MATLAB Programming

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MATLAB Programming

• COMM2M
• Harry R. Erwin, PhD
• University of Sunderland

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Sources

• James E. Gentle, 2002, Elements of Computational
  Statistics, Springer.

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Topics

• Operators and Flow Control
• M-Files
• Functions
• Input and Output
• M-File Style
• Optimization
• Tutorial
• Individual Project

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Operators and Flow Control

• Relational and Logical Operators
• Flow Control

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Relational Operators

• The six relational operators are
• (equal)
• (not equal)
• lt
• gt
• lt
• gt
• True is 1 and false is 0
• Comparisons involving matrices produce matrices.

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Logical Functions

• ischar
• isempty
• isequal
• isfinite
• isieee
• isinf

• islogical
• isnan
• isnumeric
• isreal
• issparse

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Logical Operators

• (logical and)
• (logical or)
• (logical not)
• xor (logical exclusive or)
• all (true if all elements of vector are nonzero)
• any (true if any element of vector is nonzero)

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Find

• The find() command returns the indices
  corresponding to the non-zero elements of a
  vector. Applied to a matrix M, it works with
  M().
• This can be used with any of these functions and
  operators.
• If f was generated by f find(X), then X(f) are
  the non-zero elements of X.

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If Then Else

• if expression (handled like C/C/Java)
• statements (comma separated on one line)
• elseif expression2 (optional)
• elseif statements
• else (optional)
• final set of statements
• end

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For Loop

• Convenient (but avoid if performance-critical
  use vectors instead)
• for variable expression
• for statements (, sep if 1 line)
• end
• Expression is usually isj. It can be a matrix,
  in which case the columns from first to last are
  used.

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While Loop

• while expression
• statements
• end
• As long as expression remains true (0)
• for and while loops can be terminated with a
  break.
• continue jumps back to the loop start.
• Infinite loop
• while 1, , end

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Switch Statement

• switch expression
• case value1 statements
• case value2 statements
• case value3 statements
• otherwise statements (optional)
• end
• The case value can be a value list within
  forming a cell array.
• This is different from C!!!!!

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M-Files

• Scriptsno input or output arguments and operate
  on variables in the workspace
• Functionscontain a function definition line and
  can work with input and output arguments.
  Internal variables are local unless declared
  global.

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Scripts

• Format for a script called spin.m
• SPIN
• describes what it does
• executable statements

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Functions

• function retval name(arguments)
• NAME one line description. (H1 line)
• more details including arguments
• code statements, eventually setting retval
• The name of the m-file should be the name of the
  function.
• The H1 line should omit the and a. It should
  start with a capital letter and end with ..
• There is usually a blank line after the header.
• The return command can be used to exit.

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Editing M-Files

• M-files are ASCII files, so you can use any text
  editor.
• MATLAB has a built-in editor/debugger.
• Type edit
• Or use the menu in Windows systems.
• MATLAB maintains a search path to find M-files.
  Use the path and addpath commands. There is also
  a path browser that can be called by pathtool.
• Relevant commands available include what,
  lookfor, help, type, exist, and more.

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Function Details

• Functions can be passed as argument to other
  functions. Such an argument is preceded by _at_,
  e.g., _at_fun. Handle it using feval.
• Functions can also be passed as name strings.
  This is not preferred.
• The vectorize() function can be used to convert
  multiplication, division, and exponentiation to
  array operations

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Subfunctions

• Any M-file can contain local functions after the
  first one that can be called by the first one or
  other subfunctions.
• Usually you head a subfunction with
• Subfunction
• Subfunctions can be arguments.
• Functions and subfunctions can call themselves
  recursively.

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Input and Output

• User input
• Screen display
• Reading and writing text files

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User Input

• The input function will display a prompt and wait
  for user input. Input is interpreted as a string
  if input is called with a second argument s.
• The function ginput collects data via mouse click
  coordinates.
• The function pause() suspends execution until a
  key is clicked. pause(n) waits n seconds.

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Screen Display

• If you dont append a there will be output to
  the screen.
• The disp(var) function displays var.
• The fprintf function gives more sophisticated
  control.
• The sprintf function returns a string that
  fprintf would have printed.

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Text Files

• Type help iofun for the list of functions that
  support text and binary file io.
• These are generally similar to C functions.

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M-File Style

• Be careful to fully document your files. In
  particular, provide an example of how the
  function can be used that can be cut and pasted.
• Space around logical operators and
• One statement per line
• Indentation to emphasize structure.
• Matrix names should be capitalized.

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Optimization

• You may compile M-files.
• Vectorize, dont shade your eyes
• n 5e5 x randn(n,1)
• tic, s 0 for i1n, s sx(i)2 end, toc
• Elapsed time 8.35
• tic, s sum(x.2) toc
• Elapsed time 0.06

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More Optimization

• Preallocate large arrays. Otherwise they may be
  expanded one row/column at a time.
• The repmat function is much faster than anything
  that involves manipulating individual matrix
  entries.
• Empty arrays/matrices are handled by
  extrapolating operations on non-empty ones. This
  may be very convenient.

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Grand Tour Tutorial

• When a cluster of data points is rotated,
  patterns in the data may become apparent.
• Rotations are orthogonal transformations that
  preserve the norms of the data vectors and the
  angles between.
• Simple rotation matrices start with the identity
  matrix and change the four elements aii, aij,
  aji, and ajj. aii and ajj are replaced with
  cos(?), aij becomes sin(?), and aji becomes
  -sin(?).

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Generalized Rotation Matrices

• A generalized rotation matrix, Q, is the product
  of (d2-d)/2 such simple rotation matrices.
• Q Q12Q13Q1dQ23Q24Q2dQd-1,d

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Constructing the Plot

• Rotating a plot in all directions, and projecting
  into the first two or three dimensions is called
  a Grand Tour (Asimov 1985).
• You can take for the values of ?ij,
• t?ij modulo 2?
• where the ?ij are linearly independent over the
  integers. Suitable constants are the square roots
  of the first (d2-d)/2 primes.
• Plot the first two (or three) dimensions.
• Suitable data can be found here
  lthttp//lib.stat.cmu.edu/gt
• Step time and observe the changes.

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Suitable Data Can Be Found At

• lthttp//lib.stat.cmu.edu/gt