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MATLAB Tutoriala whirlwind tourHinke Osingah.m.osinga@bris.ac.ukEngineering MathematicsQueen’s Building 2.12MATLAB Tutorial – p.1/30The BasicsMATLAB can do everything a calculator does>>(1+4)*3ans =15As is standard:+ and- are addition,/ is division and* is multiplication,ˆ is an exponentMATLAB Tutorial – p.2/30Everything is a Matrix!In MATLAB, a scalar is actually a 1×1 matrixa vector is an n×1 or 1× n matrix>>a = 3a =3a is the number 3, but also the 1×1 matrix [3]Here is how to create a row vector>>v = [1 2 3]v =1 2 3MATLAB Tutorial – p.3/30Everything is a Matrix!A semicolon tells MATLAB to start a new row, so>>w = [4; 5; 6]w =456is a column vector.With a’ you turn a column vector into a row vector>>w’ans =4 5 6MATLAB Tutorial – p.4/30Multiplication of matricesYou can multiply the vectorsv andw>>v*wans =32Recall: 1×3 times 3×1 gives 1×1Similarly, 3×1 times 1×3 gives 3×3>>A = w*vA =4 8 125 10 156 12 18MATLAB Tutorial – p.5/30Matrix operationsStandard multiplication is really matrix multiplicationDimensions must match!Try typing>>v*vHowever, MATLAB can do 1×1 times a matrix:>>3*ACheck what MATLAB does when adding a scalar anda matrix>>A + 2MATLAB Tutorial – p.6/30Elementwise operationsElementwise operations are done using a. before theoperator. For example, each element is squared using>>sqv = v.ˆ2sqv =1 4 9If two vectors (or matrices) have the same dimensionsyou can perform an elementwise ...

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Publié par

Fawyeng

Langue

English

MATLAB Tutorial

whirlwind tour

Hinke Osinga

h.m.osinga@bris.ac.uk

Engineering Mathematics

Queen's Building 2.12

MATLAB Tutorial p.1/30

The Basics

MATLAB can do everything a calculator does

>>(1+4)*3 ans =

15 As is standard:

+and-are addition, /is division and*is multiplication, ˆis an exponent

MATLAB Tutorial p.2/30

Everything is a Matrix!

In MATLAB, a scalar is actually a1×1matrix a vector is ann×1or1×nmatrix

>>a = 3 a = 3 ais the number 3, but also the1×1matrix[3] Here is how to create a row vector

>>v = [1 2 3] v = 1

MATLAB Tutorial p.3/30

Everything is a Matrix!

A semicolon tells MATLAB to start a new row, so

>>w = [4; 5; 6] w =

4 5 6

is a column vector. With a'you turn a column vector into a row vector >>w' ans =

MATLAB Tutorial p.4/30

Multiplication of matrices

You can multiply the vectorsvandw

>>v*w ans = 32

Recall:1×3times3×1gives1×1 Similarly,3×1times1×3gives3×3

>>A = w*v A =

4 8 12 5 10 15 6 12 18

MATLAB Tutorial p.5/30

Matrix operations

Standard multiplication is really matrix multiplication

Dimensions must match!

Try typing

>>v*v However, MATLAB can do1×1times a matrix:

>>3*A Check what MATLAB does when adding a scalar and a matrix

>>A + 2

MATLAB Tutorial p.6/30

Elementwise operations

lEementwiseoperationsareodnesuignabeforeteh

. operator. For example, each element is squared using

>>sqv = v.ˆ2 sqv = 1 4 9 If two vectors (or matrices) have the same dimensions you can perform an elementwise product

>>v.*sqv ans = 1

MATLAB Tutorial p.7/30

Functions operate elementwise

Functions operate on each element in a matrix:

>>exp(v) ans = 2.7183

>>log(ans) ans = 1 2

>>sqrt(v) ans = 1.0000

7.3891

1.4142

20.0855

1.7321

MATLAB Tutorial p.8/30

huonewdtituupityf

>>ans ans = 3.1416

; MATLAB saves the last output in the variableans.

>>y = tan(pi/6);

Special constants

>>pi ans = 3.1416

The variablepi

MATLAB Tutorial p.9/30

sirepaenamavtnlewiriablueπthvaerppusBAoehtsessTLMA

Dealing with Matrices

To create a matrix, you could do something like:

>>M = [-3 0 1; 2 5 -7; -1 4 8] The semicolons indicate the end of a row. All rows have to be the same length.

Theelementinthetihdror,wrstcloumn,is

M(3,1) You get the elements in rows 2 through 3 and columns 1 through 2, by typing

>>M(2:3,1:2) ans = 2 5 −1 4

MATLAB Tutorial p.10/30

Extract a submatrix

So, to get the entire second column, you type

>>M(1:3,2) which is the same as

>>M(:,2) which is literally telling MATLAB to use all rows second column

You get a whole row of a matrix with

>>M(1,:)

the

MATLAB Tutorial p.11/30

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