################################################## Exercise sheet 1

#####  Exercise 1 - Exploring a spatial point pattern

# load package splancs
library(splancs)

# load dataset southlancs contained in the package
data(southlancs)
head(southlancs)

# extract larynx cases and their locations  
larynx<-southlancs[southlancs[,3]==1,]
loclarynx<-cbind(larynx$x,larynx$y)

# plot their locations
plot(loclarynx,xlab="eastings",ylab="northings",main="Locations of larynx cancer cases",pch="+",col="red")

# borders of the study area are given as a polygon
polymap(southlancs.bdy,border="grey")

# estimate kernel density - different bandwidths
k1<-kernel2d(pts=loclarynx,poly=southlancs.bdy,h0=100,nx=100,ny=100)
k2<-kernel2d(pts=loclarynx,poly=southlancs.bdy,h0=500,nx=100,ny=100)
k3<-kernel2d(pts=loclarynx,poly=southlancs.bdy,h0=1000,nx=100,ny=100)
k4<-kernel2d(pts=loclarynx,poly=southlancs.bdy,h0=2000,nx=100,ny=100)

# plot the densities, using contour or image
par(mfrow=c(2,2))
contour(k1,nlevels=15,main="Bandwidth=100")
contour(k2,nlevels=15,main="Bandwidth=500")
contour(k3,nlevels=15,main="Bandwidth=1000")
contour(k4,nlevels=15,main="Bandwidth=2000")

par(mfrow=c(2,2))
image(k1,col=grey(seq(0.8,0,-0.1)),main="Bandwidth=100")
image(k2,col=grey(seq(0.8,0,-0.1)),main="Bandwidth=500")
image(k3,col=grey(seq(0.8,0,-0.1)),main="Bandwidth=1000")
image(k4,col=grey(seq(0.8,0,-0.1)),main="Bandwidth=2000")


# add location of the old incinerator to the plot
old.incinerator
image(k4,col=grey(seq(0.8,0,-0.1)),main="Bandwidth=2000")
points(old.incinerator,pch="+",col="red")



####### Exercise 2 - Distance to an incinerator, Poisson regression analysis
# read in dataset newyork.txt
newyork<-read.table("newyork.txt",header=TRUE)
names(newyork)

# location of the population centroids
locnewyork<-cbind(newyork[,1],newyork[,2])

plot(locnewyork,xlab="xcoord",ylab="ycoord",main="Population Centroids",pch="+")
# add incinerator to the plot
points(-0.14,-67.19,col="red")

# compute distance from each population centroid to the incinerator using rdist
library(fields)
monarch<-matrix(c(-0.14,-67.19),nrow=1,ncol=2) # to use rdist(), this must be a matrix
dm<-rdist(locnewyork,monarch)


#(*) write a function which calculates the Euklidean distance between two locations
euklid<-function(loc1,loc2){
d<-sqrt(sum((loc1-loc2)^2))
return(d)}

disteuklid<-rep(0,790)
for (i in 1:790){
disteuklid[i]<-euklid(locnewyork[i,],monarch)}


# poisson regression
# calculate the inverse distance
invdist<-1/dm

poisson.glm<-glm(newyork$ncases~invdist+offset(log(newyork$npopulation)),family="poisson")

summary(poisson.glm)


########### Exercise 3 - Mapping shapefiles in R
# load the library maptools 
library(maptools)

# read in the shapefile Switzerland
swissmap<-readShapeSpatial("switzerland/switzerland",IDvar="BEZIRKSNR")

# plot a map of all Swiss regions
plot(swissmap)

# define a vector with the ID's of the Swiss lakes
lake<-c(100,200,300,500,1000,1400,1700,1900,2000,2100,2200,2300,2400)

# define a color vector assining different colors to lakes and regions
colors<-ifelse(swissmap$BEZIRKSNR%in%lake,"blue","yellow")

# plot the Swiss map with regions and lakes
plot(swissmap,col=colors)