**Matrix: YCheng/psse2**

Description: Power system state simulation matrix, Yunzhi Cheng, UT Arlington

(bipartite graph drawing) |

Matrix properties | |

number of rows | 28,634 |

number of columns | 11,028 |

nonzeros | 115,262 |

structural full rank? | yes |

structural rank | 11,028 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | real |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | Y. Cheng |

editor | T. Davis |

date | 2007 |

kind | power network problem |

2D/3D problem? | no |

Additional fields | size and type |

b | full 28634-by-1 |

guess | full 11028-by-1 |

Notes:

Power system state simulation matrix from Yunzhi Cheng, UT Arlington. In MATLAB, the solution to x=A\b is desired, but this can be slow in MATLAB 7.3 because of the speed of sparse QR as compared to sparse Cholesky. Using x=(A'*A)\(A'*b) is faster, but of course yields slightly less accurate (but still acceptable) results. Note that an initial guess to the solution is provided, for use by an iterative method. However, sparse Cholesky with an AMD ordering is very fast for this matrix and thus iterative methods are unlikely to be competitive. In MATLAB 7.3 on a 3.2 Ghz Pentium 4 desktop, x=(A'*A)\(A'*b) takes 0.07 seconds.

Ordering statistics: | result |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 3,138,002 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 109,583 |

SVD-based statistics: | |

norm(A) | 200379 |

min(svd(A)) | 0.192744 |

cond(A) | 1.03961e+06 |

rank(A) | 11,028 |

sprank(A)-rank(A) | 0 |

null space dimension | 0 |

full numerical rank? | yes |

singular values (MAT file): | click here |

SVD method used: | s = svd (full (R)) ; where [~,R,E] = spqr (A) with droptol of zero |

status: | ok |

For a description of the statistics displayed above, click here.

*Maintained by Tim Davis, last updated 12-Mar-2014.Matrix pictures by cspy, a MATLAB function in the CSparse package.
Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.
*