BACK ISSUES OF T-S HORIZONS ARE NOW AVAILABLE

Each issue brings you approximately thirty-two pages of usable information, prograiTi listings, product reviews, programming articles, hardware projects, and applications you can use in your home or business. T-S HORIZONS features nationally kncwn writers like Gordon Young and Paul Hunter. And now you can get the back issues you missed for only $1.25 per issue!

Issue HI Creating and Saving Files, Uninterruptible Power Supply, Repeat Key Module, Numerical Analysis, and more!

Issue #2 Memory Reduction, Matrix/Cursor Input, User-Friendliness, Graphics Tutorial, Reset Switch Project, and more!!

Issue H3 Animation, Simple Loading Aid Project, File Protection, Differential Equations, Ham Radio, and more!!!

Issue H4 Bank-Switching for the TSlOOO-Part 1, Error Recovery, TS2068 Edge

Connector Schematics, Converting to T/S BASIC, Simpson's Rule, more!!!

T.cu. I - T-SHirkinj T'SHiri’tinx

I * H V* I ^ Vi H H ■ AmvMOM OgftWy tar »» Tfrwx ■ ■■ ■■■■ ■ vHBIb

I wm IIBI I kBIIdil ^ 11 * MtardtfitaOu»MytortfwTRMKConvutarUMr

I |*3ngr|'^gf|jf _ ^ ««« -o.

Aflordabta Ou»My far tfw Trwk Computar ifapr

AHordiPfa C3uaWy tar t« CompuMr UMr

s IS Eg m £ Es IS ci a fi

p p a p a o p p p a P P ii (p p a P B caa iiifDBp'ai pp m

M*TiNx/eun*o« wmjT WM HO l IHf • •

MCMOHY HtOUCTlOH

ANiMATlOM fVLM. MOTICTIOM

IBVHWt

SX MO eiLf

MAM HACK!* tlAiCt

IMMOCALO

BANK BWTTCHNQ FOR TIC T8 1000 Ppl 1 Expond To B6K • by Htfipr

Enclosed is Please send issues of T- $1.25 each.	US$ ^ the indicated -S Horizons for	mi ADDRESS
HI	H2	CITY
H3	H4	STATE.ZIP
Send to:	T-S Horizons,	Back Issues, 2002 Summit St., Portsmouth, OH 45662

T‘5 HarKinx

Affordable Quality for the Timex Computer User 2002 SUMMIT ST. PORTSMOUTH. OHIO 45662

Table o-f Contents		FORMAT	SIZE*	IX	2X
		Full page	6-1/4 X	9	$125	$119
ENTER	4	2/3 page	4-1/2 X	9	100	95
Guest Ed i tor i al	6	1/2 page	6-1/4 X	4-1/2	75	71
by Stan Ue i t			3 X	9
Reader INPUT	8	1/3 page	4-1/2 X	4-1/2	65	62
Program Tips	11		2 X	9
by Rois Harder		1/4 page	3 X	4-1/2	35	33
Numerical Analysis	12	1/6 page	2 X	4-1/2	29	21
by Ken Lewis		1/9 page	2 X	3	17	16
"WORM" Word Processor	14	2 i nch	2 X	2	12	11
by Gordon Young		1 i nch	1 X	2	6	5
TS 1000 Bank Switching	16	*No charge	■for ad 1	reduct	i on .
by Paul Hunter		FORMAT; Black and	white	only.	Ads
Graphics Program	20	may be reproduced ■	from an ad in	an-
by Johnson and Swartz		other publ i cat i on .
Reviews	21	CLOSING DATES; 15th o-f	month	pre-
T-S NEWS	27	ceedi ng i ssue date	.
USR NEWS	30	FREQUENCY ;	Monthl y	•

Ther^^s something NEU on the horizon.

QUALITY, UTILITY, ACCESSIBILITY, AFFORDABILITY. This the combination you^ve been waiting for. Don^t miss an issue. Subsribe NOU!

I want to have T*S HORIZONS delivered to my hone every month.

