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smooth.R
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> ### This used to be in example(smooth) before we had package-specific demos
> # Copyright (C) 1997-2009 The R Core Team
>
> require(stats); require(graphics); require(datasets)
> op <- par(mfrow = c(1,1))
> ## The help(smooth) examples:
> example(smooth, package="stats")
smooth> require(graphics)
smooth> ## see also demo(smooth) !
smooth>
smooth> x1 <- c(4, 1, 3, 6, 6, 4, 1, 6, 2, 4, 2) # very artificial
smooth> (x3R <- smooth(x1, "3R")) # 2 iterations of "3"
3R Tukey smoother resulting from smooth(x = x1, kind = "3R")
used 2 iterations
[1] 3 3 3 6 6 4 4 4 2 2 2
smooth> smooth(x3R, kind = "S")
S Tukey smoother resulting from smooth(x = x3R, kind = "S")
changed
[1] 3 3 3 3 4 4 4 4 2 2 2
smooth> sm.3RS <- function(x, ...)
smooth+ smooth(smooth(x, "3R", ...), "S", ...)
smooth> y <- c(1, 1, 19:1)
smooth> plot(y, main = "misbehaviour of \"3RSR\"", col.main = 3)
Hit <Return> to see next plot:
smooth> lines(sm.3RS(y))
smooth> lines(smooth(y))
smooth> lines(smooth(y, "3RSR"), col = 3, lwd = 2) # the horror
smooth> x <- c(8:10, 10, 0, 0, 9, 9)
smooth> plot(x, main = "breakdown of 3R and S and hence 3RSS")
Hit <Return> to see next plot:
smooth> matlines(cbind(smooth(x, "3R"), smooth(x, "S"), smooth(x, "3RSS"), smooth(x)))
smooth> presidents[is.na(presidents)] <- 0 # silly
smooth> summary(sm3 <- smooth(presidents, "3R"))
3R Tukey smoother resulting from
smooth(x = presidents, kind = "3R") ; n = 120
used 4 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 44.0 57.0 54.2 71.0 82.0
smooth> summary(sm2 <- smooth(presidents,"3RSS"))
3RSS Tukey smoother resulting from
smooth(x = presidents, kind = "3RSS") ; n = 120
used 5 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 44.00 57.00 55.45 69.00 82.00
smooth> summary(sm <- smooth(presidents))
3RS3R Tukey smoother resulting from
smooth(x = presidents) ; n = 120
used 7 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
24.00 44.00 57.00 55.88 69.00 82.00
smooth> all.equal(c(sm2), c(smooth(smooth(sm3, "S"), "S"))) # 3RSS === 3R S S
[1] TRUE
smooth> all.equal(c(sm), c(smooth(smooth(sm3, "S"), "3R"))) # 3RS3R === 3R S 3R
[1] TRUE
smooth> plot(presidents, main = "smooth(presidents0, *) : 3R and default 3RS3R")
Hit <Return> to see next plot:
smooth> lines(sm3, col = 3, lwd = 1.5)
smooth> lines(sm, col = 2, lwd = 1.25)
> ## Didactical investigation:
>
> showSmooth <- function(x, leg.x = 1, leg.y = max(x)) {
+ ss <- cbind(x, "3c" = smooth(x, "3", end="copy"),
+ "3" = smooth(x, "3"),
+ "3Rc" = smooth(x, "3R", end="copy"),
+ "3R" = smooth(x, "3R"),
+ sm = smooth(x))
+ k <- ncol(ss) - 1
+ n <- length(x)
+ slwd <- c(1,1,4,1,3,2)
+ slty <- c(0, 2:(k+1))
+ matplot(ss, main = "Tukey Smoothers", ylab = "y ; sm(y)",
+ type= c("p",rep("l",k)), pch= par("pch"), lwd= slwd, lty= slty)
+ legend(leg.x, leg.y,
+ c("Data", "3 (copy)", "3 (Tukey)",
+ "3R (copy)", "3R (Tukey)", "smooth()"),
+ pch= c(par("pch"),rep(-1,k)), col=1:(k+1), lwd= slwd, lty= slty)
