# Kerby Shedden October, Overview of R

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Kerby Shedden October, 2007 Overview of R

2 R R is a programming language for statistical computing, data analysis, and graphics. It is a re-implementation of the S language, which was developed in the 1980 s. R is a high level language. The core language has some superficial similarities to C, but many things are handled automatically in R that are not in C. R is one of the main computing tools used in statistical education and research. It is also widely used for data analysis and numerical computing in other fields of scientific research. 2

3 Using this document Rather than simply reading this document, you will learn R much more quickly if you type the code examples (contained in boxes) into R. Even better, experiment with variations of the code examples to see what happens. 3

4 Running R Interactive: You can use R interactively, by typing short programs directly at the R prompt. Sourcing scripts: Most of the time you should write your programs using a text editor (like WordPad on a Windows machine). Save your program as a text file with extension.r, like myprog.r, then run your program by typing source( myprog.r ) at the R prompt. You will probably need to set the directory path to point to the directory where you saved your script. Make sure you save your programs as text files. 4

5 Variables in R A variable is a symbol, like x, that holds a value. The value can be any R object. There are many types of objects in R, but we will mainly use numerical objects. In mathematical terms, these can be classified as scalars, vectors, and matrices: Scalar variable A scalar is a single number. The following code creates a scalar variable with the numeric value 5: x = 5 Vector variable A vector is a sequence of numbers. The following code creates a vector variable with the value [3, 5, 2]: x = c(3, 5, 2) The c stands for concatenate. 5

6 Matrix variable A matrix is a two-way table of numbers. The following code creates a matrix variable with the value x = matrix(c(2, 3, 4, 5, 6, 7), nrow=3, ncol=2) Note that the matrix is filled in by column. If we use x = matrix(c(2, 3, 4, 5, 6, 7), nrow=3, ncol=2, byrow=true) Then we get

7 Variable names You can use simple variable names like x, y, A, and a (note that A and a are different variable names). You can also use longer names like counter, index1, or subject id. A variable name may contain digits, but it cannot begin with a digit. It may contain underscores ( ) but not operators (* - + < > = & %) punctuation (( ) { },.) or the comment character (#). Be careful about clobbering built-in symbols with your own variable names. You could create a variable named log, but then you would no longer be able to use the logarithm function. 7

8 Function signatures A function signature specifies what arguments can be passed into a function. Functions in R have zero or more mandatory arguments, and zero or more keyword arguments. For example, the matrix function we saw earlier has the following signature: matrix(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL) For the matrix function, every argument has a default value (e.g. nrow defaults to 1). 8

9 Getting Information from R You can get some documentation about almost any R command or function using the help command. For example, the following produces some documentation about the matrix function. help(matrix) You can get the current value of a variable by typing its name at the prompt. You can also use the print function to display its value. The following displays the value of the variable x. print(x) 9

10 Comments A comment is anything you write in your program code that is ignored by the computer. Comments help other people understand your code. Anything following a # character is a comment. x = c(3, 5, 2) ## These are the doses of the new drug formulation. 10

11 Scalar arithmetic The familiar scalar arithmetic operations are +,,, and / (addition, subtraction, multiplication, and division). After the following program is run, z will have the value 12, a will have the value 2, and w will have the value 24. x = 5 y = 7 z = x + y a = y - x w = a*z Other arithmetic operations are ˆ(exponentiation) and %% (remainder). x = 5^2 y = 23 %% 5 11

12 Arithmetic expressions You can evaluate more complicated expressions by following standard mathematical conventions. If in doubt about precedence, use parentheses (but don t over-use them). x = 5 y = (x+1) / (x-1)^2 + 1/x 12

13 Modifying variable values in place It is possible (and useful) to modify the value of a variable using an expression that involves its current value. After the following program, the value of x will be 6. x = 5 x = x

14 Assignment by value Variable values are assigned by value in R. Therefore after running the following lines of code, the value of x is 5 and the value of y is 6. x = 5 y = x y = y+1 14

15 Rounding R provides several rounding functions: floor rounds to, ceiling rounds to +, round rounds to the nearest integer, and trunc rounds toward zero. v = ceiling(3.8) w = floor(3.8) x = ceiling(-3.8) y = trunc(-3.8) z = round(-3.8) 15

16 Higher mathematical functions The square root function is sqrt, and fractional powers are also allowed, so sqrt(x) is the same as xˆ0.5. The natural log function is denoted log, and the exponential function e x is denoted by exp(x). The trigonometric functions are denoted in the usual way. The mathematical constant pi is also provided. w = sqrt(2) x = exp(3) y = log(x) z = tan(pi/3) 16

17 Overflow and underflow Numbers can be represented in exponential notation in R, for example, using 1.5e7 for Representing a real number on a computer requires an approximation. These approximations are poor for very large numbers and very small numbers. For example, the value of y after running the following short program will be exactly zero. x = exp(-100) y = x^10 As another example, the value of x = tan(pi/2) should be infinity, but you will see that it is actually a very large finite number. Beware. 17

