Matrix: VDOL/orbitRaising_4

Description: orbitRaising optimal control problem (matrix 4 of 4)

VDOL/orbitRaising_4 graph
(undirected graph drawing)

VDOL/orbitRaising_4 dmperm of VDOL/orbitRaising_4
scc of VDOL/orbitRaising_4

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  • download as a MATLAB mat-file, file size: 84 KB. Use UFget(2721) or UFget('VDOL/orbitRaising_4') in MATLAB.
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    Matrix properties
    number of rows915
    number of columns915
    structural full rank?yes
    structural rank915
    # of blocks from dmperm3
    # strongly connected comp.2
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorB. Senses, A. Rao
    editorT. Davis
    kindoptimal control problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 915-by-1
    rownamefull 915-by-79
    mappingfull 915-by-1


    Optimal control problem, Vehicle Dynamics & Optimization Lab, UF       
    Anil Rao and Begum Senses, University of Florida                                                                  
    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.                            
    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.                                                                
      title={Applied Optimal Control: Optimization, Estimation, and        
      author={Bryson, Arthur Earl},                                        
      publisher={CRC Press}                                                

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD9,543
    Cholesky flop count1.4e+05
    nnz(L+U), no partial pivoting, with AMD18,171
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD13,957
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD31,414

    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.