nnls: Nonnegative Least Squares

In limSolve: Solving Linear Inverse Models

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

A	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.
B	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:

X	vector containing the solution of the nonnegative least squares problem.
residualNorm	scalar, 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.
solutionNorm	scalar, the value of the quadratic function at the solution, i.e. the value of \min(||Ax-b||^2).
IsError	logical, TRUE if an error occurred.
type	the string "nnls", such that how the solution was obtained can be traced.
numiter	the number of iterations.

Author(s)

Karline Soetaert <[e-mail]>

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)

See Also

ldei, which includes equalities

Examples

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

limSolve documentation built on Sept. 22, 2023, 1:07 a.m.