Alternatives to torch.Tensor.minimum() for Element-wise Minimum Comparisons

torch.Tensor.minimum()

In PyTorch, torch.Tensor.minimum() is a function used to perform element-wise minimum comparisons between a tensor and another tensor or a constant value. It returns a new tensor containing the smaller values from each corresponding element in the inputs.

Key Points

• Data types
  It supports most numeric data types in PyTorch, but not complex numbers.
• Output
  The resulting tensor has the same dimensions as the input tensors.
• Input types
  It can handle comparisons between two tensors or a tensor and a constant value (scalar).
• Element-wise comparison
  It operates on each element of the input tensors independently.

Example

import torch

# Create two tensors
tensor1 = torch.tensor([3, 1, 4])
tensor2 = torch.tensor([2, 5, 1])

# Element-wise minimum comparison
result = torch.minimum(tensor1, tensor2)
print(result)  # Output: tensor([2, 1, 1])

torch.min() (alternative for finding minimum across all elements)

# Find minimum value across all elements
min_value = torch.min(tensor1)
print(min_value)  # Output: tensor(1)

• NaN handling
  If either operand in the element-wise comparison is NaN (Not a Number), NaN is returned in the corresponding element of the output tensor.
• dim and keepdim arguments (advanced)
  torch.min() offers optional arguments dim and keepdim for finding minimum values along specific dimensions and preserving the original dimension if desired. Refer to the PyTorch documentation for more details on these arguments.

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Minimum with Constant Value

This example compares a tensor with a constant value (scalar) and returns the element-wise minimum:

import torch

tensor = torch.tensor([5, 2, 8, 1])
constant_value = 3

result = torch.minimum(tensor, constant_value)
print(result)  # Output: tensor([3, 2, 3, 1])

Finding Minimum Along a Dimension (with dim argument)

This code demonstrates using the dim argument with torch.min() to find the minimum value along a specific dimension:

import torch

matrix = torch.tensor([[3, 1, 4], [7, 2, 5], [0, 9, 6]])

# Find minimum values along columns (dim=1)
min_values, min_indices = torch.min(matrix, dim=1)
print(min_values)  # Output: tensor([ 1,  2,  0])
print(min_indices)  # Output: tensor([1, 1, 0])

Preserving Dimension (with keepdim argument)

This example shows how the keepdim argument in torch.min() can be used to retain the original dimension in the output:

import torch

vector = torch.tensor([4, 8, 2])

# Find minimum value, keeping dimension
min_value, min_indices = torch.min(vector.unsqueeze(0), dim=1, keepdim=True)
print(min_value)  # Output: tensor([[2]])
print(min_indices)  # Output: tensor([[2]])

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Manual Element-wise Comparison with torch.lt() and torch.where()

This approach uses a combination of functions to achieve the same result as torch.Tensor.minimum():

import torch

tensor1 = torch.tensor([3, 1, 4])
tensor2 = torch.tensor([2, 5, 1])

# Element-wise comparison using boolean mask and selection
result = torch.where(tensor1 < tensor2, tensor1, tensor2)
print(result)  # Output: tensor([2, 1, 1])

Here, torch.lt(tensor1, tensor2) creates a boolean mask where True indicates elements in tensor1 are less than those in tensor2. Then, torch.where() uses this mask to select the appropriate elements from either tensor1 or tensor2 for the output tensor.

This approach offers more flexibility but can be less concise than torch.Tensor.minimum().

Utilizing NumPy (if applicable)

If you're working with tensors that can be converted to NumPy arrays (e.g., CPU tensors), you could leverage NumPy's np.minimum() function for element-wise minimum calculations:

import torch
import numpy as np

tensor1 = torch.tensor([3, 1, 4])
tensor2 = torch.tensor([2, 5, 1])

# Convert to NumPy arrays (assuming CPU tensors)
tensor1_np = tensor1.numpy()
tensor2_np = tensor2.numpy()

# Perform minimum comparison with NumPy
result_np = np.minimum(tensor1_np, tensor2_np)
print(result_np)  # Output: [2 1 1]

# Convert back to PyTorch tensor (optional)
result_torch = torch.from_numpy(result_np)

• Keep in mind performance implications when working with large tensors, especially if using NumPy conversions.
• If you need more control over the element-wise comparison or have specific NumPy integration needs, consider the manual approach or NumPy usage.
• For clarity and efficiency within PyTorch, torch.Tensor.minimum() is generally the preferred choice.