Transcript Programming in MATLAB

ME 303
Programming in MATLAB
Outline of Lecture
• What is Matlab? Windows?
• Data Types
– arrays: char, numeric, struct, cell
• Operators
– arithmetic, relational, logical
• Flow Control
– conditionals, case, while, etc.
• M-functions
– syntax
– examples of simple functions
– writing and debugging a simple MATLAB function
What is Matlab ?
•
MATLAB® is a high-performance language for technical computing. It integrates computation,
visualization, and programming in an easy-to-use environment where problems and solutions are
expressed in familiar mathematical notation.
•
MATLAB is an interactive system whose basic data element is an array that does not require
dimensioning. This allows you to solve many technical computing problems, especially those with matrix
and vector formulations, in a fraction of the time it would take to write a program in a scalar
noninteractive language such as C or Fortran. So where other programming languages work with
numbers one at a time, MATLAB allows you to work with entire matrices quickly and easily.
FORTRAN:
real*8 A(10,10), B(10,10), C(10,10)
do i=1,10
do j=1,10
C(i,j) = A(i,j) + B(i,j)
10 continue
20 continue
MATLAB:
•
C=A+B
The name MATLAB stands for matrix laboratory.
What is Matlab ?
• A software environment for interactive (No need to declare
variables) numerical computations
• >> 2+3*4/2
• >> a=5e-3; b=1; a+b
• Examples:
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Matrix computations and linear algebra
Solving nonlinear equations
Numerical solution of differential equations
Mathematical optimization
Statistics and data analysis
Signal processing
Modelling of dynamical systems
Solving partial differential equations
Simulation of engineering systems
M-file editor/debugger window
Getting Help
To get help:
MATLAB main menu
-> Help
-> MATLAB Help
Getting Help
• Type one of the following commands in the
command window:
–
–
–
–
–
help – lists all the help topics
help topic – provides help for the specified topic
help command – provides help for the specified command
helpwin – opens a separate help window for navigation
Lookfor keyword – search all M-files for keyword
• Online resource(http://www.mathworks.com)
• >> demo in matlab
Variables
• Variable names:
– Must start with a letter.
– May contain only letters, digits, and the underscore “_”.
– MATLAB is case sensitive, for example one & ONE are different
variables.
– MATLAB only recognizes the first 31 characters in a variable name.
• Assignment statement:
– Variable = number;
– Variable = expression;
• Example: >> t = 1234;
– >> t = 1234
– t=
–
1234
Variables
• Special variables:
–
–
–
–
–
ans: default variable name for the result.
pi: π = 3.1415926 ……
eps: ε= 2.2204e-016, smallest value by which two numbers can differ
inf: ∞, infinity
NAN or nan: not-a-number
• Commands involving variables:
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who: lists the names of the defined variables
whos: lists the names and sizes of defined variables
clear: clears all variables
clear name: clears the variable name
clc: clears the command window
clf: clears the current figure and the graph window
Arrays
• A row vector in MATLAB can be created by an explicit list, starting with
a left bracket, entering the values separated by spaces (or commas) and
closing the vector with a right bracket.
• A column vector can be created the same way, and the rows are separated
by semicolons.
• Example:
– >> x = [ 0 0.25*pi 0.5*pi 0.75*pi pi]
– x=
x is a row vector.
–
0 0.7854 1.5708 2.3562 3.1416
– y=[0; 0.25*pi; 0.5*pi; 0.75*pi; pi]
– y=
y is a column vector.
–
0
–
0.7854
–
1.5708
–
2.3562
–
3.1416
Arrays
• Vector Addressing- A vector element is addressed in
MATLAB with an integer index enclosed in parentheses.
• Example:
– >> x(3)
– ans =
–
1.5708 <- 3rd element of vector X
• The colon notation may be used to address a block of
elements
•
(start:increment:end)
• Example:
– >> x(1:2:5)
– ans =
–
0 1.5708 3.1416
Arrays
• Some useful commands:
x = start:end
x = start:increment:end
Create row vector x starting with start, counting by 1 , ending at
end
Create row vector x starting with start, counting by increment,
ending at or before end
x = linspace(start,end,number)
Create linearly spaced row vector x starting with start, ending at
end, having number elements
x = logspace(start,end,number)
Create logarithmically spaced row vector x starting with start,
ending with end, having number elements
length(x)
y = x’
dot(x,y),cross(x,y)
Returns the length of vector x
Transpose of vector x
Returns the scalar dot and vector cross product of the vector x
and y
Matrices
• A matrix
–
–
–
–
–
–
rectangular array of numbers
1-by-1 matrices, which are scalars, and
to matrices with only one row or column, which are vectors.
