igi

iadpython.start.igi(sample)

Infinitesmal Generator Initialization.

igi_start() generates the starting matrix with the inifinitesimal generator method. The accuracy is O(d) and assumes that the average irradiance upwards is equal to that travelling downwards at the top and the average radiance upwards equals that moving upwards from the bottom.

Ultimately the formulas for the reflection matrix is

\[R_{ij} = a d/(4\nu_i\nu_j) hpm_{ij}\]

and

\[T_{ij} = a d/(4\nu_i\nu_j) hpp_{ij} + \delta_{ij}(1-d/\nu_i)/(2\nu_i w_i)\]