Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void FermiDiracCDF(TDenseMtxVec x, Double Mu, Double s, TDenseMtxVec y) | Fermi-Dirac cumulative distribution function (CDF). |
| 2 | Double FermiDiracCDF(Double x, Double Mu, Double s) | Fermi-Dirac normalization integral (CDF form). |
Overload 1: void FermiDiracCDF(TDenseMtxVec x, Double Mu, Double s, TDenseMtxVec y)
Fermi-Dirac cumulative distribution function (CDF).
| # | 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 cumulative distribution function (CDF).
Remarks:
The distribution arises in the study of integer spin particles in physics.
Overload 2: Double FermiDiracCDF(Double x, Double Mu, Double s)
Fermi-Dirac normalization integral (CDF form).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value. NOTE: x is ignored by this routine. |
| 2 | Mu | Location (chemical-potential) parameter, real value. |
| 3 | s | Shape parameter, real value. |
Returns: Double - the Fermi-Dirac normalization constant. The result is INDEPENDENT of x.
Remarks:
Returns the closed-form normalization integral of the Fermi-Dirac weight over (0,inf), expressed with the Lerch transcendent Phi:
F(mu,s)=e^(mu) Gamma(s+1) Phi(-e^(mu), s+1, 1)
The value does not depend on x. The internal real-valued Lerch series converges for | -e^(mu)| <= 1, i.e. mu <= 0.