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

Dragon Dictate 6.0 - Premium voice-recog...
With Dragon Dictate speech recognition software, you can use your voice to create and edit text or interact with your favorite Mac applications. Far more than just speech-to-text, Dragon Dictate lets... Read more
OmniFocus 3.11.7 - GTD task manager with...
OmniFocus is an organizer app. It uses projects to organize tasks naturally, and then add tags to organize across projects. Easily enter tasks when you’re on the go, and process them when you have... Read more
rekordbox 6.5.1.0009 - Professional DJ m...
rekordbox is the best way of preparing and managing your tracks, be it at home, in the studio, or even on the plane! It allows you to import music from other music-management software using the... Read more
1Password 7.8.1 - Powerful password mana...
1Password is a password manager that uniquely brings you both security and convenience. It is the only program that provides anti-phishing protection and goes beyond password management by adding Web... Read more
Ableton Live 10.1.35 - Record music usin...
Ableton Live lets you create and record music on your Mac. Use digital instruments, pre-recorded sounds, and sampled loops to arrange, produce, and perform your music like never before. Ableton Live... Read more
Microsoft Office 365, 2019 16.48 - Popul...
Microsoft Office 365. The essentials to get it all done. Unmistakably Office, designed for Mac Get started quickly with new, modern versions of Word, Excel, PowerPoint, Outlook and OneNote-... Read more
Adobe After Effects 18.1 - Create profes...
After Effects is available as part of Adobe Creative Cloud for $52.99/month (or $20.99/month for a single app license). The new, more connected After Effects can make the impossible possible. Get... Read more
Adobe Audition 14.1 - Professional post-...
Audition is available as part of Adobe Creative Cloud for as little as $20.99/month (or $9.99/month if you're a previous Audition customer). Adobe Audition empowers you to create and deliver... Read more
Adobe Animate 21.0.5 - Animation authori...
Animate is available as part of Adobe Creative Cloud for as little as $20.99/month (or $9.99/month if you're a previous Flash Professional customer). Animate (was Flash CC) lets you share work... Read more
Adobe Photoshop 22.3.1 - Professional im...
You can download Photoshop for Mac as a part of Creative Cloud for only $20.99/month (or $9.99/month if you have purchased an earlier software version). Adobe Photoshop is a recognized classic of... Read more

Latest Forum Discussions

See All

Moonlight Sculptor is an upcoming MMORPG...
Kakao Games and XL Games – who you might be familiar with from their previous game ArcheAge – have announced that their MMORPG Moonlight Sculptor is now available to pre-order for iOS and Android devices. Moonlight Sculptor has previously launched... | Read more »
MU Archangel is now open for pre-registr...
MU Archangel is now open for pre-registration in Southeast Asia following its massive success in other territories. Players from Singapore, Thailand, Malaysia, Indonesia, and the Philippines (except Vietnam) can now join in on the fun by applying... | Read more »
Compete, a new social media app you can...
Whoever told you you can’t get rich making videos has obviously never heard of Compete, Competitive Media Technologies Limited’s hot new social media app where you can rake in all the dough just by doing what you love. Video monetization that... | Read more »
Bethesda has released a new DOOM mobile...
Bethesda Softworks has released a new DOOM game out of the blue exclusively for mobile devices. It’s called Mighty DOOM and is currently only available as an early access title on Android but will be expanding to more users in the future. [Read... | Read more »
Anagraphs is a word puzzle game with a t...
Cinq-Mars Media has released its word puzzle game Anagraphs for iOS and Android devices. The game released last week after a short delay in getting it onto the appropriate platforms. [Read more] | Read more »
These are the top 5 best iPhone games li...
Fortnite has been the big hitter in mobile gaming this year, and it's not hard to see why. Thanks to some excellent marketing, and a polished experience that almost anyone can enjoy, it's really taken the App Store by storm. But there are other... | Read more »
The top 5 best iPhone games like Pokemon...
Pokemon GO is still the, if you'll excuse the pun, go-to game if you want some AR action on your phone. But it's not the only choice out there, and if you've got a hankering for something a bit different, then your eyes might already have started... | Read more »
The top 5 best iPhone games like Starcra...
Starcraft sits at the top of the RTS tree for a number of very good reasons. It also isn't on mobile, again, for a number of very good reasons. But that doesn't mean you can't find a way to indulge your sci-fi, competitive, massive, or engaging RTS... | Read more »
Apple Arcade: Ranked - Top 25 [Updated 4...
In case you missed it, I am on a quest to rank every Apple Arcade game there is. [Read more] | Read more »
The top 5 best iPhone games like The Roo...
The Room has had a massive impact on the world of mobile gaming. Not only is it a brilliant adventure, it also shows how the touchscreen controls on your iPhone can be turned into something far more elegant and tactile than just a bunch of buttons... | Read more »

