This document contains some information about how to use Maxent.py to do analytical continuation to imaginary-frequency Green's function data. We use Maximum Entropy Method(MEM) based on the paper: M. Jarrell and J.E. Gubernatis, Phys. Rep. 269 (1996) 133.
python installed (better ipython IDE)
matplotlib, scipy and numpy installed.
In terminal, run Maxent.py as:
python Maxent.py test.dat
or in ipython IDE,
%run Maxent.py test.dat
where test.dat is file that contains data. Here is format that required by test.dat: The first column is Matsubara frequency, the second column is the real part of Green's function, the third column is the imaginary part of the Green's function and so forth. The second and third column is the first set of Green's function data. And the forth and fifth column is the second set of Green's function data. Please see the ./test/test1/test1.dat file as a reference.
e.g.
| wn | G1.real | G1.imag | G2.real | G2.imag | ... |
|---|---|---|---|---|---|
| 0.1 | 111 | 112 | 121 | 122 | ... |
| 0.2 | 211 | 212 | 221 | 222 | ... |
| ... | ... | ... | ... | ... | ... |
After finishing running the code, it will generate the MaxEnt result graph and some files to store the data. test.dat.p is pickle file that stores dictionary data. test.datComparison.paf is the Maxent graph. test.datmaxent.dat stores the Maxent dat. The first column in it is real frequency and the second column is the spectral function A(w). test.datPalpha.dat has the posterior probability distribution of P(\alpha|G). The first column is the alpha and the second column is P(\alpha|G). These files are enough for publishing purpose.
There is also a Draw.py file to plot. Run
python Draw.py test.dat.p
will create two graphs. One is MEM result and inset is the posterior probability distribution. Another graph is the trend how spectral function evolves with regularization parameter alpha.
For different cases, the parameter used in the Maxent.py file should be changed. In the file, Maxent class has several arguments as input in the constructor.
filename: the file that stores imaginary-frequency Green's function data
column: number of column in the file, an odd number.
numMfre: number of Matsubara frequency used. (this number should be less than the rows in the file)
numRfre: the number of grid for spectral function A(w).
wmin: minimum real frequency
wmax: maximun real frequency
defaultModel: this parameter can be 'gaussian', 'straightline' or 'input'.
tol: tolerance for minimization. 1e-12 for SLSQP; 1e-5 for Bryan
std: whether or not use the standard deviation.
alphamin: value of minimun alpha in log space.
alphamax: value of maximum alpha in log space
numAlpha: number of alphas.
minimizer: "SLSQP" or "Bryan".
draw: whether or not draw the MEM result graph.
- Please contact me: yanfeit89@gmail.com if you need help.