introduction ao matlab
DESCRIPTION
Introdução ao matlabTRANSCRIPT
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Introduction to Matlab
By: .Ycel zbek
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Outline:
What is Matlab? Matlab Screen Variables, array, matrix, indexing Operators (Arithmetic, relational, logical ) Display Facilities Flow Control Using of M-File Writing User Defined Functions Conclusion
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What is Matlab? Matlab MATLAB (Matrix laboratory) is
basically a high level language which has many specialized toolboxes for making things easier for us
Assembly
High Level Languages such as
C, Pascal etc.
Matlab
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What are we interested in? Matlab (C++ and LabView) are required in
almost every research position. Advantage: Good toolbox library Disavantage:
Longer processing time Price
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Free Clones Octave Scilab
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Matlab Screen Command Window
type commands
Current Directory View folders and m-files
Workspace View program variables Double click on a variable
to see it in the Array Editor
Command History view past commands save a whole session
using diary
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Variables No need for types. i.e.,
All variables are created with double precision unless specified and they are matrices.
After these statements, the variables are 1x1 matrices with double precision
int a;double b;float c;
Example:>>x=5;>>x1=2;
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Getting help The help command >> help The help window >> helpwin The lookfor command >> lookfor CANCEL >>CTR C GOOGLE: Matlab... lookfor scholesBLSLAMBDA Black-Scholes elasticity. BLSPRICE Black-Scholes put and call pricing. BLSRHO Black-Scholes sensitivity to interest rate change. .... help blspriceBLSPRICE Black-Scholes put and call pricing. [CALL,PUT] = BLSPRICE(SO,X,R,T,SIG,Q) returns the value ofcall and put options using the Black-Scholes pricing formula.SO isthe current asset price, X is the exercise price, R is the risk-free
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lookfor scholesBLSLAMBDA Black-Scholes elasticity. BLSPRICE Black-Scholes put and call pricing. BLSRHO Black-Scholes sensitivity to interest rate change. .... help blspriceBLSPRICE Black-Scholes put and call pricing. [CALL,PUT] = BLSPRICE(SO,X,R,T,SIG,Q) returns the value ofcall and put options using the Black-Scholes pricing formula.SO isthe current asset price, X is the exercise price, R is the risk-free
....
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Array, Matrix
a vector x = [1 2 5 1]
x =1 2 5 1
a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x =1 2 35 1 43 2 -1
transpose y = x y =1251
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Long Array, Matrix
t =1:10
t =1 2 3 4 5 6 7 8 9 10
k =2:-0.5:-1
k =2 1.5 1 0.5 0 -0.5 -1
B = [1:4; 5:8]x =
1 2 3 45 6 7 8
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Generating Vectors from functions zeros(M,N) MxN matrix of zeros
ones(M,N) MxN matrix of ones
rand(M,N) MxN matrix of uniformly distributed random numbers on (0,1)
x = zeros(1,3)x =
0 0 0
x = ones(1,3)x =
1 1 1
x = rand(1,3)x =0.9501 0.2311 0.6068
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Matrix Index The matrix indices begin from 1 (not 0 (as in C)) The matrix indices must be positive integer
Given:
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)Error: ??? Index exceeds matrix dimensions.
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Concatenation of Matrices
x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1 2 4 5
B = [x ; y]
1 24 5
C = [x y ;z] Error:??? Error using ==> vertcat CAT arguments dimensions are not consistent.
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Operators (arithmetic)
+ addition- subtraction* multiplication/ division^ power complex conjugate transpose
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Matrices Operations
Given A and B:
Addition Subtraction Product Transpose
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Operators Element by Element.* element-by-element multiplication./ element-by-element division.^ element-by-element power
FIND fuctionX = [1 0 4 -3 0 0 0 8 6];
find(X > 2)ans =
3 8 9
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The use of . Element Operation
K= x^2Erorr:??? Error using ==> mpower Matrix must be square.
B=x*yErorr:??? Error using ==> mtimes Inner matrix dimensions must agree.
A = [1 2 3; 5 1 4; 3 2 1]A =
1 2 35 1 43 2 -1
y = A(:,3)
y= 3 4 -1
b = x .* y
b=3 8 -3
c = x . / y
c= 0.33 0.5 -3
d = x .^2
d= 1 4 9
x = A(1,:)
x=1 2 3
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Math Functions
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Basic Task: Plot the function sin(x) between 0x4 Create an x-array of 100 samples between 0
and 4.
Calculate sin(.) of the x-array
Plot the y-array
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>plot(y)0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
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Plot the function e-x/3sin(x) between 0x4 Create an x-array of 100 samples between 0
and 4.
