NNLS, NNT, MEM

Goal

This is a program for doing analytical continuations using one of the methods:

• Non Negative Least Squares
• Non Negative Tikhonov
• Maximum Entropy Metod

Compile

Compile by copying the example Makefile: src/Makefile_example to src/Makefile and adjust it to fit to the current machine. In the src folder, run: make and the binary NNLS_NNT_MEM should be created. LAPACK is required. Quadruple precision modified LAPACK routines are stored in the folder src/quad.

How to use it

Run the program by executing the binary. A control file called ac.inp is expected to exist in the current folder. Among many things is the Matsubara input filename specified in ac.inp. The input Matsubara data has to be Matsubara frequency data. Three columns are expected in the input file. The first should be the Matsubara frequencies, the second the real part of the function and the third column the imaginary part of the function. The ac.inp is row format strict, one can not change the order of the parameters. A typical ac.inp file exist in folder tests. Copy and adjust it for your analtyical continuation.

Tests

In the tests folder a few test models exist:

• betheU0
• betheU4
• Haverkort_wc1_dw0.5
• Sm7

A good start for using the program is to try these tests. Perhaps a good beginning is also to modify the attached ac.inp files. One thing one can do is to try both NNLS, NNT and MEM for the test models.

Output

The spectral function will be calculated. A smeared spectral function is also printed as output. It is calculated by taking the spectral function (determined just above the real axis) and using the Hilbert transform to evaluate the spectral function a distance $\delta$ above the real axis ( $\frac{-1}{\pi}\text{Im}[G(\omega+i\delta)]$ ).

Possible improvements

• Implement kernels for imaginary time
• Test MINPACK's non-linear equation solver
• Implement stochastic sampling methods