nlmrt (version 2012-12.16)

nlmrt-package: Tools for solving nonlinear least squares problems. UNDER DEVELOPMENT.

Description

The package provides some tools related to using the Nash variant of Marquardt's algorithm for nonlinear least squares.

Details

ll{ Package: nlmrt Type: Package Version: 1.0 Date: 2012-03-05 License: GPL-2 } This package includes methods for solving nonlinear least squares problems specified by a modeling expression and given a starting vector of named paramters. Note: You must provide an expression of the form lhs ~ rhsexpression so that the residual expression rhsexpression - lhs can be computed. The expression can be enclosed in quotes, and this seems to give fewer difficulties with R. Data variables must already be defined, either within the parent environment or else in the dot-arguments. Other symbolic elements in the modeling expression must be standard functions or else parameters that are named in the start vector.

The main functions in nlmrt are:

nlfb - Nash variant of the Marquardt procedure for nonlinear least squares, with bounds constraints, using a residual and optionally Jacobian described as \code{R} functions. 20120803: Todo: Make masks more consistent between nlfb and nlxb.

nlxb - Nash variant of the Marquardt procedure for nonlinear least squares, with bounds constraints, using an expression to describe the residual via an \code{R} modeling expression. The Jacobian is computed via symbolic differentiation. wrapnls - Uses nlxb to solve nonlinear least squares then calls nls() to create an object of type nls.

model2grfun.R - Generate a gradient vector function from a nonlinear model expression and a vector of named parameters.

model2jacfun.R - Generate a Jacobian matrix function from a nonlinear model expression and a vector of named parameters.

model2resfun.R - Generate a residual vector function from a nonlinear model expression and a vector of named parameters.

model2ssfun.R - Generate a sum of squares objective function from a nonlinear model expression and a vector of named parameters.

modgr.R - compute gradient of the sum of squares function using the Jacobian and residuals for a nonlinear least squares problem modss.R - computer the sum of squares function from the residuals of a nonlinear least squares problem

myfn.R, mygr.R, myjac.R, myres.R, myss.R - dummy functions that seem to be needed so there is an available handle for output of functions that generate various functions from expressions.

For testing purposes, there are also some experimental codes using different internal computations for the linear algebraic sub-problems in the inst/dev-codes/ sub-folder.

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

nls

Examples

rm(list=ls())
# library(nlmrt)

# traceval set TRUE to debug or give full history
traceval  <-  FALSE

# Data for Hobbs problem

ydat  <-  c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443, 
          38.558, 50.156, 62.948, 75.995, 91.972) # for testing
y  <-  ydat  # for testing
tdat  <-  seq_along(ydat) # for testing
# WARNING -- using T can get confusion with TRUE
tt  <-  tdat
# A simple starting vector -- must have named parameters for nlxb, nls, wrapnls.
start1  <-  c(b1=1, b2=1, b3=1)

eunsc  <-   y ~ b1/(1+b2*exp(-b3*tt))

cat("GLOBAL DATA
")

anls1g  <-  try(nls(eunsc, start=start1, trace=traceval))
print(anls1g)

cat("GLOBAL DATA AND EXPRESSION -- SHOULD FAIL
")
anlxb1g  <-  try(nlxb(eunsc, start=start1, trace=traceval))
print(anlxb1g)

rm(y)
rm(tt)

cat("LOCAL DATA IN DATA FRAMES
")
weeddata1  <-  data.frame(y=ydat, tt=tdat)
weeddata2  <-  data.frame(y=1.5*ydat, tt=tdat)
anlxb1  <-  try(nlxb(eunsc, start=start1, trace=traceval, data=weeddata1))
print(anlxb1)

anlxb2  <-  try(nlxb(eunsc, start=start1, trace=traceval, data=weeddata2))
print(anlxb2)

startf1  <-  c(b1=1, b2=1, b3=.1)

## With BOUNDS

anlxb1  <-  try(nlxb(eunsc, start=startf1, lower=c(b1=0, b2=0, b3=0), 
      upper=c(b1=500, b2=100, b3=5), trace=traceval, data=weeddata1))
print(anlxb1)

# Check nls too
anlsb1  <-  try(nls(eunsc, start=start1, lower=c(b1=0, b2=0, b3=0), 
     upper=c(b1=500, b2=100, b3=5), trace=traceval, data=weeddata1, algorithm='port'))
print(anlsb1)

tmp  <-  readline("next")

anlxb2  <-  try(nlxb(eunsc, start=start1, lower=c(b1=0, b2=0, b3=0), upper=c(b1=500, b2=100, b3=.25), trace=traceval, data=weeddata1))
print(anlxb2)


anlsb2  <-  try(nls(eunsc, start=start1, lower=c(b1=0, b2=0, b3=0), upper=c(b1=500, b2=100, b3=.25), trace=traceval, data=weeddata1, algorithm='port'))
print(anlsb2)

tmp  <-  readline("next")

cat("TEST MASKS
")

anlsmnqm  <-  try(nlxb(eunsc, start=start1, lower=c(b1=0, b2=0, b3=0), 
   upper=c(b1=500, b2=100, b3=5), masked=c("b2"), trace=traceval, data=weeddata1))
print(anlsmnqm)

cat("UNCONSTRAINED
")
an1q  <-  try(nlxb(eunsc, start=start1, trace=traceval, data=weeddata1))
print(an1q)
tmp  <-  readline("next")


cat("MASKED
")
an1qm3  <-  try(nlxb(eunsc, start=start1, trace=traceval, data=weeddata1, masked=c("b3")))
print(an1qm3)
tmp  <-  readline("next")