I have enclosed $12.00 for a one-year <12 issue) subscription. ^18.00 Canada. $20.00 other foreign.

Name _ _ _ _ _

Address ■ _ _ _ _

City _ _ ' State _ Zip ____

Hail form with check or money order to:

T-S Horizons

Subscription Dept. Please start my

2002 Summit St. subscr i pt i on wi th

Portsmouth, OH 45662 the C __i ssue .

Dear Fellow Timex and Sinclair Computer Users,

Thank you -for your patience. T-S Horizons is intended to be monthly but as you can see, you are holding the April/May issue oi T-S Horizons in your hands. Income tax matUrs were only one ot the reasons we are late. At any rate thank you tor bearing with us.

There is a lot ot news concerning the Timex computing world these days - largely bad news, but enough good news that we are encouraged. Ue hope you will be too.

I got some critical comments regarding last issue's cover, and I suppose 1 deserve it. Tm usually an optimist but Timex's lay-down-and-die attitude really upset me. The *2068 tombstone* represented the Timex Computer Corporation only, and not the TS-2068 itself, Timex users in general, or the future of T-S Horizons. Actually I'm optimistic about the last three.

Hope for the TS-2068?

Due to recent ads selling Timex products at 1/2-off and last-minute buying by TS-1000 owners, the stockpile of TS-2068's at Timex is nearly gone. All of the TS-2040 printers have been sold (except for the few being returned by dealers). Some software and TS-2020 program recorders are still available for an unknown period of time. The TS-1000 is out of production. However the TS-1500 is still being made on a limited basis for educational use. (You know, those correspondence schools that advertise in magazines like Popular Hechanics, that offer to teach you how to program and give you a free computer.)

However if you've heard rumors that someone is seeking the rights from Timex to market the TS-2068 and/or TS-1000, they're not just rumors. Our sources at Timex say no less than 20 parties are inquiring about the prospect - some of them seriously. As we understand it Timex will manufacture the 2068 if they can get a firm order for 25,000 units. It will be the same machine, but will not carry the Timex name. (This makes some sense. Timex was perfectly happy with the TS-1000 as long as it was *selling itself.* But when they really had to market it and the 2068, they dropped them.)

So it seems there is some hope for the Timex (?) computers. (Notes Clive Sinclair still has made no reassuring gestures to American users.)

Publishino - Another One Bites the Dust

- In case you haven't heard Sync has sunk.

The March/April issue was the last. When 1 heard the news, 1 called their offices to find out why. Incredibly, the guy 1 talked to said it was because Timex got out the computer business - as if they thought all of us loyal Timex users would say, *Well Timex is gone. Let's all go buy Ataris and cancel our subscriptions to Sync!* When I reminded him that when Sync was first started there was no Timex computer - only the 2X80 - a Sinclair computer importad from England, he said he never thought of it like that. 1 suspect the true reason was a falloff of advertising income due to excessive ad rates.

- Timex Sinclair User is still dead, despite rumors to the contrary. The only hope 1 see is if they get dollar signs in their eyes over Sync's dropped advertisers.

HMEX TakM A Liekiac

BAM( 8WITCHNQ FOR nc TS tOOO Fwt 1

Exftnl To MK • by PaU HiMw

S Hiriiinj

MWM* IV M Tlm« CompiMr Unr

Another one bites the dust...

- Bad news for TS User (newsletter) fans. Despite the big talk in the April issue <*If you are a (TS User) reader then you are OK. TS User is full of optimism. TS User will continue production and coverage of Timex and Sinclair Microcomputer products...), in a recent phone conversation, Derek Stubbs informed me that his company was moving on (into robotics and software development - not Timex software), and dropping the Timex market. He had offered in that same issue to establish a clearinghouse for third party merchandise but, of course, that will not materialize now.

So what's left?

T-S Horizons. To be honest 1 hate to see Sync, TSU(mag), and TSU(nl) go. They were all good resources for us at T-S Horizons and other Timex users. But TSH is here to stay. We may be late occasionally but trust us - we plan to be around for a long time.

