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

• Matrix: GHS_indef/ncvxqp9
• Description: Gould, Hu, & Scott: KKT matrix - nonconvex QP (CUTEr)
• download as a MATLAB mat-file, file size: 210 KB. Use SJget(398) or SJget('GHS_indef/ncvxqp9') in MATLAB.
• download in Matrix Market format, file size: 203 KB.
• download in Rutherford/Boeing format, file size: 200 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 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14615 to 14620 and associated error bounds.

 Matrix properties (click for a legend) number of rows 16,554 number of columns 16,554 structural full rank? yes structural rank 16,554 numerical rank 14,617 dimension of the numerical null space 1,937 numerical rank / min(size(A)) 0.88299 Euclidean norm of A 1.2705e+011 calculated singular value # 14617 0.25269 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 0.25259 calculated singular value # 14618 0.25226 gap in the singular values at the numerical rank: singular value # 14617 / singular value # 14618 1.0017 calculated condition number -2 condest 9.0537e+018 nonzeros 54,040 # of blocks from dmperm 555 # strongly connected comp. 555 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? yes positive definite? no

 author N. Gould editor N. Gould date 1994 kind optimization problem 2D/3D problem? no SJid 398 UFid 1,243

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 142,666 134,665 384,442 Cholesky flop count 1.0e+007 5.9e+006 4.0e+007 nnz(L+U), no partial pivoting 268,778 252,776 752,330 nnz(V) for QR, upper bound nnz(L) for LU 360,371 328,079 315,723 nnz(R) for QR, upper bound nnz(U) for LU 680,921 695,753 673,342

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.