**Matrix: Rajat/Raj1**

Description: Circuit simulation matrix from Raj

(bipartite graph drawing) | (graph drawing of A+A') |

Matrix properties | |

number of rows | 263,743 |

number of columns | 263,743 |

nonzeros | 1,300,261 |

structural full rank? | yes |

structural rank | 263,743 |

# of blocks from dmperm | 169 |

# strongly connected comp. | 3 |

explicit zero entries | 2,203 |

nonzero pattern symmetry | 100% |

numeric value symmetry | 58% |

type | real |

structure | unsymmetric |

Cholesky candidate? | no |

positive definite? | no |

author | Raj |

editor | T. Davis |

date | 2007 |

kind | circuit simulation problem |

2D/3D problem? | no |

Notes:

High fill-in with KLU, because the matrix is nearly singular and lots of partial pivoting occurs. If the pattern of A+A' is considered to be the nonzero pattern of a symmetric positive definite matrix, then nnz(L) has only 3,728,967 nonzeros using p=amd(A) and chol(A(p,p)), where A excludes the explicit zeros in Problem.Zeros. The flop count for the Cholesky factorization is only 340.9 million. With a pivot tolerance of 2.2e-16, KLU Version 1.0 constructs and LU factorization with about 31 million nonzeros, even though it uses AMD for the diagonal blocks of the BTF for which the expected nnz(L) is only 3.705 million (for the Cholesky factor- ization of the large diagonal block). The BTF form has little impact on the factorization.

Ordering statistics: | result |

nnz(chol(P*(A+A'+s*I)*P')) with AMD | 3,728,967 |

Cholesky flop count | 3.4e+08 |

nnz(L+U), no partial pivoting, with AMD | 7,194,191 |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 6,973,362,829 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 12,971,084,610 |

*Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2203 explicit zero entries.
*

*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.
*