Matrix properties
number of rows	15,561
number of columns	15,561
nonzeros	149,532
structural full rank?	yes
structural rank	15,561
# 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 15561-by-1
rowname	full 15561-by-82
mapping	full 15561-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/hangGlider                                                        
                                                                       
Range maximization of a hang glider optimal control problem is taken   
from Ref.~\cite{bulirsch1993combining}.  The goal of the optimal       
control problem is to determine the state and the control that         
maximize the range of the hang glider in the presence of a thermal     
updraft. The state of the system is defined by horizontal distance,    
altitude, horizontal velocity, and the vertical velocity and the       
control is the lift coefficient. The specified accuracy tolerance of   
$10^{-8}$ were satisfied after five mesh iterations. As the mesh       
refinement proceeds, the size of the KKT matrices increases from 360   
to 16011. This problem is sensitive to accuracy of the mesh and it     
requires excessive number of collocation points to be able to satisfy  
the accuracy tolerance. Thus, the size of the KKT matrices changes     
drastically.                                                           
                                                                       
@book{bulirsch1993combining,                                           
  title={Combining Direct and Indirect Methods in Optimal Control:     
     Range Maximization of a Hang Glider},                             
  author={Bulirsch, Roland and Nerz, Edda and Pesch, Hans Josef and    
     von Stryk, Oskar},                                                
  year={1993},                                                         
  publisher={Springer}                                                 
}                                                                      

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	160,356
Cholesky flop count	1.9e+06
nnz(L+U), no partial pivoting, with AMD	305,151
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	12,737,712
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	99,089,535

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.