matlab graphics n one of the best things about matlab is interactive graphics “ plot ” is the...

MATLAB GraphicsMATLAB Graphics One of the best things about MATLAB is

interactive graphics “plot” is the one you will be using most often Many other 3D plotting functions -- plot3,

mesh, surfc, etc. Use “help plot” for plotting options To get a new figure, use “figure” logarithmic plots available using semilogx,

semilogy and loglog

plot(x,y) defaults to a blue line

plot(x,y,’ro’) uses red circles

plot(x,y,’g*’) uses magenta asterisks

If you want to put two plots on the same graph, use “hold on”

plot(a,b,’r:’) (red dotted line)hold onplot(a,c,’ko’) (black circles)

Plotting CommandsPlotting Commands

plot (x, y) plot(x1, y1, x2, y2)

plot (x, y, ‘color symbol line style’)

» x = linspace(0, 2*pi);» y = sin (2.*x);» z = cos (0.5*x);» plot (x, y)» plot (x, y, x, z)» figure (2)» plot (x, y, 'r o -'); grid on» hold on» plot (x, z, 'b * :')

(red, circle, solid line)

(blue, star, dotted line)

figure or figure (#) : open a figure

Plotting CommandsPlotting Commands

» xlabel (Time)» ylabel (Temperature)» title (Temperature Record : 1900 - 2000)» text (17, 120, Record High )» text (85, -40, Record Low )» axis ([0 100 -50 140])» hold off

xlabel ( label ) ylabel ( label )title ( title of the plot )text ( x_location, y_location, text )axis ( [ x_min x_max y_min y_max ] )

- text string

Graphics CommandsGraphics Commands Axis, Labels, and Title

Color, Symbols, and Line TypesColor, Symbols, and Line Types Use “help plot” to find available Specifiers

b blue . point - solid

g green o circle : dotted

r red x x-mark -. dashdot

c cyan + plus -- dashed

m magenta * star

y yellow s square

k black d diamond

v triangle (down)

^ triangle (up)

< triangle (left)

> triangle (right)

p pentagram

h hexagram

Colors Symbols Line Types

» x=0:0.1:5;» y=2*x.^3-12*x.^2+8*x-6;» H=plot(x,y,'b',x,y,'r*');» set(H,'LineWidth',3,'MarkerSize',12)» xlabel('x'); ylabel('y');» title('f(x)=2x^3-12x^2+8x-6');» print -djpeg075 poly.jpg

element-by-element operations x.^n

Adjust line thickness, font size, marker size, etc.

» x=0:0.1:10;» y=sin(2.*pi*x)+cos(pi*x);» H1=plot(x,y,'m'); set(H1,'LineWidth',3); hold on;» H2=plot(x,y,'bO'); set(H2,'LineWidth',3,'MarkerSize',10); hold off;» xlabel('x'); ylabel('y');» title('y = sin(2\pix)+cos(\pix)');» print -djpeg075 function.jpg

» x=0:0.1:3; y1=exp(-x); y2=sqrt(x);» H=plot(x,y1,'b-',x,y2,'r--');» set(H,'LineWidth',3)» xlabel('x'); ylabel('y'); title('MATLAB Plots');» H1=text(1.8,0.2,'exp(-x)'); set(H1,'FontSize',18);» H2=text(1.8,1.3,'sqrt(x)'); set(H2,'FontSize',18);

3-D plots generate a grid containing the x and y values of each point.

x = 0:0.2:2*pi;  % create vector of points on x-axis y = 0:0.2:2*pi;  % create vector of points on y-axis

% Now if n=length(x) and m=length(y), the grid will contain % N=n*m grid points.  XX and YY are n by m matrices containing % the x and y values for each grid point respectively. [XX,YY] = meshgrid(x,y);

% The convention in numbering the points is apparent from % the following lines. x2 = 1:5; y2 = 11:15; [XX2,YY2] = meshgrid(x2,y2); XX2, YY2

% This shows that XX2(i,j) contains the jth component of the % x vector and YY2(i,j) contains the ith component of the y vector.

