nnls - Non negative least squares

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

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Updated 23 Apr 2013

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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

Cite As

Bill Whiten (2023). nnls - Non negative least squares (https://www.mathworks.com/matlabcentral/fileexchange/38003-nnls-non-negative-least-squares), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2012a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: nlcontrol

Inspired: zeroSR1, nlsq & nnnlsq Least squares

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Version Published Release Notes
1.1.0.0

Correction for case of all zero solution.

1.0.0.0