From 169ae760725c6747f3021918477b23f3813f6169 Mon Sep 17 00:00:00 2001 From: NunoSempere Date: Sat, 24 Oct 2020 23:10:16 +0200 Subject: [PATCH] Created github repository for the package --- README.md | 7 + algorithm_comparison.png | Bin 0 -> 30876 bytes cran-package/DESCRIPTION | 12 + cran-package/LICENSE | 2 + cran-package/NAMESPACE | 12 + cran-package/R/labeling.R | 881 ++++++++++++++++++++++++++ cran-package/man/extended.Rd | 40 ++ cran-package/man/extended.figures.Rd | 25 + cran-package/man/gnuplot.Rd | 26 + cran-package/man/heckbert.Rd | 27 + cran-package/man/labeling-internal.Rd | 15 + cran-package/man/labeling-package.Rd | 56 ++ cran-package/man/matplotlib.Rd | 26 + cran-package/man/nelder.Rd | 31 + cran-package/man/rpretty.Rd | 49 ++ cran-package/man/sparks.Rd | 28 + cran-package/man/thayer.Rd | 28 + cran-package/man/wilkinson.Rd | 62 ++ labeling-manual.pdf | Bin 0 -> 153416 bytes labeling_0.4.2.tar.gz | Bin 0 -> 9868 bytes 20 files changed, 1327 insertions(+) create mode 100644 README.md create mode 100644 algorithm_comparison.png create mode 100644 cran-package/DESCRIPTION create mode 100644 cran-package/LICENSE create mode 100644 cran-package/NAMESPACE create mode 100644 cran-package/R/labeling.R create mode 100644 cran-package/man/extended.Rd create mode 100644 cran-package/man/extended.figures.Rd create mode 100644 cran-package/man/gnuplot.Rd create mode 100644 cran-package/man/heckbert.Rd create mode 100644 cran-package/man/labeling-internal.Rd create mode 100644 cran-package/man/labeling-package.Rd create mode 100644 cran-package/man/matplotlib.Rd create mode 100644 cran-package/man/nelder.Rd create mode 100644 cran-package/man/rpretty.Rd create mode 100644 cran-package/man/sparks.Rd create mode 100644 cran-package/man/thayer.Rd create mode 100644 cran-package/man/wilkinson.Rd create mode 100644 labeling-manual.pdf create mode 100644 labeling_0.4.2.tar.gz diff --git a/README.md b/README.md new file mode 100644 index 0000000..54df9b0 --- /dev/null +++ b/README.md @@ -0,0 +1,7 @@ +# labeling [![](https://cranlogs.r-pkg.org/badges/labeling)](https://cran.r-project.org/package=labeling) + +This package contains functions which provide a range of axis labeling algorithms, most notably the "extended" algorithm described in Talbot et al.'s [An Extension of Wilkinson’s Algorithm for Positioning Tick Labels on Axes](http://vis.stanford.edu/files/2010-TickLabels-InfoVis.pdf). They are used in [ggplot2](https://ggplot2.tidyverse.org/), through the [scales](https://scales.r-lib.org/) package. + +![](algorithm_comparison.png) + +For implementation details, see `/cran-package/R/labeling.R`. For instructions and usage examples, see `labeling-manual.pdf`. For complaints and bugs, send me a message to the mantainer [email](https://cran.r-project.org/web/packages/labeling/) or file a Github issue. diff --git a/algorithm_comparison.png b/algorithm_comparison.png new file mode 100644 index 0000000000000000000000000000000000000000..1e0a7c31615b0500c8aad5a9be14310041afbc25 GIT binary patch literal 30876 zcmd43bySqy_dZN0NO#B3pyYs*lz@~VAxcX#AR^tZbSnr9AqW^KA~Dh_DKL~G-6`G8 zzIL4-%;9{Dn$77_!t-%L~5#c?qgtJ!@%DU zuHk?`>x^HqU|_IdsNIo&;GMZvckcm%e)`45m`xg|I)B+fBBw32o5XImTX<_G9reUd zcdg%CPN6;S6`~VA?=m!mws7$>{rP9`r%!lG?4N&TxyIJ}0#5dyPv+^!MgD$)B~n_^Qu*&vS6k!obop=GjnOf& z55vVcb2KRE)V^;Ln^;PJ^Emg|kpoE21w%&zx%Li+a>$n~_GBhssL5afbNbncokAFU zWd2nAeJirHz;{M>fP5Hl`VX?v#vqGp>b87quVDp$U>5Zt_O4}?u#eW(HXyiu`T4RND>j6zacw*i*(16p&(+?f~PN=Tp4*o0dStP5k(dgy;s zy}W>V%vL?*^Y|NZ{8*kZ!g-%7DLrH{Ht=cj3%8!uwOfhhe2%ZX<+Z_R8iewwJwI9H z;pJ6){P=p{>Dbf{)@krtvs2)1Ms0;+QG3u?dr;$o>vfNhHXQVEvztK|erM@F=C)S~ zigI&v**4eTD4x%e1RY`5pY3#^%&wht(Gn@~@bW9NA 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file mode 100644 index 0000000..f6e4091 --- /dev/null +++ b/cran-package/LICENSE @@ -0,0 +1,2 @@ +YEAR: 2020 +COPYRIGHT HOLDER: Justin Talbot diff --git a/cran-package/NAMESPACE b/cran-package/NAMESPACE new file mode 100644 index 0000000..3287f5a --- /dev/null +++ b/cran-package/NAMESPACE @@ -0,0 +1,12 @@ +importFrom("stats", "median", "runif") +importFrom("graphics", "axis", "barplot", "hist", "par") +export(heckbert) +export(wilkinson) +export(extended) +export(extended.figures) +export(nelder) +export(rpretty) +export(matplotlib) +export(gnuplot) +export(sparks) +export(thayer) diff --git a/cran-package/R/labeling.R b/cran-package/R/labeling.R new file mode 100644 index 0000000..df6fe64 --- /dev/null +++ b/cran-package/R/labeling.R @@ -0,0 +1,881 @@ +#' Functions for positioning tick labels on axes +#' +#' \tabular{ll}{ +#' Package: \tab labeling\cr +#' Type: \tab Package\cr +#' Version: \tab 0.2\cr +#' Date: \tab 2011-04-01\cr +#' License: \tab Unlimited\cr +#' LazyLoad: \tab yes\cr +#' } +#' +#' Implements a number of axis labeling schemes, including