TweetFollow Us on Twitter

MatLab
Volume Number:4
Issue Number:5
Column Tag:The Workstation Mac

MatLab Comes to the Mac II

By Paul Zarchan, Cambridge, Mass

Introduction

MATLAB is an interactive program to help with scientific and engineering numeric calculations. Although it was originally written in FORTRAN for mainframe computers, a second generation MATLAB was rewritten for smaller computers such as the Sun Workstation and the VAX computer. In the last few years a special version of MATLAB was developed to run on MS DOS compatable PC’s with math coprocessors. Typical uses for MATLAB are general purpose numeric computation, algorithm prototyping and solving special purpose problems with matrix formulations that arise in disciplines such as automatic control theory, statistics and digital signal processing. MATLAB is now available for the Mac II or for any Mac souped up with a 68020 accelerator board and a 68881 math coprocessor. For engineers this lends legitimacy to the claim that the Mac II is actually a workstation.

Unlike FORTRAN on the MAC, MATLAB is not really designed to make executable code (i.e. “double clickable” applications). As with interpretive BASIC, the MATLAB application is required on the disk to execute any file previously generated. Unlike BASIC, MATLAB is very fast because of the highly efficient algorithms. MATLAB allows engineers to solve problems almost as they are written mathematically and in addition allows easy access to libraries of some very powerful software. Some have called MATLAB “APL without the pain”. The Mac version of MATLAB takes full advantage of the Mac interface. This also means the MATLAB output can easily be incorporated into reports and presentations making MacMATLAB far more useful than the DOS version.

Matrix Examples

Matricies can be entered either in the MATLAB editor or by the carrot prompt by using brackets to define the matrix and semicolons to separate matrix rows. For example, by entering

»A=[1 2 3;4 5 6;7 8 0]

we get the MATLAB output on screen as

A =
     1     2     3
     4     5     6
     7     8     0

If we want to find the transpose of matrix A we simply type at the prompt

»B=A’

where the ‘ indicates transposition The resultant screen output is

B =
     1     4     7
     2     5     8
     3     6     0

Taking the matrix inverse of A is simple as typing

»inv(A)

which yields the screen output (nearly instantaneously)

ans =
   -1.7778    0.8889   -0.1111
    1.5556   -0.7778    0.2222
   -0.1111    0.2222   -0.1111

Many other matrix and linear algebra functions are available with MATLAB. Of course, many engineers have these functions built into their FORTRAN libraries - so why use MATLAB? Let’s do more examples to see why!

Polynomial Example

Suppose we had two polynomials and we wanted to multiply them and find the roots of the resultant expression. If the two polynomials were

x2+3x+2 and x2+x-12

we would define the polynomials in MATLAB by typing

»A=[1 3 2];
»B=[1 1 -12];

where the polynomials are expressed as vectors where the vector elements represent the polynomial coefficients in descending order. We can multiply the 2 polynomials algebraically in MATLAB by using the convolution function or

»C=conv(A,B)

which yields

»C =
     1     4    -7   -34   -24

The screen output displays the coefficients of the resultant polynomial in descending order. This means that the product of the 2 polynomials is given by

x4+4x3-7x2-34x-24

To find the roots of the resultant polynomial we simply type

»roots(C)

which yields the 4 roots as

ans =
    3.0000
   -4.0000
   -2.0000
   -1.0000

Still not impressed with MATLAB? Let’s look at more examples.

Plotting

Unlike FORTRAN, plotting functions come built into MATLAB. If we wanted to plot

y=sin(x) and z=.01x2 from -15 to 15 in increments of .05 only the following 4 MATLAB statements would be required

»x=-15:.05:15;
»y=sin(x);
»z=x.^2/100;
»plot(x,y,x,z)

The unenhanced screen output for such a set of commands appears in Fig. 1. Of course since MATLAB grpahical output is in the PICT format it can be copied to the clipboard and pasted into any Macintosh application.

Figure 1 - Plotting With MATLAB is Easy

The graph can be embellished within the MATLAB environment (with features similar to Cricket Graph) or copied onto the clipboard and pasted into MacDraw for further enhancement.

If we wanted to show that a 5 term Fourier series expansion for a square wave is accurate (Gibb’s effect) we only need the following 3 lines of MATLAB code.

»t = 0:.1:10;
»y = sin(t) + sin(3*t)/3 + sin(5*t)/5 + sin(7*t)/7 + sin(9*t)/9;
»plot(t,y)

The resultant unenhanced MATLAB output is shown below.