Some other worthy T-S dedicated publications are:

-SyncWare News, P.O.Box 5177, El Monte, CA 91734 (for the technically inclined - a nice publication). -Basic, 3705 Biscayne B1., Miami FL 33137 (BASIC programs for the ZXBl/TSl 000/1 500).

-Syntax, RD 2, Box 457, Harvard, MA 01451.

-Also see USR News for some very good Timex Sinclair user group newsletters.

In addition there are two other magazines we would like to mention:

-The Computer Trader (1704 Sam Drive, Birmingham, AL 35235). This magazine covers all computers, from Apple to 2X81. In a typical Issue there are four to six articles for the Timex-Sinclalr. Currently they are running an excellent machine code tutorial series.

-The Computer Shopper (P.O.Box F, 407 S. Washington Ave., Titusville FL 3279d). In a recent phone conversation with the magazines' editor, Stan Veit (who provided this issue's Guest Editorial), I was told that they are planning to add two new features for Timex-Sincal Ir users: a general Information-type column and a telecommunications column specifically for Timex users.

Third-Party Support

Although a few companies are getting out of the Timex-Sinclalr market (most notably Memotech), most of the significant software and peripheral companies are hanging in there. The folks at Byte-Back told us, their business has tripled since Timex 'pulled the plug.* 21st Century Electronics has a full line of TSIOOO products, and is developing many TS20d8 products. They have 5

A GUEST EDITORIAL by STAN VEIT of The Computer Shopper

It is almost two years ago since I attended a press lun¬ cheon at the Tavern On The Green in Central Park, New York City. The purpose of the meeting^vas to announce that Timex Corp had formed Timex Computers and would take over the sales of Sinclair Com¬ puters in the United States, Clive Sinclair was there in smiling fellowship with the top brass of the Timex Corp. Their message to' the press was that Timex (who had always manufactured the ZX80 and ZX81 low-cost computers), would now apply their marketing expertise to com¬ puters as well as watches. They would also provide extensive software and peripheral sup¬ port to the Sinclair machines making them highly useful to small business, education, and science.

We members of the press were impressed. Here was a company who’s watches and clocks had a reputation for low-cost and quality and they were going to bring the same qualities to low cost com¬ puters! We believed it as much as the Timex people did.

Timex upgraded the ZX-81, which they called the TS-1000 by adding-additional memory. They advertised the computer and sold thousands of them throughout the country. The Timex TS-1000 became the in¬ troduction to personal com¬ puting for many people.

A few months ago Timex fired all the people left in the Computer division and folded it into the watch operation. Then last week they complete¬ ly got out of the s^es of com- 6 puters, explaining that they

couldn’t make any money from them. Small wonder, the TS-1000 that cost me $99.00 plus $49.00 for the 16K Memory Expansion was now selling for $39.00, with the Memory Unit and some soft¬ ware!

I blame the VIC-20 and TRS-80 Color Computer and the TI 99/4A for the final death of the TS-1000. VIC-20 and CoCo showed the public that you could get a real computer for ^bout the same price as the Timex plus the expansion module. They both had real keyboards and good software. You could get reliable cassette loads, or just plug in a cart¬ ridge and use the machine. There were third party expan¬ sion units that worked. Radio Shack and Commodore even provided a printer and disk drive for those who could pay for them.

Now nobody expects a com¬ pany to stay with a money los¬ ing product, but when you sell millions of items to the public you have some responsibility toward those who bought the product on the basis of your claims about its merit.

Sinclair was not much help to the users of their machines, but they made no bones about it. You understood when you bought a ZX80 or ZX81 that you were pretty much on your own. Timex however promis¬ ed to do better, they offered help from such things as the user hotline (1-800-24TIMEX) and the COMPUTER CLUB and a Newsletter. None of it ever worked. The Hot Line was usually busy and if you got through, the chances were that they couldn’t answer your

questions and they never call¬ ed you back. The other support mechanisms for the 2068 might have worked if Timex hadn’t fired Dan Ross and his staff.