those +#' compared in An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes +#' by Talbot, Lin, and Hanrahan, InfoVis 2010. +#' +#' @name labeling-package +#' @aliases labeling +#' @docType package +#' @title Axis labeling +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @references +#' Heckbert, P. S. (1990) Nice numbers for graph labels, Graphics Gems I, Academic Press Professional, Inc. +#' Wilkinson, L. (2005) The Grammar of Graphics, Springer-Verlag New York, Inc. +#' Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes, InfoVis 2010. +#' @keywords dplot +#' @seealso \code{\link{extended}}, \code{\link{wilkinson}}, \code{\link{heckbert}}, \code{\link{rpretty}}, \code{\link{gnuplot}}, \code{\link{matplotlib}}, \code{\link{nelder}}, \code{\link{sparks}}, \code{\link{thayer}}, \code{\link{pretty}} +#' @examples +#' heckbert(8.1, 14.1, 4) # 5 10 15 +#' wilkinson(8.1, 14.1, 4) # 8 9 10 11 12 13 14 15 +#' extended(8.1, 14.1, 4) # 8 10 12 14 + +#' # When plotting, extend the plot range to include the labeling +#' # Should probably have a helper function to make this easier +#' data(iris) +#' x <- iris$Sepal.Width +#' y <- iris$Sepal.Length +#' xl <- extended(min(x), max(x), 6) +#' yl <- extended(min(y), max(y), 6) +#' plot(x, y, +#' xlim=c(min(x,xl),max(x,xl)), +#' ylim=c(min(y,yl),max(y,yl)), +#' axes=FALSE, main="Extended labeling") +#' axis(1, at=xl) +#' axis(2, at=yl) +c() + + + +#' Heckbert's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @return vector of axis label locations +#' @references +#' Heckbert, P. S. (1990) Nice numbers for graph labels, Graphics Gems I, Academic Press Professional, Inc. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +heckbert <- function(dmin, dmax, m) +{ + range <- .heckbert.nicenum((dmax-dmin), FALSE) + lstep <- .heckbert.nicenum(range/(m-1), TRUE) + lmin <- floor(dmin/lstep)*lstep + lmax <- ceiling(dmax/lstep)*lstep + seq(lmin, lmax, by=lstep) +} + +.heckbert.nicenum <- function(x, round) +{ + e <- floor(log10(x)) + f <- x / (10^e) + if(round) + { + if(f < 1.5) nf <- 1 + else if(f < 3) nf <- 2 + else if(f < 7) nf <- 5 + else nf <- 10 + } + else + { + if(f <= 1) nf <- 1 + else if(f <= 2) nf <- 2 + else if(f <= 5) nf <- 5 + else nf <- 10 + } + nf * (10^e) +} + + + +#' Wilkinson's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @param Q set of nice numbers +#' @param mincoverage minimum ratio between the the data range and the labeling range, controlling the whitespace around the labeling (default = 0.8) +#' @param mrange range of \code{m}, the number of tick marks, that should be considered in the optimization search +#' @return vector of axis label locations +#' @note Ported from Wilkinson's Java implementation with some changes. +#' Changes: 1) m (the target number of ticks) is hard coded in Wilkinson's implementation as 5. +#' Here we allow it to vary as a parameter. Since m is fixed, +#' Wilkinson only searches over a fixed range 4-13 of possible resulting ticks. +#' We broadened the search range to max(floor(m/2),2) to ceiling(6*m), +#' which is a larger range than Wilkinson considers for 5 and allows us to vary m, +#' including using non-integer values of m. +#' 2) Wilkinson's implementation assumes that the scores are non-negative. But, his revised +#' granularity function can be extremely negative. We tweaked the code to allow negative scores. +#' We found that this produced better labelings. +#' 3) We added 10 to Q. This seemed to be necessary to get steps of size 1. +#' It is possible for this algorithm to find no solution. +#' In Wilkinson's implementation, instead of failing, he returns the non-nice labels spaced evenly from min to max. +#' We want to detect this case, so we return NULL. If this happens, the search range, mrange, needs to be increased. +#' @references +#' Wilkinson, L. (2005) The Grammar of Graphics, Springer-Verlag New York, Inc. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +wilkinson <-function(dmin, dmax, m, Q = c(1,5,2,2.5,3,4,1.5,7,6,8,9), mincoverage = 0.8, mrange=max(floor(m/2),2):ceiling(6*m)) +{ + best <- NULL + for(k in mrange) + { + result <- .wilkinson.nice.scale(dmin, dmax, k, Q, mincoverage, mrange, m) + if(!is.null(result) && (is.null(best) || result$score > best$score)) + { + best <- result + } + } + seq(best$lmin, best$lmax, by=best$lstep) +} + +.wilkinson.nice.scale <- function(min, max, k, Q = c(1,5,2,2.5,3,4,1.5,7,6,8,9), mincoverage = 0.8, mrange=c(), m=k) +{ + Q <- c(10, Q) + + range <- max-min + intervals <- k-1 + granularity <- 1 - abs(k-m)/m + + delta <- range / intervals + base <- floor(log10(delta)) + dbase <- 10^base + + best <- NULL + for(i in 1:length(Q)) + { + tdelta <- Q[i] * dbase + tmin <- floor(min/tdelta) * tdelta + tmax <- tmin + intervals * tdelta + + if(tmin <= min && tmax >= max) + { + roundness <- 1 - ((i-1) - ifelse(tmin <= 0 && tmax >= 0, 1, 0)) / length(Q) + coverage <- (max-min)/(tmax-tmin) + if(coverage > mincoverage) + { + tnice <- granularity + roundness + coverage + + ## Wilkinson's implementation contains code to favor certain ranges of labels + ## e.g. those balanced around or anchored at 0, etc. + ## We did not evaluate this type of optimization in the paper, so did not include it. + ## Obviously this optimization component could also be added to our function. + #if(tmin == -tmax || tmin == 0 || tmax == 1 || tmax == 100) + # tnice <- tnice + 1 + #if(tmin == 0 && tmax == 1 || tmin == 0 && tmax == 100) + # tnice <- tnice + 1 + + if(is.null(best) || tnice > best$score) + { + best <- list(lmin=tmin, + lmax=tmax, + lstep=tdelta, + score=tnice + ) + } + } + } + } + best +} + + + + +## The Extended-Wilkinson algorithm described in the paper. + +## Our scoring functions, including the approximations for limiting the search +.simplicity <- function(q, Q, j, lmin, lmax, lstep) +{ + eps <- .Machine$double.eps * 100 + + n <- length(Q) + i <- match(q, Q)[1] + v <- ifelse( (lmin %% lstep < eps || lstep - (lmin %% lstep) < eps) && lmin <= 0 && lmax >=0, 1, 0) + + 1 - (i-1)/(n-1) - j + v +} + +.simplicity.max <- function(q, Q, j) +{ + n <- length(Q) + i <- match(q, Q)[1] + v <- 1 + + 1 - (i-1)/(n-1) - j + v +} + +.coverage <- function(dmin, dmax, lmin, lmax) +{ + range <- dmax-dmin + 1 - 0.5 * ((dmax-lmax)^2+(dmin-lmin)^2) / ((0.1*range)^2) +} + +.coverage.max <- function(dmin, dmax, span) +{ + range <- dmax-dmin + if(span > range) + { + half <- (span-range)/2 + 1 - 0.5 * (half^2 + half^2) / ((0.1 * range)^2) + } + else + { + 1 + } +} + +.density <- function(k, m, dmin, dmax, lmin, lmax) +{ + r <- (k-1) / (lmax-lmin) + rt <- (m-1) / (max(lmax,dmax)-min(dmin,lmin)) + 2 - max( r/rt, rt/r ) +} + +.density.max <- function(k, m) +{ + if(k >= m) + 2 - (k-1)/(m-1) + else + 1 +} + +.legibility <- function(lmin, lmax, lstep) +{ + 1 ## did all the legibility tests in C#, not in R. +} + + +#' An Extension of Wilkinson's Algorithm for Position Tick Labels on Axes +#' +#' \code{extended} is an enhanced version of Wilkinson's optimization-based axis labeling approach. It is described in detail in our paper. See the references. +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @param Q set of nice numbers +#' @param only.loose if true, the extreme labels will be outside the data range +#' @param w weights applied to the four optimization components (simplicity, coverage, density, and legibility) +#' @return vector of axis label locations +#' @references +#' Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes, InfoVis 2010. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +extended <- function(dmin, dmax, m, Q=c(1,5,2,2.5,4,3), only.loose=FALSE, w=c(0.25,0.2,0.5,0.05)) +{ + eps <- .Machine$double.eps * 100 + + if(dmin > dmax) { + temp <- dmin + dmin <- dmax + dmax <- temp + } + + if(dmax - dmin < eps) { + #if the range is near the floating point limit, + #let seq generate some equally spaced steps. + return(seq(from=dmin, to=dmax, length.out=m)) + } + + if((dmax - dmin) > sqrt(.Machine$double.xmax)) { + #if the range is too large + #let seq generate some equally spaced steps. + return(seq(from=dmin, to=dmax, length.out=m)) + } + + n <- length(Q) + + best <- list() + best$score <- -2 + + j <- 1 + while(j < Inf) + { + for(q in Q) + { + sm <- .simplicity.max(q, Q, j) + + if((w[1]*sm+w[2]+w[3]+w[4]) < best$score) + { + j <- Inf + break + } + + k <- 2 + while(k < Inf) # loop over tick counts + { + dm <- .density.max(k, m) + + if((w[1]*sm+w[2]+w[3]*dm+w[4]) < best$score) + break + + delta <- (dmax-dmin)/(k+1)/j/q + z <- ceiling(log(delta, base=10)) + + while(z < Inf) + { + step <- j*q*10^z + + cm <- .coverage.max(dmin, dmax, step*(k-1)) + + if((w[1]*sm+w[2]*cm+w[3]*dm+w[4]) < best$score) + break + + min_start <- floor(dmax/(step))*j - (k - 1)*j + max_start <- ceiling(dmin/(step))*j + + if(min_start > max_start) + { + z <- z+1 + next + } + + for(start in min_start:max_start) + { + lmin <- start * (step/j) + lmax <- lmin + step*(k-1) + lstep <- step + + s <- .simplicity(q, Q, j, lmin, lmax, lstep) + c <- .coverage(dmin, dmax, lmin, lmax) + g <- .density(k, m, dmin, dmax, lmin, lmax) + l <- .legibility(lmin, lmax, lstep) + + score <- w[1]*s + w[2]*c + w[3]*g + w[4]*l + + if(score > best$score && (!only.loose || (lmin <= dmin && lmax >= dmax))) + { + best <- list(lmin=lmin, + lmax=lmax, + lstep=lstep, + score=score) + } + } + z <- z+1 + } + k <- k+1 + } + } + j <- j + 1 + } + + seq(from=best$lmin, to=best$lmax, by=best$lstep) +} + + + +## Quantitative evaluation plots (Figures 2 and 3 in the paper) + + +#' Generate figures from An Extension of Wilkinson's Algorithm for Position Tick Labels on Axes +#' +#' Generates Figures 2 and 3 from our paper. +#' +#' @param samples number of samples to use (in the paper we used 10000, but that takes awhile to run). +#' @return produces plots as a side effect +#' @references +#' Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of Wilkinson's Algorithm for Positioning Tick Labels on Axes, InfoVis 2010. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +extended.figures <- function(samples = 100) +{ + oldpar <- par() + par(ask=TRUE) + + a <- runif(samples, -100, 400) + b <- runif(samples, -100, 400) + low <- pmin(a,b) + high <- pmax(a,b) + ticks <- runif(samples, 2, 10) + + generate.labelings <- function(labeler, dmin, dmax, ticks, ...) + { + mapply(labeler, dmin, dmax, ticks, SIMPLIFY=FALSE, MoreArgs=list(...)) + } + + h1 <- generate.labelings(heckbert, low, high, ticks) + w1 <- generate.labelings(wilkinson, low, high, ticks, mincoverage=0.8) + f1 <- generate.labelings(extended, low, high, ticks, only.loose=TRUE) + e1 <- generate.labelings(extended, low, high, ticks) + + figure2 <- function(r, names) + { + for(i in 1:length(r)) + { + d <- r[[i]] + + #plot coverage + cover <- sapply(d, function(x) {max(x)-min(x)})/(high-low) + hist(cover, breaks=seq(from=-0.01,to=1000,by=0.02), xlab="", ylab=names[i], main=ifelse(i==1, "Density", ""), col="darkgray", lab=c(3,3,3), xlim=c(0.5,3.5), ylim=c(0,0.12*samples), axes=FALSE, border=FALSE) + #hist(cover) + axis(side=1, at=c(0,1,2,3,4), xlab="hello", line=-0.1, lwd=0.5) + + # plot density + dens <- sapply(d, length) / ticks + hist(dens, breaks=seq(from=-0.01,to=10,by=0.02), xlab="", ylab=names[i], main=ifelse(i==1, "Density", ""), col="darkgray", lab=c(3,3,3), xlim=c(0.5,3.5), ylim=c(0,0.06*samples), axes=FALSE, border=FALSE) + axis(side=1, at=c(0,1,2,3,4), xlab="hello", line=-0.1, lwd=0.5) + } + } + + par(mfrow=c(4, 2), mar=c(0.5,1.85,1,0), oma=c(1,0,1,0), mgp=c(0,0.5,-0.3), font.main=1, font.lab=1, cex.lab=1, cex.main=1, tcl=-0.2) + figure2(list(h1,w1, f1, e1), names=c("Heckbert", "Wilkinson", "Extended\n(loose)", "Extended\n(flexible)")) + + figure3 <- function(r, names) + { + for(i in 1:length(r)) + { + d <- r[[i]] + steps <- sapply(d, function(x) round(median(diff(x)), 2)) + steps <- steps / (10^floor(log10(steps))) + tab <- table(steps) + barplot(rev(tab), xlim=c(0,0.4*samples), horiz=TRUE, xlab=ifelse(i==1,"Frequency",""), xaxt='n', yaxt='s', las=1, main=names[i], border=NA, col="gray") + } + } + + par(mfrow=c(1,4), mar=c(0.5, 0.75, 2, 0.5), oma=c(0,2,1,1), mgp=c(0,0.75,-0.3), cex.lab=1, cex.main=1) + figure3(list(h1,w1, f1, e1), names=c("Heckbert", "Wilkinson", "Extended\n(loose)", "Extended\n(flexible)")) + par(oldpar) +} + + + +#' Nelder's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @param Q set of nice numbers +#' @return vector of axis label locations +#' @references +#' Nelder, J. A. (1976) AS 96. A Simple Algorithm for Scaling Graphs, Journal of the Royal Statistical Society. Series C., pp. 94-96. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +nelder <- function(dmin, dmax, m, Q = c(1,1.2,1.6,2,2.5,3,4,5,6,8,10)) +{ + ntick <- floor(m) + tol <- 5e-6 + bias <- 1e-4 + + intervals <- m-1 + x <- abs(dmax) + if(x == 0) x <- 1 + if(!((dmax-dmin)/x > tol)) + { + ## special case handling for very small ranges. Not implemented yet. + } + + step <- (dmax-dmin)/intervals + s <- step + + while(s <= 1) + s <- s*10 + while(s > 10) + s <- s/10 + + x <- s-bias + unit <- 1 + for(i in 1:length(Q)) + { + if(x < Q[i]) + { + unit <- i + break + } + } + step <- step * Q[unit] / s + range <- step*intervals + + x <- 0.5 * (1+ (dmin+dmax-range) / step) + j <- floor(x-bias) + valmin <- step * j + + if(dmin > 0 && range >= dmax) + valmin <- 0 + valmax <- valmin + range + + if(!(dmax > 0 || range < -dmin)) + { + valmax <- 0 + valmin <- -range + } + + seq(from=valmin, to=valmax, by=step) +} + + +#' R's pretty algorithm implemented in R +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @param n number of axis intervals (specify one of \code{m} or \code{n}) +#' @param min.n nonnegative integer giving the \emph{minimal} number of intervals. If \code{min.n == 0}, \code{pretty(.)} may return a single value. +#' @param shrink.sml positive numeric by a which a default scale is shrunk in the case when \code{range(x)} is very small (usually 0). +#' @param high.u.bias non-negative numeric, typically \code{> 1}. The interval unit is determined as \code{\{1,2,5,10\}} times \code{b}, a power of 10. Larger \code{high.u.bias} values favor larger units. +#' @param u5.bias non-negative numeric multiplier favoring factor 5 over 2. Default and 'optimal': \code{u5.bias = .5 + 1.5*high.u.bias}. +#' @return vector of axis label locations +#' @references +#' Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) \emph{The New S Language}. Wadsworth & Brooks/Cole. