Matrix: Schulthess/N_pid
Description: biochemical network; left nullspace is required
(bipartite graph drawing) |
Matrix properties | |
number of rows | 3,625 |
number of columns | 3,923 |
nonzeros | 8,054 |
structural full rank? | no |
structural rank | 2,171 |
# of blocks from dmperm | 640 |
# strongly connected comp. | 1,216 |
explicit zero entries | 0 |
nonzero pattern symmetry | 0% |
numeric value symmetry | 0% |
type | integer |
structure | rectangular |
Cholesky candidate? | no |
positive definite? | no |
author | P. Schulthess |
editor | T. Davis |
date | 2012 |
kind | biochemical network |
2D/3D problem? | no |
Notes:
Matrices from Pascal Schulthess, Institute for Pathology, Chariteplatz 1, 10117 Berlin, Germany. Three large biochemical networks (N_biocarta, N_pid, and N_reactome). These are stoichiometric matrices extracted from three biochemical databases (BioCarta, PID, and REACTOME) describing cell signaling pathways and protein-protein interaction networks. The goal is to find the left nullspace of the matrix; in MATLAB notation: N = null (Problem.A') ; The matrix (Problem.A')*N will thus be essentially zero. This can be done much more efficiently with the spqr_rank toolbox by Leslie Foster and Tim Davis, as: N = spqr_null (Problem.A') ; Results: The matrix A is transposed, then N = null (A) or N = spqr_null (A) is computed. The size statistic is the memory taken by N. spqr_null can compute either an explicit matrix N, or an implicit Householder-based representation. The latter takes less memory. Matrix: N_biocarta size: 1996 by 1922 (transposed) spqr_null stats: flag: 0 rank: 1023 tol: 3.5456e-12 est_sval_upper_bounds: [0.1689 3.4534e-15] est_sval_lower_bounds: [0.1203 0] sval_numbers_for_bounds: [1023 1024] est_norm_A_times_N: 2.4349e-15 spqr_null, implicit: 0.03 sec, norm(A*N) 9e-15 size: 0.08 MB spqr_null, explicit: 0.10 sec, norm(A*N) 9e-15 size: 0.11 MB MATLAB null: 3.31 sec, norm(A*N) 2e-13 size: 13.82 MB all report dim(N) of 899. Matrix: N_pid size: 3923 by 3625 (transposed) spqr_null stats: flag: 0 rank: 2048 tol: 1.3937e-11 est_sval_upper_bounds: [0.0922 5.1310e-15] est_sval_lower_bounds: [0.0585 0] sval_numbers_for_bounds: [2048 2049] est_norm_A_times_N: 1.6751e-15 spqr_null, implicit: 0.05 sec, norm(A*N) 4e-14 size: 0.21 MB spqr_null, explicit: 0.34 sec, norm(A*N) 4e-14 size: 1.32 MB MATLAB null: 24.86 sec, norm(A*N) 9e-13 size: 45.73 MB all report dim(N) of 1577 Matrix: N_reactome size: 16559 by 10204 (transposed) spqr_null stats: flag: 0 rank: 9025 tol: 1.1766e-10 est_sval_upper_bounds: [0.6722 1.3042e-14] est_sval_lower_bounds: [0.0106 0] sval_numbers_for_bounds: [9025 9026] est_norm_A_times_N: 9.4695e-15 spqr_null, implicit: 0.95 sec, norm(A*N) 2e-13 size: 7.5 MB spqr_null, explicit: 3.53 sec, norm(A*N) 2e-13 size: 25.2 MB MATLAB null: 904.54 sec, norm(A*N) 2e-10 size: 96.2 MB all report dim(N) of 1179.
Ordering statistics: | result |
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD | 46,046 |
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD | 9,594 |
SVD-based statistics: | |
norm(A) | 20.4905 |
min(svd(A)) | 0 |
cond(A) | Inf |
rank(A) | 2,048 |
sprank(A)-rank(A) | 123 |
null space dimension | 1,577 |
full numerical rank? | no |
singular value gap | 4.16923e+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.