Lecture MATLAB fundamentals Variables, Naming Rules, Arrays (numbers, scalars, vectors, matrices), Arithmetical Operations, Defining and manipulating arrays © 2007 Daniel Valentine All rights reserved Published by Elsevier Variables  What are variables? – You name the variables (as the programmer) and assign them numerical values Variable Naming Rules Must begin with a LETTER  May only contain letters, numbers and underscores ( _ )  No spaces or punctuation marks allowed!  Only the first 63 characters are significant; beyond that the names are truncated  Case sensitive (e.g the variables a and A are not the same)  Which variable names are valid?       12oclockRock tertiarySector blue cows Eiffel65 red_bananas This_Variable_Name_Is_Quite_Possibly_Too_Lon g_To_Be_Considered_Good_Practice_However_I t_Will_Work % (the green part is not part of the recognized name) Variable Naming Conventions  There are different ways to name variables The following illustrate some of the conventions used: – lowerCamelCase – UpperCamelCase – underscore_convention  If a variable is a constant, some programmers use all caps: – CONSTANT  It does not matter which convention you choose to work with; it is up to you Variables as Arrays In MATLAB, a variable is stored as an array of numbers When appropriate, it is interpreted as a scalar, vector or matrix scalar 1×1 vector n × or × n matrix n×m The size of an array is specified by the number of rows and the number of columns in the array, with the number of rows indicated first Scalars Scalars are 1×1 arrays  They contain a single value, for example:  Vectors  A vector is a list of numbers expressed as a dimensional array A vector can be n×1 or 1×n  Columns are separated by commas (or spaces):  Rows are separated by semicolons:  Matrices  For example, this is a 4×3 matrix: A matrix is a two dimensional array of numbers Rows  Columns 3.0 1.8 3.6 4.6 -2.0 21.3 0.0 -6.1 12.8 2.3 0.3 -6.1 The equal sign assigns  Consider the command lines: >> ax = 5; >> bx = [1 2]; >> by = [3 4]; >> b = bx + by;  The equal sign (=) commands that the number computed on the right of it is input to the variable named on the left; thus, it is an assignment operation Defining (or assigning) arrays  An array can be defined by typing in a list of numbers enclosed in square brackets: – Commas or spaces separate numbers A = 12 18 -3 – Semicolons indicate a new row B = -2 2 Defining arrays continued  You can define an array in terms of another array: C = 12 18 -2 -3 2 12 18 -2 -3 2 D = 12 18 -2 -3 2 Creating Zeros & Ones arrays  Create an array of zeros: E = 0  0 0 0 0 0 0 Create an array of ones: F = 1 1 1 Note: Placing a single number inside either function will return an n × n array e.g ones(4) will return a × array filled with ones Retrieving Values in an Array  Index – a number used to identify elements in an array – Retrieving a value from an array: G = ans = ans = Changing Values in an Array  You can change a value in an element in an array with indexing: A = 12  -3 You can extend an array by defining a new element: A = 12 -3 0 – Notice how undefined values of the array are filled with zeros Colon Operator  Colon notation can be used to define evenly spaced vectors in the form: first : last H =  The default spacing is 1, so to use a different increment, use the form: first : increment : last I = – The numbers now increment by 11 Extracting Data with the Colon Operator  The colon represents an entire row or column when used in as an array index in place of a particular number G = ans = ans = 9 ans = Extracting Data with the Colon Operator Continued  The colon operator can also be used to extract a range of rows or columns: G = G = ans = Manipulating Arrays  The transpose operator, an apostrophe, changes all of an array’s rows to columns and columns to rows J = ans = 7 Manipulating Matrices Continued  The functions fliplr() and flipud() flip a matrix left-to-right and top-to-bottom, respectively – Experiment with these functions to see how they work Hands-on exercise: Create the following matrix using colon notation:  W = 10  – 18 1:5 The second row ranges from 10 to 18 in increments of 10:2:18 The third row ranges from to in increments of -1  – 16 The first row ranges from to in increments of  – 14 All three rows are evenly spaced  – 12 6:-1:2 All together: Hands-on continued  Create the following matrix using colon notation: X = 1.2 1.9   2.3 3.8 -3 3.4 5.7 -6 4.5 7.6 -9 5.6 9.5 -12 Transpose this matrix and assign it to variable Y >> Y = x’ Extract the 2nd row from Y and assign it to variable Z >> Z = Y(2,:) Summary (1 of 2) Naming a variable: Start with letter followed by any combination of letters, numbers and underscores (up to 63 of these objects are recognized)  Arrays are rows and columns of numbers  Array operations (element-by-element operations with the dot-operators)  Hierarchy of arithmetic operations  Summary (2 of 2) Command lines that assign variables numerical values start with the variable name followed by = and then the defining expression  An array of numbers is the structure of variables in MATLAB Within one variable name, a set of numbers can be stored  Array, vector and matrix operations are efficient MATLAB computational tools 