18 Boolean expressions Boolean expressions evaluate to either TRUE or FALSE. For example, < 5 is FALSE, 10-4 > 5 is TRUE, and == is TRUE (note that you must use two equals signs for testing equality to avoid confusion with assignment statements). 18

19 More Boolean expressions The & (and) operator is TRUE only if the expressions on both sides of the operator are TRUE. For example, (3 < 5) & (2 > 0) is TRUE, and (2 < 3) & (5 > 5) is FALSE. 19

20 The (or) operator is TRUE if at least one of the expressions surrounding it is TRUE. For example, (3 < 5) (2 > 3) is TRUE, and (2 < 1) (5 > 5) is FALSE. 20

21 The! operator (not) evaluates to TRUE for FALSE statements and to FALSE for TRUE statements. For example!(2 < 1) is TRUE and!(3 < 6) is FALSE. Boolean expressions can be combined, using parentheses to confirm precedence. For example, ((5>4) &!(3<2)) (6>7) is TRUE. 21

22 Generating arithmetic sequences The seq function generates an arithmetic sequence (i.e. a sequence of values with a fixed spacing between consecutive elements). For example z = seq(3, 8) creates a vector variable called z that contains the values 3, 4, 5, 6, 7, 8. You can also use z = seq(8, 3) to create the vector of values 8, 7, 6, 5, 4, 3, or z = seq(3, 8, by=2) to create the vector of values 3, 5, 7, where the by parameter causes every second value in the range to be returned. 22

23 Generating vectors using the array function Another way to create vectors in R is using the array function. One use of the array function is to create a vector with the same value repeated a given number of times. For example, z = array(3, 5) constructs a vector of 5 consecutive 3 s, [3, 3, 3, 3, 3]. You can also use the array function to concatenate several copies of an array together end-to-end. For example z = array(c(3,5), 10) creates the vector [3,5,3,5,3,5,3,5,3,5]. Note that the second parameter (10 in this case) refers to the length of the result, not the number of times that the first parameter is repeated. 23

24 Generating arrays using the array function You can reshape a vector into an array using array: V = seq(1, 11, 2) M = array(v, c(3,2)) which yields the array Note that the matrix is filled in column-wise, not row-wise. You can also convert a matrix into a vector using the array function. 24

25 Finally, you can use the array function in place of the matrix function. In the following, the values of A and B are equivalent. V = seq(1, 11, 2) A = matrix(v, nrow=3, ncol=2) B = array(v, c(3,2)) 25

26 Vector and matrix arithmetic Vectors and matrices of the same shape can be operated on arithmetically, with the operations acting element-wise. For example, x = seq(3, 12, 2) y = seq(10, 6) z = x + y calculates the vector sum x + y = z [3, 5, 7, 9, 11] + [10, 9, 8, 7, 6] = [13, 14, 15, 16, 17] 26

27 Element-wise operations on vectors and arrays Many of the mathematical functions in R act element-wise on vectors and matrices. For example, in x = c(9, 16, 25, 36) y = sqrt(x) the value of y will be y = [3, 4, 5, 6]. Other functions acting element-wise include log, exp, and the trigonometric functions. 27

28 Reducing operations on vectors and arrays The values in a vector can be summed using the sum function. For example, A = seq(1, 100, 2) x = sum(a) calculates the sum of the odd integers between 1 and 100. There is also a product function called prod, but it is rarely used. The max and min functions calculate the largest and smallest value, respectively, in a vector or matrix. A = array(seq(1, 100, 2), c(25,2)) mx = max(a) mn = min(a) The functions mean, median, sd, IQR, and var calculate the corresponding descriptive statistic from the values in a vector or matrix. 28

29 Element-wise Boolean operations Most Boolean operators act element-wise. V = c(3,2,8,6,5,6,11,0) I = (V %% 2 == 1) Creates the vector I with value [TRUE, FALSE, FALSE, FALSE, TRUE, FALSE, TRUE, FALSE]. 29

30 Counting Frequently it is useful to count how many elements within a vector satisfy some condition. For example, if we wanted to know how many of the integers between 1 and 100 are divisible by 7, we could use A = seq(100) B = (A %% 7 == 0) x = sum(b) Note that when summing the Boolean vector B, true values are counted as 1 and false values are counted as 0. 30

31 Operating on matrices by row or column The apply function applies a function to every row or to every column of a matrix. For example M = array(seq(8), c(4,2)) RS = apply(m, 1, sum) CS = apply(m, 2, sum) takes the matrix M M = and computes the row sums RS = [6, 8, 10, 12] or the column sums CS = [10, 26]. 31

32 The first argument to apply is a matrix, and the second argument is either 1 (for operating on the rows) or 2 (for operating on the columns). The third argument to apply (sum in the example), can be any function that maps vectors to scalars (e.g. mean, max, sd). If you replace sum with max in the example, you will get RS = [5, 6, 7, 8] and CS = [4, 8]. 32

