log_normal#

caf.distribute.cost_functions.log_normal(base_cost, sigma, mu, min_return_val=1e-150)#

Apply of the log normal cost function.

Parameters:
  • base_cost (np.ndarray) – Array of the base costs.

  • sigma (float) – Parameters of the log normal cost function, see Notes.

  • mu (float) – Parameters of the log normal cost function, see Notes.

  • min_return_val (float)

Return type:

ndarray

min_return_val: float

The minimum value allowed in the return. Avoid return arrays with values such as 1e-300 which lead to overflow errors when divisions are made.

Returns:

Output from the log normal equation, same shape as base_cost.

Return type:

log_normal_costs

Parameters:
  • base_cost (ndarray)

  • sigma (float)

  • mu (float)

  • min_return_val (float)

Notes

Formula used for this function is:

\[f(C_{ij}) = \frac{1}{C_{ij} \cdot \sigma \cdot \sqrt{2\pi}} \cdot \exp\left(-\frac{(\ln C_{ij}-\mu)^2}{2\sigma^2}\right)\]

where:

  • \(C_{ij}\): cost from i to j.

  • \(\sigma, \mu\): calibration parameters.