Matrix: VDOL/reorientation_4

Description: reorientation optimal control problem (matrix 4 of 8)

VDOL/reorientation_4 graph
(undirected graph drawing)


VDOL/reorientation_4 dmperm of VDOL/reorientation_4
scc of VDOL/reorientation_4

  • Home page of the UF Sparse Matrix Collection
  • Matrix group: VDOL
  • Click here for a description of the VDOL group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups
  • download as a MATLAB mat-file, file size: 250 KB. Use UFget(2725) or UFget('VDOL/reorientation_4') in MATLAB.
  • download in Matrix Market format, file size: 230 KB.
  • download in Rutherford/Boeing format, file size: 206 KB.

    Matrix properties
    number of rows2,717
    number of columns2,717
    nonzeros33,630
    structural full rank?yes
    structural rank2,717
    # of blocks from dmperm3
    # strongly connected comp.2
    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 2717-by-1
    rownamefull 2717-by-81
    mappingfull 2717-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/reorientation                                                     
                                                                           
    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.     
                                                                           
    @book{betts2010practical,                                              
      title={Practical Methods for Optimal Control and Estimation          
         Using Nonlinear Programming},                                     
      author={Betts, John T},                                              
      volume={19},                                                         
      year={2010},                                                         
      publisher={SIAM Press},                                              
      address = {Philadelphia, Pennsylvania},                              
    }                                                                      
    

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD46,496
    Cholesky flop count1.2e+06
    nnz(L+U), no partial pivoting, with AMD90,275
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,069,535
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD3,283,467

    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.