Parameters
A comprehensive dictionary about parameters.
In this part, we will provide detailed explanations of the control parameters of the ACTest toolkit. As mentioned before, the act.toml file contains two sections: [Test] and [Solver]. The parameters described here are specific to the [Test] section. They are primarily used for setting generation rules for the spectral functions and Green's functions. However, the parameters within the [Solver] section will be transferred to the ACFlow toolkit for configuring the analytic continuation methods. They will be explained in the documentation of the ACFlow toolkit.
Contents
solver
Definition:
Specify analytic continuation solver. Possible values include
- MaxEnt
- BarRat
- NevanAC
- StochAC
- StochSK
- StochOM
- StochPX
They are the analytic continuation methods supported by the ACFlow toolkit. This parameter is only relevant for the acflow.jl and acplot.jl scripts.
Type:
String.
Examples:
solver = "MaxEnt"
Comment:
This parameter is mandatory.
ptype
Definition:
Specify type of peaks. Possible values include
- gauss
- lorentz
- delta
- rectangle
- risedecay
They are corresponding to the Gaussian, Lorentzian, $\delta$-like, rectangular, and Rise-And-Decay peaks, respectively. This parameter is only relevant for the acgen.jl script.
Type:
String.
Examples:
ptype = "gauss"
Comment:
This parameter is mandatory.
ktype
Definition:
Specify kernel function. Possible values include
- fermi
- boson
- bsymm
They are corresponding to the fermionic, bosonic, and symmetric bosonic kernels, respectively.
Type:
String.
Examples:
ktype = "fermi"
Comment:
This parameter is mandatory.
grid
Definition:
Specify grid for the Green's functions. Possible values include
- ftime
- btime
- ffreq
- bfreq
Here, the characters f and b mean fermionic and bosonic, respectively. The strings time and freq mean imaginary time and Matsubara frequency axes, respectively.
Type:
String.
Examples:
grid = "ftime"
Comment:
This parameter is mandatory.
mesh
Definition:
Specify mesh for the spectral function. Possible values are
- linear
- tangent
- lorentz
- halflorentz
They are corresponding to the linear, tangent, Lorentzian, and half-Lorentzian meshes, respectively.
Type:
String.
Examples:
mesh = "linear"
Comment:
This parameter is mandatory.
ngrid
Definition:
Number of imaginary time or Matsubara frequency points for the Green's function. It denotes $N_{\tau}$ or $N$.
Type:
Integer.
Examples:
ngrid = 10
Comment:
This parameter is mandatory.
nmesh
Definition:
Number of mesh points for the spectral function. It is $N_{\omega}$.
Type:
Integer.
Examples:
nmesh = 101
Comment:
This parameter is mandatory.
ntest
Definition:
How many spectral functions and corresponding Green's functions are generated by the ACTest toolkit? It is the size of the testing dataset for analytic continuation methods or codes.
Type:
Integer.
Examples:
ntest = 100
Comment:
This parameter is mandatory.
wmax
Definition:
Right boundary of the real frequency mesh ($\omega_{\text{max}}$).
Type:
Float.
Examples:
wmax = 8.0
Comment:
This parameter is mandatory.
wmin
Definition:
Left boundary of the real frequency mesh ($\omega_{\text{min}}$).
Type:
Float.
Examples:
wmin = -8.0
Comment:
This parameter is mandatory.
pmax
Definition:
Right boundary of features in the spectrum. It is used to restrict the centers of Gaussian and Lorentzian peaks. $\texttt{wmin} < \texttt{pmin} < \texttt{pmax} < \texttt{wmax}$.
Type:
Float.
Examples:
pmax = 4.0
Comment:
This parameter is mandatory.
pmin
Definition:
Left boundary of features in the spectrum. It is used to restrict the centers of Gaussian and Lorentzian peaks. $\texttt{wmin} < \texttt{pmin} < \texttt{pmax} < \texttt{wmax}$.
Type:
Float.
Examples:
pmin = -4.0
Comment:
This parameter is mandatory.
beta
Definition:
Inverse temperature of the system $\beta$ ($\equiv 1/T$). It is used to define the imaginary time or Matsubara frequency grids for Green's functions.
Type:
Float.
Examples:
beta = 40.0
Comment:
This parameter is mandatory.
noise
Definition:
The noise level, i.e., the $\delta$ parameter.
Type:
Float.
Examples:
noise = 1e-6
Comment:
This parameter is mandatory.
offdiag
Definition:
Specify whether the spectral function is positive definite or not. If offdiag is true, it implies that the spectral function is not positive definite and the ACTest toolkit will generate off-diagonal Green's function.
Type:
Bool.
Examples:
offdiag = true
Comment:
This parameter is mandatory.
lpeak
Definition:
It is an integer array that sets the number of peaks (features) that the synthetic spectral function may contain. For example: lpeak = [1,2,3,4,5], then the ACTest toolkit can generate spectral functions with the number of peaks ranging from 1 to 5. This parameter is only relevant for the acgen.jl script.
Type:
Array (Integer).
Examples:
lpeak = [1,2,3,5]
Comment:
This parameter is mandatory.