MATLAB demo - SAMSI

Introduction to Matlab
Xueying Wang
SAMSI Undergraduate Workshop Spring 2010
February 26, 2010
Xueying Wang
Introduction to Matlab

Introduction
MATLAB is an interactive software package which was developed
to perform numerical calculations on vectors and matrices. Initially,
it was simply a MATrix LABoratory. However, today it is much
more powerful:
• can do quite sophisticated graphics.
• is quite easy to code complicated algorithms involving vectors
and matrices.
• can numerically solve a wide variety of ODEs and PDEs.
• contains various toolboxes.
Xueying Wang
Introduction to Matlab

Getting started
• To begin a MATLAB session, type matlab or click on a
MATLAB icon and wait for the prompt, i.e ” ≫ ”, to appear. You
are now in the MATLAB workspace.
• To exit MATLAB, type exit or quit.
• To get help, typing
>> help
or
>> doc
gives you complete information about the command.
Xueying Wang
Introduction to Matlab

Things to know
1 Scalar, array and matrix calculations
2 Graphics
3 MATLAB functions
4 Programming
Xueying Wang
Introduction to Matlab

Scalar, array and matrix calculations
—– Scalar:
>> (17-1/9+pi*2.1)^3
>> ans % to provide the most recent answer
>> sin(6)
>> exp(2)
>> log(10)
—– Vectors:
>> v = [2 3 4]
>> v = 2:4
To compute
9∑
i=0
1
, you can enter
i
>> 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9
Xueying Wang
Introduction to Matlab

Scalar, array and matrix calculations, ctd
A simpler way is
>> x=1:9
>> 1./x % element-wise division
>> sum(ans) (i.e.>> sum(1./[1:9]))
—– Matrices:
>> A=rand(3) % a 3-by-3 matrix consisting of random
% numbers uniformly distributed on [0,1]
>> M=randn(2,6) % a 2-by-6 matrix containing random
% numbers which are drawn from
% the standard normal
>> zeros(4,7) % the 4-by-7 matrix of zeros
>> size(M) % the dimension of the matrix M
>> eye(3) % the 3-by-3 identity matrix
>> ones(4) % the 4-by-4 matrix of 1s
Xueying Wang
Introduction to Matlab

Scalar, array and matrix calculations, ctd
>> whos % list all variables in workspace
>> B=[1 2 3; 4 5 6; 7 8 9];
>> A*B % matrix multiplication
>> A.*B % element-wise multiplication
>> sqrt(B)
>> det(A) % the determinant of matrix A
>> inv(A) % the inverse of matrix A
>> b = rand(3,1);
To solve equations A x = b, we can type
>> x = inv(A)*b
or
>> x = A\b
Xueying Wang
Introduction to Matlab

Scalar, array and matrix calculations, ctd
>> % eigenvalues and eigenvectors of matrix A (A*V=V*D)
>> [V,D] = eig(A)
>> whos
>> save % save workspace variables to ’matlab.mat’
>> clear % removes all variables from the workspace
>> U = rand(1000,1);
>> N = randn(10^3,1)*3+1;
>> [mean(N),std(N)]
>> [min(N),max(N)]
>> norm(N)
Xueying Wang
Introduction to Matlab

Graphics: 2-d plot
>> n = 100;
>> x = 2*pi*[1:n]/n;
>> y1 = sin(x); y2 = 2*cos(x);
>> plot(x,y1)
>> hold on;
>> plot(x,y2);
>> hold off;
>> plot(x,y1,x,y2,’r.’)
>> xx = linspace(0, 2*pi,n);
>> figure;
>> plot(xx, sin(xx),’b*’, xx,2*cos(x),’r-’)
>> subplot(2,2,1); ezplot(@exp)
>> subplot(2,2,2); semilogy(x,exp(x));
>> subplot(2,2,3:4); loglog(x,exp(x));
Xueying Wang
Introduction to Matlab

Graphics: 3-d plot
>> x = [-3:0.1:3]’;
>> y = [-2:0.1:2]’;
>> [X, Y] = meshgrid(x, y);
>> Z = (X + Y).*exp( -X.*X - 2*Y.*Y );
>> mesh(X, Y, Z)
>> surf(X, Y, Z)
>> xlabel(’X’)
>> ylabel(’Y’)
>> zlabel(’Z’)
>> contour(X,Y,Z)
Xueying Wang
Introduction to Matlab

MATLAB functions
⊛ MATLAB has lots of built-in functions.
⊛ We can create our own MATLAB functions. Type
>> edit
The first line of MATLAB function files is of the form
function = (, ..., )
or
function [, ..., ] = (,
..., )
Xueying Wang
Introduction to Matlab

Programming
The general form of the for loop is
for =
...
end
Xueying Wang
Introduction to Matlab

Programming, ctd
The second MATLAB loop structure is the while statement. The
general form of the while loop is
>> while
...
end
Xueying Wang
Introduction to Matlab

Programming, ctd
The simplest form of the if statement is
>> if
...
end
where the < statements > are evaluated as long as the
< logicalexpression > is true.
Xueying Wang
Introduction to Matlab