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######################### triangle.plot ######################################
"triangle.plot" <- function (ta, label = as.character(1:nrow(ta)), clabel = 0, cpoint = 1,
draw.line = TRUE, addaxes = FALSE, addmean = FALSE, labeltriangle = TRUE,
sub = "", csub = 0, possub = "topright", show.position = TRUE,
scale = TRUE, min3 = NULL, max3 = NULL, box = FALSE)
{
seg <- function(a, b, col = par("col")) {
segments(a[1], a[2], b[1], b[2], col = col)
}
nam <- names(ta)
ta <- t(apply(ta, 1, function(x) x/sum(x)))
d <- triangle.param(ta, scale = scale, min3 = min3, max3 = max3)
opar <- par(mar = par("mar"))
on.exit(par(opar))
A <- d$A
B <- d$B
C <- d$C
xy <- d$xy
mini <- d$mini
maxi <- d$maxi
if (show.position)
add.position.triangle(d)
par(mar = c(0.1, 0.1, 0.1, 0.1))
plot(0, 0, type = "n", xlim = c(-0.8, 0.8), ylim = c(-0.6,
1), xlab = "", ylab = "", xaxt = "n", yaxt = "n", asp = 1,
frame.plot = FALSE)
seg(A, B)
seg(B, C)
seg(C, A)
text(C[1], C[2], labels = paste(mini[1]), pos = 2)
text(C[1], C[2], labels = paste(maxi[3]), pos = 4)
if (labeltriangle)
text((A + C)[1]/2, (A + C)[2]/2, labels = nam[1], cex = 1.5,
pos = 2)
text(A[1], A[2], labels = paste(maxi[1]), pos = 2)
text(A[1], A[2], labels = paste(mini[2]), pos = 1)
if (labeltriangle)
text((A + B)[1]/2, (A + B)[2]/2, labels = nam[2], cex = 1.5,
pos = 1)
text(B[1], B[2], labels = paste(maxi[2]), pos = 1)
text(B[1], B[2], labels = paste(mini[3]), pos = 4)
if (labeltriangle)
text((B + C)[1]/2, (B + C)[2]/2, labels = nam[3], cex = 1.5,
pos = 4)
if (draw.line) {
nlg <- 10 * (maxi[1] - mini[1])
for (i in 1:(nlg - 1)) {
x1 <- A + (i/nlg) * (B - A)
x2 <- C + (i/nlg) * (B - C)
seg(x1, x2, col = "lightgrey")
x1 <- A + (i/nlg) * (B - A)
x2 <- A + (i/nlg) * (C - A)
seg(x1, x2, col = "lightgrey")
x1 <- C + (i/nlg) * (A - C)
x2 <- C + (i/nlg) * (B - C)
seg(x1, x2, col = "lightgrey")
}
}
if (cpoint > 0)
points(xy, pch = 20, cex = par("cex") * cpoint)
if (clabel > 0)
scatterutil.eti(xy[, 1], xy[, 2], label, clabel)
if (addaxes) {
pr0 <- dudi.pca(ta, scale = FALSE, scannf = FALSE)$c1
w1 <- triangle.posipoint(apply(ta, 2, mean), mini, maxi)
points(w1[1], w1[2], pch = 16, cex = 2)
a1 <- pr0[, 1]
x1 <- a1[1] * A + a1[2] * B + a1[3] * C
seg(w1 - x1, w1 + x1)
a1 <- pr0[, 2]
x1 <- a1[1] * A + a1[2] * B + a1[3] * C
seg(w1 - x1, w1 + x1)
}
if (addmean) {
m <- apply(ta, 2, mean)
w1 <- triangle.posipoint(m, mini, maxi)
points(w1[1], w1[2], pch = 16, cex = 2)
w2 <- triangle.posipoint(c(m[1], mini[2], 1 - m[1] -
mini[2]), mini, maxi)
w3 <- triangle.posipoint(c(1 - m[2] - mini[3], m[2],
mini[3]), mini, maxi)
w4 <- triangle.posipoint(c(mini[1], 1 - m[3] - mini[1],
m[3]), mini, maxi)
points(w2[1], w2[2], pch = 20, cex = 2)
points(w3[1], w3[2], pch = 20, cex = 2)
points(w4[1], w4[2], pch = 20, cex = 2)
seg(w1, w2)
seg(w1, w3)
seg(w1, w4)