# Note that the parameters are put in out of order to test code.
an1qm123  <-  try(nlxb(eunsc, start=start1, trace=traceval, data=weeddata1, masked=c("b2","b1","b3")))
print(an1qm123)
tmp  <-  readline("next")


cat("BOUNDS")
start2  <-  c(b1=100, b2=10, b3=0.1)
an1qb1  <-  try(nlxb(eunsc, start=start2, trace=traceval, data=weeddata1, lower=c(0,0,0), upper=c(200, 60, .3)))
print(an1qb1)
tmp  <-  readline("next")


cat("BOUNDS and MASK")
an1qbm2  <-  try(nlxb(eunsc, start=start2, trace=traceval, data=weeddata1, lower=c(0,0,0), upper=c(200, 60, .3), masked=c("b2")))
print(an1qbm2)
tmp  <-  readline("next")


escal  <-   y ~ 100*b1/(1+10*b2*exp(-0.1*b3*tt))
suneasy  <-  c(b1=200, b2=50, b3=0.3)
ssceasy  <-  c(b1=2, b2=5, b3=3)
st1scal  <-  c(b1=100, b2=10, b3=0.1)


cat("EASY start -- unscaled")
anls01  <-  try(nls(eunsc, start=suneasy, trace=traceval, data=weeddata1))
print(anls01)
anlmrt01  <-  try(nlxb(eunsc, start=ssceasy, trace=traceval, data=weeddata1))
print(anlmrt01)

cat("All 1s start -- unscaled")
anls02  <-  try(nls(eunsc, start=start1, trace=traceval, data=weeddata1))
if (class(anls02) == "try-error") {
   cat("FAILED:")
   print(anls02)
} else {
   print(anls02)
}
anlmrt02  <-  nlxb(eunsc, start=start1, trace=traceval, data=weeddata1)
print(anlmrt02)

cat("ones start -- scaled")
anls03  <-  try(nls(escal, start=start1, trace=traceval, data=weeddata1))
print(anls03)
anlmrt03  <-  nlxb(escal, start=start1, trace=traceval, data=weeddata1)
print(anlmrt03)

cat("HARD start -- scaled")
anls04  <-  try(nls(escal, start=st1scal, trace=traceval, data=weeddata1))
print(anls04)
anlmrt04  <-  nlxb(escal, start=st1scal, trace=traceval, data=weeddata1)
print(anlmrt04)

cat("EASY start -- scaled")
anls05  <-  try(nls(escal, start=ssceasy, trace=traceval, data=weeddata1))
print(anls05)
anlmrt05  <-  nlxb(escal, start=ssceasy, trace=traceval, data=weeddata1)
print(anlmrt03)


shobbs.res  <-  function(x){ # scaled Hobbs weeds problem -- residual
# This variant uses looping
    if(length(x) != 3) stop("hobbs.res -- parameter vector n!=3")
    y  <-  c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443, 38.558, 50.156, 62.948,
         75.995, 91.972)
    tt  <-  1:12
    res  <-  100.0*x[1]/(1+x[2]*10.*exp(-0.1*x[3]*tt)) - y
}
 
shobbs.jac  <-  function(x) { # scaled Hobbs weeds problem -- Jacobian
    jj  <-  matrix(0.0, 12, 3)
    tt  <-  1:12
    yy  <-  exp(-0.1*x[3]*tt)
    zz  <-  100.0/(1+10.*x[2]*yy)
    jj[tt,1]   <-   zz
    jj[tt,2]   <-   -0.1*x[1]*zz*zz*yy
    jj[tt,3]   <-   0.01*x[1]*zz*zz*yy*x[2]*tt
    return(jj)
}

cat("try nlfb
")
st  <-  c(b1=1, b2=1, b3=1)
low  <-  -Inf
up <- Inf

ans1 <- nlfb(st, shobbs.res, shobbs.jac, trace=traceval)
ans1
cat("No jacobian function -- use internal approximation
")
ans1n <- nlfb(st, shobbs.res, trace=TRUE, control=list(watch=TRUE)) # NO jacfn
ans1n

