Lecture 13: M/O/F/ for Engineering Applications - Part 1 BJ Furman 26NOV2012

The Plan for Today Matlab/Octave/FreeMat (M/O/F) for engineering applications  Overview of M/O/F  Matlab/FreeMat environment  Octave command line  Basic operations  Script files  Resources for more information

Learning Objectives Explain what M/O/F are Navigate the Matlab user interface and Octave command line Use M/O/F as a scratch pad Create script files to execute a sequence of commands

Matlab and Octave M/O/F are ‘high-level’ languages  They abstract away the nitty-gritty details Numerical calculation  Oriented toward engineering, mathematical, and scientific computing Matlab (Matrix Laboratory)  Particularly good at handling arrays! Powerful graphics and analysis tools  Controls, signal processing, data analysis, and other specialized ‘toolboxes’ are available Widely used in industry Matlab is commercial software (a student version is available) Octave and FreeMat are open source and free: (main page) (main page) Key point!

Matlab (ver. 6.5) Environment (GUI) Default Window Layout Command Window Command History Window Workspace/Current Directory Window Interactive ‘scratch pad’ Workspace: lists variables Directory: files in current dir

Octave Command Line Enter commands at the prompt

QtOctave GUI Enter commands at the prompt

Matlab as a ‘scratch pad’ Variables are dynamically typed Info on variables in the workspace

Octave as a ‘scratch pad’ dynamically typed

M/O/F Basics - 1 Fundamental element: the array  even scalars are stored as 1x1 array of double floating point value How many bytes?  See Workspace Window Useful commands (see documentation for more details!)  who (information about what is in memory)  whos (more detailed information about what is in memory)  clc (clears the command window. In QtOctave, View  Clear Terminal)  clear (clears all user defined variables)  help name (provides information on command name)

M/O/F Basics - 2 Script files (.m files)  Text files containing M/O/F statements Type in a text editor (M/O/F) or use M-file editor in Matlab (File/New/M-File or Ctrl-n)  Comments Matlab: % Octave: % or # FreeMat: %  Example: look at cool_plot.m Verify directory containing cool_plot.m is in the file path  MATLAB: File | Set Path… | select folder  Octave: addpath(‘dir_path’) find from Windows Explorer

Script File Example: cool_plot.m

Octave Script File Example cool_plot.m needs to be in the ‘load path’ Octave: a ddpath(dir-path) Example (yours may be different): addpath('C:\Octave\Octave_code') Matlab: File | Set Path…

Matlab Script File Example

Ch Example See: chap. 23 of The Ch Language User's Guide and chap. 2 of The Ch Language Environment Reference

Excel Example Data needs to be equally spaced Select z-data values Insert | Other Charts | Surface Use Chart Tools | Layout tab to control display

M/O/F Basics - 3 Array creation AA = [1 2 3; 4,5,6; 7 8 9] size(A) Indexing elements AA(1,2) Adding elements AA(4,2) = 13 AA(4,2) = 13; Separate elements by spaces or commas, and rows by semicolon or carriage return Which element does this choose? Contrast with C. Index by enclosing indices in ( ) What does this do? What does this do? Contrast with C. The semicolon at the end suppresses the output

M/O/F Basics - 4 Vectors ( just 1xn or nx1 arrays) BB=[sin(pi/4), -2^3, size(A,1)] Vectors using the colon operator CC = 1 : 0.25 : 2 DD = 0 : 5 Linspace EE = linspace(0,5,3 ) Logspace FF = logspace(1,3,5) base : increment : limit start : end : n For n elements linearly spaced between start and end start : end : n For n elements logarithmically spaced between start and end For an increment of 1: base : limit Format: Note: limit is reached only if (limit-base)/increment is an integer

M/O/F Basics - 5 Manipulating arrays AAdd a row A = [ A ; [ ] ] EExtract a sub-array G = A(1:3, 1:2) Colon operator by itself means, “all the elements” CCan apply to the dimensions of the arrays to access all the elements of a row or column CCan apply to the entire array to get all the elements as a column vector WWhat order will they come out? EExamples H = [1:4; linspace(10,40,4); 400:-100:100] I = H( [1 2], : ) J = H( : ) What will this produce? Assuming A = [ 1 2 3; 4,5,6 ; ] What does this do? Matlab stores array elements in column- major order.