+ ss
+ }
> ## 4 simple didactical examples, showing different steps in smooth():
>
> for(x in list(c(4, 6, 2, 2, 6, 3, 6, 6, 5, 2),
+ c(3, 2, 1, 4, 5, 1, 3, 2, 4, 5, 2),
+ c(2, 4, 2, 6, 1, 1, 2, 6, 3, 1, 6),
+ x1))
+ print(t(showSmooth(x)))
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
x 4 6 2 2 6 3 6 6 5 2
3c 4 4 2 2 3 6 6 6 5 2
3 4 4 2 2 3 6 6 6 5 3
3Rc 4 4 2 2 3 6 6 6 5 2
3R 4 4 2 2 3 6 6 6 5 3
sm 4 4 4 3 3 6 6 6 5 3
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 3 2 1 4 5 1 3 2 4 5 2
3c 3 2 2 4 4 3 2 3 4 4 2
3 2 2 2 4 4 3 2 3 4 4 4
3Rc 3 2 2 4 4 3 3 3 4 4 2
3R 2 2 2 4 4 3 3 3 4 4 4
sm 2 2 2 2 3 3 3 3 4 4 4
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 2 4 2 6 1 1 2 6 3 1 6
3c 2 2 4 2 1 1 2 3 3 3 6
3 2 2 4 2 1 1 2 3 3 3 3
3Rc 2 2 2 2 1 1 2 3 3 3 6
3R 2 2 2 2 1 1 2 3 3 3 3
sm 2 2 2 2 2 2 2 3 3 3 3
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 4 1 3 6 6 4 1 6 2 4 2
3c 4 3 3 6 6 4 4 2 4 2 2
3 3 3 3 6 6 4 4 2 4 2 2
3Rc 4 3 3 6 6 4 4 4 2 2 2
3R 3 3 3 6 6 4 4 4 2 2 2
sm 3 3 3 3 4 4 4 4 2 2 2
> par(op)
>
>
> demo(smooth)
demo(smooth)
---- ~~~~~~
Type <Return> to start :
> ### This used to be in example(smooth) before we had package-specific demos
> # Copyright (C) 1997-2009 The R Core Team
>
> require(stats); require(graphics); require(datasets)
> op <- par(mfrow = c(1,1))
> ## The help(smooth) examples:
> example(smooth, package="stats")
smooth> require(graphics)
smooth> ## see also demo(smooth) !
smooth>
smooth> x1 <- c(4, 1, 3, 6, 6, 4, 1, 6, 2, 4, 2) # very artificial
smooth> (x3R <- smooth(x1, "3R")) # 2 iterations of "3"
3R Tukey smoother resulting from smooth(x = x1, kind = "3R")
used 2 iterations
[1] 3 3 3 6 6 4 4 4 2 2 2
smooth> smooth(x3R, kind = "S")
S Tukey smoother resulting from smooth(x = x3R, kind = "S")
changed
[1] 3 3 3 3 4 4 4 4 2 2 2
smooth> sm.3RS <- function(x, ...)
smooth+ smooth(smooth(x, "3R", ...), "S", ...)
smooth> y <- c(1, 1, 19:1)
smooth> plot(y, main = "misbehaviour of \"3RSR\"", col.main = 3)
Hit <Return> to see next plot:
smooth> lines(sm.3RS(y))
smooth> lines(smooth(y))
smooth> lines(smooth(y, "3RSR"), col = 3, lwd = 2) # the horror
smooth> x <- c(8:10, 10, 0, 0, 9, 9)
smooth> plot(x, main = "breakdown of 3R and S and hence 3RSS")
Hit <Return> to see next plot:
smooth> matlines(cbind(smooth(x, "3R"), smooth(x, "S"), smooth(x, "3RSS"), smooth(x)))
smooth> presidents[is.na(presidents)] <- 0 # silly
smooth> summary(sm3 <- smooth(presidents, "3R"))
3R Tukey smoother resulting from
smooth(x = presidents, kind = "3R") ; n = 120
used 4 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 44.0 57.0 54.2 71.0 82.0
smooth> summary(sm2 <- smooth(presidents,"3RSS"))
3RSS Tukey smoother resulting from
smooth(x = presidents, kind = "3RSS") ; n = 120
used 5 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 44.00 57.00 55.45 69.00 82.00
smooth> summary(sm <- smooth(presidents))
3RS3R Tukey smoother resulting from
smooth(x = presidents) ; n = 120
used 7 iterations
Min. 1st Qu. Median Mean 3rd Qu. Max.
