@@ -164,7 +164,7 @@ Comparison of CPU times (1e6 repetitions):
See also [this comparison](issues/30) of the two integrators.
## Integrator
The main advantages of the integrator are that it is numerically reliable and it yields results for all three tabulations, including GEANT which is readily available for any ion-target combinations. Another advantage is that it can separate the energy loss into its electronic and nuclear components. The main drawbacks are that it is slow (the thicker the material, the longer it takes) and that it systematically underestimates the energy loss of light ions at low energies because it does not take into account angular straggling (see Figure 1 below). It is possible to speed up the integrator by adjusting various parameters such as the minimum step size. The complete list of adjustable parameters can be found in [GslIntegrator.h](https://gitlab.au.dk/ausa/ausalib/-/blob/gsl-integrator/include/ausa/eloss/GslIntegrator.h)(GSL integrator) and [EnergyLossIntegrator.h](https://gitlab.au.dk/ausa/ausalib/-/blob/gsl-integrator/include/ausa/eloss/EnergyLossIntegrator.h)(home-made integrator).
The main advantages of the integrator are that it is numerically reliable and it yields results for all three tabulations, including GEANT which is readily available for any ion-target combinations. Another advantage is that it can separate the energy loss into its electronic and nuclear components. The main drawbacks are that it is slow (the thicker the material, the longer it takes) and that it systematically underestimates the energy loss of light ions at low energies because it does not take into account angular straggling (see Figure 1 below). It is possible to speed up the integrator by adjusting various parameters such as the minimum step size. The complete list of adjustable parameters can be found in [GslIntegrator.h](https://gitlab.au.dk/ausa/ausalib/-/blob/master/include/ausa/eloss/GslIntegrator.h)(GSL integrator) and [EnergyLossIntegrator.h](https://gitlab.au.dk/ausa/ausalib/-/blob/gsl-master/include/ausa/eloss/EnergyLossIntegrator.h)(home-made integrator).
## Range inverter
The main advantages of the integrator are that it is fast and does not suffer from the above mentioned systematic error. The main drawbacks are that it only yields results for SRIM and that it has some numerical problems around the maximum of the stopping power curve (see Figures 1 and 2 below). Also it does not allow separation of the energy loss into electronic and nuclear components. The numerical problems can be improved but not fully eliminated, at the cost of computational speed, by using B-spline least-squares fitting instead of cubic spline interpolation to determine the range function. The implementation of the B-spline least-square fitting has been taken from [Geometric Tools Engine](http://www.geometrictools.com/Source/CurvesSurfacesVolumes.html)(see also [license agreement](http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt)) while the implementation of the cubic spline interpolation has been taken from [ROOT](http://project-mathlibs.web.cern.ch/project-mathlibs/sw/5_18_00/html/group__Interpolation.html).
