• SJSU Singular Matrix Database
• Matrix group: QY
• Click here for a description of the QY group.
• Click here for a list of all matrices
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• Matrix: QY/case9
• Description: Transient stabilty constrained interior pt. optimal power flow, J. Quanyuan
• download as a MATLAB mat-file, file size: 10 MB. Use SJget(695) or SJget('QY/case9') in MATLAB.
• download in Matrix Market format, file size: 10 MB.
• download in Rutherford/Boeing format, file size: 9 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,rr, 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,spnrank.pdf"> spnrank, version 1.0 with opts.tol_eigs = 1e-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 14442 to 14447 and associated error bounds.   Matrix properties (click for a legend) number of rows 14,454 number of columns 14,454 structural full rank? yes structural rank 14,454 numerical rank 14,444 dimension of the numerical null space 10 numerical rank / min(size(A)) 0.99931 Euclidean norm of A 5306.2 calculated singular value # 14444 1.4283e-008 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 1.3146e-008 calculated singular value # 14445 1.1652e-008 gap in the singular values at the numerical rank: singular value # 14444 / singular value # 14445 1.2258 calculated condition number -2 condest 3.1256e+012 nonzeros 147,972 # of blocks from dmperm 2 # strongly connected comp. 2 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? no positive definite? no

 author J. Quanyuan editor T. Davis date 2008 kind power network problem sequence 2D/3D problem? no SJid 695 UFid 2,214

 Additional fields size and type b sparse 14454-by-1 A cell 12-by-1 b1 cell 12-by-1 b2 cell 12-by-1

Notes:

```Transient stabilty constrained interior pt. optimal power flow, J. Quanyuan
Two problem sets from Dr. Jiang Quanyuan from Zhejiang University,
Hangzhou, China, March, 2008, used in an electrical power system.
Each matrix A is solved sequentially with two right-hand-sides, b1 and
b2, one at a time.  In the UF collection, the sequence of all first
and second right-hand-sides is in Problem.aux.b2 and Problem.aux.b1.
These matrices are symmetric indefinite (x=A\b uses MA57)
Note that the last matrices in the sequence are ill-conditioned.

Transient Stability Constrained Interior Point Optimal Power Flow Program
Version 1.0 -- Developed by Dr. Jiang Quanyuan, March 2008

case9.m - TSOPF converges after 12 iterations
object    = 3.945939E+03
max_equ   = 3.287326E-11
low_inequ = None
up_inequ  = None
```

 Ordering statistics: AMD METIS DMPERM+ nnz(chol(P*(A+A'+s*I)*P')) 178,786 211,362 - Cholesky flop count 2.6e+006 3.8e+006 - nnz(L+U), no partial pivoting 343,118 408,270 - nnz(V) for QR, upper bound nnz(L) for LU 17,856,448 8,290,763 17,856,447 nnz(R) for QR, upper bound nnz(U) for LU 26,478,449 28,095,620 26,478,449

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.