fdc2s(SECP)
fdc2s()所属R语言包：SECP
Mass fractal dimension of a 2D cluster
质量分形维数的二维簇
译者：生物统计家园网 机器人LoveR
描述----------Description----------
fdc2s() function uses a linear regression model for statistical estimation of the mass fractal dimension of a cluster on 2D square lattice with iso- & anisotropic sets cover.
fdc2s()函数使用线性回归模型的二维正方晶格上的丛集异各向异性套盖的质量分形维数的统计估计。
用法----------Usage----------
fdc2s(acc=ssi20(x=95), bnd=isc2s(k=12, x=dim(acc)))
参数----------Arguments----------
参数：acc
an accessibility matrix for 2D square percolation lattice.
可达性矩阵二维方形渗透格。
参数：bnd
bounds for the iso- or anisotropic set cover.
异或各向异性集合覆盖的界限。
Details
详细信息----------Details----------
The mass fractal dimension for a cluster is equal to the coefficient of linear regression between log(n) and log(r), where n is an absolute frequency of the total cluster sites which are bounded elements of iso- & anisotropic sets cover.
的质量的分形维数为聚类是等于log(n)和log(r)，其中n是一个绝对频率是有界的异元素的总簇网站之间的线性回归系数和各向异性套覆盖。
The isotropic set cover on 2D square lattice is formed from scalable squares with variable sizes 2r+1 and a fixed point in the lattice center.
二维正方晶格上的各向同性集合覆盖形成具有可变大小的2r+1中的固定点的晶格中心从可伸缩的平方。
The anisotropic set cover on 2D square lattice is formed from scalable rectangles with variable sizes r+1 and a fixed edge along the lattice boundary.
二维正方晶格的各向异性盖是由可变大小的可扩展的矩形r+1和一个固定的晶格边界的边缘。
The percolation is simulated on 2D square lattice with uniformly weighted sites and the constant parameter p.
的渗透是模拟二维正方晶格均匀加权的网站和常量参数p。
The isotropic cluster is formed from the accessible sites connected with initial sites subset.
的各向同性聚类形成从与初始网站子集连接的可访问的站点。
If acc[e]<p then e is accessible site; if acc[e]==1 then e is non-accessible site; if acc[e]==2 then e belong to a sites cluster.
如果acc[e]<p然后e是可访问的网站;如果acc[e]==1然后e是不可访问的网站，如果acc[e]==2然后e属于一个网站聚类。
值----------Value----------
A linear regression model for statistical estimation of the mass fractal dimension of a cluster on 2D square lattice with iso- & anisotropic sets cover.
线性回归模型的聚类二维正方晶格与异各向异性套盖的质量分形维数的统计估计。
（作者）----------Author(s)----------
Pavel V. Moskalev
参考文献----------References----------
Statistical estimation of percolation cluster parameters. Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies, No.1 (January-June), pp.29-35; arXiv:1105.2334v1 [cond-mat.stat-mech]; in Russian.
参见----------See Also----------
fdc3s, fds2s, fds3s
fdc3s，fds2s，fds3s
实例----------Examples----------
# # # # # # # # # # # # # # # # #[＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃]
# Example 1: Isotropic set cover[例1：各向同性集合覆盖]
# # # # # # # # # # # # # # # # #[＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃]
pc <- .592746
p1 <- pc - .03
p2 <- pc + .03
lx <- 33; ss <- (lx+1)/2
set.seed(20120627); ac1 <- ssi20(x=lx, p=p1)
set.seed(20120627); ac2 <- ssi20(x=lx, p=p2)
bnd <- isc2s(k=9, x=dim(ac1))
fd1 <- fdc2s(acc=ac1, bnd=bnd)
fd2 <- fdc2s(acc=ac2, bnd=bnd)
n1 <- fd1$model[,"n"]; n2 <- fd2$model[,"n"]
r1 <- fd1$model[,"r"]; r2 <- fd2$model[,"r"]
rr <- seq(min(r1)-.2, max(r1)+.2, length=100)
nn1 <- predict(fd1, newdata=list(r=rr), interval="conf")
