Concatenation
• MATLAB lets you construct a new vector by
concatenating other vectors:
– A = [B C D ... X Y Z]
where the individual items in the brackets may be
any vector defined as a constant or variable, and
the length of A will be the sum of the lengths of the
individual vectors.
– A = [1 2 3 42]
is a special case where all the component elements
are scalar quantities.
Slicing (generalized indexing)
• A(4) actually creates an anonymous 1 × 1
index vector, 4, and then using it to extract
the specified element from the array A.
• In general,
B(<rangeB>) = A(<rangeA>)
where <rangeA> and <rangeB> are both index
vectors, A is an existing array, and B can be an
existing array, a new array, or absent altogether
(giving B the name ans). The values in B at the
indices in <rangeB> are assigned the values of A
from <rangeA> .
Example:
Exercise: Write Matlab code to create an array
oddv of odd indices from a vector v.
For example:
>> v = [1 4 9 16 25]
>> oddv = < your code here>
>> oddv
ans =
[1 9 25]
etc.
4.2. Matrices
Example: The following 2 x 3 matrix (matA) can be
created in Matlab as follows:
Dimension of a matrix can be accessed by function
called size.
Accessing and modifying array elements
Accessing and modifying array elements
Accessing and modifying array elements
Matrix operations
Matrix addition, multiplication, inverse, determinant etc.
Matrix operations
Matrix addition, multiplication, inverse, determinant, transpose
etc.
Logical indexing in 2-dim matrices
Exercise: Solve a linear system of equations:
3x + 5y – 6z= 11
4x – 6y + z = 9
-2x + 3y + 5z = –13
Sum, max, min, size etc.
4.3. Mixed Data Types
Discussions and exercises, Chapter 4
Exercise 4.1
Exercise 4.2
Write statements to do the following operations on a
vector x:
1) Return the odd indexed elements.
Exercise 4.2
Write statements to do the following operations on a
vector x:
2) Return the first half of x.
Exercise 4.2
Write statements to do the following operations on a
vector x:
3) Return the vector in the reverse order.
Exercise 4.3
Given a vector v, and a vector k of indices, write a
one or two statement code in Matlab that removes
the elements of v in positions specified by k.
Example:
>> v = [1, 3, 5, 7, 11, 9, 19]
>> k = [2, 4, 5]
>> < your code here>
>> v
ans =
1, 5, 9, 19
Exercise 4.3
Given a vector v, and a vector k of indices, write a
one or two statement code in Matlab that removes
the elements of v in positions specified by k.
Exercise 4.4 what does Matlab output for the
following commands?
1) 6 ~= 1 : 10
2) (6 ~= 1) : 10
Exercise 4.4 what does Matlab output for the
following commands?
1) 6 ~= 1 : 10
2) (6 ~= 1) : 10
Exercise 4.5. (This is quite tricky, especially without
using a loop construct like while or for.)
Write a statement to return the elements of a vector
randomly shuffled.
Hint provided is a useful one.
First understand how sort function works.
Array Manipulation
We consider the following basic operations on
vectors:
–
–
–
–
Creating an array
Extracting data from an array by indexing
Shortening an array
Mathematical and logical operations on arrays
Creating an Array – Constant Values
• Entering the values directly, e.g.
A = [2, 5, 7; 1, 3, 42] the semicolon
identifies the next row, as would a new
line in the command
• Using the functions zeros( rows, cols),
ones(rows, cols), rand(rows, cols) and
randn(rows, cols) to create vectors filled with
0, 1, or random values between 0 and 1
Indexing an Array
• The process of extracting values from an
array, or inserting values into an array
• Syntax:
– A(row, col) returns the element(s) at the
location(s) specified by the array row and
column indices.
– A(row, col) = value replaces the elements at the
location(s) specified by the array row and
column indices.
• The indexing row and column vectors may
contain either numerical or logical values
Operating on Arrays
Four techniques extend directly from
operations on vectors:
■ Arithmetic operations
■ Logical operations
■ Applying library functions
■ Slicing (generalized indexing)
The following deserves an additional word
because of the nature of arrays:
■ Concatenation
Array Concatenation
• Array concatenation can be accomplished
horizontally or vertically:
– R = [A B C] succeeds as long as A, B and C have
the same number of rows; the columns in R will
be the sum of the columns in A, B and C.
– R = [A; B; C] succeeds as long as A, B and C have
the same number of columns; the rows in R will
be the sum of the rows in A, B and C.
Reshaping Arrays
• Arrays are actually stored in column order in
Matlab. So internally, a 2 × 3 array is stored
as a column vector: A(1,1)
A(2,1)
A(1,2)
A(2,2)
A(1,3)
A(2,3)
• Any n × m array can be reshaped into any p ×
q array as long as n*m = p*q using the
reshape function.
Engineering Example—Computing Soil
Volume
• Consider the example where you are given the
depth of soil from a survey in the form of a
rectangular array of soil depth.
• You are also given the footprint of the foundations
of a building to be built on that site and the depth
of the foundation.
• Compute the volume of soil to be removed.
Survey Data
Building Footprint
Solution
clear
clc
% soil depth data for each square produced
% by the survey
dpth = [8 8 9 8 8 8 8 8 7 8 7 7 7 7 8 8 8 7
8 8 8 8 8 8 8 7 7 7 7 7 8 7 8 8 8 7
. . .
9 8 8 7 7 8 7 7 7 7 8 8 9 9 9 8 7 8];
% estimated proportion of each square that should
% be excavated
area = [1 1 1 1 1 1 1 1 1 1 .3 0 0 0 0 0 0 0
. . .
0 0 0 0 0 0 .4 .8 .9 1 1 1 1 1 1 1 1 .6];
square_volume = dpth .* area;
total_soil = sum(sum(square_volume))
Summary
This chapter introduced you to vectors and arrays. For
each collection, you saw how to:
■ Create them by concatenation and a variety of specialpurpose functions
■ Access and remove elements, rows, or columns
■ Perform mathematical and logical operations on them
■ Apply library functions, including those that summarize
whole columns or rows
■ Move arbitrary selected rows and columns from one
array to another
■ Reshape and linearize arrays