nlxb {nlmrt} | R Documentation |
Nash variant of Marquardt nonlinear least squares solution via qr linear solver.
Description
Given a nonlinear model expressed as an expression of the form lhs ~ formula_for_rhs and a start vector where parameters used in the model formula are named, attempts to find the minimum of the residual sum of squares using the Nash variant (Nash, 1979) of the Marquardt algorithm, where the linear sub-problem is solved by a qr method.
Usage
nlxb(formula, start, trace=FALSE, data, lower=-Inf, upper=Inf,
masked=NULL, control, ...)
Arguments
formula |
This is a modeling formula of the form (as in |
start |
A named parameter vector. For our example, we could use start=c(b1=1, b2=2.345, b3=0.123) |
trace |
Logical TRUE if we want intermediate progress to be reported. Default is FALSE. |
data |
A data frame containing the data of the variables in the formula. This data may, however, be supplied directly in the parent frame. |
lower |
Lower bounds on the parameters. If a single number, this will be applied to all parameters. Default -Inf. |
upper |
Upper bounds on the parameters. If a single number, this will be applied to all parameters. Default Inf. |
masked |
Character vector of quoted parameter names. These parameters will NOT be altered by the algorithm. |
control |
A list of controls for the algorithm. These are:
|
... |
Any data needed for computation of the residual vector from the expression rhsexpression - lhsvar. Note that this is the negative of the usual residual, but the sum of squares is the same. |
Details
nlxb
attempts to solve the nonlinear sum of squares problem by using
a variant of Marquardt's approach to stabilizing the Gauss-Newton method using
the Levenberg-Marquardt adjustment. This is explained in Nash (1979 or 1990) in
the sections that discuss Algorithm 23. (?? do we want a vignette. Yes, because
folk don't have access to book easily, but finding time.)
In this code, we solve the (adjusted) Marquardt equations by use of the
qr.solve()
. Rather than forming the J'J + lambda*D matrix, we augment
the J matrix with extra rows and the y vector with null elements.
Value
A list of the following items
coefficients |
A named vector giving the parameter values at the supposed solution. |
ssquares |
The sum of squared residuals at this set of parameters. |
resid |
The residual vector at the returned parameters. |
jacobian |
The jacobian matrix (partial derivatives of residuals w.r.t. the parameters) at the returned parameters. |
feval |
The number of residual evaluations (sum of squares computations) used. |
jeval |
The number of Jacobian evaluations used. |
Note
Special notes, if any, will appear here.
Author(s)
John C Nash <nashjc@uottawa.ca>
References
Nash, J. C. (1979, 1990) _Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation._ Adam Hilger./Institute of Physics Publications
others!!
See Also
Function nls()
, packages optim
and optimx
.
Examples
cat("See examples in nlmrt-package.Rd\n")