https://github.com/cran/pracma
Revision b5e4bf28fcba9f5eaffbeecfb0bc307452d074ee authored by Hans W. Borchers on 01 November 2014, 00:00:00 UTC, committed by Gabor Csardi on 01 November 2014, 00:00:00 UTC
1 parent d57c14d
Tip revision: b5e4bf28fcba9f5eaffbeecfb0bc307452d074ee authored by Hans W. Borchers on 01 November 2014, 00:00:00 UTC
version 1.7.7
version 1.7.7
Tip revision: b5e4bf2
direct1d.R
direct1d <- function(f, a, b, maxiter = 20, ...) {
if (!is.numeric(a) || !is.numeric(b) ||
length(a) != 1 || length(b) != 1)
stop("Endpoints 'a', 'b' must be numeric and of length 1.")
if (a >= b || !is.finite(a) || !is.finite(b))
stop("Endpoints 'a', 'b' must be finite and a < b must hold.")
fun <- match.fun(f)
f <- function(x) fun(x, ...)
#(1) initialize
c0 <- (b-a)/2
f0 <- f(c0); fcnt <- 1
m <- 1
B <- matrix(c(m, a, b, c0, f0), nrow = 1)
xmin <- c0; fmin <- f0; tmin <- (b-a)/2
niter <- 0
while(niter < maxiter) {
#(2) identify potentially optimal intervals
s <- .identify_optimal(B)
S <- B[s, , drop = FALSE]
#(3) select all intervals j in S
for (i in 1:nrow(S)) {
k <- S[i, 1]
#(4) divide into three parts
d <- (S[i, 3] - S[i, 2])/3
c1 <- S[i, 4] - d; c2 <- S[i, 4] + d
f1 <- f(c1); f2 <- f(c2); fcnt <- fcnt + 2
# fmin <- min(f1, fmin, f2)
if (f1 < fmin) {
xmin <- c1; fmin <- f1; tmin <- d
} else if (f2 < fmin) {
xmin <- c2; fmin <- f2; tmin <- d
}
#(5) Add and update intervals
m <- m+1; B <- rbind(B, c(m, S[i, 2], S[i, 2] + d, c1, f1))
m <- m+1; B <- rbind(B, c(m, S[i, 2] + 2*d, S[i, 3], c2, f2))
B[k, 2:3] <- c(S[i, 2] + d, S[i, 3] - d)
}
#(6) S is empty now
#(7) check iteration limit
niter <- niter + 1
}
return(list(xmin = xmin, fmin = fmin))
}
.identify_optimal <- function(B) {
P <- cbind(B[, 1], (B[, 3] - B[, 2])/2, B[, 5])
i0 <- 1
for (i in 1:nrow(P)) {
if ( P[i, 2] < P[i0, 2] ||
(P[i, 2] == P[i0, 2] && P[i, 3] < P[i0, 3]) ) i0 <- i
}
I <- P[i0, 1]
p2 <- P[i0, 2]; p3 <- P[i0, 3]
P <- P[P[, 2] > p2, , drop = FALSE]
while (!isempty(P)) {
t <- atan2(P[, 3, drop = FALSE] - p3, P[, 2] - p2)
ti <- which.min(t)
i0 <- P[ti, 1]
I <- c(I, i0)
p2 <- P[ti, 2]; p3 <- P[ti, 3]
P <- P[P[, 2] > p2, , drop = FALSE]
}
return(I)
}
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