It begins with [, and end with ]
Spaces or commas are used to separate elements in a row
Semicolon or enter is used to separate rows
• A = [1,2,3;4,-5,6;5,-6,7]
• MATLAB has other ways of storing both numeric and
nonnumeric data, but in the beginning, it is usually best to
think of everything as a matrix.
Matrices
Indexing Matrices
•Indexing using parentheses
•>> A(2,3)
•Index submatrices using vectors
of row and column indices
•>> A([2 3],[1 2])
•Ordering of indices is important!
•>> B=A([3 2],[2 1])
•>> B=[A(3,2),A(3,1);A(2,2);A(2,1)]
Matrices
Indexing Matrices
•Index complete row or column using
the colon operator
•>> A(1,:)
•Can also add limit index range
•>> A(1:2,:)
•>> A([1 2],:)
•General notation for colon operator
•>> v=1:5
•>> w=1:2:5
Matrices
• Element-by-Element Array-Array Mathematics
operation
Algebraic Form
MATLAB
Addition
a+b
a+b
Subtraction
a–b
a–b
Multiplication
axb
a .* b
Division
a/b
a ./ b
Exponentiation
ab
a .^ b
• Example:
•
•
•
•
•
>> x = [1 2 3];
>> y = [4 5 6];
>> z = x .* y
z =
4 10 18
Matrices
zeros(n)
Returns a n X n matrix of zeros
zeros(m,n)
Returns a m X n matrix of zeros
ones(n)
Returns a n X n matrix of ones
ones(m,n)
Returns a m X n matrix of ones
size(A)
For a m X n matrix A, returns the row vector [m,n] containing the number of rows
and columns in matrix
length(A)
Returns the larger of the number of rows or columns in A
Transpose
B=A’
Identity Matrix
Addition and Subtraction
eye(n) -> returns an n X n identity matrix
eye(m,n) -> returns an m X n matrix with ones on the main diagonal and zeros
elsewhere
C =A +B
C =A - B
Scalar Multiplication
B = α A, where α is a scalar
Matrix Multiplication
C =A* B
Matrix Inverse
B = inv(A), A must be a square matrix in this case
Matrix powers
B = A * A , A must be a square matrix
Determinant
det(A), A must be a square matrix
Expressions
Variables
S=5, Ali=6, a=4
A=3
a=?
Variables are stored in the workspace
who – list current variables
whos – detailed list of variables
clear – removes all variables from the workspace
Numbers
3
9.6397238
1i
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-99
0.0001
1.60210e-20 6.02252e23
-3.14159j
3e5i
All numbers are stored internally using the long format.
16 significant decimal digits and
a finite range of roughly 10-308 to 10+308.
Functions
Help elfun
Help specfun
Help elmat
Data Types in MATLAB
Data Types in MATLAB
Uint8 and Doubles(Numeric)
• Double
– almost all MATLAB functions
• expect doubles as arguments
• return doubles
• e.g.,
• need to convert uint8 to
double before performing
any math operations
» a = 1:10
a=
1 2 3 4 5 6 7 8 9 10
» b = uint8(a)
b=
1 2 3 4 5 6 7 8 9 10
» whos
Name
Size
Bytes Class
a
b
1x10
1x10
80 double array
10 uint8 array
» b*2
??? Error using ==> *
Function '*' not defined for variables of class 'uint8'.
