mindspore.nn.LGamma

class mindspore.nn.LGamma[source]

Calculates LGamma using Lanczos’ approximation referring to “A Precision Approximation of the Gamma Function”. The algorithm is:

\[\begin{split}\begin{array}{ll} \\ lgamma(z + 1) = \frac{(\log(2) + \log(pi))}{2} + (z + 1/2) * log(t(z)) - t(z) + A(z) \\ t(z) = z + kLanczosGamma + 1/2 \\ A(z) = kBaseLanczosCoeff + \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{z + k} \end{array}\end{split}\]

However, if the input is less than 0.5 use Euler’s reflection formula:

\[lgamma(x) = \log(pi) - lgamma(1-x) - \log(abs(sin(pi * x)))\]

And please note that

\[lgamma(+/-inf) = +inf\]

Thus, the behaviour of LGamma follows:

  • when x > 0.5, return log(Gamma(x))

  • when x < 0.5 and is not an integer, return the real part of Log(Gamma(x)) where Log is the complex logarithm

  • when x is an integer less or equal to 0, return +inf

  • when x = +/- inf, return +inf

Inputs:

  • x (Tensor) - The input tensor. Only float16, float32 are supported.

Outputs:

Tensor, has the same shape and dtype as the x.

Raises

TypeError – If dtype of x is neither float16 nor float32.

Supported Platforms:

Ascend GPU

Examples

>>> x = Tensor(np.array([2, 3, 4]).astype(np.float32))
>>> op = nn.LGamma()
>>> output = op(x)
>>> print(output)
[3.5762787e-07 6.9314754e-01 1.7917603e+00]