mindspore.nn.LGamma

class mindspore.nn.LGamma

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

$$\begin{array}{r}\begin{array}{l}\\ lgamma(z+1)=\frac{(\log (2)+\log (pi))}{2}+(z+1/2)\ast log(t(z))-t(z)+A(z)\\ t(z)=z+kLanczosGamma+1/2\\ A(z)=kBaseLanczosCoeff+\sum _{k=1}^n\frac{kLanczosCoefficients[i]}{z+k}\end{array}\end{array}$$

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

$$lgamma(x)=\log (pi)-lgamma(1-x)-\log (abs(sin(pi\ast x)))$$

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]