Array of all zeros>> zeros(2,3) rows,columns ans =
0 0 0
0 0 0
Array of all ones>> ones(3,1)
ans =
1
1
1
Manipulating vectors
Concatenating arrays>> x = [1,2]; y = [3,4];
>> [x, y]
ans =
1 2 3 4
>> [x; y]
ans =
1 2
3 4
Manipulating vectors� Extracting elements from arrays
>> x = [1 5 2 10];>> x(2)ans = Ones-based like Fortran 5 (not zeros-based like C)>> x(end)ans = 10>> x([3, 1]) You can also index with vectorsans = 2 1>> x(2:4) index by (start:end)ans = 5 2 10
Manipulating vectors� Finding elements in arrays
>> x = [-1 5 -2 10];
>> indx = find(x<0)
indx =
1 3 Returns indices of negative elements
>> x(indx) = 0
x =
0 5 0 10 The negative values have been set to zero
Vectorized computation
LOOPS(well, almost)
Vectorized computation� Example: y = cos x
Using Cint n, N;
float pi;
float x[100], y[100];
pi = 3.1415926;
N = 100;
dx = 2*pi/N;
x[0] = dx;
for(n=1;n<N;n++) {
y[n] = cos(x[n]);x[n+1] = x[n]+dx;
}
Using MATLAB
N = 100;
dx = 2*pi/N;
x = dx * (0:N-1);y = cos(x);
All mathematical functions are applied element-by-element to arrays!
#8^O
Vectorized computation� Vectorization is one key to Matlab’s power
� Example: y = e-2x cos xN = 101;x = linspace(0, 2*pi, N);y = exp(-2*x) .* cos(x);
Specialized toolboxes at Thayer forSignal and image processing (help signal, help images)Statistics Partial Differential EquationsOptimization (?)
Matlab programming
Matlab programs are called M-files
� Script M-filesA script is a list of Matlab commands
Create with Matlab editor, save as “myscript.m”
>> myscript executes the commands
Scripts are nice for hacking solutions together
Matlab programming� Function M-files
A function takes arguments and returns values function Tc = fahr2cel(Tf)
% FAHR2CEL Convert Fahrenheit to Celsius
% Tc = fahr2cel(Tf)
% Tf = temperature in Fahrenheit
% Tc = temperature in Celsius
Tc = 5/9 * (Tf - 32);
Matlab programmingUse fahr2cel.m like any other Matlab function
>> Tf = [-40 32 212];
>> fahr2cel(Tf)
ans =
-40 0 100
The first set of comments are its online help>> help fahr2cel
FAHR2CEL Convert Fahrenheit to Celsius
Tc = fahr2cel(Tf)
Tf = temperature in Fahrenheit
Tc = temperature in Celsius
Matlab programming� Matlab has if-else-end and if-elseif-else-end
IF expression statements
ELSEIF expression statementsELSE statementsEND
Also: switch (case)SWITCH switch_expression
CASE case_expression, statements .... OTHERWISE, statementsEND
Matlab programming
Sometimes (often) you really need a loopFOR expression
statements
END
WHILE expression
statements
END
Matlab programmingTo learn more about how functions are written, you can
list the M-files of many Matlab commands.
>> type fliplr%FLIPLR Flip matrix in left/right direction.% FLIPLR(X) returns X with row preserved and columns flipped% in the left/right direction.% % X = 1 2 3 becomes 3 2 1% 4 5 6 6 5 4
if ndims(x)~=2, error('X must be a 2-D matrix.'); end[m,n] = size(x);y = x(:,n:-1:1);
Advanced programming� Debugger� Profiler� File import/export� String manipulation� Data structures� Functions with variable numbers of arguments
Time for lab� Work through the examples� Write a function mybox(x) which implements the function
It can be done efficiently in three lines.� Back here at 11:00
�y = 1, |x| <= .5
0, otherwise{
Solutionfunction y = mybox(x)
% MYBOX Implement the lab assignment
y = zeros(size(x)); % Default to zeros
indx = find(abs(x) <= 0.5); % Find the points which will be 1
y(indx) = 1; % Change them
or
y(indx) = ones(size(indx));
Two-dimensional graphics� Basic plot
>> x = linspace(0, 2*pi, 51);
>> y = cos(x);
>> plot(x,y)
Two-dimensional graphics
Adding labelsLabelling commands
>> xlabel(‘x’);
>> ylabel(‘y’);
>> title(‘My First Graph’)
Interactively
Two-dimensional graphics� Points and curves
>> x = linspace(0, 2*pi, 21);
>> y = cos(x);
>> plot(x,y, x,y,’o’)
Two-dimensional graphics
� Points only>> plot(x,y,’o’)
or
>> stem(x, y)
Two-dimensional graphics� Multiple plots on the same axis
>> x = linspace(0, 2*pi, 51);
>> y = cos(x);
>> w = sin(x);
>> plot(x,y, x,w)
or
>> plot(x, y)
>> hold on This way is nice when you want to build
>> plot(x, w) a plot one graph at a time.
>> hold off
Two-dimensional graphics� Multiple plots in the same window
>> subplot(2,1,1) (m x n matrix of axes selecting pth axis)
