Matrix: LPnetlib/lp_fit2d
Description: Netlib LP problem fit2d: minimize c'*x, where Ax=b, lo<=x<=hi
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| (bipartite graph drawing) |
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| Matrix properties | |
| number of rows | 25 |
| number of columns | 10,524 |
| nonzeros | 129,042 |
| structural full rank? | yes |
| structural rank | 25 |
| # 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 25-by-1 |
| c | full 10524-by-1 |
| lo | full 10524-by-1 |
| hi | full 10524-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
FIT2D 26 10500 138018 482330 B -6.8464293294E+04
BOUND-TYPE TABLE
FIT2D UP
Supplied by Bob Fourer.
When included in Netlib: Cost coefficients negated.
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.
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)
FIT2D -6.8464293232E+04
Added to Netlib on 31 Jan. 1990
| Ordering statistics: | result |
| nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 262,500 |
| nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 325 |
| SVD-based statistics: | |
| norm(A) | 17513.2 |
| min(svd(A)) | 10.088 |
| cond(A) | 1736.04 |
| rank(A) | 25 |
| 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 (R)) ; where [~,R,E] = spqr (A') with droptol of zero |
| 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.