Please follow the following exercises to get familiar with R. Parts of the exercises follow A (very) short introduction to R by Paul Torfs & Claudia Brauer, Hydrology and Quantitative Water Management Group Wageningen University, The Netherlands
Compute the difference between 2012 and the year you started at your university and divide this by the difference between 2012 and the year you were born. Multiply this with 100 to get the percentage of your life you have spent at this university. Use brackets if you need them.
(2012 - 2004)/(2012 - 1984) * 100
## [1] 28.57
Find help for the log function.
?log
Repeat Task 1, but with several steps in between. You can give the variables any name you want, but the name has to start with a letter. Additionally, calculate the following:
\[ \frac{5}{5+345} \]
\[ 2 \cdot \sin (90°) \] Mind the conversion between degrees and radians!
\[ \sqrt{16}+\sqrt{25} \]
\[ \frac{\frac{5}{5+345}+2 \cdot \sin (90°)}{\sqrt{16}+\sqrt{25}} \]
atUni <- 2012 - 2004
alive <- 2012 - 1984
atUni/alive * 100
## [1] 28.57
a <- 5/(5 + 345)
a
## [1] 0.01429
b <- 2 * sin(90 * pi/180)
b
## [1] 2
c <- sqrt(16) + sqrt(25)
c
## [1] 9
(a + b)/c
## [1] 0.2238
Compute the sum of 4, 5, 8 and 11 by first combining them into a vector and then using the function sum. What are mean and median of this series?
vec <- c(4, 5, 8, 11)
sum(vec)
## [1] 28
mean(vec)
## [1] 7
median(vec)
## [1] 6.5
Plot 100 random numbers following a Gaussian distribution with mean 11 and standard deviation 42 as a series of connected points and add their the mean as a horizontal grey line. Additionally, plot these random numbers in a histogram (showing densities on the y-axis) and as box plot.
vec <- rnorm(100, 11, 42)
plot(vec, type = "b")
abline(h = mean(vec), col = "gray")
hist(vec, n = 10, freq = F)
boxplot(vec)
Put the numbers 31 to 60 in a vector named p and in a matrix with 6 rows and 5 columns named q. Calculate the row- and column-wise sum of q.
p <- 31:60
q <- matrix(p, 6, 5)
q
## [,1] [,2] [,3] [,4] [,5]
## [1,] 31 37 43 49 55
## [2,] 32 38 44 50 56
## [3,] 33 39 45 51 57
## [4,] 34 40 46 52 58
## [5,] 35 41 47 53 59
## [6,] 36 42 48 54 60
q <- matrix(p, 6, 5, byrow = T)
q
## [,1] [,2] [,3] [,4] [,5]
## [1,] 31 32 33 34 35
## [2,] 36 37 38 39 40
## [3,] 41 42 43 44 45
## [4,] 46 47 48 49 50
## [5,] 51 52 53 54 55
## [6,] 56 57 58 59 60
apply(q, 1, sum)
## [1] 165 190 215 240 265 290
apply(q, 2, sum)
## [1] 261 267 273 279 285
Construct three random standard normal vectors of length 100. Call these vectors x1, x2 and x3. Make a data frame called t with three columns (called Va, Vb and Vc) containing respectively x1, x1+x2 and x1+x2+x3. Call the following functions for this data frame: plot(t) and cov(t). For each column call the function sd. Can you understand the results?
x1 <- rnorm(100)
x2 <- rnorm(100)
x3 <- rnorm(100)
t <- data.frame(Va = x1, Vb = x1 + x2, Vc = x1 + x2 + x3)
str(t)
## 'data.frame': 100 obs. of 3 variables:
## $ Va: num -1.683 -0.239 1.321 -0.417 0.33 ...
## $ Vb: num -1.611 -2.613 0.558 -0.809 0.821 ...
## $ Vc: num -1.418 -2.427 0.814 -0.718 1.52 ...
plot(t)
cov(t)
## Va Vb Vc
## Va 0.8454 0.9047 0.8312
## Vb 0.9047 2.1204 1.9499
## Vc 0.8312 1.9499 2.8123
apply(t, 2, sd)
## Va Vb Vc
## 0.9194 1.4561 1.6770
lapply(t, sd)
## $Va
## [1] 0.9194
##
## $Vb
## [1] 1.456
##
## $Vc
## [1] 1.677
sapply(t, sd)
## Va Vb Vc
## 0.9194 1.4561 1.6770
Compute the mean of the square root of a vector of 100 random numbers. What happens?
