Matrix: Williams/cant

Description: FEM/Cantilever: FEM cantilever. Williams et al.

Williams/cant graph
(undirected graph drawing)

Williams/cant dmperm of Williams/cant

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  • Matrix group: Williams
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  • download as a MATLAB mat-file, file size: 4 MB. Use UFget(2375) or UFget('Williams/cant') in MATLAB.
  • download in Matrix Market format, file size: 8 MB.
  • download in Rutherford/Boeing format, file size: 3 MB.

    Matrix properties
    number of rows62,451
    number of columns62,451
    structural full rank?yes
    structural rank62,451
    # of blocks from dmperm244
    # strongly connected comp.244
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

    editorS. Williams, L. Oliker, R. Vuduc, J. Shalf, K. Yelick, J. Demmel
    kind2D/3D problem
    2D/3D problem?yes


    Matrices used by S. Williams et al for sparse matrix multiplication on GPUs.   
    14 matrices were used in the following paper:                                  
        S. Williams, L. Oliker, R. Vuduc, J. Shalf, K. Yelick, J. Demmel,          
        "Optimization of Sparse Matrix-Vector Multiplication on Emerging Multicore 
        Platforms", Parallel Computing Volume 35, Issue 3, March 2009, Pages       
        178-194.  Special issue on Revolutionary Technologies for Acceleration of  
        Emerging Petascale Applications.                                           
    This same set of 14 matrices was also used in a subsequent technical report by 
                                                                                   "Efficient Sparse
        Matrix-Vector Multiplication on CUDA" Nathan Bell and Michael Garland, in, 
        "NVIDIA Technical Report NVR-2008-004", December 2008                      
    file            Name            dim*    nnz     description                    
    dense2          Dense           2K      4.0M    dense matrix in sparse format  
    pdb1HYS         Protein         36K     4.3M    protein data bank 1HYS         
    consph          FEM/Spheres     83K     6.0M    FEM concentric spheres         
    cant            FEM/Cantilever  62K     4.0M    FEM cantilever                 
    pwtk            Wind Tunnel     218K    11.6M   pressurized wind tunnel        
    rma10           FEM/Harbor      47K     2.37M   3D CFD of Charleston Harbor    
    qcd5_4          QCD             49K     1.90M   quark propagators (QCD/LGT)    
    shipsec1        FEM/Ship        141K    3.98M   FEM Ship section / detail      
    mac_econ_fwd500 Economics       207K    1.27M   Macroeconomic model            
    mc2depi         Epidemiology    526K    2.1M    2D Markov model of epidemic    
    cop20k_A        FEM/Accelerator 121K    2.62M   Accelerator cavity design      
    scircuit        Circuit         171K    959K    Motorola circuit simulation    
    webbase-1M      webbase         1M      3.1M    Web connectivity matrix        
    rail4284        LP              4Kx1.1M 11.3M   Railways set cover,            
                                                    constraint matrix              
    (*) the matrix is square if only one dimension listed.                         
    Six of the matrices are nearly identical to the matrices already in the        
    UF Collection.  They are thus not included in the UF Collection.  See          
    the README.txt file for this collection for details.                           

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD28,946,396
    Cholesky flop count2.1e+10
    nnz(L+U), no partial pivoting, with AMD57,830,341
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD16,727,557
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD33,159,456

    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.