demo/cyq_test.R In Rcgmin2: EXPERIMENTAL Conjugate gradient minimization of nonlinear functions with box constraints

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

rm(list = ls())
library(Rcgmin)
# 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
for (k in 1:n) {
z7 <- 1
z2 <- 2 * x[k] - 1
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/(i * i - 1)
}
res[i] <- rr
}  # end loop on i
res
}

cyq.jac <- function(x) {
n <- length(x)
cj <- matrix(0, n, n)
for (i in 1:n) {
# loop over rows
for (k in 1:n) {
# loop over columns (parameters)
z5 <- 0
cj[i, k] <- 2
z8 <- 2 * x[k] - 1
z2 <- z8
z7 <- 1
j <- 1
while (j < i) {
# recurrence loop
z4 <- z5
z5 <- cj[i, k]
cj[i, k] <- 4 * z8 + 2 * z2 * z5 - z4
z6 <- z7
z7 <- z8
z8 <- 2 * 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 * rv %*% cj)
}

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

nn <- c(2, 3, 5, 8, 10, 20, 30)

for (n in nn) {
cat("Chebyquad in ", n, " parameters\n")
afname <- paste("acyq", n, "G.txt", sep = "")
lower <- rep(-10, n)
upper <- rep(10, n)
bdmsk <- rep(1, n)  # free all parameters
x0 <- 1:n
x0 <- x0/(n + 1)  # Initial value suggested by Fletcher
ut <- system.time(ans <- Rcgmin(x0, cyq.f, cyq.g, lower,
upper, bdmsk, control = list(trace = 1)))[1]
print(ans)
cat("time = ", ut, "\n")
}
```

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Rcgmin2 documentation built on May 2, 2019, 4:41 p.m.