Mathematical Operations with Tensors
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:
123456789101112131415import 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:
123456import 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:
12345import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[5, 6], [7, 8]]) 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.
12345678910import 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 toaxisin NumPy) along which the operation is applied. By default, ifdimis not provided, the operation is applied to all elements of the tensor;keepdim: a boolean flag (Falseby default). If set toTrue, the reduced dimension is retained as a size1dimension in the output, preserving the original number of dimensions.
12345678import 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.
123456import torch 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.
1234567tensor = 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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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:
123456789101112131415import 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:
123456import 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:
12345import torch x = torch.tensor([[1, 2], [3, 4]]) y = torch.tensor([[5, 6], [7, 8]]) 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.
12345678910import 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 toaxisin NumPy) along which the operation is applied. By default, ifdimis not provided, the operation is applied to all elements of the tensor;keepdim: a boolean flag (Falseby default). If set toTrue, the reduced dimension is retained as a size1dimension in the output, preserving the original number of dimensions.
12345678import 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.
123456import torch 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.
1234567tensor = 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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