Analysis Tools - ALF — Algorithms for Lattice Fermions

Post-processing simulation output: error analysis, Fourier transforms, and analytic continuation.

Overview¶

After a simulation completes, raw bin data must be analyzed to extract physical observables with error bars. The workflow depends on whether HDF5 output was enabled.

Analysis Workflow¶

With HDF5 (recommended)¶

$ALF_DIR/Analysis/ana_hdf5.out              # analyze all observables
$ALF_DIR/Analysis/ana_hdf5.out Ener_scal    # analyze a specific observable

Results are written to a res/ subdirectory. The input is a single data.h5 file containing all observables.

Without HDF5¶

$ALF_DIR/Analysis/ana.out *          # analyze all observables
$ALF_DIR/Analysis/ana.out Ener_scal  # analyze a specific observable

ana.out dispatches to the appropriate analysis routine based on the observable name suffix:

Suffix	Analysis	Output
`_scal`	Scalar covariance (`cov_scal`)	`<name>J` (Jackknife mean ± error)
`_eq`	Equal-time correlations (`cov_eq`)	`<name>JR` (real space), `<name>JK` (k-space)
`_tau`	Time-displaced correlations (`cov_tau`)	`<name>_kx_ky/g_dat` (k-resolved, τ-dependent)

Legacy Script Workflow¶

For fine-grained control, the individual analysis programs can be called directly. The script Scripts_and_Parameters_files/analysis.sh demonstrates this:

# Scalar observables
for i in *_scal; do $ALF_DIR/Analysis/cov_scal.out < $i; done

# Equal-time observables
for i in *_eq; do ln -sf $i ineq && $ALF_DIR/Analysis/cov_eq.out; done

# Time-displaced observables (particle channel)
for i in Green_tau; do ln -sf $i intau && $ALF_DIR/Analysis/cov_tau.out; done

# Time-displaced observables (particle-hole channel)
for i in SpinZ_tau Den_tau; do ln -sf $i intau && $ALF_DIR/Analysis/cov_tau_ph.out; done

Available Analysis Programs¶

Program	Input	Purpose
`ana.out`	Plain-text bin files	All-in-one dispatcher
`ana_hdf5.out`	`data.h5`	All-in-one dispatcher (HDF5)
`Max_SAC.out`	Analyzed τ-dependent data	MaxEnt / Stochastic Analytic Continuation
`convert_bins.py`	Plain-text bins	Convert plain-text output to HDF5 format

Legacy Programs¶

The following programs are called internally by ana.out / ana_hdf5.out. They are rarely needed directly.

Program	Input	Purpose
`cov_scal.out`	`*_scal` files	Scalar observable Jackknife analysis
`cov_eq.out`	`*_eq` files	Equal-time correlation analysis + Fourier transform
`cov_tau.out`	`*_tau` files	Time-displaced correlation analysis (particle channel)
`cov_tau_ph.out`	`*_tau` files	Time-displaced correlation analysis (particle-hole channel)
`cov_mut.out`	Mutual information data	Mutual information covariance analysis

Sub-Pages¶

[[HDF5 Output Format]] — Structure of data.h5
[[Bin Conversion]] — Converting plain-text output to HDF5
[[Analytic Continuation]] — Maximum entropy and stochastic analytic continuation