1. Laboratory in Oceanography: Data and Methods
Introduction to Matlab ® Programming Software
MAR599, Spring 2009
Miles A. Sundermeyer

2. Introduction to Matlab
The name MATLAB stands for matrix laboratory
Fundamentally a programming language – does not need compiling, runs off interactive command line or command scripts
Matlab Website:
Starting and quitting Matlab …
Windows: double click the Matlab icon …
Linux: run “matlab” on command line
Type ‘exit’ to quit (works in either)

3. Introduction to Matlab
.m files / coding
% Code for generating plot of example of system of equations - this case
% stage vs. flow rating curve, with observations at different times. %
% Written by Miles A. Sundermeyer, 1/27/09
% set the variables
time = [ ];
stage = [ ];
flow = [ ];
% create plot
plot(stage,flow,'b*')
xlabel('stage(m)')
ylabel('flow (m^3s)')
title('Stage vs. Discharge Rating Curve')
set(gca,'xlim',[ ])
set(gca,'ylim',[ ])
% fit line to data
% create X matrix for linear fit
X = [stage' ones(size(time'))];
B = X\discharge'; % left divide y = Xb by X to solve for B=[m b]'
% (need to transpose stage to column vector first)
% now B contains both the slope, m, and intercept, b
stagefit = [min(stage) max(stage)];
hold on
plot(stagefit,[stagefit' ones(size(stagefit'))]*B,'r-');

4. Introduction to Matlab
.m files / coding
Best Programming Practices
Use .m files for all your code for sake of documentation and repeatability
Include header summarizing what code does, inputs and outputs, author, and date written/modified.
Use vertical and horizontal whitespace generously. Indentation and spacing should reflect the block structure of the code.
Comments should describe what is happening, how it is being done, what parameters mean, which globals are used, and any restrictions or bugs. Avoid unnecessary comments.
Variable names
length trades off with clarity of expression
use descriptive names whenever possible for clarity, simple names for things like ‘for’ loops.
give units where appropriate (as comments, e.g., % (m/s)
Function names should reflect what they do and what they return
***** Ended here on Lecture 2 *****

5. Introduction to Matlab
Getting Started / Introduction / Product Overview
Desktop Tools and Development Environment
MATLAB desktop and Command Window
editor & debugger, code analyzer, help browser, viewer for workspace & files
Mathematical Function Library
Computational algorithms from basic (e.g., sum, sine, cosine, complex arithmetic) to sophisticated functions (e.g., matrix inverse, matrix eigenvalues, Bessel functions, FFTs).
The Language
A high-level matrix/array language with control flow statements, functions, data structures, input/output, and object-oriented programming features.
Graphics
Extensive graphing / annotation: incl. 2-D, 3-D, image processing, animation
Ability to build graphical user interfaces on MATLAB applications
External Interfaces
Libraries for writing C and Fortran programs to interact with MATLAB
Ability to call external routines from MATLAB and vice versa

6. Introduction to Matlab
Getting Started / Matrices and Arrays / Expressions
Variables
Declarations or dimension not required
Variable names consist of a letter, followed by any number of letters, digits, or underscores
Case sensitive.
e.g.,
> num_students = 25
creates a 1-by-1 matrix named num_students and stores the value 25 in its single element
Numbers
Conventional decimal notation
Scientific notation uses the letter ‘e’ to specify a power-of-ten scale factor
Imaginary numbers use either i or j as a suffix (read more for rules on imag numbers)
e-20
e23 1i j 3e5i

7. Introduction to Matlab
Getting Started / Matrices and Arrays / Expressions
Operators (see also ‘help <any operator>’ for list – worth doing once to see)
+ Addition-Subtraction
* Multiplication
/ Division
\ Left division (described in Linear Algebra in MATLAB documentation)
^ Power
‘ Complex conjugate transpose
( ) Specify evaluation order
Functions
standard elementary math functions (abs, sqrt, exp, sin)
special functions for useful constants pi
i,j Imaginary unit,
Inf Infinity (e.g., 1/0)
nan Not-a-number (e.g., 0/0, inf/inf, 0*inf)

8. Introduction to Matlab
Getting Started / Matrices and Arrays / Expressions
Examples of Matlab Expressions
> rho = (1+sqrt(5))/2
rho =
> a = abs(3+4i)
a = 5
> z = sqrt(besselk(4/3,rho-i))
z = i