nn2 <- predict(fd2, newdata=list(r=rr), interval="conf")
s1 <- paste(round(confint(fd1)[2,], digits=3), collapse=", ")
s2 <- paste(round(confint(fd2)[2,], digits=3), collapse=", ")
x <- y <- seq(lx)
par(mfrow=c(2,2), mar=c(3,3,3,1), mgp=c(2,1,0))
image(x, y, ac1, cex.main=1,
main=paste("Isotropic set cover and a 2D cluster of\n",
"sites with (1,0)-neighborhood and p=",
round(p1, digits=3), sep=""))
rect(bnd["x1",], bnd["y1",], bnd["x2",], bnd["y2",])
abline(h=ss, lty=2); abline(v=ss, lty=2)
image(x, y, ac2, cex.main=1,
main=paste("Isotropic set cover and a 2D cluster of\n",
"sites with (1,0)-neighborhood and p=",
round(p2, digits=3), sep=""))
rect(bnd["x1",], bnd["y1",], bnd["x2",], bnd["y2",])
abline(h=ss, lty=2); abline(v=ss, lty=2)
plot(r1, n1, pch=3, ylim=range(c(n1,n2)), cex.main=1,
main=paste("0.95 confidence interval for the mass\n",
"fractal dimension is (",s1,")", sep=""))
matlines(rr, nn1, lty=c(1,2,2), col=c("black","red","red"))
plot(r2, n2, pch=3, ylim=range(c(n1,n2)), cex.main=1,
main=paste("0.95 confidence interval for the mass\n",
"fractal dimension is (",s2,")", sep=""))
matlines(rr, nn2, lty=c(1,2,2), col=c("black","red","red"))
# # # # # # # # # # # # # # # # #[＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃]
# Example 1: Anisotropic set cover, dir=2[例1：各向异性集合覆盖，DIR = 2]
# # # # # # # # # # # # # # # # #[＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃＃]
pc <- .592746
p1 <- pc - .03
p2 <- pc + .03
lx <- 33; ss <- (lx+1)/2; ssy <- seq(lx+2, 2*lx-1)
set.seed(20120627); ac1 <- ssi20(x=lx, p=p1, set=ssy, all=FALSE)
set.seed(20120627); ac2 <- ssi20(x=lx, p=p2, set=ssy, all=FALSE)
bnd <- asc2s(k=9, x=dim(ac1), dir=2)
fd1 <- fdc2s(acc=ac1, bnd=bnd)
fd2 <- fdc2s(acc=ac2, bnd=bnd)
n1 <- fd1$model[,"n"]; n2 <- fd2$model[,"n"]
r1 <- fd1$model[,"r"]; r2 <- fd2$model[,"r"]
rr <- seq(min(r1)-.2, max(r1)+.2, length=100)
nn1 <- predict(fd1, newdata=list(r=rr), interval="conf")
nn2 <- predict(fd2, newdata=list(r=rr), interval="conf")
s1 <- paste(round(confint(fd1)[2,], digits=3), collapse=", ")
s2 <- paste(round(confint(fd2)[2,], digits=3), collapse=", ")
x <- y <- seq(lx)
par(mfrow=c(2,2), mar=c(3,3,3,1), mgp=c(2,1,0))
image(x, y, ac1, cex.main=1,
main=paste("Anisotropic set cover and a 2D cluster of\n",
"sites with (1,0)-neighborhood and p=",
round(p1, digits=3), sep=""))
rect(bnd["x1",], bnd["y1",], bnd["x2",], bnd["y2",])
abline(v=ss, lty=2)
image(x, y, ac2, cex.main=1,
main=paste("Anisotropic set cover and a 2D cluster of\n",
"sites with (1,0)-neighborhood and p=",
round(p2, digits=3), sep=""))
rect(bnd["x1",], bnd["y1",], bnd["x2",], bnd["y2",])
abline(v=ss, lty=2)
plot(r1, n1, pch=3, ylim=range(c(n1,n2)), cex.main=1,
main=paste("0.95 confidence interval for the mass\n",
"fractal dimension is (",s1,")", sep=""))
matlines(rr, nn1, lty=c(1,2,2), col=c("black","red","red"))
plot(r2, n2, pch=3, ylim=range(c(n1,n2)), cex.main=1,
main=paste("0.95 confidence interval for the mass\n",
"fractal dimension is (",s2,")", sep=""))
matlines(rr, nn2, lty=c(1,2,2), col=c("black","red","red"))
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-29 23:53:19