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +rpretty <- function(dmin, dmax, m=6, n=floor(m)-1, min.n=n%/%3, shrink.sml = 0.75, high.u.bias=1.5, u5.bias=0.5 + 1.5*high.u.bias) +{ + ndiv <- n + h <- high.u.bias + h5 <- u5.bias + + dx <- dmax-dmin + if(dx==0 && dmax==0) + { + cell <- 1 + i_small <- TRUE + U <- 1 + } + else + { + cell <- max(abs(dmin), abs(dmax)) + U <- 1 + ifelse(h5 >= 1.5*h+0.5, 1/(1+h), 1.5/(1+h5)) + i_small = dx < (cell * U * max(1, ndiv) * 1e-07 * 3) + } + + if(i_small) + { + if(cell > 10) + { + cell <- 9+cell/10 + } + cell <- cell * shrink.sml + if(min.n > 1) cell <- cell/min.n + } + else + { + cell <- dx + if(ndiv > 1) cell <- cell/ndiv + } + + if(cell < 20 * 1e-07) + cell <- 20 * 1e-07 + + base <- 10^floor(log10(cell)) + + unit <- base + + if((2*base)-cell < h*(cell-unit)) + { + unit <- 2*base + if((5*base)-cell < h5*(cell-unit)) + { + unit <- 5*base + if((10*base)-cell < h*(cell-unit)) + unit <- 10*base + } + } + + # track down lattice labelings... + + ## Maybe used to correct for the epsilon here?? + ns <- floor(dmin/unit + 1e-07) + nu <- ceiling(dmax/unit - 1e-07) + + ## Extend the range out beyond the data. Does this ever happen?? + while(ns*unit > dmin+(1e-07*unit)) ns <- ns-1 + while(nu*unit < dmax-(1e-07*unit)) nu <- nu+1 + + + ## If we don't have quite enough labels, extend the range out to make more (these labels are beyond the data :( ) + k <- floor(0.5 + nu-ns) + if(k < min.n) + { + k <- min.n - k + if(ns >=0) + { + nu <- nu + k/2 + ns <- ns - k/2 + k%%2 + } + else + { + ns <- ns - k/2 + nu <- nu + k/2 + k%%2 + } + ndiv <- min.n + } + else + { + ndiv <- k + } + + graphmin <- ns*unit + graphmax <- nu*unit + + seq(from=graphmin, to=graphmax, by=unit) +} + +#' Matplotlib's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @return vector of axis label locations +#' @references +#' \url{http://matplotlib.sourceforge.net/} +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +matplotlib <- function(dmin, dmax, m) +{ + steps <- c(1,2,5,10) + nbins <- m + trim <- TRUE + + vmin <- dmin + vmax <- dmax + params <- .matplotlib.scale.range(vmin, vmax, nbins) + scale <- params[1] + offset <- params[2] + + vmin <- vmin-offset + vmax <- vmax-offset + + rawStep <- (vmax-vmin)/nbins + scaledRawStep <- rawStep/scale + + bestMax <- vmax + bestMin <- vmin + + scaledStep <- 1 + chosenFactor <- 1 + + for (step in steps) + { + if (step >= scaledRawStep) + { + scaledStep <- step*scale + chosenFactor <- step + bestMin <- scaledStep * floor(vmin/scaledStep) + bestMax <- bestMin + scaledStep*nbins + if (bestMax >= vmax) + break + } + } + if (trim) + { + extraBins <- floor((bestMax-vmax)/scaledStep) + nbins <- nbins-extraBins + } + graphMin <- bestMin+offset + graphMax <- graphMin+nbins*scaledStep + + seq(from=graphMin, to=graphMax, by=scaledStep) +} + +.matplotlib.scale.range <- function(min, max, bins) +{ + threshold <- 100 + dv <- abs(max-min) + maxabsv<-max(abs(min), abs(max)) + if (maxabsv == 0 || dv/maxabsv<10^-12) + return(c(1, 0)) + + meanv <- 0.5*(min+max) + + if ((abs(meanv)/dv) < threshold) + offset<- 0 + else if (meanv>0) + { + exp<-floor(log10(meanv)) + offset = 10.0^exp + } else + { + exp <- floor(log10(-1*meanv)) + offset <- -10.0^exp + } + exp <- floor(log10(dv/bins)) + scale = 10.0^exp + c(scale, offset) +} + + + +#' gnuplot's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @return vector of axis label locations +#' @references +#' \url{http://www.gnuplot.info/} +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +gnuplot <- function(dmin, dmax, m) +{ + ntick <- floor(m) + power <- 10^floor(log10(dmax-dmin)) + norm_range <- (dmax-dmin)/power + p <- (ntick-1) / norm_range + + if(p > 40) + t <- 0.05 + else if(p > 20) + t <- 0.1 + else if(p > 10) + t <- 0.2 + else if(p > 4) + t <- 0.5 + else if(p > 2) + t <- 1 + else if(p > 0.5) + t <- 2 + else + t <- ceiling(norm_range) + + d <- t*power + graphmin <- floor(dmin/d) * d + graphmax <- ceiling(dmax/d) * d + + seq(from=graphmin, to=graphmax, by=d) +} + + + +#' Sparks' labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @return vector of axis label locations +#' @references +#' Sparks, D. N. (1971) AS 44. Scatter Diagram Plotting, Journal of the Royal Statistical Society. Series C., pp. 327-331. