An Introduction to Scientific Computer Programmingzrw/compshop/R_intro.pdf · 2014-07-07 · Dr. S. Vaughan and Prof. R. Willingale Programming with R Department of Physics and Astronomy

Dr. S. Vaughan and Prof. R. Willingale Department of Physics and Astronomy Programming with R

An Introduction to Scientific Computer Programming


R Programming Workshop An introduction to computer programming Using the R computing environment Creating computer programs Solving problems using a computer Using computers as a tool for:

–  Plotting graphs and pictures – Analysis of data –  Learning maths and physics…


Log on

Click on Start

Click on Program Installer

Scroll down, select Rstudio

Click on install Then close the Program Installer


Programming to do what?

Arithmetic – manipulating numbers Lexical analysis – characters and words Algebra – manipulating symbols Syntax – sentences and grammar Logic – Boolean algebra Procedure – algorithms, decision, repetition


x = 0 0.1000 0.200 0.300 0.400 0.500 0.600 0.70 0.800 0.900 y = 0 0.0997 0.198 0.295 0.388 0.477 0.561 0.64 0.712 0.776




What is R?

R is an open-source environment for –  statistical computing –  visualisation (plotting graphs, pictures…)

R is an excellent general programming environment beyond statistics R is free and freely available

–  http://www.r-project.org/

Download R onto your PC/Mac and use it!


Getting started with R Logon to a UoL computer.

Start ! All Programs ! RStudio [click]

Type commands at the ‘prompt’ in the R ‘console’.



The console – Type new commands here



Editor - Write “scripts” here



Editor - Write “scripts” here Help files, history,

memory manager here



Editor - Write “scripts” here Help files, history,

memory manager here

graphics – Plots appear here


The R Working Directory, and Quitting

> setwd("Rwork") set the working directory

> getwd() get the working directory [1] "Z:/My Documents/Rwork"

> list.files() list files in the working directory

> q() quit R – don’t save workspace

NOTE: empty brackets


Getting Help

From the windows – click “Help” menu at the top of GUI screen – select “R Help”

From the console – type ? plot for help with the “plot” command

From the web - http://www.r-project.org/ Or http://stackoverflow.com/questions/tagged/r


Making the computer do something

> pi [1] 3.141593 > 3*pi [1] 9.424778 > sin(pi/2) [1] 1 > plot(1:20)

Inspect the object called ‘pi’

This is the answer



> pi [1] 3.141593 > 3*pi [1] 9.424778 > sin(pi/2) [1] 1 > plot(1:20)

Evaluate ‘3×pi’ and then inspect the result

This is the answer



> pi [1] 3.141593 > 3*pi [1] 9.424778 > sin(pi/2) [1] 1 > plot(1:20)

Evaluate sin(pi/2), and inspect the result

This is the answer

NOTE: function(…)



> pi [1] 3.141593 > 3*pi [1] 9.424778 > sin(pi/2) [1] 1 > plot(1:20)

Generate a plot using the plot(…) function

NOTE: function(…)


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778

Evaluate this bit

Assign the result to an object called x

type the name of a variable to see its contents


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778 > x <- 1:5 > x [1] 1 2 3 4 5

x is a list (or vector) containing 5 values


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778 > x <- 1:5 > x [1] 1 2 3 4 5 > y <- sin(x) > y [1] 0.8414710 0.9092974 0.1411200 -0.7568025 -0.9589243

computes sin(x) for each value of x


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778 > x <- 1:5 > x [1] 1 2 3 4 5 > y <- sin(x) > y [1] 0.8414710 0.9092974 0.1411200

-0.7568025 -0.9589243 > y[2] [1] 0.9092974

the second element of the object y


Variables, Objects and Assignment > x <- 3*pi > x [1] 9.424778 > x <- 1:5 > x [1] 1 2 3 4 5 > y <- sin(x) > y [1] 0.8414710 0.9092974 0.1411200

-0.7568025 -0.9589243 > y[3] [1] 0.14112

the third element of the object y


Plotting Graphs

> x <- 1:100 > y <- sin(x)*exp(-x/100) > plot(x, y, type="l")

Note: this is the letter l – for line


R Script Files

Edit a script file and save (“mysource.R”) –  File ! New file ! R Script –  File ! Save / Save As (in working directory) –  File ! Open

Source the script file (run the script) > source(“mysource.R”) – Or click on Source button in editor window


Brownian motion & random walks Einstein (1905) developed physical theory of Brownian motion


A 1-dimensional random walk

-4 -3 -2 -1 0 1 2 3 4

start here [x=0] y=0



-4 -3 -2 -1 0 1 2 3 4

randomly jump +1 or -1 now at y=1

move ahead to x=1



-4 -3 -2 -1 0 1 2 3 4

randomly jump +1 or -1 now at y=0

move ahead to x=2



-4 -3 -2 -1 0 1 2 3 4

randomly jump +1 or -1 now at y= -1

move ahead to x=3



-4 -3 -2 -1 0 1 2 3 4

randomly jump +1 or -1 now at y= -2

move ahead to x=4

what happens to y as we keep advancing x…?


