Tensor Manipulation I

Key-points

• 텐서(Tensor)

• 넘파이(NumPy)

• 텐서 조작(Tensor Manipulation)

• 브로드캐스팅(Broadcasting)

Learning

• Vector, Matrix and Tensor

• Numpy Review

• PyTorch Tensor Allocation

• Matrix Multiplication

• Other Basic Ops

Vector, Matrix and Tensor

*Preview

*2D Tensor(Typical Simple Setting)

• |t| = (batch size, dim)

*3D Tensor(Typical Computer Vision)

• |t| = (batch size, width, height)

*3D Tensor(Typical NLP)

• |t| = (batch size, length, dim)

Numpy Review

Numpy와 Pytorch는 서로 호환이 너무 잘 되어서 직관적 이해가 편합니다.

#파이토치 설치
! pip install torchvision

#필요 라이브러리 import

import numpy as np
import torch

#1D Array with Numpy

t = np.array([0., 1., 2., 3., 4., 5., 6.])
print(t) #[0,1,2,3,4,5,6]

print('Rank of t :', t.ndim) #t의 차원, Rank of t: 1
print('Shape of t:', t.shape)#행렬 형태, Shape of : (7,)


print('t[0] t[1] t[-1] = ', t[0], t[1], t[-1])#Element, t[0] t[1] t[-1] =  0.0 1.0 6.0

print('t[2:5] t[4:-1] = ', t[2:5], t[4:-1]) #Slicing, t[2:5] t[4:-1] =  [2. 3. 4.] [4. 5.]

print('t[:2] t[3:] = ', t[:2], t[3:])#Slicing, t[:2] t[3:] =  [0. 1.] [3. 4. 5. 6.]

#1D Array with PyTorch

a = torch.FloatTensor([0.,1.,2.,3.,4.,5.,6.])
print(a) #tensor([0., 1., 2., 3., 4., 5., 6.])


print(a.dim()) # rank, 차원 , 1
print(a.shape) #shape 행렬, torch.Size([7])
print(a.size()) # shape, torch.Size([7])
print(a[0], a[1], a[-1]) #Element, tensor(0.) tensor(1.) tensor(6.)
print(a[2:5], a[4:-1]) #Slicing, tensor(0.) tensor(1.) tensor(6.)
print(a[:2], a[3:])#Slicing, tensor([0., 1.]) tensor([3., 4., 5., 6.])

#2D Array with Numpy

k = np.array([[1., 2., 3.], [4., 5., 6.],[7.,8.,9.], [10.,11.,12.]])
print(k)

#[[ 1.  2.  3.]
 [ 4.  5.  6.]
 [ 7.  8.  9.]
 [10. 11. 12.]]
 
print('Rank of k: ', k.ndim)#k차원, Rank of k:  2
print('Shape of k: ', k.shape)#행렬 형태, Shape of k:  (4, 3)

#2D Array with PyTorch

b = torch.FloatTensor([[1., 2., 3.],
                       [4., 5., 6.],
                       [7., 8., 9.],
                       [10., 11., 12.]])
print(b)

##tensor([[ 1.,  2.,  3.],
        [ 4.,  5.,  6.],
        [ 7.,  8.,  9.],
        [10., 11., 12.]])
        
print(b.dim()) #rank 
print(b.size()) #shape
print(b[:, 1])
print(b[:, 1].size())
print(b[:, :-1])

#
2
torch.Size([4, 3])
tensor([ 2.,  5.,  8., 11.])
torch.Size([4])
tensor([[ 1.,  2.],
        [ 4.,  5.],
        [ 7.,  8.],
        [10., 11.]])

Broadcasting

 #Same shape

a =  torch.FloatTensor([[3,3]])
b = torch.FloatTensor([[2,2]])

print(a + b) # tensor([[5., 5.]])

#Vector + Scalar

a1 = torch.FloatTensor([[1, 2]])
a2 = torch.FloatTensor([3]) # 3 --> [[3,3]]

# 사이즈가 달라도 사이즈를 맞혀준다
print(a1 + a2) #tensor([[4., 5.]])

# 2 x 1 vector + 1 x 2 vector

b1 = torch.FloatTensor([[1, 2]])
b2 = torch.FloatTensor([[3], [4]])#[3,3], [4,4]
print(b1 + b2) 

#tensor([[4., 5.],
        [5., 6.]])

Multiplication vs Matrix Multiplication

print()
print('-----------')
print('Mul vs Matmul')
print('-----------')

a = torch.FloatTensor([[1, 2], [3, 4]])
b = torch.FloatTensor([[1], [2]])

print('Shape of Matrix 1: ', a.shape) #2x2
print('Shape of Matrix 2: ', b.shape) #2x1
print(a.matmul(b)) #2x1

c = torch.FloatTensor([[1, 2], [3, 4]])
d = torch.FloatTensor([[1], [2]])

print('Shape of Matrix 1: ', c.shape) #2x2
print('Shape of Matrix 2: ', d.shape) #2x1
print(c.mul(d)) #2x1

Mean

k = torch.FloatTensor([1,2])
print(k.mean()) #tensor(1.5000)

#Can't use mean() on integers

k1 = torch.LongTensor([1, 2])

try:
    print(k1.mean())
    
except Exception as exc:
    print(exc)

#mean(): input dtype should be either floating point or complex dtypes. Got Long instead.

k2 = torch.FloatTensor([[1, 2], [3, 4]])
print(k2) 

# tensor([[1., 2.],
        [3., 4.]])
        
print(k2.mean())
print(k2.mean(dim=0))
print(k2.mean(dim=1))
print(k2.mean(dim=-1)) 

#결과

tensor(2.5000)
tensor([2., 3.])
tensor([1.5000, 3.5000])
tensor([1.5000, 3.5000])

Max and Argmax

r = torch.FloatTensor([[10, 20], [30, 40]])
print(r)

#결과

tensor([[10., 20.],
        [30., 40.]])

print(r.max())# Returns on value: max , tensor(40.)

print(r.max(dim = 0))
print('Max: ', r.max(dim=0)[0])
print('Argmax: ', r.max(dim=0)[1])

#결과

torch.return_types.max(
values=tensor([30., 40.]),
indices=tensor([1, 1]))
Max:  tensor([30., 40.])
Argmax:  tensor([1, 1])


print(r.max(dim=1))
print(r.max(dim=-1))

#결과

torch.return_types.max(
values=tensor([20., 40.]),
indices=tensor([1, 1]))
torch.return_types.max(
values=tensor([20., 40.]),
indices=tensor([1, 1]))