The notice of the complete demise of the Timex Com¬ puters came through a one page P.R, Release from Ruder, Finn & Rotman who do the public relations for Timex. It was dated February 21, 1984 and said that Timex was withdrawing from the home computer business. It quoted Mr. C.M. Jacobi, Vice Presi¬ dent of Marketing and Sales for Timex whP said,’ We believe instability in the market will cause the value of inventories to decline, making it difficult to make a reasonable profit. Further, we are concern^ that those conditions will strain trade relations between manufacturers and retailers, a relationship which the com¬ pany values very highly.’ Note that he says nothing about rela¬ tionships between the com¬ pany and computer users! In regard to service of Timex Computers, Mr. Jacobi said, ’Consequently, the company has decided to withdraw from the retail portion of the home computer busisness. Consumer warranties will be honored and out of warranty service will continue’.

We called Mr. Jacobi to ask him to expand on the com¬ pany’s support policies. We asked questions about the level of support that Timex would continue to offer for software and the sale of proprietary chips and peripherals. We never got to speak with Mr. Jacobi. His spokesperson said

‘We are considering the answers to your questions, we will call you when we have answers for you’. They never called back.

We then called the P.R. firm who said, ‘We can not give you any additional information, call Mr. Jacobi at Timex <

I wish you could see some of the letters we have received from Timex/Sinclair users. They believed in the product and spent a lot of money on it. I myself, taught a course in Timex/Sinclair Programming and purchased a computer for $99, a 16K Memory Expansion for $49, a Printer for $99, a lot of books and software. I have about $400 invested in this machine and I know others who spent a lot more. We never expected a company like Timex to ditch us without any consideration. If they were as concerned for their customers as they are for their dealers, they would still be in the com¬ puter business.

Is the Federal Government going to let them get away with this one? Are Computer Owners as important as Snail Darters? It is one thing for a Company to go Chapter 10 or Chapter 11 (Bankrupt) and end belly-up, its another thing for a solvent company to just dump customers who bought their products in good faith. We are consumers who need protection, the Very Low Cost Computer User is an En¬ dangered Species!

. Don’t write me about it, write your Congressman!

secured the rights to Tintex's word processor for the 20d8, which they say is as good as an/ UP for an/ computer on the market. (2l5t Century, 6813 Polk St., Guttenburg NJ 07093,

210-869-2616). Gesang Associates (P.O.Box 452, Randallstown,

MD 21133, 301-922-0767) also has a full line of TSIOOO and 2068 products.

All of the following companies are expanding their product lines or maintaining status quo (in addition to those who have ads in this issue); 6. Russell Electronics, E-Z Key, Aerco, E. Arthur Brown, Computer-Wear, Paul Hunter, Rorapak. Thomas Woods has been especially vocal about his support for the Timex computer line.

The Future?

There are encouraging signs for Timex-Sinclair users.

-Timex User Groups are as active as ever.

-New companies with new products are still coming out; JRC Software (see T-S News); Hinny Electronics Graphics and 64K

package for the TSIOOO (see last issue)} Interface Design High Speed Interface (see TSH #3).

-Some companies and user groups are trying to 'import* support for the TSIOOO and 2068 from English Sinclair users who weren't subjected to Timex's demise.

Hopefully some good will come of it.

-As 1 stated above the TSIOOO and 2068 may be resurrected in the near future under a new name.

One thing that is important for us to do now is to 'strengthen the things that remain.' Companies that are now supporting TS-related products need to know there are people 'out there* who are hanging on and will buy their products. I think if we all band together we come through this in great shape.

Rick Duncan

50BB

TIMEX

QUICKSILVA THOMAS B. WOODS

? ?

21st CENTURY ^

ELECTRONICS Banta ,

BYTE-BACK Sonw^UtE

- o. misscii E-z

_ ?_ JRC ?

,6,,i,R20 ? SOFTSYIMC

Dear Rick,

K E H L-' t H!

