Matrix properties
number of rows	1,834
number of columns	1,834
nonzeros	28,757
structural full rank?	yes
structural rank	1,834
# 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 1834-by-1
rowname	full 1834-by-81
mapping	full 1834-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/spaceShuttleEntry                                                 
                                                                       
Space shuttle launch vehicle reentry optimal control problem is taken  
from Ref.~\cite{betts2010practical}. The goal of the optimal control   
problem is to determine the state and the control that maximize the    
cross range (maximize the final latitude) during the atmospheric       
entry of a reusable launch vehicle. State of the system is defined by  
the position, velocity, and the orientation of the space shuttle and   
the control of the system is the angle of attack and the bank angle    
of the space shuttle. The specified accuracy tolerance of $10^{-8}$    
were satisfied after two mesh iterations. As the mesh refinement       
proceeds, the size of the KKT matrices increases from 560 to 2450.     

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	38,794
Cholesky flop count	1.1e+06
nnz(L+U), no partial pivoting, with AMD	75,754
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	397,700
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	1,512,170

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.