MATLAB Function Reference 
Note
The nnls function was replaced by lsqnonneg in Release 11 (MATLAB 5.3). In Release 12 (MATLAB 6.0), nnls displays a warning message and calls lsqnonneg .

Syntax
Description
x = nnls(A,b)
solves the system of equations in a least squares sense, subject to the constraint that the solution vector x
has nonnegative elements . The solution x
minimizes subject to x
>=
0.
x = nnls(A,b,tol)
solves the system of equations, and specifies a tolerance tol
. By default, tol
is: max(size(A))*
norm(A,1)*
eps.
[x,w] = nnls(A,b)
also returns the dual vector w
, where when and when .
[x,w] = nnls(A,b,tol)
solves the system of equations, returns the dual vector w
, and specifies a tolerance tol
.
Examples
Compare the unconstrained least squares solution to the nnls
solution for a 4by2 problem:
A =0.0372
0.2869
0.6861
0.7071
0.6233
0.6245
0.6344
0.6170 b =
0.8587
0.1781
0.0747
0.8405 [A\b
nnls(A,b)]
= 2.5627
0
3.1108
0.6929 [norm(A*(a\b)b)
norm(A*nnls(a,b)b)]
=
0.6674
0.9118
The solution from nnls
does not fit as well, but has no negative components.
Algorithm
The nnls
function uses the algorithm described in [1], Chapter 23. The algorithm starts with a set of possible basis vectors, computes the associated dual vector w
, and selects the basis vector corresponding to the maximum value in w
to swap out of the basis in exchange for another possible candidate, until w
<=
0.
See Also
\
Matrix left division (backslash)
References
[1] Lawson, C. L. and R. J. Hanson, Solving Least Squares Problems,
PrenticeHall, 1974, Chapter 23.
nextpow2  nnz 