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Rcgminu <- function(par, fn, gr, control = list(trace=0), ...) {
## An R version of the conjugate gradient minimization
## using the Dai-Yuan and Hager-Zhang ideas
# This version is for unconstrained functions.
#
# Input:
# par = a vector containing the starting point
# fn = objective function (assumed to be sufficeintly
# differentiable)
# gr = gradient of objective function
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# control = list of control parameters. Rcgmin uses:
# maxit = a limit on the number of iterations (default 500)
# trace = 0 (default) for no output,
# >0 for output (bigger => more output)
# eps=1.0e-7 (default) for use in computing numerical gradient approximations.
# dowarn=TRUE by default. Set FALSE to suppress warnings.
# ?? others
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# Output:
# A list with components:
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# par: The best set of parameters found.
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# value: The value of 'fn' corresponding to 'par'.
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# counts: A two-element integer vector giving the number of
# calls to
# 'fn' and 'gr' respectively. This excludes those calls
# needed
# to compute the Hessian, if requested, and any calls to
# 'fn'
# to compute a finite-difference approximation to the
# gradient.
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# convergence: An integer code. '0' indicates successful
# convergence.
# Error codes are
# '0' converged
# '1' indicates that the function evaluation count
# 'maxfeval'
# was reached.
# '2' indicates initial point is infeasible
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# message: A character string giving any additional
# information returned
# by the optimizer, or 'NULL'.
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# Author: John C Nash
# Date: April 2, 2009; revised July 28, 2009
# Major rework November 20, 2018 onwards
#################################################################
bvec <- par # copy the parameter vector
n <- length(bvec) # number of elements in par vector
# control defaults
ctrl <- list(
maxfeval = 500*round(sqrt(n+1)), # limit on function evaluations
maxit = 500,
tol = n * (n * .Machine$double.eps), # for gradient test.
# Note -- integer overflow if n*n*.Machine$double.eps,
trace = 0,
cgoffset = 10000, # offset for test (a + reltest) == (b + reltest)
cgstepredn = 0.25,
cgminstep = 1e-5,
cgoldstep = 1,
cgstinflate = 1.125,
cgstep0max = 10,
qiilev = 0, # how many abs(fmin) to add to fmin allowed for quad inv interp??
acctol = 1e-6) # acceptable point tolerance
namc <- names(control)
if (!all(namc %in% names(ctrl)))
if(ctrl$trace > 0) stop("unknown names in control: ", namc[!(namc %in% names(ctrl))])
ctrl[namc] <- control
grNULL <- is.null(gr)
#############################################
# gr MUST be provided
if (is.null(gr)) { # if gr function is not provided STOP (Rvmmin has definition)
stop("A gradient calculation (analytic or numerical) MUST be provided for Rcgmin")
}
if ( is.character(gr) ) {
# Convert string to function call, assuming it is a numerical gradient function
mygr<-function(par=par, userfn=fn, ...){
do.call(gr, list(par, userfn, ...))
}
} else { mygr<-gr }
############# end test gr ####################
## Set working parameters (See CNM Alg 22)
if (ctrl$trace > 0) {
cat("Rcgminu -- J C Nash 2009 - unconstrained version CG min\n")
cat("an R implementation of Alg 22 with Yuan/Dai modification\n")
}
ig <- 0 # count gradient evaluations
ifn <- 1 # count function evaluations (we always make 1 try below)
# for ceps
cyclimit <- min(2.5 * n, 10 + sqrt(n)) # upper bound on when we restart CG cycle
# This does not appear to be in Y H Dai & Y Yuan, Annals of
# Operations Research 103, 33--47, 2001
# in Alg 22 pascal, we can set this as user. Do we wish to allow that?
## Note -- integer overflow if n*n*d.eps
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######## check bounds and masks #############
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# At this point, we have full bounds in play
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# Initial function value
if (ctrl$trace > 2) {
cat("Try function at initial point:")
print(bvec)
}
f <- try(fn(bvec, ...), silent = TRUE) # Compute the function at initial point.
