Matrix: LPnetlib/lp_maros_r7
Description: Netlib LP problem maros_r7: minimize c'*x, where Ax=b, lo<=x<=hi
|
| (bipartite graph drawing) |
 |
| Matrix properties | |
| number of rows | 3,136 |
| number of columns | 9,408 |
| nonzeros | 144,848 |
| structural full rank? | yes |
| structural rank | 3,136 |
| # 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 | I. Maros |
| editor | D. Gay |
| date | 1994 |
| kind | linear programming problem |
| 2D/3D problem? | no |
| Additional fields | size and type |
| b | full 3136-by-1 |
| c | full 9408-by-1 |
| lo | full 9408-by-1 |
| hi | full 9408-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
MAROS-R7 3137 9408 151120 4812587 1.4971851665E+06
From Istvan Maros.
Concerning the problems he submitted, Istvan Maros says that
MAROS-R7 is "an interesting
real-life LP problem which appeared hard to some solvers." It "is an
image restoration problem done via a goal programming approach. It is
structured, namely, its first section is a band matrix with the
dominating number of nonzeros, while the second section is also a band
matrix with bandwidth equals 2 and coefficients +1, -1. The problem is
a representative of a family of problems in which the number of rows and
the bandwidth of the first section can vary. This one is a medium size
problem from the family. MAROS-R7 became available in cooperation with
Roni Levkovitz and Carison Tong."
Added to Netlib on 17 Jan. 1994
| Ordering statistics: | result |
| nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 9,862,844 |
| nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 853,785 |
| SVD-based statistics: | |
| norm(A) | 3.40327 |
| min(svd(A)) | 1.46495 |
| cond(A) | 2.32313 |
| rank(A) | 3,136 |
| 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.