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +sparks <- function(dmin, dmax, m) +{ + fm <- m-1 + ratio <- 0 + key <- 1 + kount <- 0 + r <- dmax-dmin + b <- dmin + + while(ratio <= 0.8) + { + while(key <= 2) + { + while(r <= 1) + { + kount <- kount + 1 + r <- r*10 + } + while(r > 10) + { + kount <- kount - 1 + r <- r/10 + } + + b <- b*(10^kount) + if( b < 0 && b != trunc(b)) b <- b-1 + b <- trunc(b)/(10^kount) + r <- (dmax-b)/fm + kount <- 0 + key <- key+2 + } + + fstep <- trunc(r) + if(fstep != r) fstep <- fstep+1 + if(r < 1.5) fstep <- fstep-0.5 + fstep <- fstep/(10^kount) + ratio <- (dmax - dmin)*(fm*fstep) + kount <- 1 + key <- 2 + } + fmin <- b + c <- fstep*trunc(b/fstep) + if(c < 0 && c != b) c <- c-fstep + if((c+fm*fstep) > dmax) fmin <- c + + seq(from=fmin, to=fstep*(m-1), by=fstep) +} + + +#' Thayer and Storer's labeling algorithm +#' +#' @param dmin minimum of the data range +#' @param dmax maximum of the data range +#' @param m number of axis labels +#' @return vector of axis label locations +#' @references +#' Thayer, R. P. and Storer, R. F. (1969) AS 21. Scale Selection for Computer Plots, Journal of the Royal Statistical Society. Series C., pp. 206-208. +#' @author Justin Talbot \email{jtalbot@@stanford.edu} +#' @export +thayer <- function(dmin, dmax, m) +{ + r <- dmax-dmin + b <- dmin + kount <- 0 + kod <- 0 + + while(kod < 2) + { + while(r <= 1) + { + kount <- kount+1 + r <- r*10 + } + while(r > 10) + { + kount <- kount-1 + r <- r/10 + } + b <- b*(10^kount) + if(b < 0) + b <- b-1 + ib <- trunc(b) + b <- ib + b <- b/(10^kount) + r <- dmax-b + a <- r/(m-1) + kount <- 0 + while(a <= 1) + { + kount <- kount+1 + a <- a*10 + } + while(a > 10) + { + kount <- kount-1 + a <- a/10 + } + ia <- trunc(a) + if(ia == 6) ia <- 7 + if(ia == 8) ia <- 9 + + aa <- 0 + if(a < 1.5) aa <- -0.5 + a <- aa + 1 + ia + a <- a/(10^kount) + + test <- (m-1) * a + test1 <- (dmax-dmin)/test + if(test1 > 0.8) + kod <- 2 + + if(kod < 2) + { + kount <- 1 + r <- dmax-dmin + b <- dmin + kod <- kod + 1 + } + } + + iab <- trunc(b/a) + if(iab < 0) iab <- iab-1 + c <- a * iab + d <- c + (m-1)*a + if(d >= dmax) + b <- c + + valmin <- b + valmax <- b + a*(m-1) + + seq(from=valmin, to=valmax, by=a) +} + diff --git a/cran-package/man/extended.Rd b/cran-package/man/extended.Rd new file mode 100644 index 0000000..5235cc8 --- /dev/null +++ b/cran-package/man/extended.Rd @@ -0,0 +1,40 @@ +\name{extended} +\alias{extended} +\title{An Extension of Wilkinson's Algorithm for Position Tick Labels on Axes} +\usage{ + extended(dmin, dmax, m, Q = c(1, 5, 2, 2.5, 4, 3), + only.loose = FALSE, w = c(0.25, 0.2, 0.5, 0.05)) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} + + \item{Q}{set of nice numbers} + + \item{only.loose}{if true, the extreme labels will be + outside the data range} + + \item{w}{weights applied to the four optimization + components (simplicity, coverage, density, and + legibility)} +} +\value{ + vector of axis label locations +} +\description{ + \code{extended} is an enhanced version of Wilkinson's + optimization-based axis labeling approach. It is + described in detail in our paper. See the references. +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of + Wilkinson's Algorithm for Positioning Tick Labels on + Axes, InfoVis 2010. +} + diff --git a/cran-package/man/extended.figures.Rd b/cran-package/man/extended.figures.Rd new file mode 100644 index 0000000..7e16f61 --- /dev/null +++ b/cran-package/man/extended.figures.Rd @@ -0,0 +1,25 @@ +\name{extended.figures} +\alias{extended.figures} +\title{Generate figures from An Extension of Wilkinson's Algorithm for Position Tick Labels on Axes} +\usage{ + extended.figures(samples = 100) +} +\arguments{ + \item{samples}{number of samples to use (in the paper we + used 10000, but that takes awhile to run).} +} +\value{ + produces plots as a side effect +} +\description{ + Generates Figures 2 and 3 from our paper. +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Talbot, J., Lin, S., Hanrahan, P. (2010) An Extension of + Wilkinson's Algorithm for Positioning Tick Labels on + Axes, InfoVis 2010. +} + diff --git a/cran-package/man/gnuplot.Rd b/cran-package/man/gnuplot.Rd new file mode 100644 index 0000000..c31d749 --- /dev/null +++ b/cran-package/man/gnuplot.Rd @@ -0,0 +1,26 @@ +\name{gnuplot} +\alias{gnuplot} +\title{gnuplot's labeling algorithm} +\usage{ + gnuplot(dmin, dmax, m) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} +} +\value{ + vector of axis label locations +} +\description{ + gnuplot's labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + \url{http://www.gnuplot.info/} +} + diff --git a/cran-package/man/heckbert.Rd b/cran-package/man/heckbert.Rd new file mode 100644 index 0000000..31c4d23 --- /dev/null +++ b/cran-package/man/heckbert.Rd @@ -0,0 +1,27 @@ +\name{heckbert} +\alias{heckbert} +\title{Heckbert's labeling algorithm} +\usage{ + heckbert(dmin, dmax, m) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} +} +\value{ + vector of axis label locations +} +\description{ + Heckbert's labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Heckbert, P. S. (1990) Nice numbers for graph labels, + Graphics Gems I, Academic Press Professional, Inc. +} + diff --git a/cran-package/man/labeling-internal.Rd b/cran-package/man/labeling-internal.Rd new file mode 100644 index 0000000..2c739ce --- /dev/null +++ b/cran-package/man/labeling-internal.Rd @@ -0,0 +1,15 @@ +\name{labeling-internal} +\title{Internal labeling objects} +\alias{.coverage} +\alias{.coverage.max} +\alias{.density} +\alias{.density.max} +\alias{.floored.mod} +\alias{.heckbert.nicenum} +\alias{.legibility} +\alias{.simplicity} +\alias{.simplicity.max} +\alias{.wilkinson.nice.scale} +\description{Internal labeling objects.