Lecture 2MATLAB fundamentals

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Variables, Naming Rules, Arrays (numbers, scalars, vectors, matrices), Arithmetical Operations, Defining and manipulating arrays Variables What are variables? You name the variables (as the programmer) and assign them numerical values.

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Lecture 2 Lecture 2 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 Variables  What are variables? – You name the variables (as the programmer) and assign them numerical values.
Variable Naming Rules 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 Which variable names are valid? 12oclockRock  tertiarySector  blue cows  Eiffel65  red_bananas  This_Variable_Name_Is_Quite_Possibly_Too_L  ong_To_Be_Considered_Good_Practice_Howev er_It_Will_Work % (the green part is not part of the recognized name)
Variable Naming Conventions 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 variable numbers. When appropriate, it is interpreted as a scalar, vector or matrix. scalar vector matrix scalar vector matrix 1×1 n × 1 or 1 × n n×m The size of an array is specified by the number of The rows and the number of columns in the array, with the number of rows indicated first. the
Scalars  Scalars are 1×1 arrays.  They contain a single value, for example: r=6 height = 5.3 width = 9.07
Vectors Vectors A vector is a list of numbers expressed as a 1 vector  dimensional array. dimensional A vector can be n×1 or 1×n.  Columns are separated by commas (or spaces): Columns commas  h = [1, 2, 3] Rows are separated by semicolons: Rows semicolons  v = [1; 2; 3]
Matrices Columns 1 2 3 A matrix is a two  1 3.0 1.8 3.6 dimensional array of numbers. 2 4.6 2.0 21.3 Rows 3 0.0 6.1 12.8 For example, this is a  4×3 matrix: 4 2.3 0.3 6.1 m = [3.0, 1.8, 3.6; 4.6, -2.0, 21.3; 0.0, 2.0, -6.1, 12.8; 2.3, 0.3, -6.1] 6.1,
Indexedlocation of numbers in an array Columns Each item in an array 1 2 3  is located in the (row, column). 1 3.0 1.8 3.6 m(2,3) m(2,3) 2 4.6 2.0 21.3 Rows ans = ans 21.3000 21.3000 3 0.0 6.1 12.8 4 2.3 0.3 6.1
Examples  Enter the following into MATLAB: – Scalar: a=1 – Vectors: b = [1, 0, 2] c = [1 0 2] – Matrix: d = [5, 4, 3; 0, 2, 8]
Examples Examples Enter (input) the following matrix into MATLAB:  7 21 6 2 32 0 whiteRabbit = 5 0 18.5
Scalar Operations Scalar Operations Operation Algebraic MATLAB Syntax Syntax a + b a+b Addition a b a–b Subtraction a × b a .* b Multiplication a ÷ b a ./ b Division ab a .^ b Exponentiation
Array Operations Array Operations Arrays of numbers in MATLAB can be interpreted as  vectors and matrices if vector or matrix algebra is to be applied. Recall that matrices are mathematical objects that can be multiplied by the rules of matrices. To do matrix multiplication, you need to use the standard *, /, and ^ operators [without the preceding . (dot)]. They are operators [without the preceding not for array multiplication, division and exponentiation. To deal with arrays on an elementbyelement level we  need to use the following array or dotoperators: .* , ./ .^ .* ./ and and
Array operations & dotoperators Array operations & dotoperators .* , ./ .^ ./ and and  Because scalars are equivalent to a 1×1 array, you can either use the standard or the dotoperators when doing multiplication, division and exponentiation of scalars (i.e., of single numbers).  It is okay for you to always use the dot operators, unless you intend to perform vector or matrix multiplication or division.
Array vs. Matrix Operations Example:  x = [ 2, 1; 3, 4] y = [ 5, 6; 7, 8] z = x .* y results in [10, 6; 21, 32]; this is array multiplication z=x*y results in [17, 20; 43, 50]; this is matrix multiplication So, do NOT forget the dot when doing array operations! (.* ./ .^)
Hierarchy of Operations Hierarchy of Operations Just like in mathematics the operations are done in the following order: Left to right doing what is in Parentheses & Exponents first, followed by Multiplication & Division, and then Addition & Subtraction last. An example: c = 2+3^2+1/(1+2) 1st c = 2+3^2+1/3 c = 2+3^2+1/(1+2) 2nd c = 2+9+1/3 c = 2+3^2+1/(1+2) 3rd c = 2+9+0.33333 c = 2+3^2+1/(1+2) 4th c = 11+0.33333 11 c = 2+3^2+1/(1+2) 5th c = 11.33333 2+3^2 11.33333
Handson Handson  Enter these two arrays into MATLAB: a= b= 10 5 5 1 0 2 10 2 9 0 0 0 0 6 8 8 1 1 0  Multiply, elementbyelement, a × b. – Since this is an array operation, the .* multiplication operation is implied by the request.
Defining & manipulating arrays Defining & manipulating arrays  All variables in MATLAB are arrays! – Single number array & scalar: 1×1 – Row array & row vector: 1×n – Column array & column vector: nx1 – Array of n rows x m columns & Matrix: n×m – Naming rules – Indexed by (row, column) Indexed  Remark: vectors and matrices are special mathematical objects, arrays are lists or tables of numbers. tables