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

  • Matrix: Mulvey/pfinan512
  • Description: Portfolio optim, 512 scenarios, Ed Rothberg, SGI, John Mulvey,Princeton
  • download as a MATLAB mat-file, file size: 887 KB. Use SJget(473) or SJget('Mulvey/pfinan512') in MATLAB.
  • download in Matrix Market format, file size: 881 KB.
  • download in Rutherford/Boeing format, file size: 701 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 71612 to 71617 and associated error bounds.


    Matrix properties (click for a legend)  
    number of rows74,752
    number of columns74,752
    structural full rank?yes
    structural rank74,752
    numerical rank 71,614
    dimension of the numerical null space3,138
    numerical rank / min(size(A))0.95802
    Euclidean norm of A 13.742
    calculated singular value # 716147.5304e-005
    numerical rank defined using a tolerance
    max(size(A))*eps(norm(A)) =
    calculated singular value # 716151.2973e-013
    gap in the singular values at the numerical rank:
    singular value # 71614 / singular value # 71615
    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. Berger, J. Mulvey, E. Rothberg, R. Vanderbei
    editorE. Rothberg
    kindduplicate economic problem
    2D/3D problem?no


    This matrix is the nonzero pattern of Mulvey/finan512

    Ordering statistics:AMD METIS
    nnz(chol(P*(A+A'+s*I)*P'))2,837,714 1,852,549
    Cholesky flop count6.3e+008 1.7e+008
    nnz(L+U), no partial pivoting5,600,676 3,630,346
    nnz(V) for QR, upper bound nnz(L) for LU7,132,462 6,391,002
    nnz(R) for QR, upper bound nnz(U) for LU15,382,253 14,889,295

    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.