## -----------------------------------------------------------------------------
x <- 0:7
y <- 0:7
xy <- expand.grid(x, y)
colnames(xy) <- c("x", "y")
head(xy)


## -----------------------------------------------------------------------------
z <- 2*xy[,1] + 3*xy[,2]
zm <- matrix(z, ncol=8)


## -----------------------------------------------------------------------------
detproc <- function(x, y) {
  z <- 2*x + 3*y
  return(z)
}

v <- detproc(xy[,1], xy[,2])
zm <- matrix(v, ncol=8)


## ----p4-1---------------------------------------------------------------------
plot(x, y, type="n")
text(xy[,1], xy[,2], z)
contour(x, y, zm, add=TRUE, lty=2)


## ----p4-2, fig.width=8, fig.height=3------------------------------------------
library(terra)
r <- rast(xmin=0, xmax=7, ymin=0, ymax=7, ncol=8, nrow=8)
X <- init(r, "x")
Y <- init(r, "y")
par(mfrow=c(1,2))
plot(X, main="x")
plot(Y, main="y")


## -----------------------------------------------------------------------------
Z <- 2*X + 3*Y


## ----p4-3, fig.cap="", fig.width=6, fig.height=5------------------------------
plot(Z)
text(Z, cex=.75)
contour(Z, add=TRUE, labcex=1, lwd=2, col="red")


## ----p4-4, fig.height=5-------------------------------------------------------
set.seed(987)
s <- sample(c(-1, 1), ncell(r), replace=TRUE)
s[1:8]
R <- setValues(r, s)
plot(R)


## ----p4-5, fig.height=5-------------------------------------------------------
Z <- 2*X + 3*Y + R
plot(Z)
text(Z, cex=.75)
contour(Z, add=T, labcex=1, lwd=2, col="red")


## -----------------------------------------------------------------------------
f <- function() {
	s <- sample(c(-1, 1), ncell(r), replace=TRUE)
	S <- setValues(r, s)
	Z <- 2*X + 3*Y + S
	return(Z)
}


## ----p4-6, fig.width=8, fig.height=6.5----------------------------------------
set.seed(777)
par(mfrow=c(2,2), mai=c(0.5,0.5,0.5,0.5))
for (i in 1:4) {
	pattern <- f()
	plot(pattern)
	text(pattern, cex=.75)
	contour(pattern, add=TRUE, labcex=1, lwd=2, col="red")
}


## ----p4-7---------------------------------------------------------------------
csr <- function(n, r=99, plot=FALSE) {
	x <- runif(n, max=r)
	y <- runif(n, max=r)
	if (plot) {
		plot(x, y, xlim=c(0,r), ylim=c(0,r))
	}
}


## ----p4-8, fig.width=6, fig.height=6------------------------------------------
set.seed(0)
par(mfrow=c(2,2), mai=c(.5, .5, .5, .5))
for (i in 1:4) {
	csr(50, plot=TRUE)
}


## -----------------------------------------------------------------------------
events <- 0:10
combinations <- choose(10, events)
prob1 <- (1/8)^events
prob2 <- (7/8)^(10-events)
Pk <- combinations * prob1 * prob2
d <- data.frame(events, combinations, prob1, prob2, Pk)
round(d, 8)
sum(d$Pk)


## -----------------------------------------------------------------------------
b <- dbinom(0:10, 10, 1/8)
round(b, 8)


## -----------------------------------------------------------------------------
set.seed(1234)
x <- runif(50) * 99
y <- runif(50) * 99


## -----------------------------------------------------------------------------
r <- rast(xmin=0, xmax=99, ymin=0, ymax=99, ncol=10, nrow=10)
quads <- as.polygons(r)


## ----p4-9, fig.cap=""---------------------------------------------------------
plot(quads, border="gray", pax=list(las=1))
points(x, y, col="red", pch=20)


## ----p4-10, fig.cap="", fig.width=6, fig.height=5-----------------------------
vxy <- vect(cbind(x,y))
vxy$v <- 1
p <- rasterize(vxy, r, "v", fun=length, background=0)

plot(p)
plot(quads, add=TRUE, border="gray")
points(x, y, pch=20)