33 Element access and slicing To access the 5 th element of the vector V, use V[5]. To access the value in row 3, column 2 of a matrix M, use M[3,2]. To access the entire third row of a matrix M use M[3,]. To access the entire second column of a matrix M use M[,2]. To access the 2 3 submatrix spanning rows 3 and 4, and columns 5, 6 and 7 of a matrix M, use M[3:4,5:7]. 33

34 Here are some examples of element access and slicing: M = array(seq(10), c(5,2)) M[4,] = -1 ## Change every value in the fourth row to -1 M[1,2] = -9 ## Change the value in the upper-right corner to -9 M[2:3,] = 0 ## Change every value in the middle 2x2 submatrix to 0 34

35 Creating an empty vector You can create an empty vector by assigning to NULL, e.g. A = NULL. You can then access elements of A by indexing in the usual way, e.g. A[5]. The length of A will automatically grow to the largest index to which you have assigned, with unassigned positions having the value NA. M = NULL M[3] = 1 ## M will now be c(na, NA, 1) 35

36 Learning the shape of a vector or array The length function returns the length of a vector. The dim function tells you how many rows and columns an array has. dim returns a vector of two values. The first return value is the number of rows and the second return value is the number of columns. M = seq(10) M = array(m, c(5,2)) ## d will be c(5,2) d = dim(m) ## nrow will be 5, and ncol will be 2 nrow = dim(m)[1] ncol = dim(m)[2] 36

37 Extending arrays You can append a row to a matrix with rbind, and a column to a matrix with cbind. M = array(seq(10), c(5,2)) ## Create a new array which is M extended by one row at ## its lower edge. A = rbind(m, c(37,38)) ## Create a new array which is M extended by one column at ## its right edge. B = cbind(m, c(37,38,39,40,41)) Note that a row you are appending to a matrix M should have the same number of elements M has columns, and a column you are appending to M should have the same number of elements as M has rows. 37

38 Removing elements and slices from vectors To remove the value in a specific position from a vector, use a negative index: M = c(3, 1, 2, 6, 5, 8, 7, 9) ## Remove the value in the third position (which is 2) ## Note: does not remove all 3 s from the vector. ## The value of A will be c(3,1,6,5,8,7,9) A = M[-3] ## Remove a slice: the value of B will be c(3, 1, 9) B = M[-3:-7] ## Remove everything from the third position to the end of ## the array. The value of C will be c(6, 5, 8, 7, 9). C = M[-3:0] 38

39 Loops Loops are used to carry out a sequence of related operations without having to write the code for each step explicitly. Suppose we want to sum the integers from 1 to 10. following. We could use the x = 0 for (i in 1:10) { x = x + i } The for statement creates a loop in which the looping variable i takes on the values 1, 2,..., 10 in sequence. For each value of the looping variable, the code inside the braces {} is executed (this code is called the body of the loop). Each execution of the loop body is called an iteration. 39

40 In the above program, x is an accumulator variable, meaning that its value is repeatedly updated while the program runs. It s important to remember to initialize accumulator variables (to zero in the example). To clarify, we can add a print statement inside the loop body. x = 0 for (i in 1:10) { x = x + i print(c(i,x)) } 40

41 Run the above code. The output (to the screen) should look like this:

42 More on loops Loops can run over any vector of values. For example, x = 1 for (v in c(3, 4, 7, 2)) { x = x*v } calculates the product = 168. Loops can be nested. For example, x = 0 for (i in seq(4)) { for (j in seq(i)) { x = x+i*j } } 42

43 calculates the following sum of products: = 65. which can be represented as a triangular array, as follows. 1 1 i j 43

44 while loops A while loop is used when it is not known ahead of time how many loop iterations are needed. For example, suppose we wish to calculate the partial sums of the harmonic series n 1/j j=1 until the partial sum exceeds 5. It is a fact that the harmonic series diverges: 1/j =, so eventually the partial sum must exceed any given constant. j=1 44

45 The following program will produce the first value n such that n j=1 1/j > 5. n = 1 ## Don t forget x = 0 ## to initialize while (x < 5) { x = x + 1/n ## Note that the order of these two statements n = n+1 ## in the block is important. } 45

46 Conditional execution ( if blocks) An if block can be used to make on-the-fly decisions about what statements of a program get executed. For example, y = 7 if (y < 10) { x = 2 } else { x = 1 } The value of x after executing the previous code is 2. This doesn t appear very useful, but if statements can be very useful inside a loop. For example, the following program places the sum of the even integers up to 100 in A and the sum of the odd integers up to 100 in B. A = 0 B = 0 for (k in 1:100) { if (k %% 2 == 1) { A = A + k } else { B = B + k } } 46

47 The following demonstrates an even more complicated if construction. A = 0 B = 0 C = 0 D = 0 for (k in (1:100)) { ## An if construct. if ((k %% 2 == 1) & (k < 50)) { A = A + k } else if ((k %% 2 == 1) & (k >= 50)) { B = B + k } else { C = C + k } } ## An independent if construct. if (k >= 50) { D = D + k } The preceding program places the sum of odd integers between 1 and 49 in A, the sum of odd integers between 50 and 100 in B, the sum of even integers between 1 and 100 in C, and the sum of all integers greater than or equal to 50 in D. 47