} +\details{These are not to be called by the user.} +\keyword{internal} \ No newline at end of file diff --git a/cran-package/man/labeling-package.Rd b/cran-package/man/labeling-package.Rd new file mode 100644 index 0000000..0d9501c --- /dev/null +++ b/cran-package/man/labeling-package.Rd @@ -0,0 +1,56 @@ +\docType{package} +\name{labeling-package} +\alias{labeling} +\alias{labeling-package} +\title{Axis labeling} +\description{ + Functions for positioning tick labels on axes +} +\details{ + \tabular{ll}{ Package: \tab labeling\cr Type: \tab + Package\cr Version: \tab 0.2\cr Date: \tab 2011-04-01\cr + License: \tab Unlimited\cr LazyLoad: \tab yes\cr } + + Implements a number of axis labeling schemes, including + those compared in An Extension of Wilkinson's Algorithm + for Positioning Tick Labels on Axes by Talbot, Lin, and + Hanrahan, InfoVis 2010. +} +\examples{ +heckbert(8.1, 14.1, 4) # 5 10 15 +wilkinson(8.1, 14.1, 4) # 8 9 10 11 12 13 14 15 +extended(8.1, 14.1, 4) # 8 10 12 14 +# When plotting, extend the plot range to include the labeling +# Should probably have a helper function to make this easier +data(iris) +x <- iris$Sepal.Width +y <- iris$Sepal.Length +xl <- extended(min(x), max(x), 6) +yl <- extended(min(y), max(y), 6) +plot(x, y, + xlim=c(min(x,xl),max(x,xl)), + ylim=c(min(y,yl),max(y,yl)), + axes=FALSE, main="Extended labeling") +axis(1, at=xl) +axis(2, at=yl) +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Heckbert, P. S. (1990) Nice numbers for graph labels, + Graphics Gems I, Academic Press Professional, Inc. + Wilkinson, L. (2005) The Grammar of Graphics, + Springer-Verlag New York, Inc. Talbot, J., Lin, S., + Hanrahan, P. (2010) An Extension of Wilkinson's Algorithm + for Positioning Tick Labels on Axes, InfoVis 2010. +} +\seealso{ + \code{\link{extended}}, \code{\link{wilkinson}}, + \code{\link{heckbert}}, \code{\link{rpretty}}, + \code{\link{gnuplot}}, \code{\link{matplotlib}}, + \code{\link{nelder}}, \code{\link{sparks}}, + \code{\link{thayer}}, \code{\link{pretty}} +} +\keyword{dplot} + diff --git a/cran-package/man/matplotlib.Rd b/cran-package/man/matplotlib.Rd new file mode 100644 index 0000000..2653210 --- /dev/null +++ b/cran-package/man/matplotlib.Rd @@ -0,0 +1,26 @@ +\name{matplotlib} +\alias{matplotlib} +\title{Matplotlib's labeling algorithm} +\usage{ + matplotlib(dmin, dmax, m) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} +} +\value{ + vector of axis label locations +} +\description{ + Matplotlib's labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + \url{https://matplotlib.org/} +} + diff --git a/cran-package/man/nelder.Rd b/cran-package/man/nelder.Rd new file mode 100644 index 0000000..4f1bbab --- /dev/null +++ b/cran-package/man/nelder.Rd @@ -0,0 +1,31 @@ +\name{nelder} +\alias{nelder} +\title{Nelder's labeling algorithm} +\usage{ + nelder(dmin, dmax, m, + Q = c(1, 1.2, 1.6, 2, 2.5, 3, 4, 5, 6, 8, 10)) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} + + \item{Q}{set of nice numbers} +} +\value{ + vector of axis label locations +} +\description{ + Nelder's labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Nelder, J. A. (1976) AS 96. A Simple Algorithm for + Scaling Graphs, Journal of the Royal Statistical Society. + Series C., pp. 94-96. +} + diff --git a/cran-package/man/rpretty.Rd b/cran-package/man/rpretty.Rd new file mode 100644 index 0000000..941548d --- /dev/null +++ b/cran-package/man/rpretty.Rd @@ -0,0 +1,49 @@ +\name{rpretty} +\alias{rpretty} +\title{R's pretty algorithm implemented in R} +\usage{ + rpretty(dmin, dmax, m = 6, n = floor(m) - 1, + min.n = n\%/\%3, shrink.sml = 0.75, high.u.bias = 1.5, + u5.bias = 0.5 + 1.5 * high.u.bias) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} + + \item{n}{number of axis intervals (specify one of + \code{m} or \code{n})} + + \item{min.n}{nonnegative integer giving the + \emph{minimal} number of intervals. If \code{min.n == 0}, + \code{pretty(.)} may return a single value.} + + \item{shrink.sml}{positive numeric by a which a default + scale is shrunk in the case when \code{range(x)} is very + small (usually 0).} + + \item{high.u.bias}{non-negative numeric, typically + \code{> 1}. The interval unit is determined as + \code{\{1,2,5,10\}} times \code{b}, a power of 10. Larger + \code{high.u.bias} values favor larger units.