• SJSU Singular Matrix Database
• Matrix group: Regtools

• Matrix: Regtools/shaw_200
• Description: SHAW 200x200 Test problem: one-dimensional image restoration model.
• download as a MATLAB mat-file, file size: 297 KB. Use SJget(254) or SJget('Regtools/shaw_200') in MATLAB.

Routine svd from Matlab 7.6.0.324 (R2008a) used to calculate the singular values.

 Matrix properties (click for a legend) number of rows 200 number of columns 200 structural full rank? yes structural rank 200 numerical rank 20 dimension of the numerical null space 180 numerical rank / min(size(A)) 0.1 Euclidean norm of A 2.9933 calculated singular value # 20 6.9115e-013 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 8.8818e-014 calculated singular value # 21 1.5968e-015 gap in the singular values at the numerical rank: singular value # 20 / singular value # 21 432.84 calculated condition number 3.9746e+019 condest 5.3147e+020 nonzeros 40,000 # of blocks from dmperm 1 # strongly connected comp. 1 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 Shaw editor Per Christian Hansen date 1972 kind ill-posed problem 2D/3D problem? no SJid 254 UFid -

 Additional fields size and type b full 200-by-1 x full 200-by-1

Notes:

```    Constructed by the call [A,b,x]= shaw(200)

where shaw is from Regularization Tools. The description of
shaw from http://www2.imm.dtu.dk/~pch/Regutools/ is:

[A,b,x] = shaw(n)

Discretization of a first kind Fredholm integral equation with
[-pi/2,pi/2] as both integration intervals.  The kernel K and
the solution f, which are given by
K(s,t) = (cos(s) + cos(t))*(sin(u)/u)^2
u = pi*(sin(s) + sin(t))
f(t) = a1*exp(-c1*(t - t1)^2) + a2*exp(-c2*(t - t2)^2) ,
are discretized by simple quadrature to produce A and x.
Then the discrete right-hand b side is produced as b = A*x.

The order n must be even.
```

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 20,100 20,100 Cholesky flop count 2.7e+006 2.7e+006 nnz(L+U), no partial pivoting 40,000 40,000 nnz(V) for QR, upper bound nnz(L) for LU 20,100 20,100 nnz(R) for QR, upper bound nnz(U) for LU 20,100 20,100

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.