我们可以尝试以下方法:
library(cluster)
d <- matrix(c(1,2,3,1,3,2),ncol=2)
e <- ellipsoidhull(d)
eg <- eigen(e$cov)
axes <- sqrt(eg$values)
angle <- atan(eg$vectors[1,1]/eg$vectors[2,1]) # angle of major axis with x axis
# check if the point (xp, yp) belongs to the ellipse with parameters a,b,... with tolerance eps
belongs.to <- function (xp, yp, a, b, x0, y0, alpha, eps=1e-3) {
return(abs((cos(alpha)*(xp-x0)+sin(alpha)*(yp-y0))^2/a^2+(sin(alpha)*(xp-x0)-cos(alpha)*(yp-y0))^2/b^2 - 1) <= eps)
}
# check if the point (xp, yp) is inside the ellipse with parameters a,b,...
is.inside <- function (xp, yp, a, b, x0, y0, alpha) {
return((cos(alpha)*(xp-x0)+sin(alpha)*(yp-y0))^2/a^2+(sin(alpha)*(xp-x0)-cos(alpha)*(yp-y0))^2/b^2 <= 1)
}
# plot ellipse
plot(e$loc, xlim=c(0,4), ylim=c(0,4), main = "ellipsoidhull", xlab='x', ylab='y')
lines(predict(e), col="blue")
points(rbind(e$loc), col = "red", cex = 3, pch = 13)
x0 <- e$loc[1] # centroid locations
y0 <- e$loc[2]
a <- sqrt(e$d2) * axes[1] # major axis length
b <- sqrt(e$d2) * axes[2] # minor axis length
alpha <- angle
xp <- 3
yp <- 2.9
is.inside(xp, yp, a, b, x0, y0, alpha)
# [1] TRUE
points(xp, yp, pch=19, col='green')
xp <- 3
yp <- 3.1
is.inside(xp, yp, a, b, x0, y0, alpha)
# [1] FALSE
points(xp, yp, pch=19, col='blue')
xp <- 3
yp <- 3
belongs.to(xp, yp, a, b, x0, y0, alpha)
# [1] TRUE
points(xp, yp, pch=19, col='pink')
# distance of a point from the center of the ellipse
sqrt((xp-x0)^2+(yp-y0)^2)
太好了!谢谢。你不仅帮助我解决了我的问题,而且还明确了椭圆的de协方差表示与我理解的表示之间的关系。谢谢。我想我可以自己解决距离问题。 – user2345448