def where(condition: Tensor, t1: Tensor=None, t2: Tensor=None):
"""
Numpy where function equivalent.
## Parameters:
condition: `Tensor` - condition tensor
t1: `Tensor` - tensor from which to take elements if condition is met, defaults to None
t2: `Tensor` - tensor from which to take elements if condition is not met, defaults to None
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t1 = Tensor([1, 2, 3])
t2 = Tensor([4, 5, 6])
x = fn.where(t1 < 2, t1, t2)
```
"""
t1 = to_tensor(t1) if t1 is not None else None
t2 = to_tensor(t2) if t2 is not None else None
data = np.where(condition.data, t1.data if t1 else None, t2.data if t2 else None)
t1g = to_tensor(t1).requires_grad if t1 else False
t2g = to_tensor(t2).requires_grad if t2 else False
requires_grad = (t1g or t2g) and not Tensor.NO_GRAD
nodes = []
if t1g:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1, df=lambda x: np.where(condition.data, x, np.zeros_like(x))))
if t2g:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1, df=lambda x: np.where(condition.data, np.zeros_like(x), x)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def mul(t1: Tensor, t2: Tensor):
"""
Multiplites two tensors (dot-product).
## Parameters:
t1: `Tensor` - first tensor
t2: `Tensor` - second tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t1 = Tensor([1, 2, 3])
t2 = Tensor([4, 5, 6])
x = fn.mul(t1, t2)
```
"""
data = t1.data * t2.data
requires_grad = (t1.requires_grad or t2.requires_grad) and not Tensor.NO_GRAD
nodes = []
if t1.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1, df=lambda x: _broadcast(t1.grad.data, t2.data*x)))
if t2.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t2, df=lambda x: _broadcast(t2.grad.data, t1.data*x)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def conv(x: Tensor, w: Tensor, stride: tuple, padding: tuple):
"""
Performs convolution.
## Parameters
x: `Tensor` - input tensor
w: `Tensor` - filter
stride: `tuple` - (vertical stride, horizontal stride)
padding: `tuple` - (vertical padding, horizontal padding)
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
import numpy as np
x = Tensor(data=np.random.rand(32, 1, 28, 28), requires_grad=True)
w = Tensor(data=np.random.rand(10, 1, 5, 5), requires_grad=True)
output = fn.conv(x, w, (1, 1), (0, 0))
```
"""
data = _conv(x.data, w.data, stride, padding)
requires_grad = (x.requires_grad or w.requires_grad) and not Tensor.NO_GRAD
nodes = []
if x.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=x, df=lambda g: _conv_grad(0, g, x.data, w.data, stride, padding)))
if w.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=w, df=lambda g: _conv_grad(1, g, x.data, w.data, stride, padding)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def power(t1: Tensor, t2: Tensor):
"""
Raises first tensor to the power of second tensor.
## Parameters:
t1: `Tensor` - first tensor
t2: `Tensor` - second tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t1 = Tensor([1, 4, 3])
t2 = Tensor([2, 5, 6])
x = fn.power(t1, t2)
```
"""
data = np.power(t1.data, t2.data)
requires_grad = (t1.requires_grad or t2.requires_grad) and not Tensor.NO_GRAD
nodes = []
if t1.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1,
df=lambda x: _broadcast(t1.data, x*t2.data*(t1.data**np.where(t2.data, t2.data-1, 1.)))))
if t2.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t2,
df=lambda x: _broadcast(t2.data, x * np.log((np.where(t1.data, t1.data, 1.)) * data))))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def minimum(t1: Tensor, t2: Tensor):
"""
Element-wise minimum of two tensor.
## Parameters:
t1: `Tensor` - first tensor
t2: `Tensor` - second tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t1 = Tensor([1, 4, 3])
t2 = Tensor([2, 5, 6])
x = fn.minimum(t1, t2)
```
"""
data = np.minimum(t1.data, t2.data)
requires_grad = (t1.requires_grad or t2.requires_grad) and not Tensor.NO_GRAD
nodes = []
def min_grad(x, z, y):
return (x == z) / (1.0 + (x == y))
if t1.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1, df=lambda x: _broadcast(t1.data, x * min_grad(t1.data, data, t2.data))))
if t2.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t2, df=lambda x: _broadcast(t2.data, x * min_grad(t2.data, data, t1.data))))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def matmul(t1: Tensor, t2: Tensor):
"""
Matrix multiplications of two tensors.
