Matrix properties
number of rows	2,871
number of columns	2,871
nonzeros	32,022
structural full rank?	yes
structural rank	2,871
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	no
positive definite?	no

author	B. Senses, A. Rao
editor	T. Davis
date	2015
kind	optimal control problem
2D/3D problem?	no

Additional fields	size and type
b	full 2871-by-1
rowname	full 2871-by-101
mapping	full 2871-by-1

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/dynamicSoaring                                                    
                                                                       
Dynamic soaring optimal control problem is taken from                  
Ref.~\cite{zhao2004optimal} where the dynamics of a glider is          
derived using a point mass model under the assumption of a flat        
Earth and stationary winds. The goal of the dynamic soaring            
problem is to determine the state and the control that minimize        
the average wind gradient slope that can sustain a powerless           
dynamic soaring flight.  The state of the system is defined by the     
air speed, heading angle, air-realtive flight path angle,              
altitude, and the position of the glider and the control of the        
system is the lift coefficient. The specified accuracy tolerance       
of $10^{-7}$ were satisfied after eight mesh iterations. As the        
mesh refinement proceeds, the size of the KKT matrices increases       
from  647 to 3543.                                                     
                                                                       
@article{zhao2004optimal,                                              
  title={Optimal Patterns of Glider Dynamic Soaring},                  
  author={Zhao, Yiyuan J},                                             
  journal={Optimal Control applications and methods},                  
  volume={25},                                                         
  number={2},                                                          
  pages={67--89},                                                      
  year={2004},                                                         
  publisher={Wiley Online Library}                                     
}                                                                      

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	56,011
Cholesky flop count	1.7e+06
nnz(L+U), no partial pivoting, with AMD	109,151
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	362,892
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	1,153,511

For a description of the statistics displayed above, click here.

Maintained by Tim Davis, last updated 04-Jun-2015.
Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.