## ---- include = FALSE--------------------------------------------------------- knitr::opts_chunk$set(collapse = TRUE,comment = "#>",fig.width=6, fig.height=4, fig.align = "center") ## ----setup, message=FALSE, results='hide'------------------------------------- library(pcds) ## ----SPch1-------------------------------------------------------------------- A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C) n<-5 #try also n<-10, 20, 50 or 100 ## ----CSR1T, eval=F, fig.cap="Scatterplot of the uniform points in the triangle $T=T(A,B,C)$ with vertices $A=(1,1)$, $B=(2,0)$, and $C=(1.5,2)$."---- # set.seed(123) # Xdt<-runif.tri(n,Tr) # Xdt # #> Call: # #> runif.tri(n = n, tri = Tr) # #> # #> Type: # #> [1] "Uniform Distribution in the Triangle with Vertices (1,1), (2,0) and (1.5,2)" # summary(Xdt) # #> Call: # #> runif.tri(n = n, tri = Tr) # #> # #> Type of the Pattern : [1] "Uniform Distribution in the Triangle with Vertices (1,1), (2,0) and (1.5,2)" # #> # #> Study Window # #> range in x-coordinate = 1 2 # #> range in y-coordinate = 0 2 # #> # #> Vertices of the Support of the Uniform Distribution # #> [,1] [,2] # #> A 1.0 1 # #> B 2.0 0 # #> C 1.5 2 # #> # #> 5 uniform points in the triangle with vertices (1,1), (2,0) and (1.5,2) # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> [1,] 1.408977 1.7660348 # #> [2,] 1.940467 0.0911130 # #> [3,] 1.528105 1.7848381 # #> [4,] 1.551435 0.9132295 # #> [5,] 1.677571 1.1452668 # #> # #> Number of points # #> nx ny # #> 5 3 # #> nx : the number of uniform points # #> ny : the number of vertices of the support region # plot(Xdt) ## ----SPch2-------------------------------------------------------------------- nx<-10; ny<-5 #try also nx<-40; ny<-5 or nx<-100; #try also nx<-1000; ny<-10; set.seed(1) Yp<-cbind(runif(ny,0,10),runif(ny,0,10)) ## ----CSRmT, fig.cap="Scatterplot of the uniform $X$ points in the Delaunay triangles based on 5 $Y$ points."---- Xdt<-runif.multi.tri(nx,Yp) #data under CSR in the convex hull of Ypoints Xdt summary(Xdt) plot(Xdt) ## ----SPch3, eval=F------------------------------------------------------------ # set.seed(11) # A<-sample(1:12,3); B<-sample(1:12,3); C<-sample(1:12,3); D<-sample(1:12,3) # tetra<-rbind(A,B,C,D)/6 # n<-5 #try also n<-10, 20, 50, or 100 ## ----CSR1th, eval=F, fig.cap="Scatterplot of the uniform $X$ points in the tetrahedron $T=T(A,B,C,D)$."---- # Xdt<-runif.tetra(n,tetra) # Xdt # #> Call: # #> runif.tetra(n = n, th = tetra) # #> # #> Type: # #> [1] "Uniform Distribution in the Tetrahedron with Vertices (1.67,0.33,1.33), (1.5,0.17,0.83), (2,1,0.83) and (1,1.17,0.83)" # summary(Xdt) # #> Call: # #> runif.tetra(n = n, th = tetra) # #> # #> Type of the Pattern : [1] "Uniform Distribution in the Tetrahedron with Vertices (1.67,0.33,1.33), (1.5,0.17,0.83), (2,1,0.83) and (1,1.17,0.83)" # #> # #> Study Window # #> range in x-coordinate = 1 2 # #> range in y-coordinate = 0.1666667 1.166667 # #> # #> Vertices of the Support of the Uniform Distribution # #> [,1] [,2] [,3] # #> A 1.666667 0.3333333 1.3333333 # #> B 1.500000 0.1666667 0.8333333 # #> C 2.000000 1.0000000 0.8333333 # #> D 1.000000 1.1666667 0.8333333 # #> # #> 5 uniform points in the tetrahedron with vertices (1.67,0.33,1.33), (1.5,0.17,0.83), (2,1,0.83) and (1,1.17,0.83) # #> (first 6 or fewer are printed) # #> [,1] [,2] [,3] # #> [1,] 1.398149 0.6715843 0.9971730 # #> [2,] 1.642032 0.4435400 0.8851113 # #> [3,] 1.502856 0.7644274 1.0461309 # #> [4,] 1.425548 0.5928684 0.9355892 # #> [5,] 1.239314 0.9320898 0.9298472 # #> # #> Number of points # #> nx ny # #> 5 4 # #> nx is the number of Uniform points # #> ny is the number of vertices of the support region # plot(Xdt) ## ----SPch4-------------------------------------------------------------------- A<-c(1,1); B<-c(2,0); C<-c(1.5,7/3); Tr<-rbind(A,B,C) del<-.4 n<-10 #try also n<-100 or 1000 ## ----seg1T, eval=F, fig.cap="Scatterplot of the points segregated (in a type I fashion) from the vertices of the triangle $T=T(A,B,C)$ with vertices $A=(1,1)$, $B=(2,0)$, and $C=(1.5,2)$."