Figure 2 - MATLAB Output For Gibb’s Effect

Still not impressed? Suppose we wanted to evaluate the function

over the range

-2¾x¾2, -2¾y¾3

All we have to do is use the following 3 MATLAB statements to get a 3 dimensional plot (with all the hidden line algorithms transparent to the user) of the function.

»[x,y]=meshdom(-2:.2:2,-2:.2:3);
»z=x.*exp(-x.^2-y.^2);
»mesh(z)

Figure 3 - MATLAB 3 Dimensional Plot

Incidentally, the plot took only a few seconds to generate. Try doing that in FORTRAN!

Signal Processing

Noisy signals can be analyzed with MATLAB. For example, we can make 750 gaussian distributed random numbers with zero mean and unity standard deviation with the statements

»rand(‘normal’)
»y=rand(750,1);

We can then analyze and display the frequency content of the 750 random numbers with a MATLAB histogram statement or

»[n,x]=hist(y);
»plot(x,n,’+’)

As expected, the MATLAB output, shown in Fig. 4, demonstrates that the 750 random numbers follow the standard “bell-shaped” curve or well known gaussian distribution.

Figure 4 - MATLAB Can Make Histograms

As was mentioned in the introduction, MATLAB comes with very powerful algorithms. The next example shows a simple use of the FFT (Fast Fourier Transform) function. A common use of the FFT is to find the frequency components buried in a noisy time domain signal. Consider data sampled at 1000 Hz. We can form a signal containing 50 Hz and 120 Hz and corrupt it with gaussian noise (zero mean and unity standard deviation) with the following 5 MATLAB statements.

»t=0:.001:.5;
»x=sin(2*pi*50*t)+sin(2*pi*120*t);
»rand(‘normal’)
»y=x+2*rand(t);
»plot(y(1:50))

Figure 5 - Noisy Signal in Time Domain

It is difficult, if not impossible, to identify the frequency components by looking at the original signal in the time domain. Converting to the frequency domain, the discrete Fourier transform of the noisy signal y is found by taking the FFT. In MATLAB code this means

»Y=fft(y);

The power spectral density, a measurement of the energy at various frequencies, is:

»Pyy=Y.*conj(Y);

We can plot the power spectral density by forming a frequency axis for the first 256 points (the other 256 points are symmetric) with the MATLAB statements

»f=1000*(0:255)/512;
»plot(f,Pyy(1:256))

From the resultant output in Fig. 6 we can clearly see the frequency components at 50 Hz and 120 Hz of the signal.

Figure 6 - Frequency Domain Output

Control Analysis

MATLAB can also be used in the analysis of control systems from both a modern and classical point of view. We can find and plot the root locus of the transfer function

for gains 0 to 10 in steps of .5 with the following MATLAB statements

»num = [.2  .3  1];
»den1 = [1 .4 1];
»den2 = [1 .5];
»den = conv(den1,den2);
»k = 0:.5:10;
»r = rlocus(num,den,k); 
»plot(r,’x’), title(‘Root-locus’),xlabel(‘Real part’),ylabel(‘Imag part’)

The resultant root locus is shown in Fig. 7.

Figure 7 - Root Locus Example With MATLAB

We could find the step response for the same system by typing the additional statements

»[a,b,c,d] = tf2ss(num,den)
»t = 0:.3:15;
»y = step(a,b,c,d,1,t); 
»plot(t,y),title(‘Step response’),xlabel(‘time(sec)’)

yielding the output of Fig. 8

Figure 8 - Step Response Output

Another example of the control system analysis capability of MATLAB consider a second order quadratic transfer function with natural frequency 1 rad/sec and damping of .2. The MATLAB program required to display the magnitude characteristics is shown below and the resultant output is displayed in Fig. 9.

»[a,b,c,d]=ord2(1,.2);
»w=logspace(-1,1);
»[mag,phase]=bode(a,b,c,d,1,w);
»mag1=20*log10(mag);
»semilogx(w,mag1)

Figure 9 - Sample Magnitude Bode Plot For Quadratic Transfer Function

More Details

If you already used MATLAB in the DOS world and have a collection of many files there is no problem in porting them to the MAC. Just use a file transfer program (I used PC to MAC and Back) and the conversion routine (going from ASCII files to .m files) provided by MATLAB. The danger in doing this is that the DOS version of MATLAB will seem very primitive once you have used the MAC version. Incidentally the MAC version of MATLAB runs about 5 times faster than the IBM/AT version and at about the same speed as the Sun-3 Workstation version.