INPUT

I would like to clear up a misconception that Art Gindin has about VU-CALC (TS-Horizons #3 Memocalc). I also experienced the same difficulty trying to get a print out on my Seikosha GP-IOOA printer and I also blamed the software.

I believe the letter points out sufficient problems to warrent making future 2068 users aware of.

Mr. Heifner has been a valuable asset to our group in evaluating and reviewing new pro¬ grams for our newsletter. I hope you find his article as valuable as I did.

The truth is that the Memotech interface and Seikosha printer will not accept Sinclair graphics (in this case the black bars that make up the grind in VU-CALG) . Many Sinclair programs will not print on the Seikosha and those that do will print in a 32 column format. (Syber Software makes a cassette program called MEMOSHA which will correct this problem but I have not been able to get it to work and it requires extensive program modifications which I think would be beyond the capability of the type of reader Art is aiming his articles at). VU-CALC should not be "abandoned" however because it will accept text in the grid which Memocalc will not. The problem is not in the documentation. It works fine with the Timex 2040 printer and the ZX-81 printer . I have encountered many people who have run .into this problem and it may be worth mentioning in your magazine. I did hear of one individual who reprogrammed VU-CALC with an acceptable ASCII symbol such as "$" instead of the graphic bars.

I hope you will forward this information to Art and hopefully to your readers. Apparent¬ ly Memotech, Sinclair and Timex are not giving it out.

Very truly yours,

James A. McKnight

3708 Strayhorn

Mesquite, Texas 75150

Gentlemen,

Enclosed please find article on Timex Program 8 VU-CALC for the T/S 2068.

Peter J Callinicos President

MILE HIGH CHAPTER TIMEX USERS

FROM: Mark A. Heifner

37 E. Colorado Ave.

Denver, CO 80210 (303) 744-1137 (303) 722-9067

TO: Timex Computer Corporation

Several weeks ago I purchased a copy of the Vu-Calc for the 2068 and was eager to use it for my business application, having found the Vu-Calc for the TS 1000 very useful, but rather limited. I was immediately impressed by the expanded number of rows and columns, the more creative method of working with data, and especially the almost limitless number of formulae that could be entered - a severe problem with the TSIOOO program. After a few minutes I realized that the program was essentially useless for any serious applications and I had to return it for a refund.

Two aspects in the 2068 Vu-Calc make it difficult to use. One is the lack of sepa¬ ration between the boxes. When all the boxes are filled on a certain portion of the display the only way to distinguish between one box and an adjacent one is to move the cursor around. All the numbers run together, end to end. Although that problem is manage¬ able but a nuisance in comparison to Vu-Calc for the 1000, one other problem cannot be remedied in any way.

In writing the program it apparently was decided that a display of 4 columns instead of 3 was important. Because of the limited space on the 2068 display in normal mode it was necessary to drop the lines separating the boxes and reduce the number of numeric entries in each box to 7 from the 8 as in the 1000 version.

Vu“Calc, like its big brothers and sisters Visicalc and its variations for the larger computers, is most useful for working with dollars and cents. Seven entries, including the decimal point, limits the program to values less than $10,000.00 whereas the 1000 version allows figures up to $100,000.00. I am sure you can see that this limitation makes the program useless for all but the simplest application.

As I see it, the deficiencies of the 1000 program were corrected quite well, but in the process nobody apparently noticed that a new set of problems had been created that pro¬ duced a program which is almost useless. The 2068 is a very capable machine with lots of dandy features and I was both surprised and disappointed that such a trashy program had been allowed to go out on the open market. A few suggestions might be helpful to correct- ing this situation with this program.

A lot of people I know that have the 2068 have gone to using monitors rather than a TV. The picture is so much better on the monitor and good monitors are nearly as cheap as a good black and white TV. Why not produce a Vu-Calc which uses the expanded display modes? If a printout is needed on the 2040 printer I am sure it could be worked out that two consecutive printouts would be sent to the printer with each printout showing half the screen. Alternatively, you might return to a 3 column display with separations or even a 2 column, dual screen display or some variation on that. The Important thing is to maintain many of the features already there but allow at least 8 numeric entries per box. Maybe it could be worked out that the user would even be allowed to select the number of entries per box, up to some reasonable limit ^ and the display would adjust itself accord¬

ingly. I doubt that having more than 9 entries per box would be useful. I do feel that a minimum eight is needed.

