ktsolve {ktsolve}

Configurable Function for Solving Families of Nonlinear Equations Version: 1.3

Description

This function is designed for use with an arbitrary set of equations with an arbitrary set of unknowns. The user selects "fixed" values for enough unknowns to leave as many variables as there are equations, which in most cases means the system is properly defined and a unique solution exists. The function, the fixed values, and initial values for the remaining unknowns are fed to a nonlinear backsolver. As of version 1.3, supports BB and nleqslv

Usage

ktsolve(yfunc, known = list(), guess, 
tool = c("BB", "nleqslv"), show = TRUE, ...)

Arguments

yfunc

a function which accepts a vector of length n and produces an output vector of length n. See the rules for constructing yfunc below.

known

A list of known values. The elements must be named and the names must match variable names in yfunc.

guess

A list or vector of initial guesses for the unknown values. The elements must be named and the names must match variable names in yfunc. AND length(guess) must be same as the number of y[j] equations in yfunc, to avoid having an over- or under-defined system.

tool

name of package which holds the solver to be used. Currently only BB::BBsolveand nleqslv::nleqslv are supported.

show

if TRUE, the solution values are printed in brief form to the console.

...

additional arguments to pass to the selected tool package.

Details

The input form of yfunc is a function of the form:

 yfunc<-function(x) {
y<-vector()
y[1]<-f1(known,guess)
y[2]<-f2(known,guess)
.
.
.
y[n]<-fn(known,guess)
}

where y[j] are dummies which will be driven to zero, and x is a dummy vector which is used (with the "guess" values) to run the solver. So, eqns in the form A=f(x) must be entered as y[j] <- f(x)-A

For example, d = a + sqrt(b) and a = sin(a/b) + g*exp(f*a) become

y[1]<- a - d +sqrt(b) and y[2]<- sin(a/b) +g*exp(f*a) -a ,

and e.g. known <- list(a=3,d=5,g=.1) are the fixed parameters and

guess <- list(b=1,f=1) are the initializers for the solver.

Note that it is not necessary to have any known values if the function in question has as many (independent) equations as unknowns. One of the handy things about ktsolve is the ease with which one can swap 'known' and 'guess' inputs to evaluate the system over different parameter sets.

Value

results

The output returned from the called solver package. As such, the contents and structure depend on which package was invoked via the tools argument.

tool

Echoes back the selected solver package used for reference.

yfunc

Returns the modified yfunc as a function for the user to review and /or use to process additional data, using the fit values generated.

Note

The original version of TK!Solver provided a very nice GUI-based version of what I've done in ktsolver. Over the years, it's turned into a very large, powerful, and,sadly, expensive application. You can find it at https://www.uts.com/Products/Tksolver

Author(s)

Carl Witthoft, [e-mail]

See Also

BBsolve , nleqslv

Examples

zfunc<-function(x) {
	z<-vector()
z[1]<- 4*var1 -3*var2 +5*var3
z[2]<-8*var1 +5*var2 -2*var3
z
}

 known=list(var2=5)
 guess=list(var1=2,var3=0)
 solv1 <- ktsolve(zfunc,known=known,guess=guess)
#   Successful convergence.
# solution is:
#      var1      var3 
# -1.979167  4.583333 
# "known" inputs were:
#       var2
# known 5  
 eval(solv1$yfunc)(solv1$results$par)

 
 known=list(var1=5)
 guess=list(var2=2,var3=0)
 solv2<- ktsolve(zfunc,known=known,guess=guess)
#   Successful convergence.
# solution is:
#      var2      var3 
# -12.63158 -11.57895 
# "known" inputs were:
#       var1
# known 5   
eval(solv2$yfunc)(solv2$results$par)