**Matrix: LPnetlib/lp_shell**

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

(bipartite graph drawing) |

Matrix properties | |

number of rows | 536 |

number of columns | 1,777 |

nonzeros | 3,558 |

structural full rank? | yes |

structural rank | 536 |

# of blocks from dmperm | 1 |

# strongly connected comp. | 1 |

explicit zero entries | 0 |

nonzero pattern symmetry | 0% |

numeric value symmetry | 0% |

type | integer |

structure | rectangular |

Cholesky candidate? | no |

positive definite? | no |

author | J. Reid |

editor | D. Gay |

date | 1978 |

kind | linear programming problem |

2D/3D problem? | no |

Additional fields | size and type |

b | full 536-by-1 |

c | full 1777-by-1 |

lo | full 1777-by-1 |

hi | full 1777-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 ------------------------------------------------------------------------------ This LP problem is the source of three sparse matrices in the Harwell/Boeing sparse matrix collection: SHL_0, SHL_200, and SHL_400. Those three matrices are square, nonsingular basis matrices that occured during the solution of SHELL. ------------------------------------------------------------------------------ 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 SHELL 537 1775 4900 38049 B 1.2088253460E+09 BOUND-TYPE TABLE SHELL UP LO FX From John Reid.

Ordering statistics: | result |

nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 56,680 |

nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 4,266 |

SVD-based statistics: | |

norm(A) | 16.0004 |

min(svd(A)) | 1.57846e-14 |

cond(A) | 1.01367e+15 |

rank(A) | 535 |

sprank(A)-rank(A) | 1 |

null space dimension | 1 |

full numerical rank? | no |

singular value gap | 2.41422e+13 |

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.
*