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.