In conclusion, spreadsheet programs are so very useful it seems a shame to produce a program for the 2068, a very capable machine, that is essentially useless when compared to the similar program for the 1000.

INVASION OF RUSSIA, JULY, 1941

16K, 32K, or TS2068

You command the German Invasion of Russia to take Moscow.

T/S 2068 Game has:

• Large map of Eastern Europe and U.S.S.R.

• Diyisional and Brigade Strength-Panzer, Infantry, Calvary, etc.

• Supply lines • Zone of Control

• Effects of terrain and weather

• Actual Reinforcements

• No fast reflexes required.

32K-IDENTICAL TO TS/2068, EXCEPT:

• large 4 screen map board • No effects of terrain 16K-IDENTICAI TO 32K GAME, EXCEPT:

1 screen map board T/S 2068 -

00 S « H

32K

16K

- $17.9^V

- 17.95 1+ $2.1

- 14.95/

VISA & Mastercard Accepted

Dealer inquiries welcome

SHARP’S

127 NINE MILE RD. SANDSTON, VA 23150 (804) 737-4895

A message from THOMAS B. WOODS

Dear Fellow Timex Computer Owner,

The bad news that Timex has dropped out of the personal computer market comes to me as a Itremendous disappointment. I put my faith in their machines and for the last two years have worked long and hard to build a software business with a reputation that I think is one of the best in the industry.

In the current situation all of us are wondering what will happen next. There is one thing I'll say, however. When the dust settles, I intend to still be here. I am determined to continue providing quality software for both the TSIOOO and the new TS2068.

I owe my business to you who use these two marvelous machines, and you deserve far more than to be simply dropped and forgotten. I for one. Intend to keep my computer running. From me, you can expect to see an optimistic future of more programs and more applications for the Timex.

It is in this rallying spirit that I announce my latest product: PRO/FILE 2068. The original, release date was scheduled for June 1984, but with circumstances being what they are, I feel that this program released now, will demonstrate my dedication to the support of the TS2068.

The manual for PRO/FILE 2068 is not yet complete, but the program itself is finished, extensively tested, and is ready to be shipped with abbreviated operating in¬ structions and a promise that the manual- -expected to be 100 pages — will be mailed to every customer just as soon as it is printed.

Enclosed is a detailed description of PRO/FILE 2068. You'll notice right away that this program is a significant advance over the older but still extremely popular ZX Pro/File used on the TSIOOO and 1500.

PRO/FILE 2068 is a masterpiece if I say so myself!

By pulling together, by communicating, and by sharing ideas and talent, I am convinced that we Timex computerists will emerge from the present chaotic state unscathed, and the computer itself will be as strong and popular

las ever.

FOB JTIST YOU CAN

QRAB THE BOLL EY THK HORIIS

TOCO TECHNOLOQY

•nnounces Stock Market Software for your TIMEX 1000 and TS g066

The TECHNI-ETOCK SOFTWARE SYSTEM la a stock market analysis program designed by a pro trader for use by pros and beginners alike. The program analyzes your favorite stocks using statistical and technical averages In order to predict future stock price trends.

The System Includes:

1 ) HANDSOME BINDER

2) 26 PAGE INFO GUIDE

3) RESEARCHED WORKSHEET

4) REFERENCE SYSTEM

«:) PR0®A>D1ED CASSETTE

To Order: Send us the names of your favorite 6 stocks along with a check for $24.9? for the TIMEX 1000 version (9 stocks and $34.9? -TS 2066) to:

for use 1 6K or more

TCX:0 TECHNOLOGY $3

POBOXBB shipping

SAN1 A CLAUS. IN 47S7»

As always, GOOD COMPUTING!

