nnls: Nonnegative Least Squares

Description

Solves the following inverse problem: $$\min(||Ax-b||^2)$$ subject to $$x>=0$$

Uses subroutine nnls (FORTRAN) from Linpack

Usage

nnls(A, B, tol = sqrt(.Machine$double.eps), verbose = TRUE)

Arguments

numeric matrix containing the coefficients of the equality constraints $Ax~=B$; if the columns of A have a names attribute, the names will be used to label the output.

numeric vector containing the right-hand side of the equality constraints.

tol

tolerance (for singular value decomposition and for the "equality" constraints).

verbose

logical to print nnls error messages.

Value

a list containing:
Xvector containing the solution of the nonnegative least squares problem.
residualNormscalar, the sum of absolute values of residuals of violated inequalities (i.e. sumof x[<0]); should="" be="" zero="" or="" very="" small="" if="" the="" problem="" is="" feasible.<="" description="">
solutionNormscalar, the value of the quadratic function at the solution, i.e. the value of $\min(||Ax-b||^2)$.
IsErrorlogical, TRUE if an error occurred.
typethe string "nnls", such that how the solution was obtained can be traced.

References

Lawson C.L.and Hanson R.J. 1974. Solving Least Squares Problems, Prentice-Hall

Lawson C.L.and Hanson R.J. 1995. Solving Least Squares Problems. SIAM classics in applied mathematics, Philadelphia. (reprint of book)

Examples

Run this code

A <- matrix(nrow = 2, ncol = 3, data = c(3, 2, 2, 4, 2, 1))
B <- c(-4, 3)
nnls(A, B)