Calculate sin(.) of the x-array
Calculate e-x/3 of the x-array
Multiply the arrays y and y1
>>x=linspace(0,4*pi,100);
>>y=sin(x);
>>y1=exp(-x/3);
>>y2=y*y1;
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Plot the function e-x/3sin(x) between 0x4 Multiply the arrays y and y1 correctly
Plot the y2-array>>y2=y.*y1;
>>plot(y2)
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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Display Facilities
plot(.)
stem(.)
Example:>>x=linspace(0,4*pi,100);>>y=sin(x);>>plot(y)>>plot(x,y)
Example:>>stem(y)>>stem(x,y)
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80 90 100-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
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Display Facilities
title(.)
xlabel(.)
ylabel(.)
>>title(This is the sinus function)
>>xlabel(x (secs))
>>ylabel(sin(x))0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1This is the sinus function
x (secs)
s
i
n
(
x
)
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Display Facilities
HOLD ON holds the current plot HOLD OFF releases hold on current plot HOLD toggles the hold state SUBPLOT- display multiple axes
subplot(#rows, #cols, index)
subplot(2,2,1);
subplot(2,2,2) ...
subplot(2,2,3) ...
subplot(2,2,4) ...
subplot(2,2,1);
subplot(2,2,2) ...
subplot(2,2,3) ...
subplot(2,2,4) ...
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Alternative Scales for Axes
SEMILOGYlog Ylinear X
PLOTYY2 sets oflinear axes
LOGLOGBoth axes logarithmic
SEMILOGXlog Xlinear Y
other_axes
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Surface Plot Example
t = 0.001:0.001:0.03; s = 90:0.2:100; [gt, gs] = meshgrid(t,s); r = 0.1; k = 95; [call, put] =
blsprice(gs,k,r,gt,0.3); surf(t,s,call) xlabel('Time to Maturity') ylabel('Spot Price);
t = 0.001:0.001:0.03; s = 90:0.2:100; [gt, gs] = meshgrid(t,s); r = 0.1; k = 95; [call, put] =
blsprice(gs,k,r,gt,0.3); surf(t,s,call) xlabel('Time to Maturity') ylabel('Spot Price);
surface_ex
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3-D Surface Plotting
surf_3d
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Specialized Plotting Routines
spec_plots
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Operators (relational, logical)
== Equal to ~= Not equal to < Strictly smaller > Strictly greater = Greater than equal to & And operator | Or operator
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Flow Control
if for while break .
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Control Structures
If Statement Syntax
if (Condition_1)Matlab Commands
elseif (Condition_2)Matlab Commands
elseif (Condition_3)Matlab Commands
elseMatlab Commands
end
Some Dummy Examples
if ((a>3) & (b==5))Some Matlab Commands;
end
if (a
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Control Structures
For loop syntax
for i=Index_ArrayMatlab Commands
end
Some Dummy Examples
for i=1:100Some Matlab Commands;
end
for j=1:3:200Some Matlab Commands;
end
for m=13:-0.2:-21Some Matlab Commands;
end
for k=[0.1 0.3 -13 12 7 -9.3]Some Matlab Commands;
end
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Control Structures
While Loop Syntax
while (condition)Matlab Commands
end
Dummy Example
while ((a>3) & (b==5))Some Matlab Commands;
end
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Use of M-FileClick to create a new M-File
Extension .m A text file containing script or function or program to run
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Use of M-File
If you include ; at the end of each statement,result will not be shown immediately
Save file as Denem430.m
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Use of M-File
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Writing User Defined Functions
Functions are m-files which can be executed by specifying some inputs and supply some desired outputs.
The code telling the Matlab that an m-file is actually a function is
You should write this command at the beginning of the m-file and you should save the m-file with a file name same as the function name
function out1=functionname(in1)function out1=functionname(in1,in2,in3)function [out1,out2]=functionname(in1,in2)
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Writing User Defined Functions
Examples Write a function : out=squarer (A, ind)
Which takes the square of the input matrix if the input indicator is equal to 1
And takes the element by element square of the input matrix if the input indicator is equal to 2
Same Name
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Writing User Defined Functions Another function which takes an input array and returns the sum and product
of its elements as outputs
The function sumprod(.) can be called from command window or an m-file as
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Notes: % is the neglect sign for Matlab (equaivalent
of // in C). Anything after it on the same line is neglected by Matlab compiler.