text(w2[1], w2[2], labels = as.character(round(m[1],
digits = 3)), cex = 1.5, pos = 2)
text(w3[1], w3[2], labels = as.character(round(m[2],
digits = 3)), cex = 1.5, pos = 1)
text(w4[1], w4[2], labels = as.character(round(m[3],
digits = 3)), cex = 1.5, pos = 4)
}
if (csub > 0)
scatterutil.sub(sub, csub, possub)
if (box) box()
return(invisible(xy))
}
######################### triangle.posipoint ######################################
"triangle.posipoint" <- function (x, mini, maxi) {
x <- (x - mini)/(maxi - mini)
x <- x/sum(x)
x1 <- (x[2] - x[1])/sqrt(2)
y1 <- (2 * x[3] - x[2] - x[1])/sqrt(6)
return(c(x1, y1))
}
######################### add.position.triangle ######################################
"add.position.triangle" <- function (d) {
par(mar = c(0.1, 0.1, 0.1, 0.1))
w <- matrix(0, 3, 3)
w[1, 1] <- d$mini[1]
w[1, 2] <- d$mini[2]
w[1, 3] <- d$maxi[3]
w[2, 1] <- d$maxi[1]
w[2, 2] <- d$mini[2]
w[2, 3] <- d$mini[3]
w[3, 1] <- d$mini[1]
w[3, 2] <- d$maxi[2]
w[3, 3] <- d$mini[3]
A <- triangle.posipoint(c(0, 0, 1), c(0, 0, 0), c(1, 1, 1))
B <- triangle.posipoint(c(1, 0, 0), c(0, 0, 0), c(1, 1, 1))
C <- triangle.posipoint(c(0, 1, 0), c(0, 0, 0), c(1, 1, 1))
a <- triangle.posipoint(w[1, ], c(0, 0, 0), c(1, 1, 1))
b <- triangle.posipoint(w[2, ], c(0, 0, 0), c(1, 1, 1))
c <- triangle.posipoint(w[3, ], c(0, 0, 0), c(1, 1, 1))
plot(0, 0, type = "n", xlim = c(-0.71, 4 - 0.71), ylim = c(-4 +
0.85, 0.85), xlab = "", ylab = "", xaxt = "n", yaxt = "n",
asp = 1, frame.plot = FALSE)
polygon(c(A[1], B[1], C[1]), c(A[2], B[2], C[2]))
polygon(c(a[1], b[1], c[1]), c(a[2], b[2], c[2]), col = grey(0.75))
par(new = TRUE)
}
######################### triangle.biplot ######################################
"triangle.biplot" <- function (ta1, ta2, label = as.character(1:nrow(ta1)), draw.line = TRUE,
show.position = TRUE, scale = TRUE)
{
seg <- function(a, b, col = 1) {
segments(a[1], a[2], b[1], b[2], col = col)
}
nam <- names(ta1)
ta1 <- t(apply(ta1, 1, function(x) x/sum(x)))
ta2 <- t(apply(ta2, 1, function(x) x/sum(x)))
d <- triangle.param(rbind(ta1, ta2), scale = scale)
opar <- par(mar = par("mar"))
on.exit(par(opar))
A <- d$A
B <- d$B
C <- d$C
xy <- d$xy
mini <- d$mini
maxi <- d$maxi
if (show.position)
add.position.triangle(d)
par(mar = c(0.1, 0.1, 0.1, 0.1))
plot(0, 0, type = "n", xlim = c(-0.8, 0.8), ylim = c(-0.6,
1), xlab = "", ylab = "", xaxt = "n", yaxt = "n", asp = 1,
frame.plot = FALSE)
seg(A, B)
seg(B, C)
seg(C, A)
text(C[1], C[2], labels = paste(mini[1]), pos = 2)
text(C[1], C[2], labels = paste(maxi[3]), pos = 4)
text((A + C)[1]/2, (A + C)[2]/2, labels = nam[1], cex = 1.5,
pos = 2)
text(A[1], A[2], labels = paste(maxi[1]), pos = 2)
text(A[1], A[2], labels = paste(mini[2]), pos = 1)
text((A + B)[1]/2, (A + B)[2]/2, labels = nam[2], cex = 1.5,
pos = 1)
text(B[1], B[2], labels = paste(maxi[2]), pos = 1)
