Unlocking Polygamma in PyTorch Tensors: Loop-based Approach, SciPy Integration, and Future Possibilities

What it is

• torch.Tensor.polygamma is not actually a documented method in PyTorch. There seems to be a mismatch between what you might have encountered and the official PyTorch documentation.

Polygamma Function

• PyTorch offers the polygamma function within the torch.special module, but it doesn't currently allow element-wise computation for tensors (as of PyTorch 1.13). This means you cannot directly apply polygamma to each element of a tensor.
• The polygamma function, denoted by polygamma(n, x), is a generalization of the derivative of the logarithm of the gamma function (digamma). It represents the nth derivative of ln(Gamma(x)).

Alternative Approaches

1. • If you need polygamma values for multiple elements, you can iterate through a tensor and calculate polygamma for each element separately:

   import torch
   
   def polygamma_loop(n, x):
       y = torch.empty_like(x)
       for i in range(x.size(0)):
           for j in range(x.size(1)):  # Assuming a 2D tensor
               y[i, j] = torch.special.polygamma(n, x[i, j])
       return y
   
   n = 1  # Order of the polygamma function
   x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
   y = polygamma_loop(n, x)
   print(y)
   

2. Using scipy (if available)
   

   • If you have scipy installed, you can leverage its special.polygamma function, which supports element-wise computations on NumPy arrays. However, this requires converting your PyTorch tensors to NumPy arrays and back:

   import torch
   import numpy as np
   from scipy.special import polygamma
   
   n = 1
   x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
   x_numpy = x.detach().cpu().numpy()  # Detach and move to CPU
   y_numpy = polygamma(n, x_numpy)
   y = torch.from_numpy(y_numpy)
   print(y)
   

Future Considerations

---

Loop-based approach (improved readability)

import torch

def polygamma_loop(n, x):
    """Calculates polygamma values element-wise for a tensor.

    Args:
        n (int): Order of the polygamma function.
        x (torch.Tensor): Input tensor.

    Returns:
        torch.Tensor: Output tensor containing polygamma values.
    """

    y = torch.empty_like(x)
    for i in range(x.size(0)):
        for j in range(x.size(1)):  # Assuming a 2D tensor
            y[i, j] = torch.special.polygamma(n, x[i, j])
    return y

# Example usage
n = 1  # Order of the polygamma function
x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
y = polygamma_loop(n, x)
print(y)

Using scipy (if available, with error handling)

import torch
import numpy as np
from scipy.special import polygamma

def polygamma_scipy(n, x):
    """Calculates polygamma values using scipy (if available).

    Args:
        n (int): Order of the polygamma function.
        x (torch.Tensor): Input tensor.

    Returns:
        torch.Tensor: Output tensor containing polygamma values.

    Raises:
        ImportError: If `scipy` is not installed.
    """

    try:
        x_numpy = x.detach().cpu().numpy()  # Detach and move to CPU
        y_numpy = polygamma(n, x_numpy)
        y = torch.from_numpy(y_numpy)
        return y
    except ImportError:
        raise ImportError("`scipy` is required for this function.")

# Example usage with error handling
try:
    n = 1
    x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
    y = polygamma_scipy(n, x)
    print(y)
except ImportError as e:
    print(e)

import torch

def polygamma_tensor(n, x):
    """Calculates polygamma values element-wise for a tensor (if implemented).

    Args:
        n (int): Order of the polygamma function.
        x (torch.Tensor): Input tensor.

    Returns:
        torch.Tensor: Output tensor containing polygamma values.

    Raises:
        NotImplementedError: If element-wise polygamma is not supported.
    """

    if not hasattr(torch.special, 'polygamma'):
        raise NotImplementedError("Element-wise polygamma not supported in PyTorch yet.")
    y = torch.special.polygamma(n, x)
    return y

# Example usage (assuming future PyTorch version with element-wise polygamma)
try:
    n = 1
    x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
    y = polygamma_tensor(n, x)
    print(y)
except NotImplementedError as e:
    print(e)

---

1. Loop-based implementation
   

   This approach iterates through each element of the tensor and calls torch.special.polygamma individually. It's a good option for small tensors, but can be inefficient for large ones.

   import torch
   
   def polygamma_loop(n, x):
       y = torch.empty_like(x)
       for i in range(x.size(0)):
           for j in range(x.size(1)):  # Assuming a 2D tensor
               y[i, j] = torch.special.polygamma(n, x[i, j])
       return y
   
   n = 1  # Order of the polygamma function
   x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
   y = polygamma_loop(n, x)
   print(y)
   

2. Using scipy (if available)
   

   If you have scipy installed, you can leverage its special.polygamma function, which supports element-wise computations on NumPy arrays. However, this requires converting your PyTorch tensors to NumPy arrays and back, which might introduce overhead.

   import torch
   import numpy as np
   from scipy.special import polygamma
   
   n = 1
   x = torch.tensor([[1.0, 2.5], [3.14, 4.2]])
   x_numpy = x.detach().cpu().numpy()  # Detach and move to CPU
   y_numpy = polygamma(n, x_numpy)
   y = torch.from_numpy(y_numpy)
   print(y)
   

• If you're working with large tensors and want to avoid data conversion, keep an eye out for future PyTorch updates that might include element-wise polygamma support.
• If you need element-wise calculations and have scipy installed, consider using it.
• For small tensors, the loop-based approach might be sufficient.