• SJSU Singular Matrix Database
  • Matrix group: Andrianov
  • Click here for a description of the Andrianov group.
  • Click here for a list of all matrices
  • Click here for a list of all matrix groups

  • Matrix: Andrianov/lpl1
  • Description: lpl1 matrix from Alexander Andrianov, SAS Institute Inc.
  • download as a MATLAB mat-file, file size: 620 KB. Use SJget(508) or SJget('Andrianov/lpl1') in MATLAB.
  • download in Matrix Market format, file size: 538 KB.
  • download in Rutherford/Boeing format, file size: 378 KB.


    A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

    Routine svds_err, version 1.0, used with Matlab (R2008a) to calculate the 6 largest singular values and associated error bounds.
    Routine spnrank, version 1.0, used with Matlab (R2008a) to calculate singular values 31141 to 31146 and associated error bounds.


    dmperm of Andrianov/lpl1

    Matrix properties (click for a legend)  
    number of rows32,460
    number of columns32,460
    structural full rank?yes
    structural rank32,460
    numerical rank 31,143
    dimension of the numerical null space1,317
    numerical rank / min(size(A))0.95943
    Euclidean norm of A 45.987
    calculated singular value # 311437.5967e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 311443.0347e-014
    gap in the singular values at the numerical rank:
    singular value # 31143 / singular value # 31144
    calculated condition number-2
    # of blocks from dmperm3
    # strongly connected comp.3
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

    authorA. Andrianov
    editorT. Davis
    kindoptimization problem
    2D/3D problem?no

    Ordering statistics:AMD METIS DMPERM+
    nnz(chol(P*(A+A'+s*I)*P'))968,227 1,083,572 968,227
    Cholesky flop count1.6e+008 2.0e+008 1.6e+008
    nnz(L+U), no partial pivoting1,903,994 2,134,684 1,903,994
    nnz(V) for QR, upper bound nnz(L) for LU19,297,162 20,962,372 21,686,759
    nnz(R) for QR, upper bound nnz(U) for LU36,796,010 40,838,677 37,074,045

    Maintained by Leslie Foster, last updated 24-Apr-2009.

    Entries 5 through 14 in the table of matrix properties and the singular
    value plot were created using SJsingular code. The other plots
    and statistics are produced using utilities from the SuiteSparse package.
    Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.