**Matrix: VDOL/orbitRaising_4**

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

(undirected graph drawing) |

Matrix properties | |

number of rows | 915 |

number of columns | 915 |

nonzeros | 7,790 |

structural full rank? | yes |

structural rank | 915 |

# of blocks from dmperm | 3 |

# strongly connected comp. | 2 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | B. Senses, A. Rao |

editor | T. Davis |

date | 2015 |

kind | optimal control problem |

2D/3D problem? | no |

Additional fields | size and type |

b | full 915-by-1 |

rowname | full 915-by-79 |

mapping | full 915-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/orbitRaising 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. @book{bryson1975applied, title={Applied Optimal Control: Optimization, Estimation, and Control}, author={Bryson, Arthur Earl}, year={1975}, publisher={CRC Press} }

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 9,543 |

Cholesky flop count | 1.4e+05 |

nnz(L+U), no partial pivoting, with AMD | 18,171 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 13,957 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 31,414 |

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.
*