mindspore.nn.DiGamma

class mindspore.nn.DiGamma

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

\[\begin{split}\begin{array}{ll} \\ digamma(z + 1) = log(t(z)) + A'(z) / A(z) - kLanczosGamma / t(z) \\ t(z) = z + kLanczosGamma + 1/2 \\ A(z) = kBaseLanczosCoeff + \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{z + k} \\ A'(z) = \sum_{k=1}^n \frac{kLanczosCoefficients[i]}{{z + k}^2} \end{array}\end{split}\]

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

\[digamma(x) = digamma(1 - x) - pi * cot(pi * x)\]

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]