if (class(f) == "try-error") {
msg <- "Initial point is infeasible."
if (ctrl$trace > 0) cat(msg, "\n")
ans <- list(par, NA, c(ifn, 0), 2, msg)
names(ans) <- c("par", "value", "counts", "convergence", "message")
return(ans)
}
if (ctrl$trace > 0) cat("Initial function value=", f, "\n")
fmin <- f # save the value
if (ctrl$trace > 2) print(bvec)
# Start the minimization process
keepgoing <- TRUE
msg <- "not finished" # in case we exit somehow
oldstep <- ctrl$cgoldstep #?? Why this choice?
####################################################################
fdiff <- NA # initially no decrease
cycle <- 0 # cycle loop counter
kf <- 0
while (keepgoing) { # main loop -- must remember to break out of it!!
# (Re)start with steepest descent by zeroing last gradient and last searchdir
t <- as.vector(rep(0, n)) # zero step vector
c <- t # zero 'last' gradient
while (keepgoing && (cycle < cyclimit)) { ## cycle loop
cycle <- cycle + 1
if (ctrl$trace > 0) cat("f, g, kf, cycle:",ifn, " ", ig, " ",kf, " ", cycle, " ", fmin,
" last decrease=", fdiff, "\n")
if (ctrl$trace > 2) {print(bvec); cat("\n")}
if (ifn > ctrl$maxfeval) {
msg <- paste("Too many function evaluations (> ", ctrl$maxfeval, ") ", sep = "")
if (ctrl$trace > 0) cat(msg, "\n")
ans <- list(par, fmin, c(ifn, ig), 1, msg) # 1 indicates not converged in function limit
names(ans) <- c("par", "value", "counts", "convergence", "message")
return(ans)
}
par <- bvec # save best parameters
ig <- ig + 1 # count gradient evaluations
if (ig > ctrl$maxit) {
msg <- paste("Too many gradient evaluations (> ", ctrl$maxit, ") ", sep = "")
if (ctrl$trace > 0) cat(msg, "\n")
ans <- list(par, fmin, c(ifn, ig), 1, msg) # 1 indicates not converged in function or gradient limit
names(ans) <- c("par", "value", "counts", "convergence", "message")
return(ans)
}
g <- mygr(bvec, ...) # Note: not checked by try(). May want to do that
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g1 <- sum(g * (g - c)) # gradient * grad-difference
g2 <- sum(t * (g - c)) # oldsearch * grad-difference
gradsqr <- sum(g * g)
if (ctrl$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("ctrl$tol, fmin, ctrl$cgoffset:", ctrl$tol, fmin, ctrl$cgoffset, "\n")
if (gradsqr > ctrl$tol * (abs(fmin) + ctrl$cgoffset)) { # ensure we haven't got a "small" gradient
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)
} #?? What if g2 <= 0?
} else {
msg <- paste("Very small gradient -- gradsqr =", gradsqr, sep = " ")
if (ctrl$trace > 0) cat(msg, "\n")
keepgoing <- FALSE # done loops -- break
break # to leave inner loop
}
if (ctrl$trace > 2) cat("Betak = g3 = ", g3, "\n")
if (g3 == 0 || cycle >= cyclimit) { # we are resetting to gradient in this case
if (ctrl$trace > 0) {
if (cycle < cyclimit) cat("Yuan/Dai cycle reset\n")
else cat("Cycle limit reached -- reset\n")
}
fdiff <- NA
cycle <- 0
break # to quit inner loop
} else { # drop through if not Yuan/Dai or cycle limit reset
t <- t * g3 - g # t starts at zero, later is search vector
gradproj <- sum(t * g) # gradient projection
if (ctrl$trace > 1) cat("Gradproj =", gradproj, "\n")
accpoint <- FALSE
if (gradproj < 0) {
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#### Line search ####
if (ctrl$trace > 2) cat("backtracklsq oldstep=", oldstep," ")
stl <- min(oldstep*ctrl$cgstinflate, ctrl$cgstep0max)
if (ctrl$trace > 2) cat("stl=", stl," ")
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maxstep <- 2 * ctrl$cgstep0max # This is pure heuristic! ??