48 break and next in loops A break statement is used to exit a loop when a certain condition is met. A next statement results in the current iteration being aborted, but the loop continues with the next iteration. The following program sums the odd integers between 1 and 49. x = 0 for (k in seq(100)) { if (k %% 2 == 0) { next } ## Skip even numbers, but keep looping. if (x >= 50) { break } ## Quit looping when the sum exceeds 50. x = x + k } 48

49 Defining your own functions You can define you own functions with the function construct. The body of the function (the code in the braces) is executed whenever the function is called. The return statement produces a value that is returned when the function is called. f = function(x, y) { return(x / (1+y^2)) } ## a will be 0.2. a = f(1, 2) 49

50 Hashes A list is a collection of values that are indexed by arbitrary keys (unlike vectors which are indexed by integer keys). A list in R is equivalent to an associative array, hash table, or dictionary as found in other high-level languages. ## Creat a list with two values. A = list() A\$apple = 3 A\$pear = 4 ## Add a third value based on the other two values. A\$fruit = A\$apple + A\$pear ## An alternate way to use the key. A[[ fruit ]] = A[[ apple ]] + A[[ pear ]] 50

### b) lower case always use lower case for all matlab commands. This is what matlab recognizes.

1 Matlab 1) Fundamentals a) Getting Help for more detailed help on any topic, typing help, then a space, and then the matlab command brings up a detailed page on the command or topic. For really difficult

### Matrix Algebra in R A Minimal Introduction

A Minimal Introduction James H. Steiger Department of Psychology and Human Development Vanderbilt University Regression Modeling, 2009 1 Defining a Matrix in R Entering by Columns Entering by Rows Entering

### Name: Class: Date: 9. The compiler ignores all comments they are there strictly for the convenience of anyone reading the program.

Name: Class: Date: Exam #1 - Prep True/False Indicate whether the statement is true or false. 1. Programming is the process of writing a computer program in a language that the computer can respond to

### Command lookfor followed by a key word (which can be anything and not only a command) gives help related to the key word.

1 Using MatLab Help Command help provides a short description of all functions. For example, to get help on the diary command, type help diary. For more information type help -i diary. Command lookfor

### 6.096 Lab 1. Due: 7 January 12:30:00. September 20, 2011

6.096 Lab 1 Due: 7 January 1:30:00 September 0, 011 1 Additional Material 1.1 Constants A constant is an expressions with a fixed value. Kinds of constants: Literals: used to express particular values

### Using Casio Graphics Calculators

Using Casio Graphics Calculators (Some of this document is based on papers prepared by Donald Stover in January 2004.) This document summarizes calculation and programming operations with many contemporary

### Introduction to Matlab

Introduction to Matlab Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course provides

### TI-83 Plus Graphing Calculator Keystroke Guide

TI-83 Plus Graphing Calculator Keystroke Guide In your textbook you will notice that on some pages a key-shaped icon appears next to a brief description of a feature on your graphing calculator. In this

Basic R Commands: Comments If you want to insert a comment (i.e., non-executable commands) anywhere in a program, you need to preface the line of code with a # sign. Everything in the line after the #

### Repetition and Loops. Additional Python constructs that allow us to effect the (1) order and (2) number of times that program statements are executed.

New Topic Repetition and Loops Additional Python constructs that allow us to effect the (1) order and (2) number of times that program statements are executed. These constructs are the 1. while loop and

### Exercise 1: Python Language Basics

Exercise 1: Python Language Basics In this exercise we will cover the basic principles of the Python language. All languages have a standard set of functionality including the ability to comment code,

### CHAPTER 3 Numbers and Numeral Systems

CHAPTER 3 Numbers and Numeral Systems Numbers play an important role in almost all areas of mathematics, not least in calculus. Virtually all calculus books contain a thorough description of the natural,

### VB.NET Programming Fundamentals

Chapter 3 Objectives Programming Fundamentals In this chapter, you will: Learn about the programming language Write a module definition Use variables and data types Compute with Write decision-making statements

### A.2. Exponents and Radicals. Integer Exponents. What you should learn. Exponential Notation. Why you should learn it. Properties of Exponents

Appendix A. Exponents and Radicals A11 A. Exponents and Radicals What you should learn Use properties of exponents. Use scientific notation to represent real numbers. Use properties of radicals. Simplify

### 6. Control Structures

- 35 - Control Structures: 6. Control Structures A program is usually not limited to a linear sequence of instructions. During its process it may bifurcate, repeat code or take decisions. For that purpose,

### Moving from CS 61A Scheme to CS 61B Java

Moving from CS 61A Scheme to CS 61B Java Introduction Java is an object-oriented language. This document describes some of the differences between object-oriented programming in Scheme (which we hope you

