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)
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
nnls may fail to conserve on singular cases.
to regularise the problem by removing the singularity.
Can try different values for reg.
nnls Failed to converge in 965 iterations
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!
Actual acknowledgement should be:
Lawson & Hanson, Solving Least Squares Problems, Ch 23.
Correction for case of all zero solution.