Matrix properties
number of rows	19,728
number of columns	29,856
nonzeros	148,416
structural full rank?	yes
structural rank	19,728
# 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	S. Karisch, F. Rendl
editor	H. Mittelmann
date	1995
kind	linear programming problem
2D/3D problem?	no

Additional fields	size and type
b	full 19728-by-1
c	full 29856-by-1
lo	full 29856-by-1
hi	full 29856-by-1
z0	full 1-by-1

Notes:

Hans Mittelmann test set, http://plato.asu.edu/ftp/lptestset           
minimize c'*x, subject to A*x=b and lo <= x <= hi                      
                                                                       
NUG:  computing LP lower bounds for quadratic assignment problems.  see
S.E. KARISCH and F. RENDL. Lower bounds for the quadratic assignment   
problem via triangle decompositions.  Mathematical Programming,        
71(2):137-152, 1995.                                                   
K.G. Ramakrishnan, M.G.C. Resende, B. Ramachandran, and J.F. Pekny,    
"Tight QAP bounds via linear programming," Combinatorial and Global    
Optimization, P.M. Pardalos, A. Migdalas, and R.E. Burkard, eds.,      
World Scientific Publishing Co., Singapore, pp. 297-303, 2002.         

Ordering statistics:	result
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	184,473,912
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	114,635,182

SVD-based statistics:
norm(A)	8.11519
min(svd(A))	4.76129e-118
cond(A)	1.70441e+118
rank(A)	18,270
sprank(A)-rank(A)	1,458
null space dimension	1,458
full numerical rank?	no
singular value gap	2.98861e+13

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.