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

Hopper Disassembler 4.2.5- - Binary disa...
Hopper Disassembler is a binary disassembler, decompiler, and debugger for 32-bit and 64-bit executables. It will let you disassemble any binary you want, and provide you all the information about... Read more
BetterTouchTool 2.261 - 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
Sketch 44.1 - Design app for UX/UI for i...
Sketch is an innovative and fresh look at vector drawing. Its intentionally minimalist design is based upon a drawing space of unlimited size and layers, free of palettes, panels, menus, windows, and... Read more
BetterTouchTool 2.260 - 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
Chromium 59.0.3071.115 - Fast and stable...
Chromium is an open-source browser project that aims to build a safer, faster, and more stable way for all Internet users to experience the web. Version 59.0.3071.115: This update has no Flash plug... Read more
SyncTwoFolders 2.2.3 - Syncs two user-sp...
SyncTwoFolders simply synchronizes two folders. It supports synchronization across mounted network drives and it is a possibility to run a simulation showing in a log what will be done. Please visit... Read more
Myriad 4.1 - $79.00
Myriad is, simply put, one of the best audio batch processors. Totally redesigned, it looks beautiful and delivers incredible performance. Let Myriad do the heavy lifting while you get back to doing... Read more
Suitcase Fusion 7 18.2.4 - Font manageme...
Suitcase Fusion 7 is the creative professional's font manager. Every professional font manager should deliver the basics: spectacular previews, powerful search tools, and efficient font organization... Read more
SoftRAID 5.6.1 - High-quality RAID manag...
SoftRAID allows you to create and manage disk arrays to increase performance and reliability. SoftRAID allows the user to create and manage RAID 4 and 5 volumes, RAID 1+0, and RAID 1 (Mirror) and... Read more
BetterTouchTool 2.25 - Customize Multi-T...
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

Latest Forum Discussions

See All

Ravenscroft 275 Piano (Music)
Ravenscroft 275 Piano 1.0.0 Device: iOS Universal Category: Music Price: $35.99, Version: 1.0.0 (iTunes) Description: Experience the splendor of a Ravenscroft Grand with the most realistic sounding piano ever created for iOS. Launch... | Read more »
This War of Mine gets a new ending and m...
This War of Mine just got a big new update, featuring free DLC that adds a new ending to the game, among other exciting changes. The update is celebrating the game's two-year release anniversary. Apart from the new ending, which will be quite... | Read more »
Summon eight new heroes in Fire Emblem H...
Nintendo keeps coming at us with Fire Emblem Heroes updates, and it doesn't look like that trend is stopping anytime soon. The folks behind the game have just announced the new War of the Clerics Voting Gauntlet, expected to start next Tuesday. [... | Read more »
The best deals on the App Store this wee...
iOS publishers are pulling out all the stops this week -- there's a huge number of seriously great games at discounted prices this week. Let's not waste any time and get right down to business. [Read more] | Read more »
The House of da Vinci (Games)
The House of da Vinci 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: Enter The House of Da Vinci, a new must-try 3D puzzle adventure game. Solve mechanical puzzles, discover hidden... | Read more »
Solve the disappearance of history’s gre...
Blue Brain Games invites you to indulge in an immersive hands-on 3D puzzle adventure in similar vein to The Room series, with its debut release The House of Da Vinci. Set during the historic period of the Italian Renaissance (when Leonardo himself... | Read more »
Age of Rivals (Games)
Age of Rivals 3.3 Device: iOS Universal Category: Games Price: $.99, Version: 3.3 (iTunes) Description: Deep civilization-building strategy in a fast-paced card game! | Read more »
Panthera Frontier (Games)
Panthera Frontier 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: | Read more »
Angry Birds Evolution beginner's gu...
Angry Birds changes things up a fair bit in its latest iteration, Angry Birds Evolution. The familiar sling-shot physics mechanics are still there, but the game now features team-based gameplay, RPG elements, and a new top-down view. With all of... | Read more »
Sega Forever is for the retro game fans
Sega is launching a new retro games service titled Sega Forever, in a move that's sure to delight games enthusiasts with a bit of nostalgia. Sega's releasing five classic games for free. The titles include Sonic the Hedgehog, Phantasy Star II,... | Read more »

