import torch

Tensors

Tenson is a number, vector, matrix, or any N- Dimensional array.

t1 = torch.tensor(4.)
t1

tensor(4.)
t1.dtype

torch.float32
t2 = torch.tensor([1., 2, 3, 4])
print(t2)                                       # ALl the tensor elements are of same data type

# Matrix - 2D tensor

t3 = torch.tensor([[5, 6],
                   [7,8],
                   [9,10]])

print(t3)

tensor([1., 2., 3., 4.])
tensor([[ 5,  6],
        [ 7,  8],
        [ 9, 10]])

# most of the time we will use floating point numbers

t4 = torch.tensor([
    [[11,12,13],
     [13,14,15]],
    [[15,16,17],
    [17,18,19.]]
])

t4

tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])

Tensors can have any number of dimensions and different lengths along each dimension. we can inspect length using .shape property

print(t1)
t1.shape

tensor(4.)

torch.Size([])
print(t2)
t2.shape

tensor([1., 2., 3., 4.])

torch.Size([4])
print(t3)
t3.shape

tensor([[ 5,  6],
        [ 7,  8],
        [ 9, 10]])

torch.Size([3, 2])
print(t4)
t4.shape

# start from outer most bracket and count number of elements in that ie. here 2 elements both matrices than we go 1 bracket in and there is also 2 list elements and so on .....

tensor([[[11., 12., 13.],
         [13., 14., 15.]],

        [[15., 16., 17.],
         [17., 18., 19.]]])

torch.Size([2, 2, 3])

we can not make a tensor with an improper shape

Tensor Operations and Gradients 

x = torch.tensor(3.)
w = torch.tensor(4., requires_grad=True) #
b = torch.tensor(5., requires_grad=True)

x,w,b

(tensor(3.), tensor(4., requires_grad=True), tensor(5., requires_grad=True))
y = w * x + b
y

tensor(17., grad_fn=<AddBackward0>)
    
y.backward()

# derivatives of y w.r.t each of input tensors are stored in .grad property of respective tensors

print('dy/dx', x.grad)
print('dy/dw', w.grad)
print('dy/db', b.grad)

dy/dx None
dy/dw tensor(3.)
dy/db tensor(1.)

we have not specified requires_grad=True in x, this tells pytorch that we are not intrested in drivatives of any future output w.r.t x but we are intrested for w and b .... so requires_grad property is important to save millions of usless coputations of derrivatives as per requirement

"grad" in w.grad is short for gradient, which is another term for derivative primarily used while dealing with vectors and matrices

Tensor Functions 

t6 = torch.full((3,2), 42)
t6

tensor([[42, 42],
        [42, 42],
        [42, 42]])
t7 = torch.cat((t3,t6))
t7

tensor([[ 5,  6],
        [ 7,  8],
        [ 9, 10],
        [42, 42],
        [42, 42],
        [42, 42]])
t8 = torch.sin(t7)
t8

tensor([[-0.9589, -0.2794],
        [ 0.6570,  0.9894],
        [ 0.4121, -0.5440],
        [-0.9165, -0.9165],
        [-0.9165, -0.9165],
        [-0.9165, -0.9165]])
t9 = t8.reshape(3,2,2)
t9

tensor([[[-0.9589, -0.2794],
         [ 0.6570,  0.9894]],

        [[ 0.4121, -0.5440],
         [-0.9165, -0.9165]],

        [[-0.9165, -0.9165],
         [-0.9165, -0.9165]]])

Inter-operability with Numpy 

import numpy as np

x = np.array([[1,2],[3, 4.]])
x

array([[1., 2.],
       [3., 4.]])
y = torch.from_numpy(x)
y

tensor([[1., 2.],
        [3., 4.]], dtype=torch.float64)
x.dtype, y.dtype

(dtype('float64'), torch.float64)
z = y.numpy()
z

array([[1., 2.],
       [3., 4.]])