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

  • Matrix: Gupta/gupta1
  • Description: Linear programming matrix (A*A'), Anshul Gupta, anshul@watson.ibm.com
  • download as a MATLAB mat-file, file size: 2 MB. Use SJget(520) or SJget('Gupta/gupta1') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.


    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 with opts.tol_eigs = 1e-008, used with Matlab (R2008a) to calculate singular values 30780 to 30785 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows31,802
    number of columns31,802
    structural full rank?yes
    structural rank31,802
    numerical rank 30,782
    dimension of the numerical null space1,020
    numerical rank / min(size(A))0.96793
    Euclidean norm of A 420.32
    calculated singular value # 307821.1571e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 307831.4385e-013
    gap in the singular values at the numerical rank:
    singular value # 30782 / singular value # 30783
    calculated condition number-2
    # of blocks from dmperm1
    # strongly connected comp.1
    entries not in dmperm blocks0
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?no

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

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))2,298,971 2,037,481
    Cholesky flop count2.9e+008 2.9e+008
    nnz(L+U), no partial pivoting4,566,140 4,043,160
    nnz(V) for QR, upper bound nnz(L) for LU163,090,890 -
    nnz(R) for QR, upper bound nnz(U) for LU332,044,906 -

    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.