24.00 44.00 57.00 55.88 69.00 82.00
smooth> all.equal(c(sm2), c(smooth(smooth(sm3, "S"), "S"))) # 3RSS === 3R S S
[1] TRUE
smooth> all.equal(c(sm), c(smooth(smooth(sm3, "S"), "3R"))) # 3RS3R === 3R S 3R
[1] TRUE
smooth> plot(presidents, main = "smooth(presidents0, *) : 3R and default 3RS3R")
Hit <Return> to see next plot:
smooth> lines(sm3, col = 3, lwd = 1.5)
smooth> lines(sm, col = 2, lwd = 1.25)
> ## Didactical investigation:
>
> showSmooth <- function(x, leg.x = 1, leg.y = max(x)) {
+ ss <- cbind(x, "3c" = smooth(x, "3", end="copy"),
+ "3" = smooth(x, "3"),
+ "3Rc" = smooth(x, "3R", end="copy"),
+ "3R" = smooth(x, "3R"),
+ sm = smooth(x))
+ k <- ncol(ss) - 1
+ n <- length(x)
+ slwd <- c(1,1,4,1,3,2)
+ slty <- c(0, 2:(k+1))
+ matplot(ss, main = "Tukey Smoothers", ylab = "y ; sm(y)",
+ type= c("p",rep("l",k)), pch= par("pch"), lwd= slwd, lty= slty)
+ legend(leg.x, leg.y,
+ c("Data", "3 (copy)", "3 (Tukey)",
+ "3R (copy)", "3R (Tukey)", "smooth()"),
+ pch= c(par("pch"),rep(-1,k)), col=1:(k+1), lwd= slwd, lty= slty)
+ ss
+ }
> ## 4 simple didactical examples, showing different steps in smooth():
>
> for(x in list(c(4, 6, 2, 2, 6, 3, 6, 6, 5, 2),
+ c(3, 2, 1, 4, 5, 1, 3, 2, 4, 5, 2),
+ c(2, 4, 2, 6, 1, 1, 2, 6, 3, 1, 6),
+ x1))
+ print(t(showSmooth(x)))
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
x 4 6 2 2 6 3 6 6 5 2
3c 4 4 2 2 3 6 6 6 5 2
3 4 4 2 2 3 6 6 6 5 3
3Rc 4 4 2 2 3 6 6 6 5 2
3R 4 4 2 2 3 6 6 6 5 3
sm 4 4 4 3 3 6 6 6 5 3
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 3 2 1 4 5 1 3 2 4 5 2
3c 3 2 2 4 4 3 2 3 4 4 2
3 2 2 2 4 4 3 2 3 4 4 4
3Rc 3 2 2 4 4 3 3 3 4 4 2
3R 2 2 2 4 4 3 3 3 4 4 4
sm 2 2 2 2 3 3 3 3 4 4 4
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 2 4 2 6 1 1 2 6 3 1 6
3c 2 2 4 2 1 1 2 3 3 3 6
3 2 2 4 2 1 1 2 3 3 3 3
3Rc 2 2 2 2 1 1 2 3 3 3 6
3R 2 2 2 2 1 1 2 3 3 3 3
sm 2 2 2 2 2 2 2 3 3 3 3
Hit <Return> to see next plot:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
x 4 1 3 6 6 4 1 6 2 4 2
3c 4 3 3 6 6 4 4 2 4 2 2
3 3 3 3 6 6 4 4 2 4 2 2
3Rc 4 3 3 6 6 4 4 4 2 2 2
3R 3 3 3 6 6 4 4 4 2 2 2
sm 3 3 3 3 4 4 4 4 2 2 2