Matrix: VDOL/reorientation_2

Description: reorientation optimal control problem (matrix 2 of 8)

VDOL/reorientation_2 graph
(undirected graph drawing)

VDOL/reorientation_2 dmperm of VDOL/reorientation_2
scc of VDOL/reorientation_2

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  • download as a MATLAB mat-file, file size: 151 KB. Use UFget(2723) or UFget('VDOL/reorientation_2') in MATLAB.
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    Matrix properties
    number of rows1,544
    number of columns1,544
    structural full rank?yes
    structural rank1,544
    # 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 1544-by-1
    rownamefull 1544-by-80
    mappingfull 1544-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.                            
    Minimum-time reorientation of an asymmetric rigid body optimal         
    control problem is taken from Ref.~\cite{betts2010practical}. The      
    goal of the problem is to determine the state and the control that     
    minimize the time that is required to reorient a rigid body. The       
    state of the system is defined by quaternians that gives the           
    orientation of the spacecraft and the angular velocity of the          
    spacecraft and the control of the system is torque. The vehicle data   
    that is used to model the dynamics are taken from NASA X-ray Timing    
    Explorer spacecraft.  The specified accuracy tolerance of $10^{-8}$    
    were satisfied after eight mesh iterations. As the mesh refinement     
    proceeds, the size of the KKT matrices increases from 677 to 3108.     
      title={Practical Methods for Optimal Control and Estimation          
         Using Nonlinear Programming},                                     
      author={Betts, John T},                                              
      publisher={SIAM Press},                                              
      address = {Philadelphia, Pennsylvania},                              

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD23,381
    Cholesky flop count5.3e+05
    nnz(L+U), no partial pivoting, with AMD45,218
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD385,123
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD1,068,246

    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.