# tmp <- readline("Try with bounds at 2")
time2 <- system.time(ans2 <- nlfb(st, shobbs.res, shobbs.jac, upper=c(2,2,2), trace=traceval))
ans2
time2


cat("BOUNDS")
st2s <- c(b1=1, b2=1, b3=1)
an1qb1 <- try(nlxb(escal, start=st2s, trace=traceval, data=weeddata1, 
  lower=c(0,0,0), upper=c(2, 6, 3), control=list(watch=FALSE)))
print(an1qb1)
tmp <- readline("next")
ans2 <- nlfb(st2s,shobbs.res, shobbs.jac, lower=c(0,0,0), upper=c(2, 6, 3), 
   trace=traceval, control=list(watch=FALSE))
print(ans2)

cat("BUT ... nls() seems to do better from the TRACE information
")
anlsb <- nls(escal, start=st2s, trace=traceval, data=weeddata1, lower=c(0,0,0),
     upper=c(2,6,3), algorithm='port')
cat("However, let us check the answer
")
print(anlsb)
cat("BUT...crossprod(resid(anlsb))=",crossprod(resid(anlsb)),"")

tmp <- readline("next")
cat("Try wrapnls
")
traceval <- FALSE
# Data for Hobbs problem
ydat <- c(5.308, 7.24, 9.638, 12.866, 17.069, 23.192, 31.443, 
          38.558, 50.156, 62.948, 75.995, 91.972) # for testing
tdat <- seq_along(ydat) # for testing
start1 <- c(b1=1, b2=1, b3=1)
escal <-  y ~ 100*b1/(1+10*b2*exp(-0.1*b3*tt))
up1 <- c(2,6,3)
up2 <- c(1, 5, 9)

weeddata1 <- data.frame(y=ydat, tt=tdat)

an1w <- try(wrapnls(escal, start=start1, trace=traceval, data=weeddata1))
print(an1w)



cat("BOUNDED wrapnls
")

an1wb <- try(wrapnls(escal, start=start1, trace=traceval, data=weeddata1, upper=up1))
print(an1wb)


cat("BOUNDED wrapnls
")

an2wb <- try(wrapnls(escal, start=start1, trace=traceval, data=weeddata1, upper=up2))
print(an2wb)

cat("TRY MASKS ONLY
")

an1xm3 <- try(nlxb(escal, start1, trace=traceval, data=weeddata1, masked=c("b3")))
print(an1xm3)
an1fm3 <- try(nlfb(start1, shobbs.res, shobbs.jac, trace=traceval, data=weeddata1, maskidx=c(3)))
print(an1fm3)

an1xm1 <- try(nlxb(escal, start1, trace=traceval, data=weeddata1, masked=c("b1")))
print(an1xm1)
an1fm1 <- try(nlfb(start1, shobbs.res, shobbs.jac, trace=traceval, data=weeddata1, maskidx=c(1)))
print(an1fm1)

# Need to check when all parameters masked.??

cat("Now check conversion of expression to function

")
cat("K Vandepoel function
")

x <- c(1,3,5,7) # data
y <- c(37.98,11.68,3.65,3.93)
penetrationks28 <- data.frame(x=x,y=y)

cat("Try nls() -- note the try() function!
")

fit0  <-  try(nls(y ~ (a+b*exp(1)^(-c * x)), data = penetrationks28, 
    start = c(a=0,b = 1,c=1), trace = TRUE))
print(fit0)

cat("")


fit1  <-  nlxb(y ~ (a+b*exp(-c*x)), data = penetrationks28, 
   start = c(a=0,b=1,c=1), trace = TRUE) 
print(fit1)

mexprn <- "y ~ (a+b*exp(-c*x))"
pvec <- c(a=0,b=1,c=1)
bnew <- c(a=10,b=3,c=4)

k.r <- model2resfun(mexprn , pvec)
k.j <- model2jacfun(mexprn , pvec)
k.f <- model2ssfun(mexprn , pvec)
k.g <- model2grfun(mexprn , pvec)


cat("At pvec:")
print(pvec)
rp <- k.r(pvec, x=x, y=y)
cat("rp=")
print(rp)
rf <- k.f(pvec, x=x, y=y)
cat("rf=")
print(rf)
rj <- k.j(pvec, x=x, y=y)
cat("rj=")
print(rj)
rg <- k.g(pvec, x=x, y=y)
cat("rg=")
print(rg)
cat("modss at pvec gives ")
print(modss(pvec, k.r, x=x, y=y))
cat("modgr at pvec gives ")
print(modgr(pvec, k.r, k.j, x=x, y=y))
cat("")



cat("At bnew:")
print(bnew)
rb <- k.r(bnew, x=x, y=y)
cat("rb=")
print(rb)
rf <- k.f(bnew, x=x, y=y)
cat("rf=")
print(rf)
rj <- k.j(bnew, x=x, y=y)
cat("rj=")
print(rj)
rg <- k.g(bnew, x=x, y=y)
cat("rg=")
print(rg)
cat("modss at bnew gives ")
print(modss(bnew, k.r, x=x, y=y))
cat("modgr at bnew gives ")
print(modgr(bnew, k.r, k.j, x=x, y=y))
cat("")