---- # Xdt<-rseg.tri(n,Tr,del) # Xdt # #> Call: # #> rseg.tri(n = n, tri = Tr, delta = del) # #> # #> Type: # #> [1] "Type I Segregation of 10 points in the triangle with vertices (1,1), (2,0) and (1.5,2.33) and exclusion parameter delta = 0.4" # summary(Xdt) # #> Call: # #> rseg.tri(n = n, tri = Tr, delta = del) # #> # #> Type of the Pattern # #> [1] "Type I Segregation of 10 points in the triangle with vertices (1,1), (2,0) and (1.5,2.33) and exclusion parameter delta = 0.4" # #> # #> Parameters of the Pattern # #> exclusion parameter # #> 0.4 # #> # #> Study Window # #> range in x-coordinate = 1 2 # #> range in y-coordinate = 0 2.333333 # #> # #> Generated Points from Pattern of Type I Segregation of One Class from Vertices of the Triangle # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> pnt 1.587007 0.5205062 # #> pnt 1.409048 0.9539932 # #> pnt 1.669594 0.7064556 # #> pnt 1.523988 0.5721596 # #> pnt 1.271635 1.6545486 # #> pnt 1.674897 1.3032453 # #> # #> Number of points: # #> nx ny # #> 10 3 # #> nx = number of generated points according to the pattern # #> ny = number of reference (i.e. Y) points # plot(Xdt) ## ----segI--------------------------------------------------------------------- ny<-5; set.seed(1) Yp<-cbind(runif(ny),runif(ny)) del<-.4 nx<-10; #try also nx<-100 or 1000; ## ----segmT, fig.cap="Scatterplot of the $X$ points segregated (in a type I fashion) from the $Y$ points."---- Xdt<-rseg.multi.tri(nx,Yp,del) Xdt summary(Xdt) plot(Xdt) ## ----------------------------------------------------------------------------- nx<-10; #try also nx<-100 or 1000; ny<-5 e<-.15; ## ----SPch5, eval=F------------------------------------------------------------ # #with default bounding box (i.e., unit square) # set.seed(1) # Yp<-cbind(runif(ny),runif(ny)) ## ----segmTcirc, eval=F, fig.cap="Scatterplot of the $X$ points segregated (in a circular fashion) from the $Y$ points in the unit square."---- # Xdt<-rseg.circular(nx,Yp,e) # Xdt # #> Call: # #> rseg.circular(n = nx, Yp = Yp, e = e) # #> # #> Type: # #> [1] "Segregation of 10 X points from 5 Y points with circular exclusion parameter e = 0.15" # summary(Xdt) # #> Call: # #> rseg.circular(n = nx, Yp = Yp, e = e) # #> # #> Type of the Pattern # #> [1] "Segregation of 10 X points from 5 Y points with circular exclusion parameter e = 0.15" # #> # #> Parameters of the Pattern # #> exclusion parameter # #> 0.15 # #> # #> Study Window # #> range in x-coordinate = 0.05168193 1.058208 # #> range in y-coordinate = -0.08821373 1.094675 # #> # #> Generated Points from Pattern of Segregation of Class X from Class Y # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> [1,] 0.82654723 0.50050923 # #> [2,] 0.77398352 1.08510108 # #> [3,] 0.99248692 0.16272732 # #> [4,] 0.70760843 0.06030401 # #> [5,] 0.32064644 0.36851638 # #> [6,] 0.06515965 0.36410878 # #> # #> Number of points: # #> nx ny # #> 10 5 # #> nx = number of generated points according to the pattern # #> ny = number of reference (i.e. Y) points # plot(Xdt,asp=1) ## ----SPch6-------------------------------------------------------------------- A<-c(1,1); B<-c(2,0); C<-c(1.5,7/3); Tr<-rbind(A,B,C) del<-.4 n<-5 #try also n<-100 or 1000 ## ----asc1T, eval=F, fig.cap="Scatterplot of the points associated (in a type I fashion) with the vertices of the triangle $T=T(A,B,C)$ with vertices $A=(1,1)$, $B=(2,0)$, and $C=(1.5,2)$."