Matrix: Dehghani/light_in_tissue

Description: Light transport in soft tissue. Hamid Dehghani, Univ. Exeter, UK

Dehghani/light_in_tissue graph
(undirected graph drawing)


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  • download as a MATLAB mat-file, file size: 2 MB. Use UFget(1873) or UFget('Dehghani/light_in_tissue') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.

    Matrix properties
    number of rows29,282
    number of columns29,282
    structural full rank?yes
    structural rank29,282
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorH. Dehghani
    editorT. Davis
    kindelectromagnetics problem
    2D/3D problem?yes

    Additional fieldssize and type
    bsparse 29282-by-1
    Qsparse 14641-by-1
    nodesfull 14641-by-3
    elementsfull 28800-by-3


    % The problem is solving the fluence (PHI) of light in soft tissue using
    % a simplified 3rd spherical harmonic expansion (SPN3) of the Radiative 
    % Transport Equation.  There are two coupled equations to solve:        
    % M1*phi1 = Q + (M2*phi2)                                   eq(1)       
    % (M4 - (M3*inv(M1)*M2))*phi2 = -2/3*Q + M3*inv(M1)*Q       eq(2)       
    % PHI = phi1 - (1/3).*phi2                                  eq(3)       
    Problem = UFget ('Dehghani/light_in_tissue') ;                          
    A = Problem.A ;                   % get the problem                     
    Q = Problem.aux.Q ;                                                     
    k = size (A,1) / 2 ;                                                    
    M1 = A (1:k,1:k) ;                                                      
    M2 = A (1:k,k+1:end) ;                                                  
    M3 = A (k+1:end, 1:k) ;                                                 
    M4 = A (k+1:end, k+1:end) ;                                             
    elements = Problem.aux.elements ;                                       
    nodes = Problem.aux.nodes ;                                             
    Q2 = (-(2/3).*Q) + (M3*(M1\Q)) ;  % create rhs for equation 2           
    Q2 = [sparse(k,1) ; Q2] ;                                               
    phi2 = A\Q2 ;                     % solve for phi2                      
    phi2 = phi2 (end/2+1:end,:) ;                                           
    Q1 = Q + M2*phi2 ;                % calculate rhs for equation 1        
    phi1 = M1\Q1;                     % solve for phi1                      
    PHI = phi1 - (1/3).*phi2;                                               
    figure (1) ; clf                  % plot results                        
    trisurf(elements, nodes(:,1), nodes(:,2), nodes(:,3), log(abs(PHI))) ;  
    shading interp ;                                                        
    view (2) ;                                                              
    colorbar('horiz') ;                                                     
    axis equal ;                                                            
    axis off ;                                                              
    colormap hot ;                                                          

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD1,390,043
    Cholesky flop count2.0e+08
    nnz(L+U), no partial pivoting, with AMD2,750,804
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD2,925,391
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD5,672,099

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A))

    Dehghani/light_in_tissue 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.