1 Overview of the standard Matlab syntax

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1 1 Overview of the standard Matlab syntax Matlab is based on computations with matrices. All variables are matrices. Matrices are indexed from 1 (and NOT from 0 as in C!). Avoid using variable names i and j as these names are used in the representation of complex numbers. Every line in Matlab closes with a ; that does not give any output on screen. 1.1 Getting started In this section we will learn to use some basic operations in Matlab Creating Matlab variables Matlab variables are created with an assignment statement. The syntax of variable assignment is For example, variable name = a value (or an expression); >> x = expression; where expression is a combination of numerical values, mathematical operators, variables, and function calls. The expression can involve manual entry, built-in functions and/or user-defined functions Overwriting variables Once a variable has been created, it can be reassigned. In addition, if you do not wish to see the intermediate results, you can suppress the numerical output by putting a semicolon (;) at the of the line. Then the sequence of commands looks like >> x = 10 >> x = x Hierarchy of operations or precedence The order in which Matlab performs arithmetic operations is exactly that taught in high school algebra courses. Exponentiations are done first, followed by multiplications and divisions, and finally by additions and subtractions. However, the standard order of precedence of arithmetic operations can be changed by inserting parentheses. For example, the result of isquite different than the similar expression with parentheses (1+2) 3. The results are 7 and 9 respectively. Parentheses can always be used to overrule priority, and their use is recommed in some complex expressions to avoid ambiguity. Therefore, to make the evaluation of expressions unambiguous, Matlab has established a series of rules. The order in which the arithmetic operations are evaluated is given in Table 1. Matlab arithmetic operators obey the same precedence rules as those in most computer programs. For operators of equal precedence, evaluation is from left to right. 1

2 Table 1: Hierarchy of arithmetic operations Precedence First Second Third Forth Mathematical Operations The contents of all parentheses are evaluated first, starting from the innermost parentheses and working outward. All exponentials are evaluated, working from left to right. All multiplications and divisions are evaluated, working from left to right. All additions and subtractions are evaluated, starting from left to right Keeping track of your work session It is possible to keep track of everything done during a Matlab session with the diary command. or give a name to a created file, >> diary; >> diary FileName; where FileName could be any arbitrary name you choose. The function diary is useful if you want to save a complete Matlab session. They save all input and output as they appear in the Matlab window. When you want to stop the recording, enter diary off. If you want to start recording again, enter diary on. The file that is created is a simple text file. It can be opened by an editor or a word processing program and edited to remove extraneous material, or to add your comments. You can use the function type to view the diary file or you can edit in a text editor or print. This command is useful, for example in the process of preparing a homework or lab submission. 1.2 Matlab commands Here are some useful Matlab commands that can be executed in the Command Window: Matrix creation: Use the command >> A = [1 2 3; 4 5 6; 7 8 9]; to create a 3 3 matrix of the form A = After each ; a new row is started, elements in the same row are separated by a space. Row vector: To create a row vector just write the command that creates a matrix with a single row: 2

3 >> A = [1 2 3]; The result of the example command will be: [ ] A = Column vector: To create a column vector just write the command that creates a matrix with a single column: >> A = [1; 2; 3]; The result of the example command will be: 1 A = 2. 3 Matrix transpose: To create the transpose of the matrix (i.e., the matrix which is formed by turning all the rows of a given matrix into columns and vice-versa) you use the following command: >> B = A ; Matrix multiplication: The multiplication of the matrices A and B is given by the command: >> C = A * B; You should be careful with the dimensions of the matrices. That is, the columns of A should be equal to the rows of B. Element-wise matrix multiplication: If you want to calculate a matrix which is formed by element-wise multiplication of two matrices, you use the command or >> C = A.* B; >> C = times(a,b); Note that the elements of C are calculated by multiplying the corresponding elements in A and B with each other. The element-wise multiplication is feasible only when A and B have the same dimensions. Left element-wise division: If you want to divide each element of A by the corresponding element of B, use the command or >> C = A.\B; 3

4 >> C = ldivide(a,b); If A and B are arrays, then they must be the same size. If either A or B is a scalar, then Matlab expands the scalar value into an appropriately sized array. Element-wise power: If you want to raise each element of A to the corresponding power in B, use the command or >> C = A.ˆ B; >> C = power(a,b); Dimensions: To return the dimension of B as a row vector with the first element representing the number of rows and the second element the number of columns, use the command >> A = size(b); Zero matrix: To create a matrix A with m rows and n columns filled with zeros, write the following command >> A = zeros(m,n); All-ones matrix: To create a matrix A with m rows and n columns filled with ones, write the following command >> A = ones(m,n); Unit (or Identity) matrix: To create a matrix A with n n square matrix with ones on the main diagonal and zeros elsewhere, write the following command >> A = eye(n); Determinant: To compute the determinant for A, use the command >> d = det(a); Return matrix element: To return the element on row k and column l in matrix A, use the command >> elem = A(k,l); Return matrix column: command To return the element the l-th column of matrix A, use the >> col = A(:,l); Return matrix row: To return the element the k-th row of matrix A, use the command 4

5 >> r = A(k,:); Return sub-matrix: To return the sub-matrix of A specified by the rows a to b and the columns c to d, write the command >> sub = A(a:b,c:d); Cancel running command: To cancel the running command yoy should press: CTRL + C. Clear command window: To clear the command window you should write clc. Clear registered variables: To clear all the registered variables you can write the command clear. Help: To see the syntax of a command you should press help followed by the name of the command. For a more extensive description of the commands, you can browse to http: //nl.mathworks.com/help/matlab/. 1.3 Matlab statements The problem is that the commands entered in the Command Window cannot be saved and executed again for several times. Therefore, a different way of executing repeatedly commands with MATLAB is: (a) to create a file with a list of commands, (b) save the file, and (c) run the file. If needed, corrections or changes can be made to the commands in the file. The files that are used for this purpose are called script files or scripts for short. A script file is an external file that contains a sequence of Matlab statements. Script files have a filename extension.m and are often called M-files. M-files can be scripts that simply execute a series of Matlab statements, or they can be functions that can accept arguments and can produce one or more outputs. All variables created in a script file are added to the workspace. This may have undesirable effects, because (a) variables already existing in the workspace may be overwritten, and (b) the execution of the script can be affected by the state variables in the workspace. As a result, it is better to code any complicated applications using rather function M-file. Functions are programs (or routines) that accept input arguments and return output arguments. Each M-file function (or function for short) has its own area of workspace, separated from the MATLAB base workspace. To write a function in an.m file you should write according to the following syntax: [variable1,..., variablem] = FunctionName(parameter1,...,parameterN)...(statements using parameter1,...,parametern ) variable1 =......(output variables) variablem... The function returns the values of the output variables variable1,..., variablem when you are using as input variables (or parameters) the parameter1,...,parametern. The name of the.m file where the function is saved has to be the same as the name of the function (here FunctionName). The return value is set by an assignment in the function. 5

6 Since Matlab is a programming language, the most relevant statements are the followings: Comment region: To indicate the beginning of a comment line use the symbol % at the beginning of the line (equivalent with // in C). E.g., % this is a comment region for clarifying the code. For loop: To execute statements specified number of times, use the following syntax for index = values... (statements) More information see at While loop: To repeat execution of statements while condition is true, use the following syntax while expression More information see at if, elseif, else : To execute statements if condition is true, use the following syntax if expression1 elseif expression2 else expression3 More information see at 6