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

• Matrix: Schenk_IBMSDS/3D_28984_Tetra
• Description: Olaf Schenk, Univ. Basel: IBM TJ Watson, Yorktown, semiconductor device
• download as a MATLAB mat-file, file size: 3 MB. Use SJget(517) or SJget('Schenk_IBMSDS/3D_28984_Tetra') in MATLAB.
• download in Matrix Market format, file size: 3 MB.
• download in Rutherford/Boeing format, file size: 3 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-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 844 to 849 and associated error bounds.  Matrix properties (click for a legend) number of rows 28,984 number of columns 28,984 structural full rank? yes structural rank 28,984 numerical rank 846 dimension of the numerical null space 28,138 numerical rank / min(size(A)) 0.029189 Euclidean norm of A 1.3523e+021 calculated singular value # 846 5.4744e+012 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 7.598e+009 calculated singular value # 847 182.24 gap in the singular values at the numerical rank: singular value # 846 / singular value # 847 3.0039e+010 calculated condition number -2 condest 2.6176e+042 nonzeros 285,092 # of blocks from dmperm 5,439 # strongly connected comp. 5,439 entries not in dmperm blocks 1,548 explicit zero entries 314,078 nonzero pattern symmetry 99% numeric value symmetry 36% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author IBM editor O. Schenk date 2003 kind semiconductor device problem 2D/3D problem? yes SJid 517 UFid 956

 Additional fields size and type b full 28984-by-1

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 6,646,202 4,128,442 4,317,757 Cholesky flop count 4.0e+009 1.8e+009 2.0e+009 nnz(L+U), no partial pivoting 13,263,420 8,227,900 8,608,078 nnz(V) for QR, upper bound nnz(L) for LU 8,104,405 7,059,175 7,173,130 nnz(R) for QR, upper bound nnz(U) for LU 15,049,119 13,240,927 13,418,309

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 314078 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.