LSQNONNEG function with large amount of data

Hi,

I'm trying to run the lsqnonneg function(finding least squares solution with the constraint of non-negativity).

I'm having problems when the data is huge - I'm getting this error message : "Exiting: Iteration count is exceeded, exiting LSQNONNEG.

Try raising the tolerance (OPTIONS.TolX)."

Also, the result returned is an intermediate solution, which is not non-negative and therefore not a valid solution.

I'm guessing that maybe the algorithm failes to find a solution on such huge amounts of data(at some point the positive set array is all zeros, and that is when the algorithm gets "stuck"), the question is if there is anything I can do other than reducing the amount of data.

I have attached a .mat file with the parameters C and d(where C is the matrix and the first param and d is second param).

Thanks in advance.

[Borong Liu]

Hi,

I have the same problem, have you fixed it?

Thanks in advance.

Answer 1

[John D'Errico]

No answer was made, so too late for @Neil Cohen. (Sorry about that. But @Borong Liu might gain.) Since there is still interest, I'll show one option to solve it.

whos C d
  Name           Size               Bytes  Class     Attributes

  C         257600x5             10304000  double              
  d         257600x1              2060800  double              

So it is not too huge of a problem. But lsqnonneg did have a problem.

lsqnonneg(C,d)
  Exiting: Iteration count is exceeded, exiting LSQNONNEG.
  Try raising the tolerance (OPTIONS.TolX).
  
ans =
-0.000368354710649102
0.227251353522795
0
0
0

Even so, I woud have thought lsqnonneg would handle this. So the obvious solution is to try lsqlin.

lsqlin(C,d,[],[],[],[],zeros(1,5))

Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

<stopping criteria details>
ans =
4.66053409046511e-23
0.201099498918889
0.124298333566924
0.760555144151411
0.215357073925574

No problem. However, this still begs the question as to how to get lsqnonneg to work. Perhaps I'll just take the advice it gave, since there are only two options that lsqnonneg uses anyway.

opts = optimset('lsqnonneg');
opts.TolX = 1e-12;
lsqnonneg(C,d,opts)
ans =
0
0.201099498918889
0.124298333566995
0.760555144149044
0.215357073938012

Which appears to be fundamentally the same solution that lsqlin returns.

[Arnab Paul]

Hi John

I have different problem

I have two matrix A_matrix and b

The dimension is

A_matrix = 301x16

b = 301x 255651.

To use b as vector I am using this code

x = zeros(size(A_matrix, 2), size(b, 2));
% Perform Non-Negative Least Squares 
options = optimset('TolX', 1e-12); % 
for i = 1:size(b, 2)
    x(:, i) = lsqnonneg(A_matrix, b(:, i), options);
end

now x has the dimension of 16x255651

b has NaN values in it as well as positive values and A_matrix has all the positive values.

The output x coming 0 in the matrix. Kindly help me with the problem

[Torsten]

Skip the columns of b with NaN values. Or what was your question ?

[Arnab Paul]

The output x has zero in the last row. 16 rows are the bands of satellite and the columns are pixels values. How not to get 0 values in the last row while using lsqnonneg?

I have converted NaNs to 0s.

[John D'Errico]

@Arnab Paul

That all elements in the last row are zero merely means that that component is always best chosen as zero, since it really wants to be negative. What function are you using? LSQNONNEG. If a given element strongly needs to be negative, then lsqnonneg effectively uses zero instead.

Just wanting a different result is not sufficient.

[Arnab Paul]

yes I am using lsqnonneg. Is their any way I can moify the Tolx or apply the different "Algorithm". So that I can get values instead of zero?