fdc2s | R Documentation |
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(acc=ssi20(x=95), bnd=isc2s(k=12, x=dim(acc)))
acc |
an accessibility matrix for 2D square percolation lattice. |
bnd |
bounds for the iso- or anisotropic set cover. |
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.
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.
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.
The percolation is simulated on 2D square lattice with uniformly weighted sites and the constant parameter p
.
The isotropic cluster is formed from the accessible sites connected with initial sites subset.
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.
A linear regression model for statistical estimation of the mass fractal dimension of a cluster on 2D square lattice with iso- & anisotropic sets cover.
Pavel V. Moskalev
Moskalev P.V., Grebennikov K.V. and Shitov V.V. (2011) 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; in Russian.
fdc3s, fds2s, fds3s
# # # # # # # # # # # # # # # # # # Example 1: Isotropic set cover # # # # # # # # # # # # # # # # # 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")) ## Not run: # # # # # # # # # # # # # # # # # # Example 2: Anisotropic set cover, 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")) ## End(Not run)
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