### 4. MATRICES Matrices

4. MATRICES 170 4. Matrices 4.1. Definitions. Definition 4.1.1. A matrix is a rectangular array of numbers. A matrix with m rows and n columns is said to have dimension m n and may be represented as follows:

### Texas Instruments TI-83, TI-83 Plus Graphics Calculator I.1 Systems of Linear Equations

Part I: Texas Instruments TI-83, TI-83 Plus Graphics Calculator I.1 Systems of Linear Equations I.1.1 Basics: Press the ON key to begin using your TI-83 calculator. If you need to adjust the display contrast,

### Object Oriented Software Design

Object Oriented Software Design Introduction to Java - II Giuseppe Lipari http://retis.sssup.it/~lipari Scuola Superiore Sant Anna Pisa September 14, 2011 G. Lipari (Scuola Superiore Sant Anna) Introduction

### Preview of Real Python Course 1, Intro to Python. Fundamentals: Functions and Loops

Preview of Real Python Course 1, Intro to Python If you like what you see, consider purchasing the entire course on RealPython.com - for just \$60, you will get all three courses, with over 1,200 pages

### REPETITION WITH PYTHON

REPETITION WITH PYTHON José M. Garrido Department of Computer Science May 2015 College of Computing and Software Engineering Kennesaw State University c 2015, J. M. Garrido Repetition with Python 2 Repetition

### Introduction to Python Programming. CSE 110: Introduction to Computer Science

Introduction to Python Programming CSE 110: Introduction to Computer Science Announcements Labs begin on Wednesday Labs will meet in CS 2129, NOT the CS SINC site! Homework 1 is due in class on Friday

### Lecture 3: Finding integer solutions to systems of linear equations

Lecture 3: Finding integer solutions to systems of linear equations Algorithmic Number Theory (Fall 2014) Rutgers University Swastik Kopparty Scribe: Abhishek Bhrushundi 1 Overview The goal of this lecture

### What is a Loop? Pretest Loops in C++ Types of Loop Testing. Count-controlled loops. Loops can be...

What is a Loop? CSC Intermediate Programming Looping A loop is a repetition control structure It causes a single statement or a group of statements to be executed repeatedly It uses a condition to control

VistaPro User Guide Custom Variable Expressions IES Virtual Environment Copyright 2015 Integrated Environmental Solutions Limited. All rights reserved. No part of the manual is to be copied or reproduced

### Notes on Determinant

ENGG2012B Advanced Engineering Mathematics Notes on Determinant Lecturer: Kenneth Shum Lecture 9-18/02/2013 The determinant of a system of linear equations determines whether the solution is unique, without

### 1 Description of The Simpletron

Simulating The Simpletron Computer 50 points 1 Description of The Simpletron In this assignment you will write a program to simulate a fictional computer that we will call the Simpletron. As its name implies

### 3 Some Integer Functions

3 Some Integer Functions A Pair of Fundamental Integer Functions The integer function that is the heart of this section is the modulo function. However, before getting to it, let us look at some very simple

### A Little Set Theory (Never Hurt Anybody)

A Little Set Theory (Never Hurt Anybody) Matthew Saltzman Department of Mathematical Sciences Clemson University Draft: August 21, 2013 1 Introduction The fundamental ideas of set theory and the algebra

### R Language Fundamentals

R Language Fundamentals Data Types and Basic Maniuplation Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Where did R come from? Overview Atomic Vectors Subsetting

### A First Book of C++ Chapter 2 Data Types, Declarations, and Displays

A First Book of C++ Chapter 2 Data Types, Declarations, and Displays Objectives In this chapter, you will learn about: Data Types Arithmetic Operators Variables and Declarations Common Programming Errors

### Python for Everybody. Exploring Data Using Python 3. Charles R. Severance

Python for Everybody Exploring Data Using Python 3 Charles R. Severance 4.10. FRUITFUL FUNCTIONS AND VOID FUNCTIONS 51 4.10 Fruitful functions and void functions Some of the functions we are using, such

### Object Oriented Software Design

Object Oriented Software Design Introduction to Java - II Giuseppe Lipari http://retis.sssup.it/~lipari Scuola Superiore Sant Anna Pisa October 28, 2010 G. Lipari (Scuola Superiore Sant Anna) Introduction

### 5.1 Radical Notation and Rational Exponents

Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

### Chapter 5 Functions. Introducing Functions

Chapter 5 Functions 1 Introducing Functions A function is a collection of statements that are grouped together to perform an operation Define a function Invoke a funciton return value type method name

### 2. Compressing data to reduce the amount of transmitted data (e.g., to save money).

Presentation Layer The presentation layer is concerned with preserving the meaning of information sent across a network. The presentation layer may represent (encode) the data in various ways (e.g., data

### MATH10212 Linear Algebra. Systems of Linear Equations. Definition. An n-dimensional vector is a row or a column of n numbers (or letters): a 1.

