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Update Functionals authored by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Functionals.md
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...@@ -27,7 +27,7 @@ Role of $`f_{\textrm{reg.}}`$ is to exclude from computation regions of small de ...@@ -27,7 +27,7 @@ Role of $`f_{\textrm{reg.}}`$ is to exclude from computation regions of small de
```c ```c
/** /**
* Meaningful only in case of ASLDA. * Meaningful only in case of ASLDA.
* Paremeters defining stabilization procedure of ASLDA functional. * Parameters defining stabilization procedure of ASLDA functional.
* For regions with density smaller than ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY * For regions with density smaller than ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY
* contribution from current term j^2/2n is assumed to be zero. * contribution from current term j^2/2n is assumed to be zero.
* For regions with density above ASLDA_STABILIZATION_RETAIN_ABOVE_DENSITY * For regions with density above ASLDA_STABILIZATION_RETAIN_ABOVE_DENSITY
...@@ -37,5 +37,5 @@ Role of $`f_{\textrm{reg.}}`$ is to exclude from computation regions of small de ...@@ -37,5 +37,5 @@ Role of $`f_{\textrm{reg.}}`$ is to exclude from computation regions of small de
#define ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY 1.0e-7 #define ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY 1.0e-7
``` ```
There meaning is presented on the figure below. There meaning is presented on the figure below.
![stabilization](uploads/6528cf3b55ebb0d55a3e7f62a6124a83/stabilization.png) ![stabilization](uploads/740d294dbfb30a203cabec0b140fa326/stabilization.png)
Smooth transition between densities `ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY` and `ASLDA_STABILIZATION_RETAIN_ABOVE_DENSITY` is introduced in order to avoid discontinuities for quantities, that may lead to divergences when computing derivatives. Smooth transition between densities `ASLDA_STABILIZATION_EXCLUDE_BELOW_DENISTY` and `ASLDA_STABILIZATION_RETAIN_ABOVE_DENSITY` is introduced in order to avoid discontinuities for quantities, that may lead to divergences when computing derivatives.
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