M/O/F Basics - 6 Special matrices  zeros, ones, eye K=zeros(3) L=ones(4) M=eye(3)

M/O/F Basics - 7 Matrix operations AArithmetic just like with scalars! (But need to take care that dimensions agree) N=L*7 O=N+eye(4) P=B*E P=B*E’ Q=A+B Q=B+E [1 2]*[3 ; 4] What does the ‘ do? A=[1 2 3; 4,5,6; 7 8 9] B=[sin(pi/4), -2^3, size(A,1)] E=linspace(0,5,3) L=ones(4)

M/O/F Basics - 8 Matrix operations, cont.  Matrix division Recall the circuit analysis problem  R1=10k  R2=R3=5k  V=10V Matrix solution If we had iR = V instead, we’d use ‘right’ division: ( i = R / V ) roughly the same as: i = VR -1 R2 R1 R3 +V i1 i2 i3 R = [ ; e3; 0 10e3 0]; V = [ ]’; I = R \ V

M/O/F Basics - 9 Matrix operations, cont. EElement-by-element operations use. (dot) and the operator (other than addition/subtraction) dot product of two vectors Note!! period-asterisk means element-by-element multiplication

M/O/F Basics - 10 Functions  Like script M-files, but several differences: first line must be of the form: function [output args] = function_name(input args) variables generated in the function are local to the function, whereas for script files (.m files), variables are global the file must be named, ‘function_name.m’  Make sure you add comments at the start that describe what the function does  Example: root-mean-square function, rms1.m keyword Name that you assign

M/O/F Basics Functions, cont.  Example: root-mean-square function, cont. Pseudocode:  square each element of x  sum the squares  divide by N  take the square root Expression to square each element in vector x  xs = x.^2 Sum the squares  sums = sum(xs) Divide by N  N = length(x)  ms = sums/N Take the square root  rms = sqrt(ms) Before you write the function, make sure the name you propose is not already used! help fn_name

M/O/F Basics Functions, cont.  Example: root-mean-square function, cont. function [y] = rms(v) % rms(v) root mean square of the elements of the column vector v % Function rms(v) returns the root mean square of the elements % of the column vector, v. If v is a matrix, then rms(v) returns % a row vector such that each element is the root mean square %of the elements in the corresponding column of v. vs = v.^2; % what does this line do? Also note semicolon. s = size(v); % what does this line do? y = sqrt(sum(vs,1)/s(1)); % what is s(1)? Let v=sin([0: *pi: 2*pi]’), one period of a sine wave. The RMS value of a sine wave is its amplitude*1/sqrt(2) Does rms() work with a row vector? How about a matrix? H1 comment line (used in lookfor) Comments that will be displayed by help command

M/O/F Basics Functions, cont.  Make rms function more robust to work with row or column vector or matrix with column vectors of data  Pseudocode: Test for size of v  if > 2, print error message  else  if row vector  transpose  calculate rms  See rms3.m

Vector Dot Product Example X Y Find the X and Y components of the vector, V ivv x ˆ   Back

Review

References Matlab. (2009, November 6). In Wikipedia, the free encyclopedia. Retrieved November 6, 2009, from  Matlab tutorials: GNU Octave. (2009, October 31). In Wikipedia, the free encyclopedia. Retrieved November 6, 2009, from  Octave main page: ( access to pre-built installers)  Octave tutorials: FreeMat. ftp:// ses/ENGR-25.htm ftp:// ses/ENGR-25.htm