Mathematical Operations with Tensors

We'll now explore how to perform mathematical operations with PyTorch tensors. These operations form the basis for building and training neural networks, so understanding them is essential.

Element-wise Operations

Element-wise operations are applied to each element in the tensor individually. These operations, such as addition, subtraction, and division, work similarly to how they do in NumPy:


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import torch
a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
# Element-wise addition
addition_result = a + b
print(f"Addition: {addition_result}")
# Element-wise subtraction
subtraction_result = a - b
print(f"Subtraction: {subtraction_result}")
# Element-wise multiplication
multiplication_result = a * b
print(f"Multiplication: {multiplication_result}")
# Element-wise division
division_result = a / b
print(f"Division: {division_result}")

Matrix Operations

PyTorch also supports matrix multiplication and dot product, which are performed using the torch.matmul() function:


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import torch
x = torch.tensor([[1, 2], [3, 4]])
y = torch.tensor([[5, 6], [7, 8]])
# Matrix multiplication
z = torch.matmul(x, y)
print(f"Matrix multiplication: {z}")

You can also use the @ operator for matrix multiplication:


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import torch
z = x @ y
print(f"Matrix Multiplication with @: {z}")

Aggregation Operations

Aggregation operations compute summary statistics from tensors, such as sum, mean, maximum, and minimum values, which can be calculated using their respective methods.


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import torch
tensor = torch.tensor([[1, 2, 3], [4, 5, 6]]).float()
# Sum of all elements
print(f"Sum: {tensor.sum()}")
# Mean of all elements
print(f"Mean: {tensor.mean()}")
# Maximum value
print(f"Max: {tensor.max()}")
# Minimum value
print(f"Min: {tensor.min()}")

Aggregation methods also have two optional parameters:

dim: specifies the dimension (similarly to axis in NumPy) along which the operation is applied. By default, if dim is not provided, the operation is applied to all elements of the tensor;
keepdim: a boolean flag (False by default). If set to True, the reduced dimension is retained as a size 1 dimension in the output, preserving the original number of dimensions.


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import torch
tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])
# Aggregation operations along specific dimensions
print(f"Sum along rows (dim=1): {tensor.sum(dim=1)}")
print(f"Sum along columns (dim=0): {tensor.sum(dim=0)}")
# Aggregation with keepdim=True
print(f"Sum along rows with keepdim (dim=1): {tensor.sum(dim=1, keepdim=True)}")
print(f"Sum along columns with keepdim (dim=0): {tensor.sum(dim=0, keepdim=True)}")

Broadcasting

Broadcasting allows operations between tensors of different shapes by automatically expanding dimensions. IIf you need a refresher on broadcasting, you can find more details here.


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a = torch.tensor([[1, 2, 3]])  # Shape (1, 3)
b = torch.tensor([[4], [5]])  # Shape (2, 1)
# Broadcasting addition
c = a + b
print(f"Broadcasted addition: {c}")

Useful Mathematical Functions

PyTorch also provides various mathematical functions such as exponentials, logarithms, and trigonometric functions.


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tensor = torch.tensor([1.0, 2.0, 3.0])
# Exponentiation
print(f"Exponent: {tensor.exp()}")
# Logarithm
print(f"Logarithm: {tensor.log()}")
# Sine
print(f"Sine: {tensor.sin()}")

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Sección 1. Capítulo 7