## ---- include = FALSE--------------------------------------------------------- knitr::opts_chunk$set(collapse = TRUE,comment = "#>",fig.width=6, fig.height=4, fig.align = "center") ## ----setup, message=FALSE, results='hide'------------------------------------- library(pcds) ## ----------------------------------------------------------------------------- trees<-swamptrees head(trees) Xp<-trees[trees[,3]==1,][,1:2] # coordinates of all live trees Yp<-trees[trees[,3]==0,][,1:2] # coordinates of all dead trees ## ----SwTrfig, fig.cap="The scatterplot of the Live Trees (red circles) and Dead Trees (black squares) in the Swamp Tree Dataset."---- lab.fac=as.factor(trees$live) lab=as.numeric(trees$live) plot(trees[,1:2],col=lab+1,pch=lab,xlab="x",ylab="y",main="Scatter plot of live and dead trees") ## ----SwTrDTfig, eval=F, fig.cap="The scatterplot of the live trees in the swamp trees data and the Delaunay triangulation of dead trees (dashed lines)."---- # Xlim<-range(Xp[,1],Yp[,1]) # Ylim<-range(Xp[,2],Yp[,2]) # xd<-Xlim[2]-Xlim[1] # yd<-Ylim[2]-Ylim[1] # plot(Xp,xlab="x", ylab="y",xlim=Xlim+xd*c(-.05,.05), # ylim=Ylim+yd*c(-.05,.05),pch=".",cex=3,main="Live Trees (solid squares) and Delaunay # Triangulation of Dead Treess") # #now, we add the Delaunay triangulation based on Y points # DT<-interp::tri.mesh(Yp[,1],Yp[,2],duplicate="remove") # interp::plot.triSht(DT, add=TRUE, do.points = TRUE) ## ----eval=F------------------------------------------------------------------- # num.delaunay.tri(Yp) # #> [1] 194 ## ----eval=FALSE--------------------------------------------------------------- # M<-"CC" #try also M<-c(1,1,1) #or M<-c(1,2,3) # Narcs=num.arcsAS(Xp,Yp,M) # Narcs$num.arcs # #> [1] 1849 # # #summary(Narcs) # #plot(Narcs) ## ----eval=FALSE--------------------------------------------------------------- # M<-c(1,1,1) #try also M<-c(1,2,3) #or M<-"CC" # r<-1.5 #try also r<-2 # # Narcs=num.arcsPE(Xp,Yp,r,M) # Narcs$num.arcs # #> [1] 1429 # # #summary(Narcs) # #plot(Narcs) ## ----eval=FALSE--------------------------------------------------------------- # PEarc.dens.test(Xp,Yp,r) #try also PEarc.dens.test(Xp,Yp,r,alt="l") or #PEarc.dens.test(Xp,Yp,r,ch=TRUE) # # #> Large Sample z-Test Based on Arc Density of PE-PCD for Testing Uniformity of 2D Data --- # #> without Convex Hull Correction # #> # #> data: Xp # #> standardized arc density (i.e., Z) = -1.7333, p-value = 0.08304 # #> alternative hypothesis: true (expected) arc density is not equal to 0.005521555 # #> 95 percent confidence interval: # #> 0.003780462 0.005628405 # #> sample estimates: # #> arc density # #> 0.004704434 ## ----eval=FALSE--------------------------------------------------------------- # PEdom.num(Xp,Yp,r,M) # #> $dom.num # #> [1] 198 # #> # #> $ind.mds # #> [1] 8 4 18 6 16 7 11 67 64 17 14 78 82 75 19 60 83 88 87 27 23 28 29 54 94 80 154 148 95 153 # #> [31] 152 47 30 149 144 147 50 101 45 48 143 173 105 109 31 46 117 44 79 168 169 134 140 139 128 113 172 165 161 160 # #> [61] 177 219 187 214 209 126 220 201 208 183 188 125 225 226 224 223 210 213 242 247 200 196 250 282 43 123 241 243 294 258 # #> [91] 283 284 281 289 288 300 304 298 306 308 286 321 278 277 311 314 313 312 276 273 319 317 318 316 320 363 364 339 369 333 # #> [121] 377 331 307 345 346 385 384 379 380 328 375 373 374 383 410 408 414 388 425 423 235 303 398 355 396 381 434 433 460 457 # #> [151] 412 194 329 193 445 458 507 442 514 464 482 517 519 506 541 573 530 532 562 539 491 500 490 533 568 566 590 586 578 569 # #> [181] 588 589 610 565 593 591 557 559 594 602 601 550 555 607 609 614 616 611 # #> # #> $tri.dom.nums # #> [1] 0 1 0 1 1 0 1 0 3 0 0 0 0 0 2 0 2 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 2 0 0 0 1 0 0 1 2 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 3 2 2 0 0 # #> [62] 0 2 0 1 1 0 0 2 0 1 1 0 1 