MATH10212 Linear Algebra Textbook: D. Poole, Linear Algebra: A Modern Introduction. Thompson, 2006. ISBN 0-534-40596-7. Systems of Linear Equations Definition. An n-dimensional vector is a row or a column

### Financial Econometrics MFE MATLAB Introduction. Kevin Sheppard University of Oxford

Financial Econometrics MFE MATLAB Introduction Kevin Sheppard University of Oxford October 21, 2013 2007-2013 Kevin Sheppard 2 Contents Introduction i 1 Getting Started 1 2 Basic Input and Operators 5

### Chapter 6 Operators and Flow Control

Chapter 6 Operators and Flow Control 6.1. Relational and Logical Operators MATLAB has a logical data type, with the possible values 1, representing true, and 0, representing false. Logicals are produced

### Scripting with TCL, Part 1

Scripting with TCL, Part 1 Axel Kohlmeyer Center for Molecular Modeling University of Pennsylvania SBS 2007 @ JNCASR, Bangalore The VMD Execution Model GUI (FLTK) Internal State Visualization Python Interpreter

### SYSTEMS OF EQUATIONS AND MATRICES WITH THE TI-89. by Joseph Collison

SYSTEMS OF EQUATIONS AND MATRICES WITH THE TI-89 by Joseph Collison Copyright 2000 by Joseph Collison All rights reserved Reproduction or translation of any part of this work beyond that permitted by Sections

### Exercise 4 Learning Python language fundamentals

Exercise 4 Learning Python language fundamentals Work with numbers Python can be used as a powerful calculator. Practicing math calculations in Python will help you not only perform these tasks, but also

### Lecture 4 Representing Data on the Computer. Ramani Duraiswami AMSC/CMSC 662 Fall 2009

Lecture 4 Representing Data on the Computer Ramani Duraiswami AMSC/CMSC 662 Fall 2009 x = ±(1+f) 2 e 0 f < 1 f = (integer < 2 52 )/ 2 52-1022 e 1023 e = integer Effects of floating point Effects of floating

### NUMBERING SYSTEMS C HAPTER 1.0 INTRODUCTION 1.1 A REVIEW OF THE DECIMAL SYSTEM 1.2 BINARY NUMBERING SYSTEM

12 Digital Principles Switching Theory C HAPTER 1 NUMBERING SYSTEMS 1.0 INTRODUCTION Inside today s computers, data is represented as 1 s and 0 s. These 1 s and 0 s might be stored magnetically on a disk,

### Sources: On the Web: Slides will be available on:

C programming Introduction The basics of algorithms Structure of a C code, compilation step Constant, variable type, variable scope Expression and operators: assignment, arithmetic operators, comparison,

### MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS Systems of Equations and Matrices Representation of a linear system The general system of m equations in n unknowns can be written a x + a 2 x 2 + + a n x n b a

### TI-86 Graphing Calculator Keystroke Guide

TI-86 Graphing Calculator Keystroke Guide In your textbook you will notice that on some pages a key-shaped icon appears next to a brief description of a feature on your graphing calculator. In this guide

### R: A self-learn tutorial

R: A self-learn tutorial 1 Introduction R is a software language for carrying out complicated (and simple) statistical analyses. It includes routines for data summary and exploration, graphical presentation

### CME 192: Introduction to Matlab

CME 192: Introduction to Matlab Matlab Basics Brett Naul January 7, 2015 What is Matlab? Computing & programming environment Visualization and mathematical prototyping tool Why Matlab? Comparison with

### MATLAB Programming. Problem 1: Sequential

Division of Engineering Fundamentals, Copyright 1999 by J.C. Malzahn Kampe 1 / 21 MATLAB Programming When we use the phrase computer solution, it should be understood that a computer will only follow directions;

### Maple Basics Arithmetic operations in Maple

MA310 MAPLE Example Sheet 1 Maple is a comprehensive Symbolic Computation System or Computer Algebra System for advanced Mathematics. These phrases refer to Maple s capability to manipulate information

### Chapter 2: Problem Solving Using C++

Chapter 2: Problem Solving Using C++ 1 Objectives In this chapter, you will learn about: Modular programs Programming style Data types Arithmetic operations Variables and declaration statements Common

### VISUAL GUIDE to. RX Scripting. for Roulette Xtreme - System Designer 2.0

VISUAL GUIDE to RX Scripting for Roulette Xtreme - System Designer 2.0 UX Software - 2009 TABLE OF CONTENTS INTRODUCTION... ii What is this book about?... iii How to use this book... iii Time to start...

### Going from Python to C

Going from Python to C Darin Brezeale December 8, 2011 Python is a high-level, interpreted language. C has many of the same types of programming constructs as in Python: arrays, loops, conditionals, functions,

### The PCAT Programming Language Reference Manual

The PCAT Programming Language Reference Manual Andrew Tolmach and Jingke Li Dept. of Computer Science Portland State University (revised October 8, 2004) 1 Introduction The PCAT language (Pascal Clone

### SOME EXCEL FORMULAS AND FUNCTIONS

SOME EXCEL FORMULAS AND FUNCTIONS About calculation operators Operators specify the type of calculation that you want to perform on the elements of a formula. Microsoft Excel includes four different types

### Chapter 4 C Program Control

Chapter 4 C Program Control Objectives of this chapter: Repetitions will be considered in greater detail for.. repetition do while repetition Also multiple selection switch case statement will be learned.