Macintosh MATLAB was developed by The Math Works, Inc. [20 N. Main St., Suite 250, Sherborn, Mass. 01770, (617)653-1415]. The software, including the signal processing toolbox comes on a single 800k disk (unprotected) with a list price of $895. The control and ientification toolboxes are sold separately - each with a list price of $495. Although this software is expensive by MAC word processing and spreadsheet standards - it is inexpensive by engineering software standards.

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Google Chrome 75.0.3770.142 - Modern and...
Google Chrome is a Web browser by Google, created to be a modern platform for Web pages and applications. It utilizes very fast loading of Web pages and has a V8 engine, which is a custom built... Read more
Notability 4.0.4 - Note-taking and annot...
Notability is a powerful note-taker to annotate documents, sketch ideas, record lectures, take notes and more. It combines, typing, handwriting, audio recording, and photos so you can create notes... Read more
ffWorks 1.3.1 - Convert multimedia files...
ffWorks, focused on simplicity, brings a fresh approach to the use of FFmpeg, allowing you to create ultra-high-quality movies without the need to write a single line of code on the command-line.... Read more
EtreCheck Pro 6.0.2 - For troubleshootin...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
Adobe Premiere Pro CC 2019 13.1.3 - Digi...
Premiere Pro CC 2019 is available as part of Adobe Creative Cloud for as little as $52.99/month. The price on display is a price for annual by-monthly plan for Adobe Premiere Pro only Adobe Premiere... Read more
BitTorrent 7.4.3 - Official client of th...
BitTorrent is a protocol for distributing files. It identifies content by URL and is designed to integrate seamlessly with the web. Its advantage over plain HTTP is that when multiple downloads of... Read more
BetterTouchTool 3.134 - Customize multi-...
BetterTouchTool adds many new, fully customizable gestures to the Magic Mouse, Multi-Touch MacBook trackpad, and Magic Trackpad. These gestures are customizable: Magic Mouse: Pinch in / out (zoom)... Read more
EtreCheck Pro 6.0.2 - For troubleshootin...
EtreCheck is an app that displays the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to... Read more
BitTorrent 7.4.3 - Official client of th...
BitTorrent is a protocol for distributing files. It identifies content by URL and is designed to integrate seamlessly with the web. Its advantage over plain HTTP is that when multiple downloads of... Read more
Adobe Premiere Pro CC 2019 13.1.3 - Digi...
Premiere Pro CC 2019 is available as part of Adobe Creative Cloud for as little as $52.99/month. The price on display is a price for annual by-monthly plan for Adobe Premiere Pro only Adobe Premiere... Read more

Latest Forum Discussions

See All

TEPPEN guide - Tips and tricks for new p...
TEPPEN is a wild game that nobody asked for, but I’m sure glad it exists. Who would’ve thought that a CCG featuring Capcom characters could be so cool and weird? In case you’re not completely sure what TEPPEN is, make sure to check out our review... | Read more »
Dr. Mario World guide - Other games that...
We now live in a post-Dr. Mario World world, and I gotta say, things don’t feel too different. Nintendo continues to squirt out bad games on phones, causing all but the most stalwart fans of mobile games to question why they even bother... | Read more »
Strategy RPG Brown Dust introduces its b...
Epic turn-based RPG Brown Dust is set to turn 500 days old next week, and to celebrate, Neowiz has just unveiled its biggest and most exciting update yet, offering a host of new rewards, increased gacha rates, and a brand new feature that will... | Read more »
Dr. Mario World is yet another disappoin...
As soon as I booted up Dr. Mario World, I knew I wasn’t going to have fun with it. Nintendo’s record on phones thus far has been pretty spotty, with things trending downward as of late. [Read more] | Read more »
Retro Space Shooter P.3 is now available...
Shoot-em-ups tend to be a dime a dozen on the App Store, but every so often you come across one gem that aims to shake up the genre in a unique way. Developer Devjgame’s P.3 is the latest game seeking to do so this, working as a love letter to the... | Read more »
Void Tyrant guide - Guildins guide
I’ve still been putting a lot of time into Void Tyrant since it officially released last week, and it’s surprising how much stuff there is to uncover in such a simple-looking game. Just toray, I finished spending my Guildins on all available... | Read more »
Tactical RPG Brown Dust celebrates the s...
Neowiz is set to celebrate the summer by launching a 2-month long festival in its smash-hit RPG Brown Dust. The event kicks off today, and it’s divided into 4 parts, each of which will last two weeks. Brown Dust is all about collecting, upgrading,... | Read more »
Flappy Royale is an incredibly clever ta...
I spent the better part of my weekend playing Flappy Royale. I didn’t necessarily want to. I just felt like I had to. It’s a hypnotic experience that’s way too easy to just keep playing. | Read more »
Void Tyrant guide - General tips and tri...
Void Tyrant is a card-based dungeon-crawler that doesn’t fit in the mold of other games in the genre. Between the Blackjack-style combat and strange gear system alone, you’re left to your own devices to figure out how best to use everything to your... | Read more »
Webzen’s latest RPG First Hero is offici...
You might be busy sending your hulking Dark Knight into the midst of battle in Webzen’s other recent release: the long-anticipated MU Origin 2. But for something a little different, the South Korean publisher has launched First Hero. Released today... | Read more »