## ----p4-12, fig.cap=""--------------------------------------------------------
f <- freq(p)
f
barplot(p)


## ----p4-13, fig.cap=""--------------------------------------------------------
n <- 0:8
prob <- 1 / ncell(r) 
size <- 50
expected <- dbinom(n, size, prob)
round(expected, 5)
plot(n, expected, cex=2, pch="x", col="blue")


## ----p4-15, fig.cap=""--------------------------------------------------------
m <- rbind(f[,3]/100, expected[1:nrow(f)])
bp <- barplot(m, beside=T, names.arg =1:nrow(f), space=c(0.1, 0.5),
   ylim=c(0,0.7), col=c("red", "blue"))
text(bp, m, labels=round(m, 2), pos = 3, cex = .75)
legend(11, 0.7, c("Observed", "Expected"), fill=c("red", "blue"))


## ----p4-16, fig.cap=""--------------------------------------------------------
poisexp <- dpois(0:8, lambda=50/100)
poisexp
plot(expected, poisexp, cex=2)
abline(0,1)


## ----p4-rlines1---------------------------------------------------------------
randomLineInRectangle <- function(xmn=0, xmx=0.8, ymn=0, ymx=0.6, retXY=FALSE) {
	x <- runif(1, xmn, xmx)
	y <- runif(1, ymn, ymx)
	angle <- runif(1, 0, 359.99999999)
	if (angle == 0) {
		# vertical line, tan is infinite
		if (retXY) {
			xy <- rbind(c(x, ymn), c(x, y), c(x, ymx))
			return(xy)
		}
		return(ymx - ymn)
	}
	tang <- tan(pi*angle/180)
	x1 <- max(xmn, min(xmx, x - y / tang))
	x2 <- max(xmn, min(xmx, x + (ymx-y) / tang))
	y1 <- max(ymn, min(ymx, y - (x-x1) * tang))
	y2 <- max(ymn, min(ymx, y + (x2-x) * tang))
	if (retXY) {
		xy <- rbind(c(x1, y1), c(x, y), c(x2, y2))
		return(xy)
	}
	sqrt((x2 - x1)^2 + (y2 - y1)^2)
}



## ----p4-rlines2---------------------------------------------------------------
randomLineInRectangle()
randomLineInRectangle()

set.seed(999)
plot(NA, xlim=c(0, 0.8), ylim=c(0, 0.6), xaxs="i", yaxs="i", xlab="", ylab="", las=1)
for (i in 1:4) {
	xy <- randomLineInRectangle(retXY=TRUE)
	lines(xy, lwd=2, col=i)
	#points(xy, cex=2, pch=20, col=i)
}


## ----p4-rlines3---------------------------------------------------------------
r <- replicate(10000, randomLineInRectangle())
hist(r, breaks=seq(0,1,0.01), xlab="Line length", main="", freq=FALSE)


## ----p4-seats-----------------------------------------------------------------
set.seed(0)
x <- replicate(10000, abs(diff(sample(1:4, 2))))
sum(x==2) / length(x)


## ----p4-19--------------------------------------------------------------------
r <- rast(xmin=0, xmax=1, ymin=0, ymax=1, ncol=8, nrow=8)
p <- as.polygons(r)

chess <- function() {
	s <- sample(c(-1, 1), 64, replace=TRUE)
	values(r) <- s
	plot(r, col=c("black", "white"), legend=FALSE, axes=FALSE, mar=c(1,1,1,1))
	plot(p, add=T, border="gray")
}


## ----p4-20--------------------------------------------------------------------
set.seed(0)
par(mfrow=c(2,2))
for (i in 1:4) {
	chess()
}


## ----p4-21, fig.width=6, fig.height=5-----------------------------------------
r <- rast(xmin=0, xmax=1, ymin=0, ymax=1, ncol=20, nrow=20)
values(r) <- rnorm(ncell(r), 0, 2)
plot(r)
contour(r, add=T)


## ----p4-22, fig.width=6, fig.height=5-----------------------------------------
ra <- focal(r, w=matrix(1/9, nc=3, nr=3), na.rm=TRUE)
ra <- focal(ra, w=matrix(1/9, nc=3, nr=3), na.rm=TRUE)
plot(ra)