### a(1) = first.entry of a

Lecture 2 vectors and matrices ROW VECTORS Enter the following in SciLab: [1,2,3] scilab notation for row vectors [8]==8 a=[2 3 4] separate entries with spaces or commas b=[10,10,10] a+b, b-a add, subtract

### Chapter II Binary Data Representation

Chapter II Binary Data Representation The atomic unit of data in computer systems is the bit, which is actually an acronym that stands for BInary digit. It can hold only 2 values or states: 0 or 1, true

### ECONOMICS 351* -- Stata 10 Tutorial 2. Stata 10 Tutorial 2

Stata 10 Tutorial 2 TOPIC: Introduction to Selected Stata Commands DATA: auto1.dta (the Stata-format data file you created in Stata Tutorial 1) or auto1.raw (the original text-format data file) TASKS:

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS. + + x 2. x n. a 11 a 12 a 1n b 1 a 21 a 22 a 2n b 2 a 31 a 32 a 3n b 3. a m1 a m2 a mn b m

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS 1. SYSTEMS OF EQUATIONS AND MATRICES 1.1. Representation of a linear system. The general system of m equations in n unknowns can be written a 11 x 1 + a 12 x 2 +

### MATLAB Basics MATLAB numbers and numeric formats

MATLAB Basics MATLAB numbers and numeric formats All numerical variables are stored in MATLAB in double precision floating-point form. (In fact it is possible to force some variables to be of other types

### Chapter 6 Repetition

Chapter 6 Repetition 6-1 Repetition in C++ The final control/logic structure is repetition: Repetition repeating a block of code until a condition is met There are three repetition statements available

### How to Type Math Symbols in MS Word

Word has some great tools for helping you input math symbols and math equations into your assignment or Word document! On the next few pages, you will see screens and instructions for how to input various

### Mathematics of Cryptography

CHAPTER 2 Mathematics of Cryptography Part I: Modular Arithmetic, Congruence, and Matrices Objectives This chapter is intended to prepare the reader for the next few chapters in cryptography. The chapter

### Getting Started with MasteringPhysics

Getting Started with MasteringPhysics POWERED BY MYCYBERTUTOR STUDENT EDITION MasteringPhysics helps you when you need it most when you are stuck working out a problem. Designed specifically for university

### Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

### Chapter 3. if 2 a i then location: = i. Page 40

Chapter 3 1. Describe an algorithm that takes a list of n integers a 1,a 2,,a n and finds the number of integers each greater than five in the list. Ans: procedure greaterthanfive(a 1,,a n : integers)

### Introduction to MATLAB

Introduction to MATLAB Matlab is a program that allows you to carry out computations in a straightforward manner, removing much of the tedium involved in programming. It is extremely useful for creating

### Introduction to Python

Caltech/LEAD Summer 2012 Computer Science Lecture 2: July 10, 2012 Introduction to Python The Python shell Outline Python as a calculator Arithmetic expressions Operator precedence Variables and assignment

1 6 JavaScript: Introduction to Scripting 2 Comment is free, but facts are sacred. C. P. Scott The creditor hath a better memory than the debtor. James Howell When faced with a decision, I always ask,

### 26 Integers: Multiplication, Division, and Order

26 Integers: Multiplication, Division, and Order Integer multiplication and division are extensions of whole number multiplication and division. In multiplying and dividing integers, the one new issue

### MATLAB Workshop 3 - Vectors in MATLAB

MATLAB: Workshop - Vectors in MATLAB page 1 MATLAB Workshop - Vectors in MATLAB Objectives: Learn about vector properties in MATLAB, methods to create row and column vectors, mathematical functions with

### Visual Logic Instructions and Assignments

Visual Logic Instructions and Assignments Visual Logic can be installed from the CD that accompanies our textbook. It is a nifty tool for creating program flowcharts, but that is only half of the story.

### Chapter 11 Number Theory

Chapter 11 Number Theory Number theory is one of the oldest branches of mathematics. For many years people who studied number theory delighted in its pure nature because there were few practical applications

### Excel 2007 Introduction to Formulae and Functions

Excel 2007 Introduction to Formulae and Functions Page 1 of 19 Contents Creating Simple Formulae... 4 Some common formulae 4 The order of precedence 5 Editing a formula 5 Copying formulae 6 Functions...

