Matrix: VDOL/spaceShuttleEntry_1

Description: spaceShuttleEntry optimal control problem (matrix 1 of 4)

VDOL/spaceShuttleEntry_1 graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 76 KB. Use UFget(2730) or UFget('VDOL/spaceShuttleEntry_1') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 41 KB.

    Matrix properties
    number of rows560
    number of columns560
    structural full rank?yes
    structural rank560
    # of blocks from dmperm1
    # strongly connected comp.1
    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 560-by-1
    rownamefull 560-by-79
    mappingfull 560-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.                            
    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 AMD7,762
    Cholesky flop count1.3e+05
    nnz(L+U), no partial pivoting, with AMD14,964
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD20,318
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD138,709

    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.