

In [1]:

    
import torch
import numpy as np
from __future__ import print_function

What is a Tensor?

Scalar is a single number.
Vector is an array of numbers.
Matrix is a 2-D array of numbers.
Tensors are N-D arrays of numbers.



In [2]:

    
x = torch.Tensor(5, 3)
print(x)









    



 8.5289e+30  4.5849e-41  8.5289e+30
 4.5849e-41  0.0000e+00  0.0000e+00
 0.0000e+00  0.0000e+00  0.0000e+00
 0.0000e+00  0.0000e+00  0.0000e+00
 8.9683e-44  0.0000e+00  1.5695e-43
[torch.FloatTensor of size 5x3]



In [3]:

    
x.zero_()









    Out[3]:





 0  0  0
 0  0  0
 0  0  0
 0  0  0
 0  0  0
[torch.FloatTensor of size 5x3]



In [4]:

    
torch.Tensor([[1, 2, 3],  # rank 2 tensor
              [4, 5, 6],
              [7, 8, 9]])









    Out[4]:





 1  2  3
 4  5  6
 7  8  9
[torch.FloatTensor of size 3x3]



In [5]:

    
x.size()









    Out[5]:





torch.Size([5, 3])



In [6]:

    
x = torch.rand(5, 3)
print(x)









    



 0.6483  0.0793  0.5400
 0.4856  0.7982  0.0293
 0.5717  0.4678  0.6365
 0.8806  0.0632  0.2726
 0.3934  0.7143  0.9290
[torch.FloatTensor of size 5x3]



In [7]:

    
npy = np.random.rand(5, 3)
y = torch.from_numpy(npy)
print(y)









    



 0.0576  0.1174  0.9857
 0.6809  0.1037  0.7149
 0.2107  0.7510  0.7408
 0.3281  0.5182  0.5043
 0.7946  0.7321  0.0289
[torch.DoubleTensor of size 5x3]



In [40]:

    
z = x + y  #can we do this addition?



In [9]:

    
x.type(), y.type()









    Out[9]:





('torch.FloatTensor', 'torch.DoubleTensor')



In [10]:

    
z = x + y.float()
print(z)









    



 0.7059  0.1967  1.5258
 1.1665  0.9019  0.7442
 0.7824  1.2188  1.3774
 1.2087  0.5815  0.7768
 1.1880  1.4464  0.9579
[torch.FloatTensor of size 5x3]



In [11]:

    
torch.add(x, y.float())









    Out[11]:





 0.7059  0.1967  1.5258
 1.1665  0.9019  0.7442
 0.7824  1.2188  1.3774
 1.2087  0.5815  0.7768
 1.1880  1.4464  0.9579
[torch.FloatTensor of size 5x3]



In [12]:

    
x









    Out[12]:





 0.6483  0.0793  0.5400
 0.4856  0.7982  0.0293
 0.5717  0.4678  0.6365
 0.8806  0.0632  0.2726
 0.3934  0.7143  0.9290
[torch.FloatTensor of size 5x3]



In [13]:

    
x.add_(1)









    Out[13]:





 1.6483  1.0793  1.5400
 1.4856  1.7982  1.0293
 1.5717  1.4678  1.6365
 1.8806  1.0632  1.2726
 1.3934  1.7143  1.9290
[torch.FloatTensor of size 5x3]



In [14]:

    
x









    Out[14]:





 1.6483  1.0793  1.5400
 1.4856  1.7982  1.0293
 1.5717  1.4678  1.6365
 1.8806  1.0632  1.2726
 1.3934  1.7143  1.9290
[torch.FloatTensor of size 5x3]



In [15]:

    
x[:2, :2]









    Out[15]:





 1.6483  1.0793
 1.4856  1.7982
[torch.FloatTensor of size 2x2]



In [16]:

    
x * y.float()









    Out[16]:





 0.0950  0.1267  1.5181
 1.0116  0.1864  0.7359
 0.3312  1.1023  1.2124
 0.6170  0.5510  0.6417
 1.1072  1.2550  0.0557
[torch.FloatTensor of size 5x3]



In [17]:

    
torch.exp(x)









    Out[17]:





 5.1981  2.9428  4.6647
 4.4176  6.0391  2.7991
 4.8146  4.3398  5.1374
 6.5573  2.8957  3.5701
 4.0286  5.5531  6.8828
[torch.FloatTensor of size 5x3]



