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nnls - Non negative least squares

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nnls - Alternative to lsqnonneg: faster on large problems, improved convergence, optional restart

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nnls - Alternative to lsqnonneg: can be faster on large problems,
 improved convergence control, optional restart vector

Solves non negative least squares:
    min wrt x: (d-Cx)'*(d-Cx) subject to: x>=0

This version of nnls aims to solve convergance problems that can occur
with the 2011-2012 version of lsqnonneg, and provides a fast solution of
large problems. Includes an option to give initial positive terms for x
for faster solution of iterative problems using nnls.

For some large problems nnls can be faster than lsqnonneg,
see test file (nnlstest.m).

Simple usage: x=nnls(C,d)

[x,w,info]=nnls(C,d,opts)
 C Coefficient matrix
 d Rhs vector
 opts Struct containing options: (optional)
       .Accy 0 fast version, 1 refines final value (default),
                2 uses accurate steps but very slow on large cases,
                faster on small cases, result usually identical to 1
       .Order True or [], or order to initially include positive terms
                if included will supply info.Order, if x0 available use
                find(x0>0), but best saved from previous run of nnls
       .Tol Tolerance test value, default zero, use multiple of eps
       .Iter Maximum number of iterations, should not be needed.

 x Positive solution vector x>=0
 w Lagrange multiplier vector w(x==0)<= approx zero
 info Struct with extra information:
       .iter Number of iterations used
       .wsc0 Estimated size of errors in w
       .wsc Maximum of test values for w
       .Order Order variables used, use to restart nnls with opts.Order

Examples in nnlstest.m

Comments and Ratings (5)

Bill Whiten

nnls may fail to conserve on singular cases.
Try
n=size(C,2);
reg=1e-6;
x=nnls([C;reg*eye(n)],[d;zeros(n,1)]);
to regularise the problem by removing the singularity.
Can try different values for reg.

Gang Wu

nnls Failed to converge in 965 iterations

Bill Whiten

See nnnlsq Non negative non linear least squares for non linear case.

Thank you Bill for providing this function. For my particular problem, it turns out that your function can find an appropriate solution, while on the other hand the Matlab function lsqnonneg can not.

It's just a pity that i fiddeled and almost re-wrote lsqnonneg before I searched and found your implementation.

Once more: thank you!

Bill Whiten

Actual acknowledgement should be:
Lawson & Hanson, Solving Least Squares Problems, Ch 23.

Updates

1.1

Correction for case of all zero solution.

MATLAB Release
MATLAB 7.14 (R2012a)
Acknowledgements

Inspired by: nlcontrol

Inspired: zeroSR1, nlsq & nnnlsq Least squares

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