kf <- 0
if (ctrl$trace > 3) cat("qiilev =",ctrl$qiilev,"\n")
while (! isTRUE(accpoint)) {
bvec <- par + stl * t
if (identical(bvec, par)) {
msg <- "linesearch: No progress"
if (ctrl$trace > 0) cat(msg,"\n")
stl <- 0 # to ensure flagged
break
}
f <- fn(bvec, ...) # Not testing in try()
kf <- kf + 1
ifn <- ifn + 1 # should test but ...
if (ctrl$trace > 2) cat("kf=",kf," f(",stl,")=",f)
if (f < fmin + ctrl$qiilev*(abs(fmin)+.Machine$double.eps) ) { # try quad point -- note condition
aa <- (f - fmin - gradproj*stl)/(stl*stl)
sq <- -gradproj/(2*aa)
if (ctrl$trace > 2) cat(" aa, sq:",aa,sq," ")
if (sq > maxstep) {
sq <- maxstep
if (ctrl$trace > 2) cat("sq reduced to ",maxstep,"\n")
}
bq <- par + sq*t
if (! identical(bq, par)) {
fq <- fn(bq, ...)
kf <- kf + 1
ifn <- ifn + 1
if (ctrl$trace > 2) cat("fq=",fq,"\n")
if (fq < f) {
accpointq <- (fq <= fmin + gradproj * sq * ctrl$acctol)
if (ctrl$trace > 2) cat("accpointq=",accpointq,"\n")
if (accpointq) {
f <- fq
stl <- sq
bvec <- bq
} # end accpointq
} # end fq < f
} # end non-identical bq, par
} # end try quadpoint
accpoint <- (f <= fmin + gradproj * stl * ctrl$acctol)
if (ctrl$trace > 2) cat(" accpoint=", accpoint,"\n")
if (! isTRUE(accpoint)) stl <- stl*ctrl$cgstepredn # backtrack
} # end backtrack loop
oldstep <- stl
fdiff <- fmin - f
fmin <- f
par <- bvec
if (ctrl$trace > 2) cat("Have fmin=",fmin," OK accpoint with stl=",stl,"\n")
} else {
msg <- "Uphill search direction"
if (ctrl$trace > 0) cat(msg,"\n")
stl <- -1 # flag uphill (probably don't need!!)
} # gradproj test
if (stl <= 0) { # not changed on step redn, or uphill
if (cycle == 1) {
msg <- " Converged -- no progress on new CG cycle"
if (ctrl$trace > 0) cat("\n", msg, "\n")
keekpgoing <- FALSE
break #!!
}
cycle <- 0 # restart
} # end stl <= 0
} # end of test on Yuan/Dai condition
if (ctrl$trace > 2) cat("oldstep=", oldstep,"\n")
if (oldstep > ctrl$cgstep0max) { oldstep <- ctrl$cgstep0max}
if (oldstep < ctrl$cgminstep) { oldstep <- ctrl$cgminstep} # steplength
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if (ctrl$trace > 2) {
cat("end inner loop -- stl, oldstep = ",stl,oldstep,"\n")
cat("fmin =",fmin,"\n")
print(par)
}
# tmp <- readline("again")
} # end of inner loop (cycle)
if (ctrl$trace > 2) cat("End outer loop, cycle =", cycle, "\n")
} # end of outer loop
msg <- "Rcgminu seems to have converged"
if (ctrl$trace > 0) cat(msg, "after ",ifn," fn and ",ig," gr evals\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'.
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ans <- list(par, fmin, c(ifn, ig), 0, msg)
names(ans) <- c("par", "value", "counts", "convergence", "message")
return(ans)
} ## end of Rcgminu
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