» (double(b))*2
ans =
2
4
6
8 10 12 14 16 18 20
Char Data Type
» c = ['hello'];
» whos
Name
Size
Bytes Class
c
1x5
10 char array
Grand total is 5 elements using 10 bytes
» c(1)
ans =
h
name = 'Thomas R. Lee';
The class and ischar functions show name's identity as a
character array: class(name)
ans =
char
ischar(name)
ans =
1
» d = [c,' again'];
»d
d=
hello again
»
» b = ['hello';'again'];
» size(b)
ans =
2 5
»b
b=
hello
again
»
Structure Data Type
image.name = 'Tom';
» image.height = 3;
» image.width = 3;
» image.data = [8 10 2; 22 7 22; 2 4 7];
» whos
Name
image
Size
Bytes Class
1x1
590 struct array
Grand total is 18 elements using 590 bytes
>> image.name = 'Tom'
image =
name: 'Tom'
>> image.height = 3;
>> image.height = 3
image =
name: 'Tom'
height: 3
>> image.data = [8 10 2; 22 7 22; 2 4 7]
image =
name: 'Tom'
height: 3
data: [3x3 double]
>> image.width = 3
image =
name: 'Tom'
height: 3
data: [3x3 double]
width: 3
>> image
image =
name: 'Tom'
height: 3
data: [3x3 double]
width: 3
Cell Arrays Data Type
•
A cell array provides a storage mechanism for dissimilar kinds of data. You can
store arrays of different types and/or sizes within the cells of a cell array. For
example, you can store a 1-by-50 char array, a 7-by-13 double array, and a 1-by-1
uint32 in cells of the same cell array.
•
To access data in a cell array, you use the same matrix indexing as with other
MATLAB matrices and arrays. However, with cell array indexing, you use curly
braces, {}, instead of square brackets an parentheses around the array indices.
For example, A{2,5} accesses the cell in row 2 and column 5 of cell array A.
Operators
• Arithmetic
– numeric computations, e.g., 2^10
• Relational
– quantitative comparison of operands
– e.g., a < b
• Logical
– AND, OR, NOT
– return Boolean variable, 1 (TRUE) or 0 (FALSE)
Arithmetic Operators
• Transpose, a’
• Power, a^2
• Addition, multiplication, division
– a(1)*b(2)
– a*b
• works if a and b are matrices
with appropriate dimensions
(columns(a) = rows(b))
– a.*b (element by element)
• except for matrix operations, most
operands must be of the same size,
unless one is a scalar
Arithmetic Operators
• Transpose, a’
• Power, a^2
• Addition, multiplication, division
– a(1)*b(2)
– a*b
• works if a and b are matrices
with appropriate dimensions
(columns(a) = rows(b))
– a.*b (element by element)
• except for matrix operations,
operands must be of the same size,
unless one is a scalar
» a = [2 3];
» b = [4 5];
» a(1)*b(2)
ans =
10
» a*b
??? Error using ==> *
Inner matrix dimensions
must agree.
» a*b'
ans =
23
» a.*b
ans =
8 15
» b/2
ans =
2.0000 2.5000
Relational Operators
• <, <=, >, >=, ==, ~=
• compare corresponding elements
of arrays with same dimensions
• if one is scalar, one is not, the scalar
is compared with each element
• result is element by element, 1 or 0
Relational Operators
• <, <=, >, >=, ==, ~=
• compare corresponding elements
of arrays with same dimensions
• if one is scalar, one is not, the scalar
is compared with each element
• result is element by element 1 or 0
»a
a=
2
3
»b
b=
4
5
»a>b
ans =
0 0
»b>a
ans =
1 1
»a>2
ans =
0 1
Logical Operators
• Logical operators (combinations of relational operators)
• & (and)
| (or)
~ (not)
• Logical functions
xor
isempty
any
all
Flow Control
• If
– if logical_expression
–
statements
– End
if (beta(1)==0)&(alpha(1)~=0)
K(1,1)=K(1,1)-(ko*beta(1)/alpha(1));
F(1)=F(1)-(ko*gama(1)/alpha(1));
end
•Else and elseif
•The else statement has no logical condition. The statements associated with it execute
if the preceding if (and possibly elseif condition) is false (0).
•The elseif statement has a logical condition that it evaluates if the preceding if (and
possibly elseif condition) is false (0). The statements associated with it execute if its
logical condition is true (1). You can have multiple elseif statements within an if block.
if n < 0
% If n negative, display error message.
disp('Input must be positive');
elseif rem(n,2) == 0 % If n positive and even, divide by 2.
A = n/2;
else
A = (n+1)/2; % If n positive and odd, increment and divide.
end
Flow Control
• switch, case, and otherwise
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 case
end
switch input_num
case -1
disp('negative one');
case 0
disp('zero');
case 1
disp('positive one');
otherwise
disp('other value');
end
Flow Control
• Use the for statement to loop a specific number of times.