0 2 1 2 2 1 1 2 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 2 1 1 1 0 3 1 1 1 2 0 2 2 2 2 1 0 1 0 2 3 1 2 2 # #> [123] 1 0 1 2 2 2 0 2 0 0 0 0 2 2 0 1 2 1 1 1 2 3 2 1 0 1 1 3 1 3 1 2 1 1 3 3 3 3 1 1 0 1 1 3 2 2 0 2 1 2 3 1 1 0 0 2 2 2 1 1 0 # #> [184] 3 0 2 1 0 2 2 1 1 3 0 # #> # #> PEdom.num.nondeg(Xp,Yp,r) # #> $dom.num # #> [1] 198 # #> # #> $ind.mds # #> [1] 8 4 18 6 11 16 7 67 64 65 14 78 82 75 19 60 83 87 88 27 23 29 28 54 94 80 154 148 95 153 # #> [31] 152 47 30 147 144 149 101 51 48 45 173 143 105 109 32 46 118 44 79 171 169 134 139 140 113 128 172 165 161 160 # #> [61] 177 219 187 214 209 126 220 208 201 183 188 125 226 225 224 223 210 213 218 242 200 196 250 282 123 43 243 241 294 258 # #> [91] 283 284 289 281 288 300 304 298 306 308 286 321 278 277 311 314 313 312 276 273 319 317 316 318 320 364 363 339 369 333 # #> [121] 331 377 346 345 307 385 384 379 380 328 373 375 374 383 410 414 408 388 423 425 235 303 396 398 355 381 433 434 412 457 # #> [151] 460 329 193 194 445 458 507 442 464 482 514 517 519 506 541 573 530 532 562 539 490 491 500 533 568 566 590 586 578 569 # #> [181] 588 589 610 591 565 593 559 557 594 601 602 555 550 607 609 611 614 616 # #> # #> $tri.dom.nums # #> [1] 0 1 0 1 1 0 1 0 3 0 0 0 0 0 2 0 2 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 2 0 0 0 1 0 0 1 2 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 3 2 2 0 0 # #> [62] 0 2 0 1 1 0 0 2 0 1 1 0 1 0 2 1 2 2 1 1 2 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 2 1 1 1 0 3 1 1 1 2 0 2 2 2 2 1 0 1 0 2 3 1 2 2 # #> [123] 1 0 1 2 2 2 0 2 0 0 0 0 2 2 0 1 2 1 1 1 2 3 2 1 0 1 1 3 1 3 1 2 1 1 3 3 3 3 1 1 0 1 1 3 2 2 0 2 1 2 3 1 1 0 0 2 2 2 1 1 0 # #> [184] 3 0 2 1 0 2 2 1 1 3 0 ## ----eval=FALSE--------------------------------------------------------------- # PEdom.num.binom.test(Xp,Yp,r) #try also PEdom.num.binom.test(Xp,Yp,r,alt="g") # # #> Large Sample Binomial Test based on the Domination Number of PE-PCD for Testing Uniformity of 2D # #> Data --- # #> without Convex Hull Correction # #> # #> data: Xp # #> #(domination number is <= 2) = 179, p-value = 1.921e-10 # #> alternative hypothesis: true Pr(Domination Number <=2) is not equal to 0.7413 # #> 95 percent confidence interval: # #> 0.8756797 0.9560803 # #> sample estimates: # #> domination number || Pr(domination number <= 2) # #> 198.0000000 0.9226804 ## ----eval=FALSE--------------------------------------------------------------- # PEdom.num.norm.test(Xp,Yp,r) #try also PEdom.num.norm.test(Xp,Yp,r,alt="g") # # #> Normal Approximation to the Domination Number of PE-PCD for Testing Uniformity of 2D Data --- # #> without Convex Hull Correction # #> # #> data: Xp # #> standardized domination number (i.e., Z) = 5.7689, p-value = 7.977e-09 # #> alternative hypothesis: true expected domination number is not equal to 143.8122 # #> 95 percent confidence interval: # #> 186.0451 209.9549 # #> sample estimates: # #> domination number || Pr(domination number = 3) # #> 198.0000000 0.9226804 ## ----eval=FALSE--------------------------------------------------------------- # M<-c(1,1,1) #try also M<-c(1,2,3) # tau<-1.5 #try also tau<-2, and tau=.5 # # Narcs=num.arcsCS(Xp,Yp,tau,M) # Narcs$num.arcs # #> [1] 955 # # #summary(Narcs) # #plot(Narcs) ## ----eval=FALSE--------------------------------------------------------------- # CSarc.dens.test(Xp,Yp,tau) #try also CSarc.dens.test(Xp,Yp,tau,alt="l") # # #> Large Sample z-Test Based on Arc Density of CS-PCD for Testing Uniformity of 2D Data --- # #> without Convex Hull Correction # #> # #> data: Xp # #> standardized arc density (i.e., Z) = -1.7446, p-value = 0.08106 # #> alternative hypothesis: true (expected) arc density is not equal to 0.003837374 # #> 95 percent confidence interval: # #> 0.002373249 0.003922496 # #> sample estimates: # #> arc density # #> 0.003147873