# generate n.step steps n.step <- 100 jump <- 1 x <- 0:n.step

# compute the y steps dy <- jump * sample(c(-1, 1), size=n.step,

replace=TRUE) plot(dy)

# compute the cumulative y position y <- c(0, cumsum(dy))

# plot the walk plot(x, y, type="s”)

We are going to write a short program

Click in the “editor” window (top left)

Start typing the following commands

Anything starting with a # symbol is a comment – the computer ignores it

Comments are helpful to the reader/writer






# plot the walk plot(x, y, type="s")

a command may run over more than one line


A (short) random walk


Randomly choose a jump of +1 or -1





# plot the walk plot(x, y, type="s")

Add up all the jumps - cumulative sum


now change number of steps to 10000 and Source again



replace=TRUE) plot(dt)


# plot the walk plot(x, y, type="s”)


A (longer) random walk run (Source) again and again


# plot a line at y=0 abline(h=0, lty=2)

# plot the start and end points points(n.step, y[1], pch=16, cex=1.5) points(n.step, y[n.step+1], pch=16, cex=1.5)

# join with a line the start and end points lines(c(n.step, n.step), c(0, y[n.step+1]))

# compute the distance travelled r <- y[n.step+1] - y[1]

# print on the plot label <- paste("distance=", signif(r, 3)) text(max(x), max(y), labels=label, pos=2)


A (longer) random walk


Brownian motion & random walks Now let’s try in 2 dimensions

Pick a random direction to move in, call it theta

Select this from a uniform distribution from 0 to 2π radians (equal probabilities)

Step a distance (jump=1) in direction theta

Resolve into components of the motion in x and in y


# generate n.step random directions (angles) n.step <- 100 theta <- runif(n.step, 0, 2*pi) jump <- 1

# compute the x and y step sizes dx <- jump * cos(theta) dy <- jump * sin(theta)

# compute the cumulative x and y positions x <- c(0, cumsum(dx)) y <- c(0, cumsum(dy))

# plot the walk plot(x, y, type="l", bty="n", col="red")

Begin a new script file → New file → R Script


# generate n.step random directions (angles) n.step <- 100 theta <- runif(n.step, 0, 2*pi) jump <- 1

# compute the x and y step sizes dx <- jump * cos(theta) dy <- jump * sin(theta)

# compute the cumulative x and y positions x <- c(0, cumsum(dx)) y <- c(0, cumsum(dy))

# plot the walk plot(x, y, type="l", bty="n", col="red")



# plot the start and end points points(x[1], y[1], pch=16, cex=1.5) points(x[n.step+1], y[n.step+1], pch=16,

cex=1.5)

# join the start and end points lines(x[c(1, n.step+1)], y[c(1, n.step+1)],

lwd=3)

# compute the distance from start to end r <- sqrt(x[n.step+1]^2 + y[n.step+1]^2)

# print on the plot label <- paste("distance=", signif(r, 3)) text(max(x), max(y), labels=label, pos=2)



n.step <- 100 n.walks <- 1000 jump <- 1 x <- array(0, dim=n.walks) y <- array(0, dim=n.walks)

for (i in 1:n.walks) { theta <- runif(n.step, 0, 2*pi) dx <- jump * cos(theta) dy <- jump * sin(theta) x[i] <- sum(dx) y[i] <- sum(dy) }

# compute the radial distances r <- sqrt(x^2 + y^2)

# plot the end point of each walk in (x,y) coordinates plot(x, y)

this is a loop - for each of i = 1,2,3,…,n.walks do whatever is {inside}

prepare two arrays to store the outputs

Pythagoras’ theorem



# plot histogram of x's hist(x, breaks=20, col="blue",

border="white", prob=TRUE)

# compare to the Normal curve x.norm <- seq(-50, 50, by=0.2) y.norm <- dnorm(x.norm, mean=0,

sd=sqrt(n.step)*2/pi) lines(x.norm, y.norm, lwd=4)

Still want more…? add this to your 2d script