In [18]:

    
torch.transpose(x, 0, 1)









    Out[18]:





 1.6483  1.4856  1.5717  1.8806  1.3934
 1.0793  1.7982  1.4678  1.0632  1.7143
 1.5400  1.0293  1.6365  1.2726  1.9290
[torch.FloatTensor of size 3x5]



In [19]:

    
#transposing, indexing, slicing, mathematical operations, linear algebra, random numbers



In [20]:

    
torch.trace(x)









    Out[20]:





5.0830910205841064



In [21]:

    
x.numpy()









    Out[21]:





array([[ 1.64829206,  1.0793463 ,  1.54002655],
       [ 1.48560095,  1.79824984,  1.02928591],
       [ 1.57166302,  1.46782982,  1.63654912],
       [ 1.88058376,  1.06322587,  1.27258039],
       [ 1.39342725,  1.71434927,  1.9290216 ]], dtype=float32)



In [22]:

    
torch.cuda.is_available()









    Out[22]:





True



In [23]:

    
if torch.cuda.is_available():
    x_gpu = x.cuda()
    print(x_gpu)









    



 1.6483  1.0793  1.5400
 1.4856  1.7982  1.0293
 1.5717  1.4678  1.6365
 1.8806  1.0632  1.2726
 1.3934  1.7143  1.9290
[torch.cuda.FloatTensor of size 5x3 (GPU 0)]



In [24]:

    
from torch.autograd import Variable



In [25]:

    
x = torch.rand(5, 3)
print(x)









    



 0.5759  0.1624  0.1933
 0.6926  0.3969  0.3648
 0.0467  0.9384  0.9780
 0.0718  0.2979  0.9483
 0.1604  0.4656  0.2753
[torch.FloatTensor of size 5x3]



In [26]:

    
x = Variable(torch.rand(5, 3))
print(x)









    



Variable containing:
 0.7786  0.9588  0.3944
 0.2147  0.5184  0.6126
 0.2722  0.9937  0.2327
 0.9567  0.5470  0.4463
 0.6881  0.2854  0.4447
[torch.FloatTensor of size 5x3]

Each variable holds data, a gradient, and information about the function that created it. <img src="figures/intro_to_pytorch/pytorch_variable.svg",width=400,height=400>



In [28]:

    
x.data









    Out[28]:





 0.7786  0.9588  0.3944
 0.2147  0.5184  0.6126
 0.2722  0.9937  0.2327
 0.9567  0.5470  0.4463
 0.6881  0.2854  0.4447
[torch.FloatTensor of size 5x3]



In [29]:

    
# should be nothing right now
assert x.grad_fn is None
assert x.grad is None



In [31]:

    
x = Variable(torch.Tensor([2]), requires_grad=True)
w = Variable(torch.Tensor([3]), requires_grad=True)
b = Variable(torch.Tensor([1]), requires_grad=True)

z = x * w
y = z + b

y









    Out[31]:





Variable containing:
 7
[torch.FloatTensor of size 1]

Compare the above computations to the below graph.. and then the one below that!



In [32]:

    
y.backward()



In [33]:

    
y, b









    Out[33]:





(Variable containing:
  7
 [torch.FloatTensor of size 1], Variable containing:
  1
 [torch.FloatTensor of size 1])

Since the derivative of w*x wrt x is w, and vice versa:



In [34]:

    
w.grad, w









    Out[34]:





(Variable containing:
  2
 [torch.FloatTensor of size 1], Variable containing:
  3
 [torch.FloatTensor of size 1])



In [35]:

    
x.grad, x









    Out[35]:





(Variable containing:
  3
 [torch.FloatTensor of size 1], Variable containing:
  2
 [torch.FloatTensor of size 1])

$ y = 2w + b$, since $x = 2$

Say we want: $\displaystyle\frac{\partial y}{\partial w}$



In [36]:

    
a = Variable(torch.Tensor([2]), requires_grad=True)

Let's compute, $\displaystyle\frac{\partial}{\partial a}(3a^2 + 2a + 1)$ when $a = 2$



In [37]:

    
y = 3*a*a + 2*a + 1



In [38]:

    
y.backward()



In [39]:

    
a.grad









    Out[39]:





Variable containing:
 14
[torch.FloatTensor of size 1]

checks out, since $\displaystyle\frac{\partial}{\partial a}(3a^2 + 2a + 1) = 6a + 2$ and $a = 2$