introduction to matlab session 1 simopekka vänskä, thl 2010

Introduction to MATLABSession 1

Simopekka Vänskä, THL2010

About this course

Introduction to MATLAB - Session 1

Focus of this course

...in learning to use MATLAB software Not in numerical methods (but some examples)

…to get some idea of the possibilities of MATLAB

We will not go through all properties of MATLAB. To get into a position for learning application specific

features.


Schedule and passing

ScheduleFive 3-hour sessionsHomework

Session working style Introduction to the topic + exercises, learning by doing

HomeworkEstimated work load 5-10 hoursMore information later

Passing the course (2 credits, passed/failed)Attendance min 3/5 sessions + passing the homework


Contents of this course

Session 2 Some matrix commands

Logical expressions

Graphics 1

Session 3 My functions + strings, cells

Controlling program flow

Session 4 Function functions

Session 5 Graphics 2

More linear algebra

Starting homework

Session 1Genaral

Matrices

M-files

MATLAB


What is MATLAB?Matrix Labratory

Array/Matrix is the basic data element

Environment for numerical computing>> quad(@(x) exp(sqrt(x.^2+1)), 0, 1)

ans =

3.1769 not for symbolic calculus

Library of mathematical functions

Programming language

Application-specific toolboxes


MATLAB desktop view


Getting started

Basic idea Workspace

Matrices and other data

elements are storaged in

the workspace

Commands who and whos

for listing the variables

Execute commands

(functions) to manipulate the

matrices in the workspace Matlab interpretes the

commands, no compiler

1. Start MATLAB

2. Create a working directory Under your personal home

directory

3. Set ”Current directory” to

your working directory

4. Create a variable v by typing

>> v = 5

in a command window and

try who and whos.

5. Write

>> exp(v)

and check the workspace.

MATRICES


Matrices (and vectors and scalars)

Matrix: the basic data element (n,m) array

Vector (n,1) matrix = column vector (1,m) matrix = raw vector

Scalar (1,1) matrix

Two ways to create matrices:

1. List the elements = is the substitution

Use [ ] brackets

2. Built-in functions (Load from a file)

Try the following:

>> A = [1 2 3; 5,6,7]

>> [1 2 3; 5,6,7]

>> B = [1 2 3; 5,6,7];

>> B

>> C=[A; B]

>> D = ones(2,4)

>> E = zeros(3)

>> E2 = zeros(1000)

>> F = zeros(1,4)

>> G = rand(10,1)

>> H = randn(10,1)

>> I = eye(5)

>> J = [ ]


More matrices Creating vectors with :, the

colon command a:b from a to b with step one

a:d:b from a to b with step d

Multi-dimensional matrices Some scalars

i and j : complex number

eps : small number

pi : Inf, NaN

Hint: Use ; for not showing the

result on the command window Hint: Command size(A) returns

the size of matrix A

Try the following

>> 1:4

>> 0:5:20

>> v = 20:-5:0

>> rand(2,3,4)

>> i

>> 5+3*i

>> i = 5

>> 5+3*i

>> eps

>> pi

>> 5e3

>> 5.4e-3

>> beta

>> help beta


Matrix arithmetics

Matrix arithmetics A+B, A-B A+c, A-c Matrix multiplication A*B Transpose A.’ and adjoint A’ Matrix power A^c

For noninteger c with

spectral calculus

\ left matrix divide Ax=y x=A\y = inv(A)*y

/ right matrix divide

Array arithmetics A+B, A-B A+c, A-c Array multiplication A.*B

Array power A.^c, A.^B

Array divide A./B

A, B matrices, c scalar – matrix sizes must match!


Reffering to vector elements

Let

v = [v1 v2 ... vn].

