[Octave-patch-tracker] [patch #9282] add minres for sparse linear systems

[Nicholas Jankowski]

Follow-up Comment #1, patch #9282 (project octave):

Nice work. some comments:

are there any tests you could add to the end of the m-file, perhaps to verify
expected input/output handling, errors, maybe verifying results as expected
from the matlab examples? 

I did run the example given on the referenced matlab help page

n = 100; on = ones(n,1); 
A = spdiags([-2*on 4*on -2*on],-1:1,n,n);
b = sum(A,2); 
tol = 1e-10; 
maxit = 50; 
M1 = spdiags(4*on,0,n,n);

x = minres(A,b,tol,maxit,M1);
minres converged at iteration 49 to a solution with relative 
residual 4.7e-014


the output x is more or less equal to ones(100,1), with error on the order of
1e-14.

running the same on your minres produces:

>> x'
ans =
 Columns 1 through 8:
   0.97030   0.94062   0.91098   0.88142   0.85195   0.82260   0.79338  
0.76433
 Columns 9 through 16:
   0.73547   0.70681   0.67839   0.65023   0.62234   0.59476   0.56750  
0.54059
 Columns 17 through 24:
   0.51406   0.48792   0.46220   0.43692   0.41211   0.38779   0.36398  
0.34071
 Columns 25 through 32:
   0.31800   0.29586   0.27434   0.25344   0.23320   0.21363   0.19476  
0.17661
 Columns 33 through 40:
   0.15921   0.14257   0.12673   0.11171   0.09752   0.08419   0.07175  
0.06022
 Columns 41 through 48:
   0.04962   0.03998   0.03131   0.02365   0.01701   0.01142   0.00690  
0.00347
 Columns 49 through 56:
   0.00116   0.00000   0.00000   0.00116   0.00347   0.00690   0.01142  
0.01701
 Columns 57 through 64:
   0.02365   0.03131   0.03998   0.04962   0.06022   0.07175   0.08419  
0.09752
 Columns 65 through 72:
   0.11171   0.12673   0.14257   0.15921   0.17661   0.19476   0.21363  
0.23320
 Columns 73 through 80:
   0.25344   0.27434   0.29586   0.31800   0.34071   0.36398   0.38779  
0.41211
 Columns 81 through 88:
   0.43692   0.46220   0.48792   0.51406   0.54059   0.56750   0.59476  
0.62234
 Columns 89 through 96:
   0.65023   0.67839   0.70681   0.73547   0.76433   0.79338   0.82260  
0.85195
 Columns 97 through 100:
   0.88142   0.91098   0.94062   0.97030


Since it's an example we can use to test algorithm compatibility, I would
suggest adding the following test block to the end of the file in addition to
any others to catch input/output, format, etc.


## test for algorithm accuracy and compatibility from matlab doc example
%!test
%! n = 100;
%! on = ones (n, 1); 
%! A = spdiags ([-2*on 4*on -2*on], -1:1, n, n);
%! b = sum (A, 2); 
%! tol = 1e-10; 
%! maxit = 50; 
%! M1 = spdiags (4*on, 0, n, n);
%! x = minres (A, b, tol, maxit, M1);
%! assert (size (x), [100, 1]);
%! assert (x,ones(100,1),1e-13);


Some of your errors related to providing incorrect inputs (nargin<2 test for
example) should call print_usage()

Regarding usage, I don't know how mandatory this is, but usually there's a
separate line for each valid calling method. so a line for minres(A,b), then
minres(A,b,tol), etc. 

Last, a complete patch should also update the scripts/sparse/module.mk file,
the documentation file (I guess under doc/interpreter/sparse.txi), and add the
new function to /NEWS


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