## Parameters:
t1: `Tensor` - first tensor
t2: `Tensor` - second tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t1 = Tensor([1, 2, 3])
t2 = Tensor([4, 5, 6])
x = fn.matmul(t1, t2)
```
"""
data = np.matmul(t1.data, t2.data)
requires_grad = (t1.requires_grad or t2.requires_grad) and not Tensor.NO_GRAD
nodes = []
if t1.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t1, df=lambda x: np.matmul(x, t2.data.T)))
if t2.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t2, df=lambda x: np.matmul(t1.data.T, x)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def average_pool(x: Tensor, kernel: tuple, stride: tuple, padding: tuple):
"""
Performs average pooling.
## Parameters
x: `Tensor` - input tensor
kernel: `tuple` - kernel shape
stride: `tuple` - stride
padding: `tuple` - padding
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
import numpy as np
x = Tensor(data=np.random.rand(32, 10, 24, 24), requires_grad=True)
sample = fn.average_pool(x, kernel=(2, 2), stride=(2, 2), padding=(0, 0))
```
"""
data = _average_pool(x.data, kernel, stride, padding)
requires_grad = x.requires_grad and not Tensor.NO_GRAD
nodes = []
if x.requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=x, df=lambda g: _average_pool_grad(g, x.data, kernel, stride, padding)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def slice(t: Tensor, index):
"""
Return values in the tensor at the given position.
## Parameter:
t: `Tensor` - input tensor
index: `tuple` - numpy-like index
## Example usage
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([[1, 1], [2, 2]])
x = fn.slice(t, (0,...))
"""
data = t.data[index]
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
def slice_grad(x):
grad = np.zeros_like(t.data)
grad[index] = x
return grad
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: slice_grad(x)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def max(t: Tensor, axis=None, keepdims=False):
"""
Returns max elements of the input tensor alongside given axis.
## Parameters
t: `Tensor` - input tensor
axis: `int` - defaults to None
keepdims: `bool` - defaults to None
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([[1, 2, 3], [4, 5, 6]])
x = fn.max(t, axis=1, keepdims=True)
```
"""
data = np.max(t.data, axis=axis, keepdims=keepdims)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: _min_max_grad(x, data, t.data, axis, keepdims)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def mean(t: Tensor, axis=None, keepdims=False):
"""
Numpy mean function equivalent.
## Parameters:
t: `Tensor` - input tensor
axis: `int` - defaults to None
keepdims: `bool` - defaults to False
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([[1, 2, 3], [4, 5, 6]])
x = fn.mean(t, axis=1)
```
"""
data = np.mean(t.data, axis=axis, dtype=np.float, keepdims=keepdims)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
def mean_grad(x):
g, n = _match_shape(x, np.shape(t.data), axis, keepdims)
return g / n
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: mean_grad(x)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def clip(t: Tensor, min_val, max_val):
"""
Clips input tensor to minimum and maximum value.
## Parameters:
t: `Tensor` - input tensor
min_val: `float` - minimum value
max_val: `float` - maximum value
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([2, 4, 6])
x = fn.clip(t, 3, 8)
```
"""
data = np.clip(t.data, min_val, max_val)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: x * np.logical_and(data != min_val, data != max_val)))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def sum(t: Tensor, axis=None, keepdims=False):
"""
Sums all the elements in tensor along given axis
## Parameters:
t: `Tensor`
axis: `int` - defaults to None
keepdims: `bool` - defaults to False
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([1, 2, 3])
x = fn.sum(t)
```
"""
data = np.sum(t.data, axis=axis, keepdims=keepdims)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: _match_shape(x, t.data.shape, axis, keepdims)[0]))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def tan(t: Tensor):
"""
Applies tan function to all the elements of the input tensor.
## Parameters:
t: `Tensor` - input tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([1, 2, 3])
x = fn.tan(t)
```
"""
data = np.tan(t.data)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: x / np.cos(t.data)**2))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def neg(t: Tensor):
"""
Unary negation of tensor elements.
## Parameters:
t: `Tensor` - input tensor
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([1, 2, 3])
x = -t
```
"""
data = -t.data
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: -x))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)
def reshape(t: Tensor, shape):
"""
Reshapes tensor.
## Parameters:
t: `Tensor` - input tensor
shape: `tuple` - new shape
## Example usage
```python
from beacon.tensor import Tensor
from beacon.tensor import functions as fn
t = Tensor([1, 2, 3], [4, 5, 6])
x = fn.reshape(t, shape=(1, 6))
```
"""
data = np.reshape(t.data, newshape=shape)
requires_grad = t.requires_grad and not Tensor.NO_GRAD
nodes = []
if requires_grad:
nodes.append(Tensor.ComputationalGraphNode(tensor=t, df=lambda x: np.reshape(x, np.shape(t.data))))
return Tensor(data=data, requires_grad=requires_grad, nodes=nodes)