# demo/cyq_test.R In Rvmminx: Variable metric nonlinear function minimization with bounds constraints - experimental

```## cyq.R -- Fletcher's Chebyquad problem

rm(list=ls())
library(Rvmmin1104)

# Ref: Fletcher, R. (1965) Function minimization without calculating derivatives -- a review,
#         Computer J., 8, 33-41.

# Note we do not have all components here e.g., .jsd, .h

cyq.f <- function (x) {
rv<-cyq.res(x)
f<-sum(rv*rv)
}

cyq.res <- function (x) {
# Fletcher's chebyquad function m = n -- residuals
n<-length(x)
res<-rep(0,n) # initialize
for (i in 1:n) { #loop over resids
rr<-0.0
for (k in 1:n) {
z7<-1.0
z2<-2.0*x[k]-1.0
z8<-z2
j<-1
while (j<i) {
z6<-z7
z7<-z8
z8<-2*z2*z7-z6 # recurrence to compute Chebyshev polynomial
j<-j+1
} # end recurrence loop
rr<-rr+z8
} # end loop on k
rr<-rr/n
if (2*trunc(i/2) == i) { rr <- rr + 1.0/(i*i - 1) }
res[i]<-rr
} # end loop on i
res
}

cyq.jac<- function (x) {
n<-length(x)
cj<-matrix(0.0, n, n)
for (i in 1:n) { # loop over rows
for (k in 1:n) { # loop over columns (parameters)
z5<-0.0
cj[i,k]<-2.0
z8<-2.0*x[k]-1.0
z2<-z8
z7<-1.0
j<- 1
while (j<i) { # recurrence loop
z4<-z5
z5<-cj[i,k]
cj[i,k]<-4.0*z8+2.0*z2*z5-z4
z6<-z7
z7<-z8
z8<-2.0*z2*z7-z6
j<- j+1
} # end recurrence loop
cj[i,k]<-cj[i,k]/n
} # end loop on k
} # end loop on i
cj
}

cyq.g <- function (x) {
cj<-cyq.jac(x)
rv<-cyq.res(x)
gg<- as.vector(2.0* rv %*% cj)
}

cat("Fletcher chebyquad function in file cyq.R\n")

nn<-c(2,3,5,8,10,15,20) # added 15, dropped 30 20100525 to reduce testing time

for (n in nn) {
afname<-paste("acyq",n,"G.txt",sep='')
lower<-rep(-10.0, n)
upper<-rep(10.0, n)
bdmsk<-rep(1, n) # free all parameters
x0<-1:n
x0<-x0/(n+1.0) # Initial value suggested by Fletcher
ut<-system.time(ans<-Rvmminstep(x0,cyq.f,cyq.g,lower,upper,bdmsk,control=list(trace=1)))[1]
optansout(ans,afname)
print(ans)
cat("time = ",ut,"\n")
}
```

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Rvmminx documentation built on May 2, 2019, 4:47 p.m.