FLIPACK | Fast Linear Inversion PACKage

FLIPACK is a C++ library. FLIPACK has no bugs, it has no vulnerabilities and it has low support. However FLIPACK has a Non-SPDX License. You can download it from GitHub.

This is the first public release of the FLIPACK library. Date: July 26th, 2013. %% Copyleft 2013: Sivaram Ambikasaran, Ruoxi Wang, Peter Kitanidis and Eric Darve %% Developed by Sivaram Ambikasaran, Ruoxi Wang %% Contact: siva.1985@gmail.com(Sivaram) , ruoxi@stanford.edu (Ruoxi) %% %% This program is free software; you can redistribute it and/or modify it under the terms of MPL2 license. %% The Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not %% distributed with this file, You can obtain one at ###1. INTRODUCTION FLIPACK (Fast Linear Inversion PACKage) is a library for fast linear inversion as described in this article. Stochastic linear inversion is the backbone of applied inverse methods. Stochastic inverse modeling deals with the estimation of functions from sparse data, which is a problem with a nonunique solution, with the objective to evaluate best estimates, measures of uncertainty, and sets of solutions that are consistent with the data. As finer resolutions become desirable, the computational requirements increase dramatically when using conventional algorithms. The FLIPACK reduces the computational cost from O(N^2) to O(N) by modeling the large dense convariances arising in these problems as a hierarchical matrix, more specifically as a matrix. Matrix-vector products for hierarchical matrices are accelerated using the Black Box Fast Multipole Method to accelerate these matrix-vector products. ###2. LINEAR MODEL ####2.1 Prior Consider that s(x) is a function to be estimated, The basic model of the function to be estimated is taken as: The first term is the prior mean, where are known functions, typically step functions, polynomials, and are unknown coefficients where k = 1,2,...,p. The second term is a random function with zero mean and characterized through a covariance function. After discretization, s(x) is represented through an m by 1 vector s. The mean of s is . where X is a known m x p matrix, and are p unknown drift coefficients. The covariance of s is .