Matrix properties
number of rows	739
number of columns	739
nonzeros	6,526
structural full rank?	yes
structural rank	739
# of blocks from dmperm	3
# strongly connected comp.	2
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 739-by-1
rowname	full 739-by-79
mapping	full 739-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/orbitRaising                                                      
                                                                       
Orbit raising problem that is taken from                               
Ref.~\cite{bryson1975applied}. The goal of the optimal control         
problem is to determine the state and the control that maximize the    
radius of an orbit transfer in a given time. The state of the system   
is defined by radial distance of the spacecraft from the attracting    
center (e.g Earth, Mars, etc.) and velocity of the spacecraft and the  
control is the thrust direction. The specified accuracy tolerance of   
$10^{-8}$ were satisfied after four mesh iterations. As the mesh       
refinement proceeds, the size of the KKT matrices increases from 442   
to 915.                                                                
                                                                       
@book{bryson1975applied,                                               
  title={Applied Optimal Control: Optimization, Estimation, and        
     Control},                                                         
  author={Bryson, Arthur Earl},                                        
  year={1975},                                                         
  publisher={CRC Press}                                                
}                                                                      

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	7,850
Cholesky flop count	1.2e+05
nnz(L+U), no partial pivoting, with AMD	14,961
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	11,389
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	25,567

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.