% Now, we generate a function to save as a separate z-axis value % for each (x,y) 2-D grid point. Z1 = sin(XX).*sin(YY);  % calculate value of function to be plotted

% create a colored mesh plot figure; mesh(XX,YY,Z1); xlabel('x'); ylabel('y'); zlabel('z'); title('sin(x)*sin(y)');

% create a colored surface plot figure; surf(XX,YY,Z1); xlabel('x'); ylabel('y'); zlabel('z'); title('sin(x)*sin(y)');

% create a contour plot figure; contour(XX,YY,Z1); xlabel('x'); ylabel('y'); zlabel('z'); title('sin(x)*sin(y)');

% create a filled contour plot with bar to show function values figure; contourf(XX,YY,Z1); colorbar; xlabel('x'); ylabel('y'); zlabel('z'); title('sin(x)*sin(y)');

% create a 3-D contour plot figure; contour3(XX,YY,Z1); xlabel('x'); ylabel('y'); zlabel('z'); title('sin(x)*sin(y)');

subplot ( m, n, p ) --

breaks the figure window into m by n small figures, select the p-th figure for the current plot

» figure (3)» subplot (3, 2, 1)» plot (t,wv1)» subplot (3, 2, 2)» plot (t,wv2)» subplot (3, 2, 4)» plot (t, wv1+wv2)» subplot (3, 2, 6)» plot (t, wv1-wv2)

MATLAB SubplotsMATLAB Subplots

1 2

3 4

5 6

MATLAB SubplotsMATLAB Subplots Filename waves2.m (script file)

% Plot Bi-chromatic Wave Profile% Display the results in three subplotsclf % clear the graphics windowa1 = 1; a2 = 1.5; c1 = 2.0; c2 = 1.8;time = 0:0.1:100;wave1 = a1 * sin(c1*time);wave2 = a2 * sin(c2*time);wave3 = wave1 + wave2;subplot(3,1,1) % top figureplot(time,wave1,'m'); axis([0 100 -3 3]); ylabel('wave 1');subplot(3,1,2) % middle figureplot(time,wave2,'g'); axis([0 100 -3 3]); ylabel('wave 2');subplot(3,1,3) % bottom figureplot(time,wave3,'r'); axis([0 100 -3 3]);xlabel(’time'); ylabel('waves 1&2');

» x=0:0.1:10; y1=sin(pi*x); y2=sin(0.5*pi*x); y3=y1+y2;» z1=cos(pi*x); z2=cos(0.5*pi*x); z3=z1-z2;» subplot(3,2,1); H1=plot(x,y1,'b'); set(H1,'LineWidth',2);» subplot(3,2,2); H2=plot(x,z1,'b'); set(H2,'LineWidth',2);» subplot(3,2,3); H3=plot(x,y2,'m'); set(H3,'LineWidth',2);» subplot(3,2,4); H4=plot(x,z2,'m'); set(H4,'LineWidth',2);» subplot(3,2,5); H5=plot(x,y3,'r'); set(H5,'LineWidth',2);» subplot(3,2,6); H6=plot(x,z3,'r'); set(H6,'LineWidth',2);

Subplot (m,n,p)

Multiple plots

Interactive inputInteractive input The input function allows you to prompt the user

for values directly from the command window

Enter either “value” or “string”

n = input(‘promptstring’)

name = input ('Enter your name: ');

name = input('Enter your name: ','s');

sid = input('Enter your student ID: ');

phone = input('Enter your Telphone number: ','s');

email = input('Enter your Email address: ','s');

string

value

M-Files: Scripts and FunctionsM-Files: Scripts and Functions You can create and save code in text files using

MATLAB Editor/Debugger or other text editors (called m-files since the ending must be .m)

A script can be executed by typing the file name, or using the “run” command

Difference between scripts and functionsDifference between scripts and functions

Scripts share variables with the main workspace

Functions do not

Comments!!!Comments!!!

Program DocumentationProgram Documentation

You must include comments in the computer programs you turn in -- otherwise we will have great difficulty knowing what you are doing

Comments are indicated by “%” at the beginning of the line

Script FilesScript Files Script file – a series of MATLAB commands

saved on a file, can be executed by

typing the file name in the Command Window invoking the menu selections in the Edit Window:

Debug, Run

Create a script file using menu selection: menu File -> New -> M-file opens the integrated

MATLAB text editor for writing a m-file.

