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nmk <-
function(par, fn, control=list(), ...) {
ctrl <- list(tol=1.e-06, maxfeval = min(5000, max(1500, 20*length(par)^2)), regsimp=TRUE, maximize=FALSE, restarts.max=3, trace=FALSE)
namc <- match.arg(names(control), choices=names(ctrl), several.ok=TRUE)
if (!all(namc %in% names(ctrl)))
stop("unknown names in control: ", namc[!(namc %in% names(ctrl))])
if (!is.null(names(control))) ctrl[namc] <- control
ftol <- ctrl$tol
maxfeval <- ctrl$maxfeval
regsimp <- ctrl$regsimp
restarts.max <- ctrl$restarts.max
maximize <- ctrl$maximize
trace <- ctrl$trace
if (maximize) fnm <- function(par, ...) -fn(par, ...) else fnm <- function(par, ...) fn(par, ...)
x0 <- par
n <- length(par)
if (n == 1) stop(call. = FALSE, "Use `optimize' for univariate optimization")
if (n > 30) warning("Nelder-Mead should not be used for high-dimensional optimization")
V <- cbind(rep(0, n), diag(n))
f <- rep(0, n+1)
f[1] <- fnm(x0, ...)
V[, 1] <- x0
scale <- max(1, sqrt(sum(x0^2)))
if (regsimp) {
alpha <- scale / (n * sqrt(2)) * c(sqrt(n+1) + n - 1, sqrt(n+1) -1)
V[, -1] <- (x0 + alpha[2])
diag(V[, -1]) <- x0[1:n] + alpha[1]
for (j in 2:ncol(V)) f[j] <- fnm(V[,j], ...)
} else {
V[, -1] <- x0 + scale * V[, -1]
for (j in 2:ncol(V)) f[j] <- fnm(V[,j], ...)
}
f[is.nan(f)] <- Inf
nf <- n + 1
ord <- order(f)
f <- f[ord]
V <- V[, ord]
rho <- 1
gamma <- 0.5
chi <- 2
sigma <- 0.5
conv <- 1
oshrink <- 1
restarts <- 0
orth <- 0
dist <- f[n+1] - f[1]
v <- V[, -1] - V[, 1]
delf <- f[-1] - f[1]
diam <- sqrt(colSums(v^2))
# sgrad <- c(solve(t(v), delf))
sgrad <- c(crossprod(t(v), delf))
alpha <- 1.e-04 * max(diam) / sqrt(sum(sgrad^2))
simplex.size <- sum(abs(V[, -1] - V[, 1])) / max(1, sum(abs(V[, 1])))
itc <- 0
conv <- 0
message <- "Succesful convergence"
while (nf < maxfeval & restarts < restarts.max & dist > ftol & simplex.size > 1.e-06) {
fbc <- mean(f)
happy <- 0
itc <- itc + 1
xbar <- rowMeans(V[, 1:n])
xr <- (1 + rho) * xbar - rho * V[, n+1]
fr <- fnm(xr, ...)
nf <- nf + 1
if(is.nan(fr)) fr <- Inf
if (fr >= f[1] & fr < f[n]) {
happy <- 1
xnew <- xr
fnew <- fr
} else if (fr < f[1]) {
xe <- (1 + rho * chi) * xbar - rho * chi * V[, n+1]
fe <- fnm(xe, ...)
if(is.nan(fe)) fe <- Inf
nf <- nf + 1
if (fe < fr) {
xnew <- xe
fnew <- fe
happy <- 1
} else {
xnew <- xr
fnew <- fr
happy <- 1
}
} else if (fr >= f[n] & fr < f[n+1]) {
xc <- (1 + rho * gamma) * xbar - rho * gamma * V[, n+1]
fc <- fnm(xc, ...)
if(is.nan(fc)) fc <- Inf
nf <- nf + 1
if (fc <= fr) {
xnew <- xc
fnew <- fc
happy <- 1
}
} else if (fr >= f[n+1]) {
xc <- (1 - gamma) * xbar + gamma * V[, n+1]
fc <- fnm(xc, ...)
if(is.nan(fc)) fc <- Inf
nf <- nf + 1
if (fc < f[n+1]) {
xnew <- xc
fnew <- fc
happy <- 1
}
}
if (happy == 1 & oshrink == 1) {
fbt <- mean(c(f[1:n], fnew))
delfb <- fbt - fbc
armtst <- alpha * sum(sgrad^2)
if (delfb > - armtst/n) {
if (trace) cat("Trouble - restarting: \n")
restarts <- restarts + 1
orth <- 1
diams <- min(diam)
sx <- sign(0.5 * sign(sgrad))
happy <- 0
V[, -1] <- V[, 1]
diag(V[, -1]) <- diag(V[, -1]) - diams * sx[1:n]
}
}
if (happy == 1) {
V[, n+1] <- xnew
f[n+1] <- fnew
ord <- order(f)
V <- V[, ord]
f <- f[ord]
} else if (happy == 0 & restarts < restarts.max) {
if (orth == 0) orth <- 1
V[, -1] <- V[, 1] - sigma * (V [, -1] - V[, 1])
for (j in 2:ncol(V)) f[j] <- fnm(V[,j], ...) ## kmm change
nf <- nf + n
ord <- order(f)
V <- V[, ord]
f <- f[ord]
}
v <- V[, -1] - V[, 1]
delf <- f[-1] - f[1]
diam <- sqrt(colSums(v^2))
simplex.size <- sum(abs(v)) / max(1, sum(abs(V[, 1])))
f[is.nan(f)] <- Inf
dist <- f[n+1] - f[1]
# sgrad <- c(solve(t(v), delf))
sgrad <- c(crossprod(t(v), delf))
if (trace & !(itc %% 2)) cat("iter: ", itc, "\n", "value: ", f[1], "\n")
}
if (dist <= ftol | simplex.size <= 1.e-06) {
conv <- 0
message <- "Successful convergence"
} else if (nf >= maxfeval) {
conv <- 1
message <- "Maximum number of fevals exceeded"
} else if (restarts >= restarts.max) {
conv <- 2
message <- "Stagnation in Nelder-Mead"
}
return(list(par = V[, 1], value=f[1]*(-1)^maximize, feval=nf, restarts=restarts, convergence=conv, message=message))
}
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