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ncg <- function(par, fn, gr, lower=NULL, upper=NULL, bdmsk = NULL, control = list(), ...) {
## Feb 15 -- working but inefficient for exrosen
## An R version of the conjugate gradient minimization using the Dai-Yuan ideas
# ncg.R 20220212 JN
# control defaults -- idea from spg
badbd <- function(x, lo, up){
val <- any(x + control$offset < lo + control$offset) |
any(x + control$offset > up + control$offset)
if (val) {
cat("BAD! x: "); print(x)
cat("lower : "); print(lo)
cat("upper : "); print(up)
}
val
}
# print(control)
# stepredn <- 0.15 # Step reduction in line search
# stepredn <- 0.25 # Step reduction in line search
# Step reduction in line search
# ctrl <- list(maxit = 500, maximize = FALSE, trace = 0, eps = 1e-07,
# stepredn = 0.2, dowarn = TRUE, tol=0)
npar<-length(par)
ctrl <- ctrldefault(npar)
# print(ctrl)
namc <- names(control)
if (!all(namc %in% names(ctrl)))
stop("unknown names in control: ", namc[!(namc %in% names(ctrl))])
ctrl[namc] <- control
if (ctrl$tol == 0) tol <- npar * (npar * .Machine$double.eps)
# for gradient test. Note -- integer overflow if n*n*d.eps
else tol<-ctrl$tol
maxit <- ctrl$maxit # limit on function evaluations
# cat("maxit = ",maxit,"\n")
maximize <- ctrl$maximize # TRUE to maximize the function
trace <- ctrl$trace # 0 for no output, >0 for output (bigger => more output)
stepredn <- ctrl$stepredn
# cat("stepredn set to ",stepredn,"\n")
if (trace > 2) cat("trace = ", trace, "\n")
eps <- ctrl$eps
fargs <- list(...) # the ... arguments that are extra function / gradient data
grNULL <- is.null(gr)
dowarn <- ctrl$dowarn #
#############################################
if (maximize) stop("rcg does NOT maximize")
if (is.null(gr)) stop("A gradient calculation (analytic or numerical) MUST be provided for ncg")
if ( is.character(gr) ) {
# Convert string to function call, assuming it is a numerical gradient function
mygr<-function(par=par, userfn=fn, ...){
do.call(gr, list(par, userfn, ...))
}
} else { mygr<-gr }
############# end test gr ####################
## Set working parameters (See CNM Alg 22)
if (trace > 0) cat("ncg -- J C Nash 2022 - bounds constraint version of CG\n")
bvec <- par # copy the parameter vector
if (badbd(bvec, lower, upper)) stop("Initial par out of bounds")
n <- length(bvec) # number of elements in par vector
maxfeval <- round(sqrt(n + 1) * maxit) # change 091219
ig <- 0 # count gradient evaluations
ifn <- 1 # count function evaluations (we always make 1 try below)
acctol <- ctrl$acctol # acceptable point tolerance
reltest <- ctrl$reltest # relative equality test
# cat("reltest=", reltest,"\n")
ceps <- .Machine$double.eps * reltest
pceps <- ceps*max(abs(bvec))
accpoint <- as.logical(FALSE) # so far do not have an acceptable point
cyclimit <- min(2.5 * n, 10 + sqrt(n)) #!! upper bound on when we restart CG cycle
fargs <- list(...) # function arguments
if (trace > 2) {cat("Extra function arguments:"); print(fargs)}