• The while statement is more suitable for basing the loop execution on
how long a condition continues to be true or false.
• For
for index = start:increment:end
statements
end
for m = 1:5
for n = 1:100
A(m, n) = 1/(m + n - 1);
end
end
• While
while expression
statements
end
while prod(1:n) < 1e100
n = n + 1;
end
Flow Control
• Continue
• The continue statement passes control to the next iteration of
the for or while loop in which it appears, skipping any
remaining statements in the body of the loop.
• In nested loops, continue passes control to the next iteration
of the for or while loop enclosing it.
fid = fopen('magic.m', 'r');
count = 0;
while ~feof(fid)
line = fgetl(fid);
if isempty(line) | strncmp(line, '%', 1)
continue
end
count = count + 1;
end
disp(sprintf('%d lines', count));
Flow Control
• Break
• The break statement terminates the execution of a for loop
or while loop.
• When a break statement is encountered, execution continues
with the next statement outside of the loop. In nested loops,
break exits from the innermost loop only
fid = fopen('fft.m', 'r');
s = '';
while ~feof(fid)
line = fgetl(fid);
if isempty(line)
break
end
s = strvcat(s, line);
end
disp(s)
input-output
user_entry = input('prompt')
displays prompt as a prompt on the screen, waits for input from the keyboard, and returns
the value entered in user_entry.
user_entry = input('prompt','s')
returns the entered string as a text variable rather than as a variable name or numerical value
a=input('a=');
b=input('b=');
c=input(‘please neter the value…’);
reply = input('Do you want more? Y/N [Y]: ','s');
if isempty(reply)
reply = 'Y';
end
count = fprintf(fid,format,A,...)
formats the data in the real part of matrix A (and in any additional matrix arguments) under
control of the specified format string, and writes it to the file associated with file identifier
fid.
•Fid is 1 for standard output (the screen) or 2 for standard error.
•The format argument is a string containing C language conversion specifications
input-output
fprintf('A unit circle has circumference %g radians.\n',2*pi)
A unit circle has circumference 6.283186 radians.
B = [8.8 7.7; 8800 7700]
fprintf(1,'X is %6.2f meters or %8.3f mm\n',9.9,9900,B)
display the lines:
X is 9.90 meters or 9900.000 mm
X is 8.80 meters or 8800.000 mm
X is 7.70 meters or 7700.000 mm
ax 2  bx  c  0
x1  ?
x2  ?
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clear
disp('This program is written... ')
fprintf('\n')
a=input('enter a=');
while a==0
disp('a ya sifirdan farkli bir deger veriniz')
a=input('Please re-enter the value of a=');
end
Delta=b^2-4*a*c;
if Delta<0
‘No solution’
else
x1=(-b+sqrt(Delta))/(2*a);
x2=(-b-sqrt(Delta))/(2*a);
fprintf('First root=%5.5f \nSecond
root=%5.5f',x1,x2)
end
A,B,C
A=0 ?
Yes
No
Δ<0 ?
No
X1=…..
X2=…..
Yes
No solution
Plotting
• type help graph2d...