Function FileFunction FileStructured programming with functions

Function FileFunction File Function file: M-file that starts with the word function

Function can accept input arguments and return outputs

Analogous to user-defined functions in programming languages such as Fortran, C, …

Save the function file as function_name.m

User help function in command window for additional information

FunctionsFunctions One output variable

function y = function_name(input arguments) More than one output variables

function [y, z] = function_name(input arguments)

Examples: function y = my_func (x)

y = x^3 + 3*x^2 -5 * x +2 ;

Function M-FilesFunction M-Files Function M-file can return more than one result Example – mean and standard deviation of a vector

function [mean, stdev] = stats(x)

% calculate the mean and standard deviation of a vector x

n = length(x);

mean = sum(x)/n;

stdev = sqrt(sum((x-mean).^2/(n-1)));

>> x=[1.5 3.7 5.4 2.6 0.9 2.8 5.2 4.9 6.3 3.5];

>> [m,s] = stats(x)m = 3.6800s = 1.7662

Interactive M-FileInteractive M-File An interactive M-file for free-falling bungee jumper

Use input and disp functions for input/output

function velocity = freefallinteract

% freefallinteract()

% compute the free-fall velocity of a bungee jumper

% input: interactive from command window

% output: ve;ocity = downward velocity (m/s)

g=9.81; % acceleration of gravity

m = input('Mass (kg): ');

cd = input('Drag coefficient (kg/m): ');

t = input('Time (s): ');

disp(' ')

disp('Velocity (m/s):')

vel = sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t);disp([t;vel]')

Interactive M-FileInteractive M-File>> freefallinteractMass (kg): 68.1Drag coefficient (kg/m): 0.25Time (s): 0:1:20 Velocity (m/s): 0 0 1.0000 9.6939 2.0000 18.7292 3.0000 26.6148 4.0000 33.1118 5.0000 38.2154 6.0000 42.0762 7.0000 44.9145 8.0000 46.9575 9.0000 48.4058 10.0000 49.4214 11.0000 50.1282 12.0000 50.6175 13.0000 50.9550 14.0000 51.1871 15.0000 51.3466 16.0000 51.4560 17.0000 51.5310 18.0000 51.5823 19.0000 51.6175 20.0000 51.6416

Problem-Solving MethodologyProblem-Solving Methodology State the problem clearly Describe the Input/Output (I/O) Work the problem by hand or with a

calculator for a simple set of data Algorithm Develop a MATLAB Solution Debugging and Testing Optimize the program and make a document

Structured ProgrammingStructured Programming

The ideal style of programming is StructuredStructured or ModularModular programming

Break down a large goal into smaller tasks Develop a module for each task A module has a single entrance and exit Modules can be used repeatedly A subroutinesubroutine (function M-file)(function M-file) may contain several

modules Subroutines (Function M-files) called by a main

program

Algorithm DesignAlgorithm Design

The sequence of logical steps required to

perform a specific task (solve a problem)

Each step must be deterministic The process must always end after a finite

number of steps The algorithm must be general enough to deal

with any contingency

Common Program StructuresCommon Program Structures

Sequence Selection Repetition

Structured ProgrammingStructured Programming

Sequential paths Sequence – all instructions (statements) are

executed sequentially from top to bottom

Non-sequential paths Decisions (Selection) – if, else, elseif Loops (Repetition) – for, while, break

Relational OperatorsRelational Operators MATLAB provides these relational operators.

MATLAB == ~= < <= > >= & | ~

Interpretation is equal to is not equal to is less than is less than or equal to is greater than is greater than or equal to and, true if both are true or, true if either one is true not

Logical ConditionsLogical Conditions ~ (not) – logical negation of an expression ~ expression If the expression is true, the result is false.

Conversely, if the expression is false, the result is true.

& (and) – logical conjunction on two expressions

expression1 & expression2

If both expressions are true, the result is true. If either or both expressions are false, the result is false.

| (or) – logical disjunction on two expressions

expression1 | expression2

If either or both expressions are true, the result is true

True Table for Logical OperatorsTrue Table for Logical Operators Order of priority of logical operators

x y ~x x&y x|y

T T F T T

T F F F T

F T T F T

F F T F F

Logical OperatorsLogical Operators 0 - 1 matrix 0: false ; 1: True

a=[2 4 6] b=[3 5 1] c=[4 3 2] a<b ans = 1 1 0 b<c ans = 1 0 1 a ~= b ans = 1 1 1 a<b&b<c ans = 1 0 0 a <= b | b >= c ans = 1 1 0

Example of a Complex DecisionExample of a Complex Decision

If a=-1, b=2, x=1, and y=‘b’, evaluate

A * b > 0 & b == 2 & x > 7 | ~(y > ‘d’)

