**Matrix: LPnetlib/lp_fit2p**

Description: Netlib LP problem fit2p: minimize c'*x, where Ax=b, lo<=x<=hi

(bipartite graph drawing) |

Matrix properties | |

number of rows | 3,000 |

number of columns | 13,525 |

nonzeros | 50,284 |

structural full rank? | yes |

structural rank | 3,000 |

# 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 | R. Fourer |

editor | R. Fourer |

date | 1990 |

kind | linear programming problem |

2D/3D problem? | no |

Additional fields | size and type |

b | full 3000-by-1 |

c | full 13525-by-1 |

lo | full 13525-by-1 |

hi | full 13525-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 BOUND-TYPE TABLE below shows the bound types present in those problems that have bounds. 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 FIT2P 3001 13525 60784 439794 B 6.8464293232E+04 BOUND-TYPE TABLE FIT2P UP Supplied by Bob Fourer. Concerning FIT1D, FIT1P, FIT2D, FIT2P, Bob Fourer says The pairs FIT1P/FIT1D and FIT2P/FIT2D are primal and dual versions of the same two problems [except that we have negated the cost coefficients of the dual problems so all are minimization problems]. They originate from a model for fitting linear inequalities to data, by minimization of a sum of piecewise-linear penalties. The FIT1 problems are based on 627 data points and 2-3 pieces per primal pl penalty term. The FIT2 problems are based on 3000 data points (from a different sample altogether) and 4-5 pieces per pl term. Added to Netlib on 31 Jan. 1990

Ordering statistics: | result |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 14,846,550 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 4,501,500 |

SVD-based statistics: | |

norm(A) | 9377.31 |

min(svd(A)) | 2 |

cond(A) | 4688.65 |

rank(A) | 3,000 |

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 (A)) ; |

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.
*