PyTorch .igammac()

The torch.igammac() function in PyTorch computes the upper regularized incomplete gamma function. This function is commonly used in probabilistic modeling, survival analysis, and statistical machine learning applications. torch.igammac() is an alias for torch.special.gammaincc(), meaning both functions compute the same values and can be used interchangeably.

Syntax

torch.igammac(input, other, \*, out=None)

This is equivalent to:

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

Parameters:

• input (Tensor): The first non-negative input tensor representing the shape parameter (${a}$).
• other (Tensor): The second non-negative input tensor representing the integration limit (${x}$).
• out (Tensor, optional): The output tensor.

Return value:

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

Note: Supports broadcasting to a common shape and requires float inputs. The backward pass with respect to input is not currently supported.

Example 1: Basic Element-Wise Computation

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

import torch

a = torch.tensor([4.0])
x = torch.tensor([3.0, 4.0, 5.0])

result = torch.igammac(a, x)
print("Upper incomplete gamma:", result)

# Verify complementary relationship with igamma
lower = torch.igamma(a, x)
print("Sum of igamma and igammac:", lower + result)

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This code produces the following output:

Upper incomplete gamma: tensor([0.6472, 0.4335, 0.2650])
Sum of igamma and igammac: tensor([1., 1., 1.])

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Example 2: Survival Probabilities

In this example, torch.igammac() calculates the survival probability (complement of CDF) for a gamma distribution at a given time point:

import torch

shape = torch.tensor([2.0, 3.0, 4.0])
time = torch.tensor([1.5])

survival_prob = torch.igammac(shape, time)
cdf = torch.igamma(shape, time)

print("Shape parameters:", shape)
print("Time point:", time)
print("Survival probabilities:", survival_prob)
print("\nCDF values:", cdf)
print("CDF + Survival:", cdf + survival_prob)

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The output of this code is:

Shape parameters: tensor([2., 3., 4.])
Time point: tensor([1.5])
Survival probabilities: tensor([0.4422, 0.7127, 0.8221])

CDF values: tensor([0.5578, 0.2873, 0.1779])
CDF + Survival: tensor([1., 1., 1.])

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