1. Expression 1: A*b = -2 > 0 (false)

2. Expression 2: b = 2 (true)

3. Expression 3: x = 1 > 7 (false)

4. Expression 4: ‘b’ > ‘d’ (false)

5. Expression 5: ~(Expression 4) (true)

6. Expression 6: (Expression 1) & (Expression 2) (false)

7. Expression 7: (Expression 6) & (Expression 3) (false)

8. Expression 8: (Expression 7) | (Expression 5) (true)

Complex DecisionComplex Decision A step-by-step evaluation of a complex decision

any & allany(A) Returns 1 for a vector where any element of the vector is true (nonzero), and 0 if no elements are true. all(A) Returns 1 for a vector where all elements of the vector are true (nonzero), and 0 if all elements are not true. A = [0 1 2; 0 -3 8; 0 5 0];any(A)ans = 0 1 1

all(A)ans = 0 1 0

Selection Selection ((IFIF)) Statements Statements The most common form of selection

structure is a simple if statement The if statement will have a condition

associated with it The condition is typically a logical

expression that must be evaluated as either “true” or “false”

The outcome of the evaluation will determine the next step performed

Logical IF StatementsLogical IF Statements If (condition) executable_statements end

-1 1x

1

y

if (x < = -1.0 | x > = 1.0) y = 0endif (x > -1.0 & x < 0.) y = 1 + xendif (x > = 0. & x < 1.0) y = 1- xend

Nested IF StatementNested IF Statement

if (condition or experssion1) statement blockelseif (condition or experssion2) another statement blockelse another statement blockend

Structures can be nested within each other

How to use Nested IFHow to use Nested IF If the condition is true the

statements following the statement block are executed.

If the condition is not true, then the control is transferred to the next

else, elseif, or end statement at the same if level.

Else and ElseifElse and Elseifif temperature > 100

disp(‘Too hot - equipment malfunctioning.’)

elseif temperature > 75

disp(‘Normal operating range.’)

elseif temperature > 60

disp(‘Temperature below desired operating range.’)

else

disp(‘Too Cold - turn off equipment.’)

end

Nested IF StatementsNested IF Statements nested if (if, if else, if elseif)

-1 1x

1

y

if (x < = -1.0)

y = 0.

elseif (x < = 0.)

y = 1. + x

elseif (x < = 1.0)

y = 1. - x

else

y=0.

end

M-file: Evaluate StudentsM-file: Evaluate Students GradeGrade function cven302_gradename = input('Enter Student Name: ','s');sid = input('Enter Student ID: ');HW = input('Enter Homework Average (30%): ');Exam1 = input('Enter Exam I score (20%): ');Exam2 = input('Enter Exam II score (20%): ');Final = input('Enter Final Exam score (30%): ');Average= HW*0.3 + Exam1*0.2 + Exam2*0.2 + Final*0.3; fprintf('Your Semester Average is: %6.2f \n',Average)if Average >= 90 Grade = 'A';elseif Average >= 80 Grade = 'B';elseif Average >= 70 Grade = 'C';elseif Average >= 60 Grade = 'D';else Grade = 'F';endfprintf('Your Semester Grade is : '), disp(Grade)

>> cven302_grade

Enter Student Name: Jane Doe

Enter Student ID: 1234567

Enter Homework Average (30%): 96

Enter Exam I score (20%): 88

Enter Exam II score (20%): 92

Enter Final Exam score (30%): 85

Your Semester Average is: 90.30

Your Semester Grade is : A

>> cven302_grade

Enter Student Name: John Doe

Enter Student ID: 9876543

Enter Homework Average (30%): 62

Enter Exam I score (20%): 84

Enter Exam II score (20%): 80

Enter Final Exam score (30%): 91

Your Semester Average is: 78.70

Your Semester Grade is : C

Decisions (Selections)Decisions (Selections) if … elseif if … elseif

StructureStructure

switch, case, and otherwiseswitch, case, and otherwiseswitch executes certain statements based on the value of a variable or expression. Its basic form is: switch expression (scalar or string) case value1 statements % Executes if expression is value1 case value2 statements % Executes if expression is value2 . . . otherwise statements % Executes if expression does not % match any caseend

switch, case, and otherwiseswitch, case, and otherwiseswitch 'b'

case -1 disp('negative one'); case 0 disp('zero'); case 'b'

disp('positive one'); otherwise disp('other value');end

Note for C Programmers Unlike the C language the, MATLAB switch executes only the first matching case; subsequent matching cases do not execute. Therefore, break statements are not used.