9. Introduction to Matlab
Getting Started / Matrices and Arrays / Matrices and Magic Squares
Entering Matrices
> A = [ ; ; ; ]
A =
Sum, transpose, and diag
> sum(A)
ans =
> A’
ans =
(Note: may use space or comma for elements of same row)

10. Introduction to Matlab
Getting Started / Matrices and Arrays / Matrices and Magic Squares
Sum, transpose, and diag (cont’d)
> sum(diag(A))
ans = 34
> sum(diag(fliplr(A)))
> sum(A')’
ans = 34
> diag(A) 16 10 7 1

11. Introduction to Matlab
Getting Started / Matrices and Arrays / Matrices and Magic Squares
Subscripts
The element in row i and column j of A is denoted by A(i,j). For example, A(4,2) is the number in the fourth row and second column.
It is also possible to refer to the elements of a matrix with a single subscript, A(k).
If you try to use the value of an element outside of the matrix, it is an error:
> t = A(4,5)
??? Index exceeds matrix dimensions.
If you store a value in an element outside of the matrix, the size increases to accommodate the newcomer:
> X = A;
> X(4,5) = 17
X =

12. Introduction to Matlab
Getting Started / Matrices and Arrays / Matrices and Magic Squares
The Colon Operator
One of most important Matlab operators - occurs in several different forms
> 1:10
ans =
To obtain non-unit spacing, specify an increment:
> 100:-7:50
> 0:pi/4:pi

13. Introduction to Matlab
Getting Started / Matrices and Arrays / Matrices and Magic Squares
The Colon Operator (cont’d)
Subscript expressions involving colons refer to portions of a matrix:
e.g., A(1:k,j) refers to the first k elements of the jth column of A.
> sum(A(1:4,4)) % computes the sum of the fourth column.
ans = 34 or
> sum(A(:,end)) % keyword ‘end’ refers to last row or column

14. Introduction to Matlab
Useful Tidbits …
Useful Tidbits
‘who’ and ‘whos’ - returns variable names, types, sizes
<variable name> - displays variable
help <function name / operator> - displays header of function
lookfor <topic> - searches headers for keywords
up, down, left, right arrows - to repeat/modify previous commands
semicolon after command - suppresses output
Anything +-*/ nan = nan

15. Introduction to Matlab
Getting Started / Matrices and Arrays / Working with Matrices
Functions that generate basic matrices
zeros % All zeros
ones % All ones
rand % Uniformly distributed random elements
randn % Normally distributed random elements
e.g.,
> Z = zeros(2,4)
Z =
> F = 5*ones(3,3)
F =
5 5 5
> N = fix(10*rand(1,10))
N =
> R = randn(4,4)
R =

16. Introduction to Matlab
Getting Started / Matrices and Arrays / Working with Matrices
Concatenation
Joining smaller matrices to make bigger ones
e.g.,
> B = [A A+32; A+48 A+16]
B =

17. Introduction to Matlab
Getting Started / Matrices and Arrays / More about Matrices and Arrays
Build a table of squares and powers of 2:
e.g.,
> n = (0:9)';
> pows = [n n.^2 2.^n]
pows =

18. Introduction to Matlab
Getting Started / Matrices and Arrays / Working with Matrices
Deleting Rows and Columns
Delete the second column of X, use
e.g.,
> A (:,2) = [ ]
A =
Deleting a single element from a matrix
A(1,2) = [ ] % results in an error
Using a 1-d subscript deletes element(s) and reshapes remaining elements into a row vector
> X=A
X(2:2:10) = [ ]
X =

19. Introduction to Matlab
Getting Started / Matrices and Arrays / Working with Matrices
Zero out a portion of B:
e.g.,
> B(1:2,2:3) = 0
B =

20. Introduction to Matlab
Getting Started / Matrices and Arrays / More about Matrices and Arrays
Logical Subscripting
Eliminate missing data
e.g.,
> x = [ NaN ];
> x = x(isfinite(x))
x =
> x = x(abs(x-mean(x)) <= 3*std(x))
x =

21. Introduction to Matlab
Getting Started / Matrices and Arrays / More about Matrices and Arrays
The ‘find’ Function
e.g., find indices of the primes in A:
> k = find(isprime(A))'
k =
> A(k)
ans =
Note: lhs index in an assignment statement preserves matrix structure
e.g.,
> A(k) = NaN
A =
16 NaN NaN NaN
NaN 10 NaN 8
9 6 NaN 12