//********************************************************************************* // // Bayesian Spectral Reconstruction and Extended MEM // // Code: Dr. Alexander Karl Rothkopf DATE: July 14th 2021 // // Method: Dr. Yannis Burnier, Dr. Alexander Karl Rothkopf DATE: 2013 // ======================================================================== // // THIS PROGRAM IS AN IMPLEMENTATION OF TWO BAYESIAN APPROACHES // FOR THE NUMERICAL INVERSION OF THE TYPICALLY ILL DEFINED TASK // // DATA[t] = Int_-WMIN^WMAX [ K[w,t] * SPEC[w] ]dw // // WHERE THE GOAL IS TO EXTRACT THE SPECTRAL FUNCTION SPEC[w] FROM // THE PROVIDED LATTICE DATA DATA[t] USING A PREVIOUSLY SPECIFIED // KERNEL FUNCTION K[w,t]. // // References: // // Y. Burnier and A. Rothkopf, // "Bayesian Approach to Spectral Function Reconstruction for // Euclidean Quantum Field Theories" // arXiv:1307.6106 [hep-lat] // Phys. Rev. Lett. 111, 182003 (2013) // // A. Rothkopf // "Improved Maximum Entropy Analysis with an Extended Search Space" // arXiv:1110.6285 [physics.comp-ph] // J.Comput.Phys. 238 (2013) 106-114 // //********************************************************************************* //********************************************************************************* // This program uses adapted code from two libraries: // // 1. The GNU Scientific Library: // // SINGULAR VALUE DECOMPOSITION // EIGENSYSTEMS OF SYMMETRIC MATRICES // MATRIX INVERSION BASED ON QR DECOMPOSITION // SOLVER FOR Ax=b BASED ON QR DECOMPOSITION // // 2. The ALGLIB Library (MPFR part 2.6.): // // LBFGS MINIMIZER // LEVENBERG MARQUARD + LBFGS PRECONDITIONER MINIMIZER // EIGENVALUES FOR NON_SYMMETRIC MATRICES // //*********************************************************************************

{"references": ["Y. Burnier and A. Rothkopf, Phys. Rev. Lett. 111, 182003 (2013)", "A. Rothkopf, J.Comput.Phys. 238 (2013) 106-114"]}