MATLAB Introduction: Learning to Use MATLAB for Applied Mathematics and Sciences, Study notes of Computer Science

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MA/CS 375

Spring 2009

Lecture 1a Introduction to MATLAB: Some Basics Ref: Appendix B, MATLAB Tutorial

MATH/CS 375 Goals

• To learn how to effectively use compu-

tational methods together with the state-

of-the-art software package, MATLAB,

to solve problems in applied mathe-

matics and the sciences, and

• To learn something about the design

and analysis of these methods.

http://www.mathworks.com

Overview of MATLAB Windows

Matlab Variables

• In Matlab variables are not declared by

the user but are created on a need-to-

use basis by a memory manager.

• Moreover, from MATLAB’s point of

view, every simple variable is a complex

matrix indexed from unity.

• Scalars are 1x1 matrices.

Script Ex

% Script(Ex1p): Plots the function f(x) = sin(2pix) % on the interval [0,1] using 11 equally-spaced points.

% Define x-points. n = 11; x = zeros(1,n); x = [0, .1, .2, .3, .4, .5, .6, .7,... .8, .9, 1];

% Evaluate y(x) = sin(2pix) for these x-points. y = zeros(1,n); for i = 1:n y(i) = sin(2pix(i)); end

% Plot sin(2pix) vs. x on [0,1]. plot(x,y);

EX1 Plot

EX1vp Plot/Print

% Script (Ex1vp): plots and prints the function f(x) = sin(2pix) % on the interval [0,1] using 11 equally-spaced points.

% Define x- and y-points. n = 11; x = linspace(0,1,n); y = zeros(1,n); y = sin(2pix);

% Print sin(2pix) vs. x on the interval [0,1]. disp(' x sin(2pix)') for i = 1:n disp(sprintf(' %3.1f %6.4f',x(i),y(i))); end

% Plot sin(2pix) vs. x on the interval [0,1]. plot(x,y);

Ex1vp output

>> ex1pvp x sin(2pix) 0.0 0. 0.1 0. 0.2 0. 0.3 0. 0.4 0. 0.5 0. 0.6 -0. 0.7 -0. 0.8 -0. 0.9 -0. 1.0 -0. >>

Building Scalars/Vectors

• Row vector: x = [1, 2, 3];
• Column vector: y = [1; 2; 3];
• Transpose: [1, 2, 3]’ = [1; 2; 3]
• Length of a vector: length(x)
• linspace command: z = linspace(1,3,n)
  • Evaluate for n = 3
  • Evaluate for n = 5

Building a Matrix

Example of a matrix A

with 3 rows and 2

columns.

2.1 3. 4.12 1. 7.1 5

   ^       

A

>> A = zeros(3,2); >> A(1,1) = 2.1; >> A(1,2) = 3.23; >> A(2,1) = 4.12; >> A(2,2) = 1.893; >> A(3,1) = 7.1; >> A(3,2) = 5.; >> A A = 2.1000 3. 4.1200 1. 7.1000 5. >>

Now What?

In the next few Viewgraphs, we examine some standard operations with matrices that are allowed in MATLAB. +, -, , ., ^, .^, /, ./, , .\

Matrix Notation

2 3 2 22 23 2 3 32 33 3

2 3

A

M M M

N N N NM

11 1 1 1 1 1

1

A A A A

A A A A

A A A A

A A A A

Let A be an NxM matrix:

Matrix Addition in Matlab

2 1 3 2 4 2 4 1

               

A

B

C A B

>> A = [2, 1;3, 2];

>> B = [4, 2;4, 1];

>> C = A + B

C =

A Note on Matrix Addition

To add (or subtract) two matrices A and

B, the dimensions of A and B must be

the same:

of rows of A must equal # of rows of B

of columns of A must equal # of columns of B

>> A = [2, 1; 3, 2; 1, 4]; >> B = [4, 2; 4, 1]; >> C = A + B ??? Error using ==> plus Matrix dimensions must agree. >>