### 14:440:127 Introduction to Computers for Engineers. Notes for Lecture 06

14:440:127 Introduction to Computers for Engineers Notes for Lecture 06 Rutgers University, Spring 2010 Instructor- Blase E. Ur 1 Loop Examples 1.1 Example- Sum Primes Let s say we wanted to sum all 1,

### CHAPTER 5 Round-off errors

CHAPTER 5 Round-off errors In the two previous chapters we have seen how numbers can be represented in the binary numeral system and how this is the basis for representing numbers in computers. Since any

### 9.2 Summation Notation

9. Summation Notation 66 9. Summation Notation In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence. We begin with a

### Simulation Tools. Python for MATLAB Users I. Claus Führer. Automn 2009. Claus Führer Simulation Tools Automn 2009 1 / 65

Simulation Tools Python for MATLAB Users I Claus Führer Automn 2009 Claus Führer Simulation Tools Automn 2009 1 / 65 1 Preface 2 Python vs Other Languages 3 Examples and Demo 4 Python Basics Basic Operations

### Writing Control Structures

Writing Control Structures Copyright 2006, Oracle. All rights reserved. Oracle Database 10g: PL/SQL Fundamentals 5-1 Objectives After completing this lesson, you should be able to do the following: Identify

### 2+2 Just type and press enter and the answer comes up ans = 4

Demonstration Red text = commands entered in the command window Black text = Matlab responses Blue text = comments 2+2 Just type and press enter and the answer comes up 4 sin(4)^2.5728 The elementary functions

### Unix Shell Scripts. Contents. 1 Introduction. Norman Matloff. July 30, 2008. 1 Introduction 1. 2 Invoking Shell Scripts 2

Unix Shell Scripts Norman Matloff July 30, 2008 Contents 1 Introduction 1 2 Invoking Shell Scripts 2 2.1 Direct Interpretation....................................... 2 2.2 Indirect Interpretation......................................

### Paper 2917. Creating Variables: Traps and Pitfalls Olena Galligan, Clinops LLC, San Francisco, CA

Paper 2917 Creating Variables: Traps and Pitfalls Olena Galligan, Clinops LLC, San Francisco, CA ABSTRACT Creation of variables is one of the most common SAS programming tasks. However, sometimes it produces

### Control Structure. Pseudocode: Input number If number is even Then Print even Else print odd. Flowchart: Begin. End. Print Odd. number even?

Control Structure Normally, a program is executed in a sequential manner.however, in many cases, a program has to choose among alternative statements C++ provides constructs that enable the programmer

### Microsoft Excel 2010: Create or Delete a Formula

Formulas are equations that perform calculations on values in your worksheet. A formula always starts with an equal sign (=). You can create a simple formula by using constants and calculation operators.

### COMP2121: Microprocessors and Interfacing

Interfacing Lecture 3: Number Systems (I) http://www.cse.unsw.edu.au/~cs2121 Lecturer: Hui Wu Session 2, 2005 Overview Positional notation Decimal, hexadecimal and binary One complement Two s complement

### Chapter 3. Cartesian Products and Relations. 3.1 Cartesian Products

Chapter 3 Cartesian Products and Relations The material in this chapter is the first real encounter with abstraction. Relations are very general thing they are a special type of subset. After introducing

### Python as a First Programming Language

STEMBOPS Justin Stevens and Giselle Serate Page 1 Python as a First Programming Language Author: Justin Stevens Giselle Serate 1 Introduction STEMBOPS Davidson Academy of Nevada University of Nevada, Reno

### Examples of Functions

Examples of Functions In this document is provided examples of a variety of functions. The purpose is to convince the beginning student that functions are something quite different than polynomial equations.

### IB Maths SL Sequence and Series Practice Problems Mr. W Name

IB Maths SL Sequence and Series Practice Problems Mr. W Name Remember to show all necessary reasoning! Separate paper is probably best. 3b 3d is optional! 1. In an arithmetic sequence, u 1 = and u 3 =

### Udacity CS101 Python Reference

Udacity CS101 Python Reference Arithmetic Expressions Comparisons Variables and Assignment Names Assignment Statement Multiple Assignment Procedures If Statements Logical Operators Loops While Loops Break

### Getting Started with R and RStudio 1

Getting Started with R and RStudio 1 1 What is R? R is a system for statistical computation and graphics. It is the statistical system that is used in Mathematics 241, Engineering Statistics, for the following

### Mathematica Programming

program.nb Mathematica Programming Dennis Silverman Mathematical Physics B U. C. Irvine Built in Programming Mathematica already has several important built over and above standard programming languages.

### C Programming Dr. Hasan Demirel

C How to Program, H. M. Deitel and P. J. Deitel, Prentice Hall, 5 th edition (3 rd edition or above is also OK). Introduction to C Programming Dr. Hasan Demirel Programming Languages There are three types

### Getting Started with

Getting Started with MASTERINGPHYSICS IS POWERED BY MYCYBERTUTOR BY EFFECTIVE EDUCATIONAL TECHNOLOGIES STUDENT EDITION MasteringPhysics is the first Socratic tutoring system developed specifically for

### ECE 0142 Computer Organization. Lecture 3 Floating Point Representations

ECE 0142 Computer Organization Lecture 3 Floating Point Representations 1 Floating-point arithmetic We often incur floating-point programming. Floating point greatly simplifies working with large (e.g.,