Defining and Indexing Arrays

· One of the strengths of MATLAB is the capability to handle large collections of numbers, called arrays, as if they were a single variable. In fact, MATLAB handles the more familiar scalar variable as if it were an array that contains only one number or element. Indeed, in the last chapter, we saw how the range of motion of a piston is readily calculated with only a few commands for a range of values of crankshaft angle. As you work through the assigned sections of Chapter 2 you should see some of these strengths revealed in the simple examples in the text. In general, any mathematical operation that you can execute on a scalar variable can be executed on every element in an array with much the same simplicity. In order to operate on arrays, we must first know how to define arrays and extract specific subsets of data (indexing) in an array.

· Type in the lines below (all but the comment lines) one-by-one into the command window. Try to make sense of each command and MATLAB’s response as you go. Don’t rush this, it is critical stuff!!

%%% Clear everything and start fresh

clear all;close all;clc;

%%% Row vector

r1=[2 4 10 15 23]

r2=[5,6,7]

%%% Column vector

s1=[3;0;7]

s2=[2

5

8]

%%% Special array commands

x1=[2:.2:14]

x2=linspace(5,6,20)

x3=logspace(1,3,20)

%%% Setting up two dimensional arrays

M=[2 5;-3 4;-7 1]

N=[4 7 8

8 -2 -4

6 -3 0

-1 0 5]

%%% 1D Array (vector) indexing

r1=[2 4 10 15 23]

r1(1) % first element

r1(3) % element 3

r1([2:4]) % elements 2,3,4

r1([1:2:5]) % every other element 1,3,5

%%% 2D Array indexing

% Singe Elements

N(2,2)

% Column

N(:,2)

% Row

N(3,:)

%%% Special operations

% Size

[m,n]=size(N)

% Transposition

Nt=N'

% Maxima and minima

N

[x,y]=max(N)

[x,y]=min(N)

max(N)

max(N’)

% Sum (for a 2D matrix, sums columns, for a vector sums all elements).

sum(N)

sum(N’)

sum(sum(N))

% Turning a multidimensional array into a vector

Nv=N(:)

sum(Nv)