Sometimes slowing down the execution is done deliberately for observation purposes. You can use the command pause for this purpose
pause %wait until any keypause(3) %wait 3 seconds
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Complex Numbers Another function which takes an input array and returns the sum and product
of its elements as outputs
z = 2+1.5*j, real(z) to get the result
z = 2.000+1.500i
ans = 2
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Variables
>>I = int8(zeros(100)); % Creates an intermediate array
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String Arrays: Created using single quote delimiter (')
Each character is a separate matrix element (16 bits of memory per character)
Indexing same as for numeric arrays
str = 'Hi there,'str =Hi there, str2 = 'Isn''t MATLAB great?'str2 =Isn't MATLAB great?
str = 'Hi there,'str =Hi there, str2 = 'Isn''t MATLAB great?'str2 =Isn't MATLAB great?
string_array
1x9 vectorstr = H i t h e r e ,
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String Arrays: str ='Hi there,'; str1='Everyone!'; new_str=[str, ' ', str1]new_str =Hi there, Everyone! str2 = 'Isn''t MATLAB great?'; new_str2=[new_str; str2]new_str2 =Hi there, Everyone!Isn't MATLAB great?
str ='Hi there,'; str1='Everyone!'; new_str=[str, ' ', str1]new_str =Hi there, Everyone! str2 = 'Isn''t MATLAB great?'; new_str2=[new_str; str2]new_str2 =Hi there, Everyone!Isn't MATLAB great?
1x19 vector
1x9 vectors
string_cat
Using [ ] operator:Each row must be same length
Row separator:semicolon (;)
Column separator:space / comma (,)
For strings of different length: STRVCAT STR2MAT new_str3 = strvcat(str, str2)new_str3 =
Hi there, Isn't MATLAB great?
new_str3 = strvcat(str, str2)new_str3 =Hi there, Isn't MATLAB great?
2x19 matrix
2x19 matrix(zero padded)
1x19 vectors
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String Arrays: String Comparisons
STRCMP - compare whole strings STRNCMP - compare first N characters FINDSTR - finds substring within a larger
string
Converting between numeric & string arrays: NUM2STR - convert from numeric to string
array STR2NUM - convert from string to numeric
array
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File I/O : High-level routines: SAVE & LOAD
Other file formats: csvread - comma-separated ASCII
files dlmread - general ASCII delimited
files textread - read formatted data
load fnameload fname x y zload fname -asciiload fname -matload fname*
load fnameload fname x y zload fname -asciiload fname -matload fname*
save fnamesave fname x y zsave fname data*save fname -asciisave fname -v4
save fnamesave fname x y zsave fname data*save fname -asciisave fname -v4
Use wildcard (*) for similar variables
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Low-level text file I/O:
This is a magic matrix17 23 4 10 1124 5 6 12 181 7 13 19 258 14 20 21 215 16 22 3 9
ASCII text file: magic5.txt
fid=fopen('magic5.txt', 'rt'); title = fgetl(fid); [data,count]=fscanf(fid, '%i'); data = reshape(data, 5, 5); fclose(fid);
fid=fopen('magic5.txt', 'rt'); title = fgetl(fid); [data,count]=fscanf(fid, '%i'); data = reshape(data, 5, 5); fclose(fid);help fprintf
Reading data from text file:
fid = fopen('magic5.txt', 'wt'); fprintf(fid, '%s\n', 'This is a magic matrix'); fprintf(fid, '%i\t%i\t%i\t%i\t%i\n', magic(5)); fclose(fid);
fid = fopen('magic5.txt', 'wt'); fprintf(fid, '%s\n', 'This is a magic matrix'); fprintf(fid, '%i\t%i\t%i\t%i\t%i\n', magic(5)); fclose(fid);
Writing data to text file:
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% This is a comment, it starts with a %clc % Clear command windowclear all % Clear variables in MatLaby = 5*3 + 2^2; % simple arithmeticx = [1 2 4 5 6]; % create the vector xx1 = x.^2; % square each element in xE = sum(abs(x).^2); % Calculate signal energyP = E/length(x); % Calculate av signal
Basic Matlab Operations
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% Calculate av signal powerx2 = x(1:3); % Select first 3 elements in xz = 1+i; % Create a complex numbera = real(z); % Pick off real partb = imag(z); % Pick off imaginary partplot(x); % Plot the vector as a signalt = 0:0.1:100; % Generate sampled timex3=exp(-t).*cos(t); % Generate a discrete signal plot(t, x3, x);% Plot points
Basic Matlab Operations
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%This shows how to save a table in ExcelcolumnHeader = {'t', 'x3'}; xlswrite('Table_1.xls',columnHeader,'Sheet1','A1'); %Saves the heather in Excelxlswrite('Table_1.xls',[t; x3]','Sheet1','A2'); %Saves the variables in Excel
%This reads the same table in Excelexcel_data = xlsread('Table_1.xls',);
Basic Matlab Operations
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Questions
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Thank You