text(B[1], B[2], labels = paste(mini[3]), pos = 4)
text((B + C)[1]/2, (B + C)[2]/2, labels = nam[3], cex = 1.5,
pos = 4)
if (draw.line) {
nlg <- 10 * (maxi[1] - mini[1])
for (i in (1:(nlg - 1))) {
x1 <- A + (i/nlg) * (B - A)
x2 <- C + (i/nlg) * (B - C)
seg(x1, x2, col = "lightgrey")
x1 <- A + (i/nlg) * (B - A)
x2 <- A + (i/nlg) * (C - A)
seg(x1, x2, col = "lightgrey")
x1 <- C + (i/nlg) * (A - C)
x2 <- C + (i/nlg) * (B - C)
seg(x1, x2, col = "lightgrey")
}
}
nl <- nrow(ta1)
for (i in (1:nl)) {
arrows(xy[i, 1], xy[i, 2], xy[i + nl, 1], xy[i + nl,
2], length = 0.1, angle = 15)
}
points(xy[1:nrow(ta1), ])
text(xy[1:nrow(ta1), ], label, pos = 4)
}
######################### triangle.param ######################################
"triangle.param" <- function (ta, scale = TRUE, min3 = NULL, max3 = NULL) {
if (ncol(ta) != 3)
stop("Non convenient data")
if (min(ta) < 0)
stop("Non convenient data")
if ((!is.null(min3)) & (!is.null(max3)))
scale <- TRUE
cal <- matrix(0, 9, 3)
tb <- t(apply(ta, 1, function(x) x/sum(x)))
mini <- apply(tb, 2, min)
maxi <- apply(tb, 2, max)
mini <- (floor(mini/0.1))/10
maxi <- (floor(maxi/0.1) + 1)/10
mini[mini<0] <- 0
maxi[maxi>1] <- 1
if (!is.null(min3))
mini <- min3
if (!is.null(max3))
maxi <- min3
ampli <- maxi - mini
amplim <- max(ampli)
# correction d'un bug trouvé par J. Lobry 15/11/2004
if (!all(ampli==amplim)) {
for (j in 1:3) {
k <- amplim - ampli[j]
while (k > 0) {
if ((k > 0) & (maxi[j] < 1)) {
maxi[j] <- maxi[j] + 0.1
k <- k - 1
}
if ((k > 0) & (mini[j] > 0)) {
mini[j] <- mini[j] - 0.1
k <- k - 1
}
}
}
}
cal[1, 1] <- mini[1]
cal[1, 2] <- mini[2]
cal[1, 3] <- 1 - cal[1, 1] - cal[1, 2]
cal[2, 1] <- mini[1]
cal[2, 2] <- maxi[2]
cal[2, 3] <- 1 - cal[2, 1] - cal[2, 2]
cal[3, 1] <- maxi[1]
cal[3, 2] <- mini[2]
cal[3, 3] <- 1 - cal[3, 1] - cal[3, 2]
cal[4, 1] <- mini[1]
cal[4, 3] <- mini[3]
cal[4, 2] <- 1 - cal[4, 1] - cal[4, 3]
cal[5, 1] <- mini[1]
cal[5, 3] <- maxi[3]
cal[5, 2] <- 1 - cal[5, 1] - cal[5, 3]
cal[6, 1] <- maxi[1]
cal[6, 3] <- mini[3]
cal[6, 2] <- 1 - cal[6, 1] - cal[6, 3]
cal[7, 2] <- mini[2]
cal[7, 3] <- mini[3]
cal[7, 1] <- 1 - cal[7, 2] - cal[7, 3]
cal[8, 2] <- mini[2]
cal[8, 3] <- maxi[3]
cal[8, 1] <- 1 - cal[8, 2] - cal[8, 3]
cal[9, 2] <- maxi[2]
cal[9, 3] <- mini[3]
cal[9, 1] <- 1 - cal[9, 2] - cal[9, 3]
mini <- apply(cal, 2, min)
mini <- round(mini, digits = 4)
maxi <- apply(cal, 2, max)
maxi <- round(maxi, digits = 4)
ampli <- maxi - mini
if (!scale) {
mini <- c(0, 0, 0)
maxi <- c(1, 1, 1)
}
A <- c(-1/sqrt(2), -1/sqrt(6))
B <- c(1/sqrt(2), -1/sqrt(6))
C <- c(0, 2/sqrt(6))
xy <- t(apply(tb, 1, FUN = triangle.posipoint, mini = mini,
maxi = maxi))
# pour avoir en sortie une matrice des coordonnées
dimnames(xy) <- list(row.names(ta),c("x","y"))
return(list(A = A, B = B, C = C, xy = xy, mini = mini, maxi = maxi))
}
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