• Plotting a point:
1.5
1
– >>plot (variablename, ‘symbol’)
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Example: Complex variable
>>z = 1 + 0.5j;
>>plot(z,‘*')
Commands for axes:
0.5
0
-0.5
0
0.2
0.4
0.6
0.8
1
Command
Description
axis([xmin xmax ymin ymax])
Define minimum and maximum values of the axes
axis square
Produce a square plot
axis equal
Equal scaling factors for both axes
axis normal
Turn off axis square, equal
axis (auto)
Return the axis to defaults
1.2
1.4
1.6
1.8
2
Plotting
•
Plotting curves:
– plot(x,y) – generate a linear plot of the values of x (horizontal axis) and y (vertical
axis)
– semilogx(x,y) - generate a plot of the values of x (logarithmic scale) and y (linear
scale)
– semilogy(x,y) – loglog(x,y) - generate a plot of the values of x and y (both logarithmic scale)
•
Multiple curves
– plot(x,y,w,z) – multiple curves can be plotted on the same graph: y vs. x and z vs. w
– legend(‘string1’,’string2’, …) – used to distinguish between plots on the same graph
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Multiple figures
– figure(n) – use in creation of multiple plot windows before the command plot()
– close – closes the figure n window
– close all – closes all the plot windows
•
Subplots:
– subplot(m,n,p) – m by n grid of windows, with p specifying the current plot as the
pth window
Plotting
•
Example: (polynomial function)
– Plot the polynomial using linear/linear, log/linear, linear/log, log/log scale
y  2x2  7x  9
polynomial, linear/linear scale
polynomial, log/linear scale
300
300
200
200
y
y
100
0
100
0
5
0
-1
10
10
polynomial, linear/log scale
3
3
10
0
10
1
10
polynomial, log/log scale
10
2
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10
10
y
>>% generate te polynomial:
>>x=linspace(0,10,100);
>>y=2*x.^2+7*x+9;
>>% plotting the polynomial:
>>figure(1);
>>subplot(2,2,1),plot(x,y);
>>title('polynomial, linear/linear scale');
>>ylabel('y'),grid;
>>subplot(2,2,2),semilogx(x,y);
>>title('polynomial, log/linear scale');
>>ylabel('y'),grid;
>>subplot(2,2,3),semilogy(x,y);
>>title('polynomial, linear/log scale');
>>ylabel('y'),grid;
>>subplot(2,2,4),loglog(x,y);
>>title('polynomial, log/log scale');
>>ylabel('y'),grid;
y
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Plotting
Adding new curves to the exsiting graph
• Use the hold command to add lines/points to an existing plot
– hold on – retain existing axes, add new curves to current axes.
– hold off – release the current figure windows for new plots
• Grids and labels:
Command
Description
grid on
Add dashed grids lines at the tick marks
grid off
Removes grid lines (default)
Grid
Toggles grid status (off to on or on to off)
title(‘text’)
Labels top of plot with text
xlabel(‘text’)
Labels horizontal (x) axis with text
ylabel(‘text’)
Labels vertical (y) axis with text
text(x,y,’text’)
Adds text to location (x,y) on the current axes, where (x,y) is in units
from the current plot
M-Files
• Before, we have executed the commands in the command window. The
more general way is to create a M-file.
• The M-file is a text file that consists a group of MATLAB
commands.
• MATLAB can open and execute the commands exactly as if
they were entered at the MATLAB command window.
• To run the M-files, just type the file name in the command
window. (make sure the current working directory is set
correctly)
User Defined Function
• Add the following command in the beginning of your m-file:
• function [output variables] = function_name (input
variables);
– Note: the function_name should be the same as your file name to
avoid confusion.
• Calling your function:
– A user-defined function is called by the name of the m-file, not the
name given in the function definition.
– Type in the m-file name like other pre-defined commands.
• Comments:
– The first few lines should be comments, as they will be displayed if
help is requested for the function name. the first comment line is
reference by the lookfor command.
User Defined Function
• Example ( circle1.m)
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function y = circle1(center,radius,nop,style)
% circle1 draws a circle with center defined as a vector 'center'
% radius as a scalar 'radius'. 'nop' is the number of points on the circle
% 'style' is the style of the point.
% Example to use: circle1([1 3],4,500, ':');
[m,n] = size(center);
if (~((m == 1) | (n == 1)) | (m == 1 & n == 1))
error('Input must be a vector')
end
close all
x0=center(1);
y0=center(2);
t0=2*pi/nop;
axis equal
axis([x0-radius-1 x0+radius+1 y0-radius-1 y0+radius+1])
hold on
for i=1:nop+1
pos1=radius*cos(t0*(i-1))+x0;
pos2=radius*sin(t0*(i-1))+y0;
plot(pos1,pos2,style);
end
User Defined Function
•
In command window:
–
>> help circle1
–
circle1 draws a circle with center defined as a vector
'center' radius as a scalar 'radius'. 'nop' is the number of
points on the circle 'style' is the style of the point
Example to use: circle1([1 3],4,500,':');
–
•
Example: plot a circle with center (3,1), radius 5
using 500 points and style '--':
–
•
>> circle1([3 1],5,500,'--');
Result in the Figure window
References
• Matlab help
• www.mathworks.com
• 58:111 Numerical Calculations (Univ. Of Iowa)
• 2E1215 course of Mikael Johanson
• Matlab Workshop of Dr. Ali A. Jalali
• Hakan Çopur’s Introductory Matlab Presentation