RepetitionRepetition

for i=1:mfor j=1:n

a(i,j)=(i+1)^2*sin(0.2*j*pi);end

end

while condition statementsend

For LoopsFor Loopsfor index = start : step : finish statementsend

for k = 1:length(d)

if d(k) < 30

velocity(k) = 0.5 - 0.3*d(k).^2;

else

velocity(k) = 0.6 + 0.2*d(k)-0.01*d(k).^2

end

end

Ends after a specified number

of repetitions

For LoopFor Loopfunction A = for_loop(m,n)

for i = 1:m

for j = 1:n

A(i,j) = 50*exp(-0.2*i)^2*sin(0.1*j*pi);

end

end

>> A = for_loop(8,6)

A =

10.3570 19.7002 27.1150 31.8756 33.5160 31.8756

6.9425 13.2054 18.1757 21.3669 22.4664 21.3669

4.6537 8.8519 12.1836 14.3226 15.0597 14.3226

3.1195 5.9336 8.1669 9.6007 10.0948 9.6007

2.0910 3.9774 5.4744 6.4356 6.7668 6.4356

1.4017 2.6661 3.6696 4.3139 4.5359 4.3139

0.9396 1.7872 2.4598 2.8917 3.0405 2.8917

0.6298 1.1980 1.6489 1.9384 2.0381 1.9384

For LoopFor Loop M-file for computing the factorial n! MATLAB has a built-in function factorial(n) to compute n!

function fout = factor(n)

% factor(n):

% Computes the product of all the integers from 1 to n.

x=1;

for i = 1:n

x = x*i;

end

fout = x;

>> factor(12)

ans =

479001600

>> factor(100)

ans =

9.332621544394410e+157

While LoopsWhile Loops

while condition statementsend

If the statement is true, the statements are executed

If the statement is always true, the loop becomes an “infinite loop”

The “break” statement can be used to terminate the “while” or “for” loop prematurely.

Ends on the basis of a logical condition

While LoopWhile Loop Compute your checking account balancefunction checking

% Compute balance in checking account

Balance = input('Current Checking Account Balance ($) = ');

Deposit = input('Monthly Deposit ($) = ');

Subtract = input('Monthly Subtractions ($) = ');

Month = 0;

while Balance >= 0

Month = Month + 1;

Balance = Balance + Deposit - Subtract;

if Balance >= 0

fprintf('Month %3d Account Balance = %8.2f \n',Month,Balance)

else

fprintf('Month %3d Account Closed \n',Month)

end

end

While LoopWhile Loop>> checking

Current Checking Account Balance ($) = 8527.20

Monthly Deposit ($) = 1025.50

Monthly Subtractions ($) = 1800

Month 1 Account Balance = 7752.70

Month 2 Account Balance = 6978.20

Month 3 Account Balance = 6203.70

Month 4 Account Balance = 5429.20

Month 5 Account Balance = 4654.70

Month 6 Account Balance = 3880.20

Month 7 Account Balance = 3105.70

Month 8 Account Balance = 2331.20

Month 9 Account Balance = 1556.70

Month 10 Account Balance = 782.20

Month 11 Account Balance = 7.70

Month 12 Account Closed

Example: Roots of Quadratic EquationExample: Roots of Quadratic Equation

a

acbbx

cbxax

2

4

02

2

If a=0, b=0, no solution (or trivial sol. c=0)

If a=0, b0, one real root: x=-c/b

If a0, d=b2 4ac 0, two real roots

If a0, d=b2 4ac <0, two complex roots

function quad = quadroots(a,b,c)% Computes real and complex roots of quadratic equation% a*x^2 + b*x + c = 0% Output: (r1,i1,r2,i2) - real and imaginary parts of the% first and second rootif a == 0 % weird cases if b ~= 0 % single root r1 = -c/b else % trivial solution error('Trivial or No Solution. Try again') end % quadratic formulaelsed = b^2 - 4*a*c; % discriminant if d >= 0 % real roots r1 = (-b + sqrt(d)) / (2*a) r2 = (-b - sqrt(d)) / (2*a) else % complex roots r1 = -b / (2*a) r2 = r1 i1 = sqrt(abs(d)) / (2*a) i2 = -i1 endend

>> quad = quadroots(5,3,-4)

r1 =

0.6434

r2 =

-1.2434

>> quad = quadroots(5,3,4)

r1 =

-0.3000

r2 =

-0.3000

i1 =

0.8426

i2 =

-0.8426

>> quad = quadroots(0,0,5)

??? Error using ==> quadroots

Trivial or No Solution. Try again

(two real roots)

(two complex roots)

(no root)