# set default masks if not defined
if (is.null(bdmsk)) { bdmsk <- rep(1, n) }
if (trace > 2) { cat("bdmsk:"); print(bdmsk)}
# Still do checks to get nolower, noupper, bounds
if (is.null(lower) || !any(is.finite(lower))) nolower = TRUE
else nolower = FALSE
if (is.null(upper) || !any(is.finite(upper))) noupper = TRUE
else noupper = FALSE
if (nolower && noupper && all(bdmsk == 1)) bounds = FALSE
else bounds = TRUE
if (trace > 2) cat("Bounds: nolower = ", nolower, " noupper = ", noupper, " bounds = ", bounds, "\n")
if (nolower) lower <- rep(-Inf, n)
if (noupper) upper <- rep(Inf, n)
######## check bounds and masks #############
## NOTE: do this inline to avoid call to external routine
if (bounds) {
# Make sure to expand lower and upper
if (!nolower & (length(lower) < n)) { # have lower bounds, length must be 1 or n
if (length(lower) == 1) {lower <- rep(lower, n) }
else { stop("NOT 1<length(lower)<n") }
} # else lower OK
if (!noupper & (length(upper) < n)) {
if (length(upper) == 1) { upper <- rep(upper, n) }
else { stop("NOT 1<length(upper)<n") }
} # else upper OK
# At this point, we have full bounds in play
# This implementation as a loop, but try later to vectorize
for (i in 1:n) { # cat('i = ',i,'\n')
if (bdmsk[i] == 0) { # NOTE: we do not change masked parameters, even if out of bounds
if (!nolower) {
if (bvec[i] < lower[i]) {
wmsg <- paste(bvec[i], " = MASKED x[", i, "] < lower bound = ", lower[i], sep = "")
if (dowarn) warning(wmsg)
}
}
if (!noupper) {
if (bvec[i] > upper[i]) {
wmsg <- paste(bvec[i], " = MASKED x[", i, "] > upper bound = ", upper[i], sep = "")
if (dowarn) warning(wmsg)
}
}
}
else { # not masked, so must be free or active constraint
if (!nolower) {
if (bvec[i] <= lower[i]) { # changed 090814 to ensure bdmsk is set
wmsg <- paste("x[", i, "], set ", bvec[i], " to lower bound = ", lower[i], sep = "")
if (dowarn && (bvec[i] != lower[i])) warning(wmsg)
bvec[i] <- lower[i]
bdmsk[i] <- -3 # active lower bound
}
}
if (!noupper) {
if (bvec[i] >= upper[i]) {# changed 090814 to ensure bdmsk is set
wmsg <- paste("x[", i, "], set ", bvec[i], " to upper bound = ", upper[i], sep = "")
if (dowarn && (bvec[i] != upper[i])) warning(wmsg)
bvec[i] <- upper[i]
bdmsk[i] <- -1 # active upper bound
}
}
} # end not masked
} # end loop for bound/mask check
}
############## end bounds check #############
# Initial function value -- may NOT be at initial point
# specified by user.
if (trace > 2) {cat("Try function at initial point:"); print(bvec) }
f <- try(fn(bvec, ...), silent = TRUE) # Compute the function at initial point.
if (trace > 0) {cat("Initial function value=", f, "\n") }
if (inherits(f,"try-error")) {
msg <- "Initial point is infeasible."
if (trace > 0) cat(msg, "\n")
ans <- list(par, NA, c(ifn, 0), 2, msg, bdmsk)
names(ans) <- c("par", "value", "counts", "convergence", "message", "bdmsk")
return(ans)
}
fmin <- f
if (trace > 0) cat("Initial fn=", f, "\n")
if (trace > 1) print(bvec)