---- # Xdt<-rassoc.tri(n,Tr,del) # Xdt # #> Call: # #> rassoc.tri(n = n, tri = Tr, delta = del) # #> # #> Type: # #> [1] "Type I Association of 5 points in the triangle with vertices (1,1), (2,0) and (1.5,2.33) with attraction parameter delta = 0.4" # summary(Xdt) # #> Call: # #> rassoc.tri(n = n, tri = Tr, delta = del) # #> # #> Type of the Pattern # #> [1] "Type I Association of 5 points in the triangle with vertices (1,1), (2,0) and (1.5,2.33) with attraction parameter delta = 0.4" # #> # #> Parameters of the Pattern # #> attraction parameter # #> 0.4 # #> # #> Study Window # #> range in x-coordinate = 1 2 # #> range in y-coordinate = 0 2.333333 # #> # #> Generated Points from Pattern of Type I Association of One Class with Vertices of the Triangle # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> pnt 1.529720 1.8418312 # #> pnt 1.477620 2.0094888 # #> pnt 1.478545 1.7880582 # #> pnt 1.476351 2.0817961 # #> pnt 1.757087 0.4729486 # #> # #> Number of points: # #> nx ny # #> 5 3 # #> nx = number of generated points according to the pattern # #> ny = number of reference (i.e. Y) points # plot(Xdt) ## ----SPch7-------------------------------------------------------------------- ny<-5; set.seed(1) Yp<-cbind(runif(ny),runif(ny)) del<-.4 nx<-10; #try also nx<-100 or 1000; ## ----ascmT, fig.cap="Scatterplot of the $X$ points associated (in a type I fashion) with the $Y$ points."---- Xdt<-rassoc.multi.tri(nx,Yp,del) Xdt summary(Xdt) plot(Xdt) ## ----SPch8, eval=F------------------------------------------------------------ # ny<-5; # e<-.15; # #with default bounding box (i.e., unit square) # set.seed(1) # Yp<-cbind(runif(ny),runif(ny)) # nx<-10; #try also nx<-100 or 1000; ## ----ascmTcirc, eval=F, fig.cap="Scatterplot of the $X$ points associated (in a circular fashion) with the $Y$ points."---- # Xdt<-rassoc.circular(nx,Yp,e) # Xdt # #> Call: # #> rassoc.circular(n = nx, Yp = Yp, e = e) # #> # #> Type: # #> [1] "Association of 10 points with 5 Y points with circular attraction parameter e = 0.15" # summary(Xdt) # #> Call: # #> rassoc.circular(n = nx, Yp = Yp, e = e) # #> # #> Type of the Pattern # #> [1] "Association of 10 points with 5 Y points with circular attraction parameter e = 0.15" # #> # #> Parameters of the Pattern # #> attraction parameter # #> 0.15 # #> # #> Study Window # #> range in x-coordinate = 0.05168193 1.058208 # #> range in y-coordinate = -0.08821373 1.094675 # #> # #> Generated Points from Pattern of Association of one Class with Class Y # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> [1,] 0.4341972 0.8314177 # #> [2,] 0.5369080 0.6210061 # #> [3,] 0.8844546 0.7025082 # #> [4,] 0.8779856 0.6771867 # #> [5,] 0.8397240 0.5659668 # #> [6,] 0.1228222 0.0294437 # #> # #> Number of points: # #> nx ny # #> 10 5 # #> nx = number of generated points according to the pattern # #> ny = number of reference (i.e. Y) points # plot(Xdt,asp=1) ## ----SPch9, eval=F------------------------------------------------------------ # ny<-5; # e<-.15; # #with default bounding box (i.e., unit square) # set.seed(1) # Yp<-cbind(runif(ny),runif(ny)) # nx<-10; #try also nx<-100 or 1000; ## ----ascmTmat, eval=F, fig.cap="Scatterplot of the $X$ points associated (in a Matérn-like fashion) with the $Y$ points."---- # Xdt<-rassoc.matern(nx,Yp,e) # Xdt # #> Call: # #> rassoc.matern(n = nx, Yp = Yp, e = e) # #> # #> Type: # #> [1] "Matern-like Association of 10 points with 5 Y points with circular attraction parameter e = 0.15" # summary(Xdt) # #> Call: # #> rassoc.matern(n = nx, Yp = Yp, e = e) # #> # #> Type of the Pattern # #> [1] "Matern-like Association of 10 points with 5 Y points with circular attraction parameter e = 0.15" # #> # #> Parameters of the Pattern # #> attraction parameter # #> 0.15 # #> # #> Study Window # #> range in x-coordinate = 0.05168193 1.058208 # #> range in y-coordinate = -0.08821373 1.094675 # #> # #> Generated Points from Pattern of Matern-like Association of one Class with Class Y # #> (first 6 or fewer are printed) # #> [,1] [,2] # #> [1,] 0.56278796 0.75345984 # #> [2,] 0.66528156 0.66859254 # #> [3,] 0.32528878 0.83448201 # #> [4,] 0.08626992 0.07483616 # #> [5,] 0.13700582 0.06441234 # #> [6,] 0.42942439 0.83624485 # #> # #> Number of points: # #> nx ny # #> 10 5 # #> nx = number of generated points according to the pattern # #> ny = number of reference (i.e. Y) points # plot(Xdt,asp=1)