mxpfit

mxpfit -- a C++ template library for Multi-eXPonential FIT

Description

mxpfit is a library for finding optimal approximation of a function by a multi-exponential sum, which is given as

where and

The library provides mainly two application programming interfaces (APIs) for 1) recovering exponents and weights in exponential sum from sampled data on a uniform grid via modified fast ESPRIT algorithm, and 2) reducing the number of terms of a given exponential sum via modified balanced truncation algorithm. The library is written in C++ with templates, which enable us to perform the simulation using various scalar type in good performance.

Requirement

• A modern C++ compiler that supports the C++11 standard, such as GCC (>= 4.8.0) and Clang (>= 3.2).
• Eigen -- linear algebra library
• FFTW3 -- fast Fourier transform library
• CMake (cross-platform make) for building examples and tests
• Doxygen for generating source code documents [optional]

Description of Files

• include/
  • fftw3/
    • shared_plan.hpp: thread-safe wrapper classes for one-dimensional FFT plans
  • mxpfit/
    • balanced_truncation.hpp: Implements modified balanced truncation algorithm for finding exponential sum with smaller order.
    • exponential_sum.hpp: Container classes holding parameters of exponential sum function.
    • fast_esprit.hpp: Implements the fast ESPRIT algorithm for finding exponential sum approximation from sampled data on a uniform grid.
    • esprit.hpp: Implements the original ESPRIT algorithm for finding exponential sum approimxation from sampled data on a uniform grid. This algorithm is much slower than fast ESPRIT method described above. This has been implemented only for testing purpose.
    • prony_like_method_common.hpp: utility functions internally used for implementing Prony-like methods.
    • hankel_matrix.hpp: A rectangular Hankel matrix class with fast Hankel matrix-vector product.
    • jacobi_svd.hpp: One-sided Jacobi singular value decomposition algorithm.
    • matrix_free_gemv.hpp: provides interface overloading operator* for product of Hankel/Vandermonde matrix and any vector type in Eigen.
    • partial_lanczos_bidiagonalization.hpp: Find a low-rank approximation of a matrix with partial Lanczos bidiagonalization with full reorthogonalization.
    • quasi_cauchy_rrd.hpp: Computes a rank-revealing Cholesky decomposition of a self-adjoint quasi-Cauchy matrix with high-relative accuracy.
    • self_adjoint_coneigensolver.hpp: Computes con-eigenvalue decomposition of self-adjoint matrix having rank-revealing decomposition.
    • vandermonde_least_squares.hpp: Solve least square solution of overdetermined Vandermonde system.
    • vandermonde_matrix.hpp: Wonderment matrix class with matrix-vector product interface class with matrix-vector product interface.
• examples
  • balanced_truncation.cpp: an example program for BalancedTruncation class
  • fast_esprit.cpp: an example program for FastESPRIT class
  • esprit_gauss.cpp: another example program for FastESPRIT class
  • esprit_compare.cpp: compare the performance of ESPRIT and FastESPRIT classes.
• tests/: unit tests

Installation

mxpfit is a header only library. You can use it by including header files under include directory.

For building example programs, type the following commands on terminal:

$ cd {mxpfit_root_dir}
$ mkdir build
$ cd build
$ cmake -DBUILD_EXAMPLES=on -DBUILD_TEST=on ..
$ make

Usage:

See examples/fast_esprit.cpp, examples/esprit_gaussian.cpp and examples/balanced_truncation.cpp.

Licence

Copyright (c) 2017-2018 Hidekazu Ikeno

Released under the MIT license