PyTorch .igamma()

The torch.igamma() function in PyTorch computes the lower regularized incomplete gamma function, a special mathematical function often used in probability, statistics, and machine learning. torch.igamma() is an alias for torch.special.gammainc(). This means both functions compute the regularized lower incomplete gamma function and can be used interchangeably.

Syntax

torch.igamma(input, other, *, out=None)

Or, alternatively:

torch.special.gammainc(input, other, *, out=None)

Parameters:

• input (Tensor): The shape parameter a of the Gamma function.
• other (Tensor): The upper limit x of the integral.
• out (Tensor, optional): The output tensor to store results.

Return value:

Returns a tensor containing the lower regularized incomplete gamma function values for each corresponding pair of elements in input and other.

Example 1: Basic Element-Wise Computation

In this example, torch.igamma() computes the lower regularized incomplete gamma function for corresponding elements of two 1D tensors:

import torch

a = torch.tensor([2.0, 3.0, 4.0])
x = torch.tensor([1.0, 2.0, 3.0])

result = torch.igamma(a, x)
print(result)

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This example produces the following output:

tensor([0.2642, 0.3233, 0.3528])

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Example 2: Gamma Distribution CDF

In this example, torch.igamma() calculates the cumulative distribution function (CDF) of a Gamma distribution with shape ${a}$ and rate 1:

import torch

a = torch.tensor([2.0])
x = torch.linspace(0, 5, 6)
gamma_cdf = torch.igamma(a, x)

print(gamma_cdf)

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The output of this code is:

tensor([0.0000, 0.2642, 0.5940, 0.8009, 0.9084, 0.9596])

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The .igamma() function is useful for:

• Computing CDFs of Gamma, Chi-square, or Exponential distributions.
• Performing Bayesian statistical modeling (priors and posteriors).
• Implementing neural network activations and loss functions involving special functions.