%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/VDOL/reorientation_1
% name: VDOL/reorientation_1
% [reorientation optimal control problem (matrix 1 of 8)]
% id: 2722
% date: 2015
% author: B. Senses, A. Rao
% ed: T. Davis
% fields: name title A b id date author ed kind notes aux
% aux: rowname mapping
% kind: optimal control problem
%-------------------------------------------------------------------------------
% notes:
% Optimal control problem, Vehicle Dynamics & Optimization Lab, UF       
% Anil Rao and Begum Senses, University of Florida                       
% http://vdol.mae.ufl.edu                                                
%                                                                        
% This matrix arises from an optimal control problem described below.    
% Each optimal control problem gives rise to a sequence of matrices of   
% different sizes when they are being solved inside GPOPS, an optimal    
% control solver created by Anil Rao, Begum Senses, and others at in VDOL
% lab at the University of Florida.  This is one of the matrices in one  
% of these problems.  The matrix is symmetric indefinite.                
%                                                                        
% Rao, Senses, and Davis have created a graph coarsening strategy        
% that matches pairs of nodes.  The mapping is given for this matrix,    
% where map(i)=k means that node i in the original graph is mapped to    
% node k in the smaller graph.  map(i)=map(j)=k means that both nodes    
% i and j are mapped to the same node k, and thus nodes i and j have     
% been merged.                                                           
%                                                                        
% This matrix consists of a set of nodes (rows/columns) and the          
% names of these rows/cols are given                                     
%                                                                        
% Anil Rao, Begum Sense, and Tim Davis, 2015.                            
%                                                                        
% VDOL/reorientation                                                     
%                                                                        
% Minimum-time reorientation of an asymmetric rigid body optimal         
% control problem is taken from Ref.~\cite{betts2010practical}. The      
% goal of the problem is to determine the state and the control that     
% minimize the time that is required to reorient a rigid body. The       
% state of the system is defined by quaternians that gives the           
% orientation of the spacecraft and the angular velocity of the          
% spacecraft and the control of the system is torque. The vehicle data   
% that is used to model the dynamics are taken from NASA X-ray Timing    
% Explorer spacecraft.  The specified accuracy tolerance of $10^{-8}$    
% were satisfied after eight mesh iterations. As the mesh refinement     
% proceeds, the size of the KKT matrices increases from 677 to 3108.     
%                                                                        
% @book{betts2010practical,                                              
%   title={Practical Methods for Optimal Control and Estimation          
%      Using Nonlinear Programming},                                     
%   author={Betts, John T},                                              
%   volume={19},                                                         
%   year={2010},                                                         
%   publisher={SIAM Press},                                              
%   address = {Philadelphia, Pennsylvania},                              
% }                                                                      
%-------------------------------------------------------------------------------