Refer to element vj with v(j)

v(J) J can be a matrix of indeces

v(J) is a matrix of size(J) and of

elements defined by J

Hint: Command length(v) returns

the length of vector v

Try the following:

>> v = 0:5:30

>> v([1 1 3])

>> v(2) = 15

>> v(2:4) = 3:5

>> J = [1 1; 2 2];

>> v(J)

>> v(10)

>> v(10)=100;


Reffering to matrix elements

Some properties Refer to entire column/raw with

the colon : A(:,5)

A(2,:)

A(:) is the matrix A as a vector Referring with end –command

A(3,5:end)

A(2:end, : )

Let

A = [a11 a12 ... a1m

a21 a22 ... a2m

an1 an2 ... anm].

Refer to element ajk with A(j,k)

or A(n*(k-1)+j)

Consider matrix as a column

vector (columns consecutively)

A(J,K) with index matrices J,K


…Reffering to matrix elements

Try the following

>> A = [1:4;5:8;9:12]

>> A(2,4)

>> A(11)

>> A(2,1:3)

>> A(2,:)

>> A([2 3],[3 1])

>> A(2:end,3)

>> A(5:end)

>> reshape(A,4,3)

>> help reshape

M-FILES


MATLAB m-files Not practical to write all commands in the command

window use m-files Text files of type *.m

For example, test1.m

Each line of an m-file is a MATLAB command line MATLAB executes the lines of an m-file by writing the

name of the file in the command window, (or F5 from the editor)

>> test1 Visibility: m-file has to be in the MATLAB’s current directory (or

in the MATLAB root)Can be written with any text editor

…but the MATLAB editor is preferable File New m-file (blank)

ProblemsSession 1


Problems

1. Go throw the previous ”Try the following” exercises 2. Are the following vectors the same?

a = [1 -2 3] b = [1 - 2 3] c = [1-2 3]

3. How much memory does the matrix I=ones(1000) need? How about I=ones(10000)? Clear memory with ”clear” command.

4. Set a=1 and b=i. Check the memory usage (whos).5. Compute

a) log(-1), b) sqrt(-1), c) 1/0.

6. See help format, and try:>> format long >> format short>> pi >> pi


Problems

Matrix manipulation – write your answers to m-files

7.Create (5,5) –matrix of zeros. Substitute random numbers (with rand –command) to raws 3-5. Delete the first and the last columns (=substitute empty matrix). Create a vector [0 1 0 1 … 0 1] of length 20. Create a vector [1,3,5,...,999,2,4,6,...,1000]. Create a vector [2,1,4,3,6,5,...,998,997,1000,999].

8.Create a (100,100) -matrix1 2 3 4 5 … 1001 2 3 4 5 … 100 … 1 2 3 4 5 … 100

Hint: Multiplication with matrix ones(100,1).


Problems

9. Let A = [1 2; 0 3]; Compute A*ej for e1 = [1;0] and e2=[0;1]; Compute A^2 and A.^2. Solve equation Ax=y for

a) y = [1;0]; b) y= [2;3]; c) y = [ i ; 0];

10.Create a ( : ,1000) matrix a) X2 whose columns are R2 rand vectors in the unit square,

b) X3 whose columns are R3 rand vectors in the unit cube. Compute the lengths of the random vectors. Calculate the average length of the random vectors.

11.Let p be a vector of annual interest rates% and let s be a vector of initial investments. Create a table A for the values of the investments after 10 years,

A(j,k) = s(k)*(1+p(j)/100)10.You can use e.g., p= .5:.5:5 and s = 2000:2000:10000.


Problems

12.Study sparse matrices from the MATLAB help >> help sparse

13.Create a sparse matrix S of size 2000x2000 with all diagonal elements 1, S(j,j)=1, and random lower diagonal S(j+1,j) = random number, j=1,…,1999. Check that S is correct with full(S(1:10,1:10)). Set y = ones(2000,1); and S2=full(S); Compare with tic toc –commands (see help tic) the speed of

solving Sx=y by tic; x=S\y; toc

tic; x=S2\y; toc

tic; x=inv(S)*y; toc (see help inv)

Can you explain the result?

>> quit

…to exit MATLAB.

introduction to matlab session 1 simopekka vänskä, thl 2010

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