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

• Matrix: Grund/bayer01
• Description: Unsymmetric Matrix bayer01, Bayer AG, F. Grund, Apr 1996.
• download as a MATLAB mat-file, file size: 1 MB. Use SJget(418) or SJget('Grund/bayer01') in MATLAB.
• download in Matrix Market format, file size: 2 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 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0 with opts.tol_eigs = 1e-010, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 51607 to 51612 and associated error bounds.

 Matrix properties (click for a legend) number of rows 57,735 number of columns 57,735 structural full rank? yes structural rank 57,735 numerical rank 51,609 dimension of the numerical null space 6,126 numerical rank / min(size(A)) 0.89389 Euclidean norm of A 1.26e+005 calculated singular value # 51609 8.4181e-007 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 8.4015e-007 calculated singular value # 51610 8.3961e-007 gap in the singular values at the numerical rank: singular value # 51609 / singular value # 51610 1.0026 calculated condition number -2 condest 3.3364e+019 nonzeros 275,094 # of blocks from dmperm 9,133 # strongly connected comp. 1 entries not in dmperm blocks 28,203 explicit zero entries 2,680 nonzero pattern symmetry 0% numeric value symmetry 0% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author Bayer editor F. Grund date 1997 kind chemical process simulation problem 2D/3D problem? no SJid 418 UFid 452

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 230,553,822 69,960,978 898,313 Cholesky flop count 3.1e+012 2.6e+011 3.7e+007 nnz(L+U), no partial pivoting 461,049,909 139,864,221 1,767,094 nnz(V) for QR, upper bound nnz(L) for LU 762,409 820,455 714,068 nnz(R) for QR, upper bound nnz(U) for LU 1,565,498 1,655,102 1,473,688

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2680 explicit zero entries.

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.