mindspore.nn.DiGamma

class mindspore.nn.DiGamma

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

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

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

$$digamma(x)=digamma(1-x)-pi\ast cot(pi\ast x)$$

Inputs:

• x (Tensor[Number]) - 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.DiGamma()
>>> output = op(x)
>>> print(output)
[0.42278463  0.92278427 1.2561178]