smpl <- rnorm(100)
mean(sqrt(smpl))
## Warning: NaNs produced
## [1] NaN
mean(sqrt(abs(smpl)))
## [1] 0.8278
sqrtSmpl <- sqrt(smpl)
## Warning: NaNs produced
sqrtSmpl
## [1] NaN NaN 1.0123 1.4211 1.0484 NaN 0.7968 0.6534 1.2941 1.1250
## [11] NaN 0.6874 0.6137 0.4341 NaN NaN NaN NaN 1.4721 0.5469
## [21] 0.7369 NaN NaN 0.7464 NaN 0.4092 NaN NaN 0.5216 1.0074
## [31] NaN NaN NaN 0.2756 0.6043 NaN 1.4010 0.5813 0.4497 NaN
## [41] 0.8242 NaN 1.0776 NaN 0.8118 1.0131 1.2734 NaN NaN NaN
## [51] 1.2955 0.1381 0.7398 NaN NaN 0.3028 NaN 0.9976 1.2344 NaN
## [61] 1.0481 0.6593 NaN NaN NaN 0.8833 1.3619 NaN 0.7132 NaN
## [71] NaN 0.6165 NaN 0.2820 0.7753 1.3181 NaN 1.1700 0.1144 NaN
## [81] 0.4681 NaN 0.3277 0.1482 1.1542 NaN 1.4893 NaN 0.9412 NaN
## [91] NaN NaN NaN NaN 0.7589 NaN 0.9444 NaN NaN NaN
sqrtSmpl[is.nan(sqrtSmpl)] <- NA
mean(sqrtSmpl)
## [1] NA
mean(sqrtSmpl, na.rm = T)
## [1] 0.8216
Make a vector from 1 to 100. Make a for-loop which runs through the whole vector. Multiply the elements which are smaller than 5 and larger than 90 with 10 and the other elements with 0.1.
x <- 1:100
for (i in 1:length(x)) {
if (x[i] < 5 | x[i] > 90)
x[i] <- x[i] * 5 else x[i] <- x[i] * 0.1
}
x
## [1] 5.0 10.0 15.0 20.0 0.5 0.6 0.7 0.8 0.9 1.0 1.1
## [12] 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
## [23] 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3
## [34] 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4
## [45] 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5
## [56] 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6
## [67] 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7
## [78] 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
## [89] 8.9 9.0 455.0 460.0 465.0 470.0 475.0 480.0 485.0 490.0 495.0
## [100] 500.0
Write a function for the previous Task, so that you can feed it any vector you like (as argument). Use the standard R function length in the specification of the counter.
scaleFun <- function(x) {
for (i in 1:length(x)) {
if (x[i] < 5 | x[i] > 90)
x[i] <- x[i] * 5 else x[i] <- x[i] * 0.1
}
return(x)
}
scaleFun(1:100)
## [1] 5.0 10.0 15.0 20.0 0.5 0.6 0.7 0.8 0.9 1.0 1.1
## [12] 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
## [23] 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3
## [34] 3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4
## [45] 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5
## [56] 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6
## [67] 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7
## [78] 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
## [89] 8.9 9.0 455.0 460.0 465.0 470.0 475.0 480.0 485.0 490.0 495.0
## [100] 500.0
scaleFun(1:10)
## [1] 5.0 10.0 15.0 20.0 0.5 0.6 0.7 0.8 0.9 1.0
Find a suitable marginal distribution for the Nile dataset:
data(Nile)
str(Nile)
## Time-Series [1:100] from 1871 to 1970: 1120 1160 963 1210 1160 1160 813 1230 1370 1140 ...
plot(Nile)
hist(Nile, freq = F)
optFunLogNorm <- function(param) {
-sum(log(dlnorm(as.vector(Nile), param[1], param[2])))
}
lnormFit <- optim(c(1, 1), optFunLogNorm)$par
## Warning: NaNs produced
## Warning: NaNs produced
dlnormFun <- function(x) dlnorm(x, lnormFit[1], lnormFit[2])
# loglik
sum(log(dlnormFun(as.vector(Nile)))) # -654
## [1] -653.9
hist(Nile, freq = F, n = 20)
curve(dlnormFun, add = T, col = "blue")
Install all required packages for the course and take a look at their demos and data.
install.packages("copula")
install.packages("evd")
demo(package="copula")
demo(package="evd")
data(package="copula")
data(package="evd")
library("evd")
data(uccle)
str(uccle)
## 'data.frame': 35 obs. of 4 variables:
## $ day : num 33.8 27.7 60 24 72.3 50.7 18.7 41.2 26.6 27.2 ...
## $ hour: num 14 12.8 12.9 11.9 20.6 29.1 6.2 21.1 11.2 18 ...
## $ tmin: num 6.5 8.5 5 8.4 13.2 11.9 3.8 13 11.1 13 ...
## $ min : num 2.5 1 0.5 0.9 1.5 4.4 1 3 3.3 2 ...
hist(uccle$hour)
Locate your favourite data set you might want to use throughout the course and load it into R. Make sure to save it as a clean .RData file. Mind your current working directory. Set up a new RStudio project for the upcoming week.
triples <- read.csv("simulatedTriples.csv")
save(triples, file = "myData.RData")
Install optional packages:
install.packages("sp")
install.packages("spacetime")
install.packages("VineCopula")
install.packages("rgl")
install.packages("spcopula", repos="http://R-Forge.R-project.org")
check the demo doing a subset of a multivariate return period analysis in the spcopula package:
library(spcopula)
demo("MRP")