# Start the minimization process
keepgoing <- TRUE
msg <- "not finished" # in case we exit somehow
oldstep <- 0.75 #!! 2/3 #!!? WHY? formerly 0.8
####################################################################
fdiff <- NA # initially no decrease
cycle <- 0 # !! cycle loop counter
haveg <- FALSE
while (keepgoing) {
# main loop -- must remember to break out of it!!
t <- as.vector(rep(0, n)) # zero step vector
c <- t # zero 'last' gradient
while (keepgoing && (cycle < cyclimit)) {
## cycle loop
cycle <- cycle + 1
if (trace > 0) cat(ifn, " ", ig, " ", cycle, " ", fmin, " last decrease=", fdiff, "\n")
if (trace > 1) { print(bvec) }
if (ifn > maxfeval) {
msg <- paste("Too many function evaluations (> ", maxfeval, ") ", sep = "")
if (trace > 0) cat(msg, "\n")
ans <- list(par, fmin, c(ifn, ig), 1, msg, bdmsk) # 1 indicates not converged in function limit
names(ans) <- c("par", "value", "counts", "convergence", "message", "bdmsk")
return(ans)
}
if (! haveg) {
par <- bvec # save best parameters
ig <- ig + 1
if (ig > maxit) {
msg <- paste("Too many gradient evaluations (> ", maxit, ") ", sep = "")
if (trace > 0) cat(msg, "\n")
ans <- list(par, fmin, c(ifn, ig), 1, msg, bdmsk)
# 1 indicates not converged in function or gradient limit
names(ans) <- c("par", "value", "counts", "convergence", "message", "bdmsk")
return(ans)
}
g <- mygr(bvec, ...) # gradient
haveg <- TRUE
}
if (bounds) { ## Bounds and masks adjustment of gradient
## first try with looping -- later try to vectorize
if (trace > 2) { cat("bdmsk:"); print(bdmsk) }
for (i in 1:n) {
if ((bdmsk[i] == 0)) { g[i] <- 0 } # masked, so gradient component is zero
else {
if (bdmsk[i] != 1) {
if ((bdmsk[i] + 2) * g[i] < 0) { # test for -ve gradient at upper bound, +ve at lower bound
g[i] <- 0 # active mask or constraint and zero gradient component
}
else {
bdmsk[i] <- 1 # freeing parameter i
if (trace > 1) cat("freeing parameter ", i, "\n")
}
}
}
} # end masking loop on i
if (trace > 2) {cat("bdmsk adj:\n"); print(bdmsk); cat("proj-g:\n"); print(g) }
} # end if bounds
## end bounds and masks adjustment of gradient
g1 <- sum(g * (g - c)) # gradient * grad-difference
g2 <- sum(t * (g - c)) # oldsearch * grad-difference
gradsqr <- sum(g * g)
if (trace > 1) { cat("Gradsqr = ", gradsqr, " g1, g2 ", g1, " ", g2, " fmin=", fmin, "\n") }
c <- g # save last gradient
g3 <- 1 # !! Default to 1 to ensure it is defined -- t==0 on first cycle
# cat(gradsqr," ",tol," ",fmin," ",reltest,"\n")
if (gradsqr > tol * (abs(fmin) + reltest) ) {
if (g2 > 0) {
betaDY <- gradsqr/g2
betaHS <- g1/g2
g3 <- max(0, min(betaHS, betaDY)) # g3 is our new 'beta' !! Dai/Yuan 2001, (4.2)
}
}
else {
msg <- paste("Very small gradient -- gradsqr =", gradsqr, sep = " ")
if (trace > 0) cat(msg, "\n")
keepgoing <- FALSE # done loops -- should we break?
break # to leave inner loop
}
if (trace > 2) cat("Betak = g3 = ", g3, "\n")
if (g3 == 0 || cycle >= cyclimit) { # we are resetting to gradient in this case
if (trace > 0) {
if (cycle < cyclimit) cat("Yuan/Dai cycle reset\n")
else cat("Cycle limit reached -- reset\n")
}
fdiff <- NA
cycle <- 0 # but haveg == TRUE
oldstep<-0.75
break #!!
}
else { # drop through if not Yuan/Dai cycle reset
t <- t * g3 - g # t starts at zero, later is step vector
gradproj <- sum(t * g) # gradient projection
if (trace > 1) cat("Gradproj =", gradproj, "\n")
if (bounds) { ## Adjust search direction for masks
if (trace > 2) { cat("t:\n"); print(t) }
t[which(bdmsk <= 0)] <- 0 # apply mask constraint
if (trace > 2) { cat("adj-t:\n"); print(t) }
## end adjust search direction for masks
} # end if bounds
# Why do we not check gradproj size??
########################################################
#### Line search ####
#### 2022-2-12 Use backtrack only
## OKpoint <- FALSE #
accpoint <- FALSE
f1 <- fmin # to ensure it is defined
f <- fmin # and as large as fmin
if (trace > 2) cat("Start linesearch with oldstep=", oldstep, "\n")
steplength <- oldstep * 1.5 #!! try a bit bigger
stepstrt<-steplength
if (bounds) { # Box constraint -- adjust step length
for (i in 1:n) { # loop on parameters -- vectorize?