Price Scanner via MacPrices.net

Apple Releases iOS 11 Public Beta; How To Get...
The official release of Apple’s latest mobile operating system iOS 11 is vaguely slated for the fall, but as of June 26, ordinary users can download an iOS 11 public beta. To download the iOS 11... Read more
Extend Life of MacBook Pro Retina 2.0TB With...
MacSales.com/Other World Computing has announced availability of the new OWC 2.0TB Aura Pro Solid State Drive for mid-2012 to early 2013 Apple MacBook Pro with Retina display. One of the fastest... Read more
BBEdit SummerFest 2017 Discount Ends Friday,...
You can get 20% off BBEdit for a limited time in Bare Bones Software’s http://www.eastgate.com/Tinderbox/Specials/SummerFest.html?mc_cid=f2101ca260&mc_eid=[UNIQID]SummerFest 2017 sale and... Read more
Use Apple’s Education discount to save up to...
Purchase a new Mac using Apple’s Education discount, and take up to $300 off MSRP. All teachers, students, and staff of any educational institution qualify for the discount. Shipping is free: - 15″ 2... Read more
Clearance 27-inch 3.3GHz 5K iMac available fo...
Amazon clearance 27″ 3.3GHz 5K iMacs (MK482LL/A) available for $1799.90 including free shipping. Their price is $500 off original MSRP, and it’s the lowest price available for this model from any... Read more
13-inch 1.8GHz/256GB MacBook Air on sale for...
B&H Photo has the updated 2017 13″ 1.8GHz/256GB MacBook Air (MQD42LL/A) in stock and on sale for $1129 including free shipping plus NY & NJ tax only. Their price is $70 off MSRP. Read more
27-inch 3.4GHz iMac on sale for $1699, save $...
B&H Photo has the new 2017 27″ 3.4GHz iMac (MNE92LL/A) in stock and on sale for $1699 including free shipping plus NY & NJ sales tax only. Their price is $100 off MSRP. Read more
21-inch 2.3GHz iMac on sale for $1049, save $...
B&H Photo has the new 2017 21″ 2.3GHz iMac (MMQA2LL/A) in stock and on sale for $1049 including free shipping plus NY & NJ tax only. Their price is $50 off MSRP. Read more
ABBYY TextGrabber 6 for iOS Implements Instan...
ABBYY has announced the release of TextGrabber 6.0.0, an important feature update to the company’s productivity app developed for iOS and Android devices. TextGrabber 6.0 now offers Real-Time... Read more
vPhone, First Smartphone That Can’t Be Lost,...
Austin, Texas based Hypori has introduced the vPhone, a virtual smartphone that affords every business user the benefits of separate work and personal phones, conveniently delivered on a single... Read more

Jobs Board

*Apple* News Product Marketing Mgr., Publish...
…organizational consensus on strategy and vision for publisher tools, authoring, and Apple News Format.Carries this strategy and vision across the organization to Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Security Data Analyst - *Apple* Information...
…data sources need to be collected to allow Information Security to better protect Apple employees and customers from a wide range of threats.Act as the subject matter Read more
Lead *Apple* Solutions Consultant - Apple I...
…integrity, and trust.Success Metrics/Key Performance Indicators:Quantitative* Year over Year growth in Apple Product and Beyond the Box sales in the assigned Point of Read more
*Apple* Solutions Consultant till v%u00E5r...
…ethics, integrity, and trust.Success Metrics/Key Performance Indicators:QuantitativeYear over Year growth in Apple Product and Beyond the Box sales in the assigned Point Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.