Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

Matrix properties (click for a legend) | |

number of rows | 643 |

number of columns | 1,586 |

structural full rank? | no |

structural rank | 642 |

numerical rank | 642 |

dimension of the numerical null space | 944 |

numerical rank / min(size(A)) | 0.99844 |

Euclidean norm of A | 170.48 |

calculated singular value # 642 | 0.050808 |

numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = | 4.5077e-011 |

calculated singular value # 643 | 1.2221e-060 |

gap in the singular values at the numerical rank: singular value # 642 / singular value # 643 | 4.1573e+058 |

calculated condition number | 1.395e+062 |

condest | -2 |

nonzeros | 5,532 |

# of blocks from dmperm | 12 |

# strongly connected comp. | 12 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | real |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | J. Tomlin |

editor | D. Gay |

date | 1989 |

kind | linear programming problem |

2D/3D problem? | no |

SJid | 323 |

UFid | 604 |

Additional fields | size and type |

b | full 643-by-1 |

c | full 1586-by-1 |

lo | full 1586-by-1 |

hi | full 1586-by-1 |

z0 | full 1-by-1 |

Notes:

A Netlib LP problem, in lp/data. For more information send email to netlib@ornl.gov with the message: send index from lp send readme from lp/data The following are relevant excerpts from lp/data/readme (by David M. Gay): The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude slack and surplus columns and the right-hand side vector, but include the cost row. We have omitted other free rows and all but the first right-hand side vector, as noted below. The byte count is for the MPS compressed file; it includes a newline character at the end of each line. These files start with a blank initial line intended to prevent mail programs from discarding any of the data. The BR column indicates whether a problem has bounds or ranges: B stands for "has bounds", R for "has ranges". The optimal value is from MINOS version 5.3 (of Sept. 1988) running on a VAX with default options. PROBLEM SUMMARY TABLE Name Rows Cols Nonzeros Bytes BR Optimal Value BNL1 644 1175 6129 42473 1.9776292856E+03 From John Tomlin. Bob Bixby reports that the CPLEX solver (running on a Sparc station) finds slightly different optimal values for some of the problems. On a MIPS processor, MINOS version 5.3 (with crash and scaling of December 1989) also finds different optimal values for some of the problems. The following table shows the values that differ from those shown above. (Whether CPLEX finds different values on the recently added problems remains to be seen.) Problem CPLEX(Sparc) MINOS(MIPS) BNL1 1.9776295615E+03 1.9776293385E+03 On the problems supplied by John Tomlin, MINOS 5.3 reports that about 10% to 57% of its steps are degenerate: Name Steps Degen Percent BNL1 1614 169 10.47 Added to Netlib on 30 Oct. 1989

Ordering statistics: | AMD |
METIS |

nnz(V) for QR, upper bound nnz(L) for LU | 95,006 | 90,893 |

nnz(R) for QR, upper bound nnz(U) for LU | 12,073 | 13,070 |

*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.