Read Chapter 7 to help you complete the questions in this exercise.
1. Create a function to calculate the area of a circle. Test the function by finding the area of a circle with a diameter of 3.4 cm. Can you use it on a vector of data?
# area of a circle
# the equation to calculate the area of a circle is pi * radius^2
circle.area <- function(d){
pi * (d/2)^2
}
# to use your new function
circle.area(10)
# [1] 78.53982
# to test on a vector of diameters
# first create a vector with diameters ranging from 0 to 50 in steps of 10
cir.diam <- seq(from = 0, to = 50, by = 10)
# test your function
circle.area(cir.diam)
# [1] 0.00000 78.53982 314.15927 706.85835 1256.63706 1963.49541
2. Write a function to convert farenheit to centegrade (oC = (oF - 32) x 5/9). Get your function to print out your result in the following format: “Farenheit : value of oF is equivalent to value oC centigrade.”
far.cent <- function(a) {
val <- (a - 32) * 5/9
print(paste("Fahrenheit: ", round(a, digits = 3), "oF", sep = " "), quote = FALSE) # round 3dp
print(paste("Centigrade: ", round(val, digits = 3), "oC", sep = " "), quote = FALSE) # round 3dp
}
# alternative Fahrenheit to centigrade using cat function
far.cent2 <- function(a) {
val <- (a - 32) * 5/9 #calculation
cat("Fahrenheit: ", round(a, digits = 3), "oF", "\n") # use cat function
cat("Centigrade: ", round(val, digits = 3), "oC", "\n")
}
3. Create a vector of normally distributed data, of length 100, mean 35 and standard deviation of 15. Write a function to calculate the mean, median, and range of the vector, print these values out with appropriate labels. Also get the function to plot a histogram (as a proportion) of the values and add a density curve.
# Create a vector of normally distributed data
# length 100, mean 35 and standard deviation of 29
vals <- rnorm(100, 35, 15) # create some norm dist data mean 35, sd = 15
summary.fun <- function(dat){
mymean <- round(mean(dat), digits = 4) # calc mean
mymedian <- round(median(dat), digits = 4) # calc median
mymin <- round(min(dat), digits = 4) # calc min
mymax <- round(max(dat), digits = 4) # calc max
print(paste("mean:", mymean, sep = " "), quote = FALSE) # print mean
print(paste("median:", mymedian, sep = " "), quote = FALSE) # print median
print(paste("range:", "from:", mymin, "to", mymax, sep = " "), quote = FALSE)
dens <- density(dat) # estimate density curve
hist(dat, main = "",type = "l",freq = FALSE) # plot histogram
lines(dens, lty = 1, col = "red") # plot density curve
}
# use the function
summary.fun(vals)
4. Write a function to calculate the median value of a vector of
numbers (yes I know there’s a median() function already but
this is fun!). Be careful with vectors of an even sample size, as you
will have to take the average of the two central numbers (hint: use
modulo %%2 to determine whether the vector is an odd or an even size).
Test your function on vectors with both odd and even sample sizes.
# calculate a median
ourmedian <- function(x){
n <- length(x)
if (n %% 2 == 1) # odd numbers
sort(x)[(n + 1)/2] # find the middle number by adding 1 to length and div 2
else { # even numbers
middletwo <- sort(x)[(n/2) + 0:1] #find the two middle numbers
mean(middletwo)
}
}
# use the function
mydat <- sample(1:50, size = 10, replace = TRUE )
# our function
ourmedian(mydat)
# R median function
median(mydat)
5. You are a population ecologist for the day and wish to investigate the properties of the Ricker model. The Ricker model is defined as:
\[ N_{t+1} = N_{t} exp\left[r\left(1- \frac{N_{t}}{K} \right) \right] \]
5. (cont) Where Nt is the population size at time t, r is the population growth rate and K is the carrying capacity. Write a function to simulate this model so you can conveniently determine the effect of changing r and the initial population size N0. K is often set to 100 by default, but you want the option of being able to change this with your function. So, you will need a function with the following arguments; nzero which sets the initial population size, r which will determine the population growth rate, time which sets how long the simulation will run for and K which we will initially set to 100 by default.
# function to simulate Ricker model
Ricker.model <- function(nzero, r, time, K = 1) {
# sets initial parameters
N <- numeric(time + 1) # creates a real vector of length time+1 to store values of Nt+1
N[1] <- nzero # sets initial population size in first element of N
for (i in 1:time) {
# loops over time
N[i + 1] <- N[i] * exp(r * (1 - N[i]/K))
}
Time <- 0:time # creates vector for x axis
plot(Time, N, type = "o", xlim = c(0, time), xlab = "Time", ylab = "Population size (N)", main = paste("r =", r, sep = " ")) # plots output
}
# To run play around with the different parameters, especially r
Ricker.model(nzero = 0.1, r = 1, time = 100)
End of Exercise 6