[Chageset]: Add the spaugment function

[John W. Eaton]

On  2-Apr-2008, Ben Abbott wrote:

| 
| On Apr 2, 2008, at 1:12 PM, David Bateman wrote:
| > Another easy function to implement. The help string and the example  
| > took
| > longer to write :-)
| >
| > D.
| 
| David, I'm getting a failure with this one.
| 
| Is there reason for concern?
| 
| In event it is important, I built with SuiteSparse 3.1.0.
| 
| octave:5> test spaugment
|    ***** test
|   m = 11; n = 10; mn = max(m ,n);
|   a = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],[-1,0,1], m, n);
|   x0 = a \ ones (m,1);
|   s = spaugment (a);
|   [L, U, P, Q] = lu (s);
|   x1 = Q * (U \ (L \ (P  * [ones(m,1); zeros(n,1)])));
|   x1 = x1(end - n + 1 : end);
|   assert (x1, x0, 1e-10)
| !!!!! test failed
| error: assert (x1,x0,1e-10) expected
|     0.109902
|     0.099020
|     0.100097
|     0.099990
|     0.100001
|     0.100000
|     0.099990
|     0.099990
|     0.099020
|     0.099020
| but got
|     0.109902
|     0.099020
|     0.100097
|     0.099990
|     0.100001
|     0.100000
|     0.099990
|     0.099990
|     0.099020
|     0.099020
| maximum absolute error 1.655e-07 exceeds tolerance 1e-10

This looks like a case where we just need to change the tolerance.

jwe