Price Scanner via MacPrices.net

Price drop! Clearance 12″ 1.2GHz Silver MacBo...
Amazon has dropped their price on the recently-discontinued 12″ 1.2GHz Silver MacBook to $849.99 shipped. That’s $450 off Apple’s original MSRP for this model, and it’s the cheapest price available... Read more
Apple’s 21″ 3.0GHz 4K iMac drops to only $936...
Abt Electronics has dropped their price on clearance, previous-generation 21″ 3.0GHz 4K iMacs to only $936 shipped. That’s $363 off Apple’s original MSRP, and it’s the cheapest price we’ve seen so... Read more
Amazon’s Prime Day savings on Apple 11″ iPad...
Amazon has new 2018 Apple 11″ iPad Pros in stock today and on sale for up to $250 off Apple’s MSRP as part of their Prime Day sale (but Prime membership is NOT required for these savings). These are... Read more
Prime Day Apple iPhone deal: $100 off all iPh...
Boost Mobile is offering Apple’s new 2018 iPhone Xr, iPhone Xs, and Xs Max for $100 off MSRP. Their discount reduces the cost of an Xs to $899 for the 64GB models and $999 for the 64GB Xs Max. Price... Read more
Clearance 13″ 2.3GHz Dual-Core MacBook Pros a...
Focus Camera has clearance 2017 13″ 2.3GHz/128GB non-Touch Bar Dual-Core MacBook Pros on sale for $169 off Apple’s original MSRP. Shipping is free. Focus charges sales tax for NY & NJ residents... Read more
Amazon Prime Day deal: 9.7″ Apple iPads for $...
Amazon is offering new 9.7″ WiFi iPads with Apple Pencil support for $80-$100 off MSRP as part of their Prime Day sale, starting at only $249. These are the same iPads found in Apple’s retail and... Read more
Amazon Prime Day deal: 10% (up to $20) off Ap...
Amazon is offering discounts on new 2019 Apple AirPods ranging up to $20 (10%) off MSRP as part of their Prime Day sales. Shipping is free: – AirPods with Charging Case: $144.99 $15 off MSRP –... Read more
Amazon Prime Day deal: $50-$80 off Apple Watc...
Amazon has Apple Watch Series 4 and Series 3 models on sale for $50-$80 off Apple’s MSRP as part of their Prime Day deals with prices starting at only $199. Choose Amazon as the seller rather than a... Read more
Amazon Prime Day deal: 50% discount on Apple...
Amazon has Apple Smart Keyboards for current-generation 10″ iPad Airs and previous-generation 10″ iPad Pros on sale today for $79.50 shipped as part of their early Prime Day deals. That’s a 50%... Read more
Abt drops prices on clearance 2018 MacBook Ai...
Abt Electronics has dropped prices on clearance 2018 13″ MacBook Airs by $201 with models now available starting at only $998. Shipping is free: – 13″ 1.6GHz/128GB MacBook Air (Space Gray, Silver, or... Read more

Jobs Board

*Apple* Graders/Inspectors (Seasonal/Hourly/...
…requirements. #COVAentryleveljobs ## Minimum Qualifications Some knowledge of agricultural and/or the apple industry is helpful as well as the ability to comprehend, Read more
Best Buy *Apple* Computing Master - Best Bu...
**710003BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Store Associates **Location Number:** 000171-Winchester Road-Store **Job Description:** Read more
Best Buy *Apple* Computing Master - Best Bu...
**709786BR** **Job Title:** Best Buy Apple Computing Master **Job Category:** Sales **Location Number:** 000430-Orange Park-Store **Job Description:** **What does a Read more
Geek Squad *Apple* Master Consultation Agen...
**709918BR** **Job Title:** Geek Squad Apple Master Consultation Agent **Job Category:** Services/Installation/Repair **Location Number:** 000106-Palmdale-Store Read more
*Apple* Systems Architect/Engineer, Vice Pre...
…its vision to be the world's most trusted financial group. **Summary:** Apple Systems Architect/Engineer with strong knowledge of products and services related to Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.