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#############################################################################
## Copyright (c) 2010-2022 Rune Haubo Bojesen Christensen
##
## This file is part of the ordinal package for R (*ordinal*)
##
## *ordinal* is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 2 of the License, or
## (at your option) any later version.
##
## *ordinal* is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## A copy of the GNU General Public License is available at
## <https://www.r-project.org/Licenses/> and/or
## <http://www.gnu.org/licenses/>.
#############################################################################
## This file contains:
## Functions for finite difference computations of derivatives
## (gradient and Hessian) of user-specified functions.
deriv12 <- function(fun, x, delta=1e-4, fx=NULL, ...) {
### Compute gradient and Hessian at the same time (to save computing
### time)
nx <- length(x)
fx <- if(!is.null(fx)) fx else fun(x, ...)
stopifnot(length(fx) == 1)
H <- array(NA, dim=c(nx, nx))
g <- numeric(nx)
for(j in 1:nx) {
## Diagonal elements:
xadd <- xsub <- x
xadd[j] <- x[j] + delta
xsub[j] <- x[j] - delta
fadd <- fun(xadd, ...)
fsub <- fun(xsub, ...)
H[j, j] <- (fadd - 2 * fx + fsub) / delta^2
g[j] <- (fadd - fsub) / (2 * delta)
## Off diagonal elements:
for(i in 1:nx) {
if(i >= j) break
## Compute upper triangular elements:
xaa <- xas <- xsa <- xss <- x
xaa[c(i, j)] <- x[c(i, j)] + c(delta, delta)
xas[c(i, j)] <- x[c(i, j)] + c(delta, -delta)
xsa[c(i, j)] <- x[c(i, j)] + c(-delta, delta)
xss[c(i, j)] <- x[c(i, j)] - c(delta, delta)
H[i, j] <- H[j, i] <-
(fun(xaa, ...) - fun(xas, ...) -
fun(xsa, ...) + fun(xss, ...)) /
(4 * delta^2)
}
}
list(gradient = g, Hessian = H)
}
myhess <- function(fun, x, fx=NULL, delta=1e-4, ...) {
nx <- length(x)
fx <- if(!is.null(fx)) fx else fun(x, ...)
stopifnot(length(fx) == 1)
H <- array(NA, dim=c(nx, nx))
for(j in 1:nx) {
## Diagonal elements:
xadd <- xsub <- x
xadd[j] <- x[j] + delta
xsub[j] <- x[j] - delta
H[j, j] <- (fun(xadd, ...) - 2 * fx +
fun(xsub, ...)) / delta^2
## Upper triangular (off diagonal) elements:
for(i in 1:nx) {
if(i >= j) break
xaa <- xas <- xsa <- xss <- x
xaa[c(i, j)] <- x[c(i, j)] + c(delta, delta)
xas[c(i, j)] <- x[c(i, j)] + c(delta, -delta)
xsa[c(i, j)] <- x[c(i, j)] + c(-delta, delta)
xss[c(i, j)] <- x[c(i, j)] - c(delta, delta)
H[j, i] <- H[i, j] <-
(fun(xaa, ...) - fun(xas, ...) -
fun(xsa, ...) + fun(xss, ...)) /
(4 * delta^2)
}
}
H
}
mygrad <-
function(fun, x, delta = 1e-4,
method = c("central", "forward", "backward"), ...)
{
method <- match.arg(method)
nx <- length(x)
if(method %in% c("central", "forward")) {
Xadd <- matrix(rep(x, nx), nrow=nx, byrow=TRUE) + diag(delta, nx)
fadd <- apply(Xadd, 1, fun, ...)
}
if(method %in% c("central", "backward")) {
Xsub <- matrix(rep(x, nx), nrow=nx, byrow=TRUE) - diag(delta, nx)
fsub <- apply(Xsub, 1, fun, ...) ## eval.parent perhaps?
}
res <- switch(method,
"forward" = (fadd - fun(x, ...)) / delta,
"backward" = (fun(x, ...) - fsub) / delta,
"central" = (fadd - fsub) / (2 * delta)
)
res
}
grad.ctr3 <- function(fun, x, delta=1e-4, ...) {
nx <- length(x)
Xadd <- matrix(rep(x, nx), nrow=nx, byrow=TRUE) + diag(delta, nx)
Xsub <- matrix(rep(x, nx), nrow=nx, byrow=TRUE) - diag(delta, nx)
fadd <- apply(Xadd, 1, fun, ...)
fsub <- apply(Xsub, 1, fun, ...) ## eval.parent perhaps?
(fadd - fsub) / (2 * delta)
}
grad.ctr2 <- function(fun, x, delta=1e-4, ...) {
ans <- x
for(i in seq_along(x)) {
xadd <- xsub <- x
xadd[i] <- x[i] + delta
xsub[i] <- x[i] - delta
ans[i] <- (fun(xadd, ...) - fun(xsub, ...)) / (2 * delta)
}
ans
}
grad.ctr <- function(fun, x, delta=1e-4, ...) {
sapply(seq_along(x), function(i) {
xadd <- xsub <- x
xadd[i] <- x[i] + delta
xsub[i] <- x[i] - delta
(fun(xadd, ...) - fun(xsub, ...)) / (2 * delta)
})
}
grad <- grad.ctr
grad.ctr4 <- function(fun, x, delta=1e-4, ...) {
### - checking finiteness of x and fun-values
### - taking care to avoid floating point errors
### - not using h=x*delta rather than h=delta (important for small or
### large x?)
if(!all(is.finite(x)))
stop("Cannot compute gradient: non-finite argument")
ans <- x ## return values
for(i in seq_along(x)) {
xadd <- xsub <- x ## reset fun arguments
xadd[i] <- x[i] + delta
xsub[i] <- x[i] - delta
ans[i] <- (fun(xadd, ...) - fun(xsub, ...)) / (xadd[i] - xsub[i])
### NOTE: xadd[i] - xsub[i] != 2*delta with floating point arithmetic.
}
if(!all(is.finite(ans))) {
warning("cannot compute gradient: non-finite function values occured")
ans[!is.finite(ans)] <- Inf
}
ans
}
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