerate(t1.shape):
if dim == 1:
grad = grad.sum(axis=i, keepdims=True)
return grad
_ctx.append(ContextGraph(t1, grad_fn1))
if t2.requires_grad:
def grad_fn2(grad: np.ndarray) -> np.ndarray:
grad = grad * (-t1.data / (t2.data**2))
for _ in range(grad.ndim - t2.data.ndim):
grad = grad.sum(axis=0)
for i, dim in enumerate(t2.shape):
if dim == 1:
grad = grad.sum(axis=i, keepdims=True)
return grad
_ctx.append(ContextGraph(t2, grad_fn2))
return o, requires_grad, _ctx
def matmul_(t1: "Tensor",
t2: "Tensor") -> Tuple[np.ndarray, bool, List[ContextGraph]]:
o = t1.data @ t2.data
requires_grad = t1.requires_grad or t2.requires_grad
_ctx: List[ContextGraph] = []
if t1.requires_grad:
def grad_fn1(grad: np.ndarray) -> np.ndarray:
return grad @ t2.data.T
_ctx.append(ContextGraph(t1, grad_fn1))
if t2.requires_grad:
def grad_fn2(grad: np.ndarray) -> np.ndarray:
return t1.data.T @ grad
_ctx.append(ContextGraph(t2, grad_fn2))
return o, requires_grad, _ctx
def pow_(t: "Tensor", p: float) -> Tuple[np.ndarray, bool, List[ContextGraph]]:
"""Tensor to the power `p`"""
o = t.data**p
requires_grad = t.requires_grad
if requires_grad:
def grad_fn(grad: np.ndarray) -> np.ndarray:
return grad * (t.data**(p - 1)) * p
_ctx = [ContextGraph(t, grad_fn)]
else:
_ctx = []
return o, requires_grad, _ctx
def slice_(t: "Tensor", idx) -> Tuple[np.ndarray, bool, List[ContextGraph]]:
o = t.data[idx]
requires_grad = t.requires_grad
if requires_grad:
def grad_fn(grad: np.ndarray) -> np.ndarray:
partial_grad = np.zeros_like(o)
partial_grad[idx] = grad
return partial_grad
_ctx.append(ContextGraph(t, grad_fn))
else:
_ctx = []
return o, requires_grad, _ctx