Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void FermiDiracPDF(TDenseMtxVec x, Double Mu, Double s, TDenseMtxVec y) | Fermi-Dirac probability density function (PDF). |
| 2 | Double FermiDiracPDF(Double x, Double Mu, Double s) | Fermi-Dirac occupation function (PDF form). |
Overload 1: void FermiDiracPDF(TDenseMtxVec x, Double Mu, Double s, TDenseMtxVec y)
Fermi-Dirac probability density function (PDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value. |
| 2 | Mu | Location parameter, real value. |
| 3 | s | Shape parameter, real positive value. |
| 4 | y | Contains result. |
Result: stored in self (calling object)
Returns: Fermi-Dirac probability density function (PDF).
Calculates the Fermi-Dirac PDF for x using the parameters Mu and s. The distribution arises in the study of half-integer spin particles in physics. Half-integer spin particles are described by Fermi-Dirac statistics and are called FERMIONS. Fermi-Dirac PDF is defined by the following equation:
Overload 2: Double FermiDiracPDF(Double x, Double Mu, Double s)
Fermi-Dirac occupation function (PDF form).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value. |
| 2 | Mu | Location (chemical-potential) parameter, real value. |
| 3 | s | Shape parameter, real value. |
Returns: Double - the Fermi-Dirac occupation value at x for the given Mu and s. This is NOT a normalized probability density.
Computes the Fermi-Dirac statistical weight that arises in the study of half-integer-spin particles (fermions):
f(x|mu,s)=x^s/(exp(x-mu)+1)
This is the physics occupation form, not a normalized PMF; no parameter validation is performed. Unlike the Bose-Einstein form the denominator never vanishes for real x.