Matrix: VDOL/spaceShuttleEntry_3

Description: spaceShuttleEntry optimal control problem (matrix 3 of 4)

VDOL/spaceShuttleEntry_3 graph
(undirected graph drawing)


VDOL/spaceShuttleEntry_3

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  • Matrix group: VDOL
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  • download as a MATLAB mat-file, file size: 216 KB. Use UFget(2732) or UFget('VDOL/spaceShuttleEntry_3') in MATLAB.
  • download in Matrix Market format, file size: 177 KB.
  • download in Rutherford/Boeing format, file size: 150 KB.

    Matrix properties
    number of rows1,834
    number of columns1,834
    nonzeros28,757
    structural full rank?yes
    structural rank1,834
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    typereal
    structuresymmetric
    Cholesky candidate?no
    positive definite?no

    authorB. Senses, A. Rao
    editorT. Davis
    date2015
    kindoptimal control problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 1834-by-1
    rownamefull 1834-by-81
    mappingfull 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 AMD38,794
    Cholesky flop count1.1e+06
    nnz(L+U), no partial pivoting, with AMD75,754
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD397,700
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,512,170

    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.