} + + \item{u5.bias}{non-negative numeric multiplier favoring + factor 5 over 2. Default and 'optimal': \code{u5.bias = + .5 + 1.5*high.u.bias}.} +} +\value{ + vector of axis label locations +} +\description{ + R's pretty algorithm implemented in R +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) + \emph{The New S Language}. Wadsworth & Brooks/Cole. +} + diff --git a/cran-package/man/sparks.Rd b/cran-package/man/sparks.Rd new file mode 100644 index 0000000..c2f521f --- /dev/null +++ b/cran-package/man/sparks.Rd @@ -0,0 +1,28 @@ +\name{sparks} +\alias{sparks} +\title{Sparks' labeling algorithm} +\usage{ + sparks(dmin, dmax, m) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} +} +\value{ + vector of axis label locations +} +\description{ + Sparks' labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Sparks, D. N. (1971) AS 44. Scatter Diagram Plotting, + Journal of the Royal Statistical Society. Series C., pp. + 327-331. +} + diff --git a/cran-package/man/thayer.Rd b/cran-package/man/thayer.Rd new file mode 100644 index 0000000..07cbfd7 --- /dev/null +++ b/cran-package/man/thayer.Rd @@ -0,0 +1,28 @@ +\name{thayer} +\alias{thayer} +\title{Thayer and Storer's labeling algorithm} +\usage{ + thayer(dmin, dmax, m) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} +} +\value{ + vector of axis label locations +} +\description{ + Thayer and Storer's labeling algorithm +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Thayer, R. P. and Storer, R. F. (1969) AS 21. Scale + Selection for Computer Plots, Journal of the Royal + Statistical Society. Series C., pp. 206-208. +} + diff --git a/cran-package/man/wilkinson.Rd b/cran-package/man/wilkinson.Rd new file mode 100644 index 0000000..66898af --- /dev/null +++ b/cran-package/man/wilkinson.Rd @@ -0,0 +1,62 @@ +\name{wilkinson} +\alias{wilkinson} +\title{Wilkinson's labeling algorithm} +\usage{ + wilkinson(dmin, dmax, m, + Q = c(1, 5, 2, 2.5, 3, 4, 1.5, 7, 6, 8, 9), + mincoverage = 0.8, + mrange = max(floor(m/2), 2):ceiling(6 * m)) +} +\arguments{ + \item{dmin}{minimum of the data range} + + \item{dmax}{maximum of the data range} + + \item{m}{number of axis labels} + + \item{Q}{set of nice numbers} + + \item{mincoverage}{minimum ratio between the the data + range and the labeling range, controlling the whitespace + around the labeling (default = 0.8)} + + \item{mrange}{range of \code{m}, the number of tick + marks, that should be considered in the optimization + search} +} +\value{ + vector of axis label locations +} +\description{ + Wilkinson's labeling algorithm +} +\note{ + Ported from Wilkinson's Java implementation with some + changes. Changes: 1) m (the target number of ticks) is + hard coded in Wilkinson's implementation as 5. Here we + allow it to vary as a parameter. Since m is fixed, + Wilkinson only searches over a fixed range 4-13 of + possible resulting ticks. We broadened the search range + to max(floor(m/2),2) to ceiling(6*m), which is a larger + range than Wilkinson considers for 5 and allows us to + vary m, including using non-integer values of m. 2) + Wilkinson's implementation assumes that the scores are + non-negative. But, his revised granularity function can + be extremely negative. We tweaked the code to allow + negative scores. We found that this produced better + labelings. 3) We added 10 to Q. This seemed to be + necessary to get steps of size 1. It is possible for + this algorithm to find no solution. In Wilkinson's + implementation, instead of failing, he returns the + non-nice labels spaced evenly from min to max. We want + to detect this case, so we return NULL. If this happens, + the search range, mrange, needs to be increased. +} +\author{ + Justin Talbot \email{justintalbot@gmail.com} +} +\references{ + Wilkinson, L. (2005) The Grammar of Graphics, + Springer-Verlag New York, Inc. +} + diff --git a/labeling-manual.pdf b/labeling-manual.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ff2c6d47fd2ea6da285730002158475e30f03718 GIT binary patch literal 153416 zcma&NW2`VuyRAFz`AplkZQHhO+qP}nHlJzRwr%eBWUZa^?y!lE<`v@B30b4$Z(P)zvr_;!YtP~6;5bkZiaX3pmL989eE|8qgniCS1Yn>gar ziCP;tn+Tg2*%_Na@$y1BIXjvd*g&~&T&L^UZL%VV-ab+}t3k%F-``1LM;hp40#PhD ztM_bM16QtB(+KOupS6I#9D0#YWG*v^s3FsAfIv{MpLopf|9y>D_0`Preob$HU?e07 zH-BaXq7pBvw)RGzDS1sK&PRDA zGyJGAA0S8Z6Onas?5%P8w`aS>r(9W*e>~_e>05tt#7TpMBeU$mUegORJ0MQC*i$nf zh_-RK3bG^_qkxmIxO;=GM(%BEDMv5j$KM|>Oro%bH<%}V0zr%jS-~53E}s@d9&x#H zJ8rX+oT}0G(w`Aj0Avc~8$LKv#p(IRFvDOwEeEy>po{;f>SJwxi_MD7-EpT%hlA7m zbl24!yOhZe>37p5+z`K|vG zv#CK@)P`N0ja}HBqJ81=)$IVPEBkYEo6mefS}A@h(FEinBDX2tiM`pL5ghy4J%9Hx z{bRk&DadG$(PHfAh^JoG2o6IyTKHD{5e<%@I=9L^ zQxOF8D2*|v%@LQA-YU%~8^}AB>5Hhf*f8>&=-s_inL4plY__>BTOU3t1Vat9m5v5V 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