som.spectral_stats
: Statistical analysis of noisy spectral functions
Functions in this module implement the statistical analysis technique for ensembles of spectral functions described in Sections I-II of [GMPPS2017].
- som.spectral_stats.spectral_integral()
Evaluate spectral integral
\[i_m^{(j)} = \int_{-\infty}^\infty dz \bar K(m, z) A^{(j)}(z)\]for a single energy interval.
Parameters:
- Z_m:
float
, Center of the energy interval.- Delta_m:
float
, Length of the energy interval.- C:
som.Configuration
, Spectral function \(A^{(j)}(z)\).- R_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns:
float
, Value of the integral.- Signature(float z_m, float delta_m, configuration c, resolution_function r_func) -> float
Evaluate spectral integral
\[i_m^{(j)} = \int_{-\infty}^\infty dz \bar K(m, z) A^{(j)}(z)\]for a single energy interval.
Parameters:
- z_m:
float
, Center of the energy interval.- delta_m:
float
, Length of the energy interval.- c:
som.Configuration
, Spectral function \(A^{(j)}(z)\).- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns:
float
, Value of the integral.- Signature(triqs::mesh::refreq mesh, configuration c, resolution_function r_func) -> vector<double>
Evaluate spectral integrals
\[i_m^{(j)} = \int_{-\infty}^\infty dz \bar K(m, z) A^{(j)}(z)\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- c:
som.Configuration
, Spectral function \(A^{(j)}(z)\).- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(i_m^{(j)}\).
- Signature(list[std::pair<double,double>] intervals, configuration c, resolution_function r_func) -> vector<double>
Evaluate spectral integrals
\[i_m^{(j)} = \int_{-\infty}^\infty dz \bar K(m, z) A^{(j)}(z)\]for a list of real energy intervals.
Parameters:
- intervals:
list
[float
,float
], List of pairs (left interval boundary, right interval boundary).- c:
som.Configuration
, Spectral function \(A^{(j)}(z)\).- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(i_m^{(j)}\).
- som.spectral_stats.spectral_avg()
Compute spectral averages over a set of accumulated particular solutions
\[i_m = \frac{1}{J} \sum_{j=1}^J i_m^{(j)}\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- Cont:
Som
, Analytic continuation object.- I:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- Mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- R_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(i_m\).
- Signature(som_core cont, int i, triqs::mesh::refreq mesh, resolution_function r_func) -> vector<double>
Compute spectral averages over a set of accumulated particular solutions
\[i_m = \frac{1}{J} \sum_{j=1}^J i_m^{(j)}\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(i_m\).
- Signature(som_core cont, int i, list[std::pair<double,double>] intervals, resolution_function r_func) -> vector<double>
Compute spectral averages over a set of accumulated particular solutions
\[i_m = \frac{1}{J} \sum_{j=1}^J i_m^{(j)}\]for a list of real energy intervals.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- intervals:
list
[float
,float
], List of pairs (left interval boundary, right interval boundary).- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(i_m\).
- som.spectral_stats.spectral_disp()
Compute spectral dispersions of a set of accumulated particular solutions
\[\sigma^2_m = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m)^2\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- Cont:
Som
, Analytic continuation object.- I:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- Mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- Avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- R_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(\sigma_m\).
- Signature(som_core cont, int i, triqs::mesh::refreq mesh, vector<double> avg, resolution_function r_func) -> vector<double>
Compute spectral dispersions of a set of accumulated particular solutions
\[\sigma^2_m = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m)^2\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(\sigma_m\).
- Signature(som_core cont, int i, list[std::pair<double,double>] intervals, vector<double> avg, resolution_function r_func) -> vector<double>
Compute spectral dispersions of a set of accumulated particular solutions
\[\sigma^2_m = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m)^2\]for a list of real energy intervals.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- intervals:
list
[float
,float
], List of pairs (left interval boundary, right interval boundary).- avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 1D NumPy array of values \(\sigma_m\).
- som.spectral_stats.spectral_corr()
Compute spectral two-point correlators of a set of accumulated particular solutions
\[\sigma_{mm'} = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m) (i_{m'}^{(j)} - i_{m'})\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- Cont:
Som
, Analytic continuation object.- I:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- Mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- Avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- R_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 2D NumPy array of values \(\sigma_{mm'}\).
- Signature(som_core cont, int i, triqs::mesh::refreq mesh, vector<double> avg, resolution_function r_func) -> matrix<double>
Compute spectral two-point correlators of a set of accumulated particular solutions
\[\sigma_{mm'} = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m) (i_{m'}^{(j)} - i_{m'})\]for energy intervals centered around points of a regular energy mesh.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- mesh:
triqs.gf.meshes.MeshReFreq
, Real energy mesh.- avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 2D NumPy array of values \(\sigma_{mm'}\).
- Signature(som_core cont, int i, list[std::pair<double,double>] intervals, vector<double> avg, resolution_function r_func) -> matrix<double>
Compute spectral two-point correlators of a set of accumulated particular solutions
\[\sigma_{mm'} = \frac{1}{J} \sum_{j=1}^J (i_m^{(j)} - i_m) (i_{m'}^{(j)} - i_{m'})\]for a list of real energy intervals.
Parameters:
- cont:
Som
, Analytic continuation object.- i:
int
, Index of the diagonal matrix element of the observable used to constructcont
.- intervals:
list
[float
,float
], List of pairs (left interval boundary, right interval boundary).- avg:
Real 1D NumPy array of precomputed averages \(i_m\).
- r_func:
str
, Name of the resolution function \(\bar K(m, z)\), one ofrectangle
,lorentzian
,gaussian
.
Returns: Real 2D NumPy array of values \(\sigma_{mm'}\).