Price Scanner via MacPrices.net

B&H is offering clearance prices on lefto...
Apple reseller B&H Photo has clearance 2020 13″ 1.4GHz Intel-based MacBook Pros on sale today for $200-$300 off Apple’s original MSRP with prices starting at only $1099. Expedited shipping is... Read more
Roundup of Today’s Best MacBook Deals: M1 Mac...
Apple resellers are offering sale prices on Apple’s M1-powered 13″ MacBook Airs ranging up to $190 off MSRP. Here’s where to pick one up today, and as always, keep an eye on our 13″ MacBook Air Price... Read more
Apple AirPods Pro drop to new low price of on...
Amazon has Apple’s AirPods Pro on sale today for a new low price of only $197 shipped. That’s $52 off MSRP and the lowest price currently available for a set of AirPods Pro from any Apple reseller.... Read more
Apple restocks clearance 13″ Intel-based MacB...
Apple has clearance, Certified Refurbished, 2020 13″ Intel-based MacBook Airs available starting at only $809 and up to $280 off original MSRP. Each MacBook features a new outer case, comes with a... Read more
OWC drops prices on 2020 Intel multi-core Mac...
Other World Computing has clearance 2020 Intel-based Mac minis on sale starting at only $499. Both 4-core and 6-core models are in stock today. These are new, unopened, factory-sealed minis: – 3.6GHz... Read more
Save $50 off Apple’s 10.9″ iPad Air today at...
B&H Photo has new 10.9″ Apple iPad Airs in stock and on sale today for up to $50 off MSRP. Expedited shipping is free to most addresses in the US. Note that some sale prices may be restricted to... Read more
Rare Apple sale: Get a HomePod mini for $10 o...
Apple reseller Expercom has the Space Gray HomePod mini on sale today for $89 shipped. Their price is $10 off Apple’s MSRP, and it’s currently the only sale price available for a HomePod mini among... Read more
Apple has M1 Mac minis available starting at...
Apple has a full line of standard configuration M1 Mac minis available in their Certified Refurbished section starting at only $589 and up to $140 off MSRP. Each mini comes with Apple’s one-year... Read more
New sale at Amazon: $55-$70 discounts on Appl...
Amazon has 7.9″ iPad minis on sale today for up to $70 off Apple’s MSRP, each including free shipping. Prices start at $344. These are the same iPad minis sold by Apple in their retail and online... Read more
Apple offering 13″ M1 MacBook Airs for as lit...
Apple has a full line of 2020 13″ M1 MacBook Airs available, Certified Refurbished, starting at only $849 and up to $190 off original MSRP. These are the cheapest M1 MacBook Airs for sale today at... Read more

Jobs Board

*Apple* Valley 20hr Teller - Wells Fargo (Un...
…or scheduled + Ability to stand for extended periods of time **Street Address** **MN- Apple Valley:** 14325 Cedar Ave - Apple Valley, MN **Disclaimer** All offers Read more
*Apple* Valley 20hr Teller - Wells Fargo (Un...
…or scheduled + Ability to stand for extended periods of time **Street Address** **MN- Apple Valley:** 14325 Cedar Ave - Apple Valley, MN **Disclaimer** All offers Read more
Desktop Support Technician - *Apple* / Mac...
…infrastructure and internal desktop systems. Must have an IT background that includes Apple / Mac support. **Overview:** + Responds to routine technical questions or Read more
Geek Squad *Apple* Consultation Professiona...
**801042BR** **Job Title:** Geek Squad Apple Consultation Professional **Job Category:** Store Associates **Store Number or Department:** 000214-Willowbrook-Store Read more
*Apple* Mobility Specialist - Best Buy (Unit...
**800879BR** **Job Title:** Apple Mobility Specialist **Job Category:** Store Associates **Store Number or Department:** 000803-Lansing-Store **Job Description:** Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.