Matrix: Schulthess/N_biocarta

Description: biochemical network; left nullspace is required

Schulthess/N_biocarta graph
(bipartite graph drawing)

Schulthess/N_biocarta dmperm of Schulthess/N_biocarta
scc of Schulthess/N_biocarta

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  • download as a MATLAB mat-file, file size: 11 KB. Use UFget(2552) or UFget('Schulthess/N_biocarta') in MATLAB.
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    Matrix properties
    number of rows1,922
    number of columns1,996
    structural full rank?no
    structural rank1,185
    # of blocks from dmperm347
    # strongly connected comp.800
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorP. Schulthess
    editorT. Davis
    kindbiochemical network
    2D/3D problem?no


    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') ;                                         
    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 COLAMD7,931
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD4,139

    SVD-based statistics:
    null space dimension899
    full numerical rank?no
    singular value gap5.50622e+13

    singular values (MAT file):click here
    SVD method used:s = svd (full (R)) ; where [~,R,E] = spqr (A') with droptol of zero

    Schulthess/N_biocarta svd

    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.