A singular value of A is guaranteed^{1} to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0,rr, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.

Routine spnrank, version 1.0,spnrank.pdf"> spnrank, version 1.0 with opts.tol_eigs = 1e-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14442 to 14447 and associated error bounds.

Matrix properties (click for a legend) | |

number of rows | 14,454 |

number of columns | 14,454 |

structural full rank? | yes |

structural rank | 14,454 |

numerical rank | 14,444 |

dimension of the numerical null space | 10 |

numerical rank / min(size(A)) | 0.99931 |

Euclidean norm of A | 5306.2 |

calculated singular value # 14444 | 1.4283e-008 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 1.3146e-008 |

calculated singular value # 14445 | 1.1652e-008 |

gap in the singular values at the numerical rank: singular value # 14444 / singular value # 14445 | 1.2258 |

calculated condition number | -2 |

condest | 3.1256e+012 |

nonzeros | 147,972 |

# of blocks from dmperm | 2 |

# strongly connected comp. | 2 |

entries not in dmperm blocks | 0 |

explicit zero entries | 0 |

nonzero pattern symmetry | symmetric |

numeric value symmetry | symmetric |

type | real |

structure | symmetric |

Cholesky candidate? | no |

positive definite? | no |

author | J. Quanyuan |

editor | T. Davis |

date | 2008 |

kind | power network problem sequence |

2D/3D problem? | no |

SJid | 695 |

UFid | 2,214 |

Additional fields | size and type |

b | sparse 14454-by-1 |

A | cell 12-by-1 |

b1 | cell 12-by-1 |

b2 | cell 12-by-1 |

Notes:

Transient stabilty constrained interior pt. optimal power flow, J. Quanyuan Two problem sets from Dr. Jiang Quanyuan from Zhejiang University, Hangzhou, China, March, 2008, used in an electrical power system. Each matrix A is solved sequentially with two right-hand-sides, b1 and b2, one at a time. In the UF collection, the sequence of all first and second right-hand-sides is in Problem.aux.b2 and Problem.aux.b1. These matrices are symmetric indefinite (x=A\b uses MA57) Note that the last matrices in the sequence are ill-conditioned. Transient Stability Constrained Interior Point Optimal Power Flow Program Version 1.0 -- Developed by Dr. Jiang Quanyuan, March 2008 case9.m - TSOPF converges after 12 iterations object = 3.945939E+03 max_equ = 3.287326E-11 low_inequ = None up_inequ = None

Ordering statistics: | AMD |
METIS |
DMPERM+ |

nnz(chol(P*(A+A'+s*I)*P')) | 178,786 | 211,362 | - |

Cholesky flop count | 2.6e+006 | 3.8e+006 | - |

nnz(L+U), no partial pivoting | 343,118 | 408,270 | - |

nnz(V) for QR, upper bound nnz(L) for LU | 17,856,448 | 8,290,763 | 17,856,447 |

nnz(R) for QR, upper bound nnz(U) for LU | 26,478,449 | 28,095,620 | 26,478,449 |

*Maintained by Leslie Foster, last updated 24-Apr-2009.*

Entries 5 through 14 in the table of matrix properties and the singular

value plot were created using SJsingular code. The other plots

and statistics are produced using utilities from
the SuiteSparse package.

Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.