# $\chi^2$ calculations

## Image plane optimization

With option `forme < 0`, Lenstool performs image plane optimization. These calculations are done in parallel with OpenMP. However, allowing a large number of CPUs not necessarily increases the efficiency of the calculations. Managing the multithreading might take more time than doing the calculations themselves. 

Here is a little benchmark (thanks to Benjamin Clement), that tells us how Lenstool scales up with the number of images per system. 

For instance, with $2$ systems of $2$ images each, Lenstool effectively uses 2 CPUs. Here are some other examples:

- Sum of images per system = Total number of images ==> CPUs effectively used
- $2+2 = 4$ => $2$
- $2+3 = 6$ => $2$
- $3+3 = 8$ => $3$
- $4+3 = 10$ => $3$
- $4+3+2 = 12$ => $4$