if ((bdmsk[i] == 1) && (abs(t[i]) > pceps)) { # only free params and search != 0
if (t[i] < 0) { # going downhill. Look at lower bound
trystep <- (lower[i] - par[i])/t[i] # t[i] < 0 so this is positive
}
else { # going uphill, check upper bound
trystep <- (upper[i] - par[i])/t[i] # t[i] > 0 so this is positive
}
# if (trace > 3) cat("steplength, trystep:", steplength, trystep, "\n")
steplength <- min(steplength, trystep) # reduce as necessary
} # end steplength reduction
else {t[i] <- 0} # small dirn gets set to zero just in case
} # end loop on i to reduce step length
bdlim <- (steplength < stepstrt) # TRUE if bound limits step
stepstrt <- steplength # save this value
if (trace > 1) cat("reset steplength (",bdlim,") = ", steplength, "\n")
# end box constraint max step length
} # end if bounds
changed <- TRUE # Need to set so loop will start
accpoint <- FALSE
while ((f >= fmin) && changed && ! accpoint) {
# may need f test to stop cycling
# while (changed && ! accpoint) {
bvec <- par + steplength * t
# ?? see if we can remove this test ?? Should be able to avoid
if (badbd(bvec, lower, upper)) stop("Top of backtrack")
# changed <- (! identical((bvec + reltest), (par + reltest)))
changed <- any(par+reltest != bvec+reltest)
if (trace > 1 && changed) cat("CHANGED - ")
if (trace > 1) {cat("trial bvec:"); print(bvec)}
if (changed) {
f <- fn(bvec, ...) # Because we need the value for linesearch, don't use try()??
# instead preferring to fail out, which will hopefully be unlikely.
ifn <- ifn + 1
if (is.na(f) || (!is.finite(f))) {
warning("ncg - undefined function")
f <- .Machine$double.xmax
}
savestep<-steplength
if (f < fmin) { f1 <- f } # Hold onto value (not needed for backtrack only??)
else {
steplength <- steplength * stepredn # reduce step size
if (steplength >= savestep) changed<-FALSE
if (trace > 0) cat("*")
}
accpoint <- (f1 <= fmin + gradproj * steplength * acctol) # changed MUST be TRUE or f1>...
## OKpoint <- (f1 < fmin)
} # changed
} # end while. At this point f == f1 < fmin if changed TRUE
if (accpoint) {
fdiff <- fmin - f
fmin <- f
par <- bvec
haveg <- FALSE # want new cycle
if (trace > 2) { cat("new fmin=",fmin,"\n"); print(bvec)}
oldstep <- steplength
}
else {
msg <- "No acceptable point -- exit loop"
if (trace > 0) cat("\n", msg, "\n")
if (cycle == 1) {
msg <- " Converged -- no progress on new CG cycle"
if (trace > 0) cat("\n", msg, "\n")
}
keekpgoing <- FALSE
break #!! ?? where does this lead?
}
} # end of test on Yuan/Dai condition
#### End line search ####
if (bounds) { ## Reactivate constraints? -- should check for infinite bounds!!?
for (i in 1:n) {
if (bdmsk[i] == 1) { # only interested in free parameters
if (is.finite(lower[i])) {# JN091020 -- need to use abs in case bounds negative
if ((bvec[i] - lower[i]) < ceps * (abs(lower[i]) + 1)) { # are we near or lower than lower bd
if (trace > 2) cat("(re)activate lower bd ", i, " at ", lower[i], "\n")
bdmsk[i] <- -3
} # end lower bd reactivate
}
if (is.finite(upper[i])) { # JN091020 -- need to use abs in case bounds negative
if ((upper[i] - bvec[i]) < ceps * (abs(upper[i]) + 1)) { # are we near or above upper bd
if (trace > 2) cat("(re)activate upper bd ", i, " at ", upper[i], "\n")
bdmsk[i] <- -1
} # end upper bd reactivate
}
} # end test on free params
} # end reactivate constraints loop
} # end if bounds
# ?? try step reset here
if (oldstep < acctol) { oldstep <- acctol } # steplength
if (oldstep > 1) { oldstep <- 1 }
} # end of inner loop (cycle)
if (trace > 1) cat("End inner loop, cycle =", cycle, "\n")
} # end of outer loop
msg <- "ncg seems to have converged"
if (trace > 0)
cat(msg, "\n")
# par: The best set of parameters found.
# value: The value of 'fn' corresponding to 'par'.
# counts: number of calls to 'fn' and 'gr' (2 elements)
# convergence: An integer code. '0' indicates successful
# convergence.
# message: A character string or 'NULL'.
ans <- list(par, fmin, c(ifn, ig), 0, msg, bdmsk)
names(ans) <- c("par", "value", "counts", "convergence",
"message", "bdmsk")
return(ans)
} ## end of ncg
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