Thomas B. Woods

P.O.Box 64, Jefferson, NH 03583

ZX PRO/FILE

A machine language information storage and retrieval tool for 16-64K.

* Multi-word search capability A Instant file access

* Ordered displays

* Definable printer functions

* Totally flexible file size

* 59 page tutorial manual

* Newsletter updates

THE MOST ADVANCED FiLE MANAGER YOU CAN GET FOR THE TIMEX

Ask for free specifications or send $16.95 for cassette and manual to:

THOMAS B. WOODS

P.O. Box 64, Jefferson, NH 03583 Phone: (603) 586-7734

Vi<ui Mastercard welcome

^^^AstfFreeTSIOOO

orTSZOBB

.j?** ^*®^j**9

i??i/aa@8®8!i‘.iaesi4 with catalog

FREF MC i)rog(<»ni UsItriQ and raiai'oq wiin S A S F. I'JOc onsl i

Ron LeMon, 1601 W 400 S. #86, Sail Lake City. UT 84104

TIMEX-SINCLAIR programs to save you money. I Payoff shows how much credit card and charge accounts really cost, how to pay them off and save $$$. Payout shows where your hard-earned money is going. On cassette, $12.95 each post¬ paid. Specify TS-1000 w/16K, TS-1500 or TS- 2068. Ace Software, 2 East Oak Avenue, Moorestown, NJ 08057

GOLFERS

GOLF HANDICAPPER is a menu driven 16K BASIC program for your TS 1000, 1500, ZX81 which computes/saves/ updates USGA handicaps for up to 48 players. With a printer attached you can print out scores and handicaps for all players. High quality cassette tape shipped in hard box and accompanied by full documentation. Send $20 ck/mo to John Carson 11200 Lockwood Dr. #307 Silver Spring, MD 20901

*****MICR0-L0AD*****

HAS

UNUSUAL SOFTWARE FOR TS1000/ZX81 BOX 1095, T OR C, NM 87901

Send. BASE for information.

CLASSIFIED AD

PR06IWIS for SCIENCE/HEALTH/ MATH/ELECTRONI CS/HOME . Free

catalog tor SASE and 40 cents postage. MAH Software, 341 West Eagle Lake Drive, Maple Grove, m 55369. 1 1

NUHERICfiL QNhLYSIS

LEAST SQUARES METHOD OF CURVE-FITTING POINT DATA TO

y=ax+b or y=be by Ken lewi s

The standard approach to fittinf^ a

set of data points to a line y=ax+b

is to use the method of least

squares. The least squares method

provides an unambiguous fitting

procedure which minimizes the

deviation of the data points frcxn

the fitted line in the following

sense. Let Y. represent an

experimental value and let be a

value from the equation y=ax^+b,

where xj is a particular value of

the variable which is assumed to be

free of error. It is desired to

obtain the "best" values of a and b

such that for e. = Y . -y . =Y . -ax . -b , 1 1^11 1 ’

N 2 N 2

the error E= 5 eT= ;jg(Y.-ax.-b)'^ is

i 1 j 1 1

a minimum, where N is the number of data points. Since xi and Yj[ are unaffected by the choices of a and b, the minimizing relations are dE/da=0 and dE/db=0. These result in the two equations:

both sides to get In y=ln bt-ax, and define y^=ln y and b^=ln b. Now we have y'=ax+b’ , so the method outlined above applies.

THE PROGRAM

To execute, this program, enter the "RUN" mode. The first prompt is "INPUT PAIRS OF DATA" and "ENTER POINT 1". The point is entered as follows: x^, enter, y^, enter. The new prompt is "ENTER POINT 2" and

the answer then appears with a and b expressed numerically.

EXAMPLE

Fit a straight line to the given data using the least-squares criterion .

X	1.1	2.9	4.3	6.2
f(x)	50	43	28	25 .

a Sx?+b Sx.= Sx.Y ]_ 1 11

a 2 Xj. + bN = S Y^

Solving for a and b, these values can be expressed in terms of the input data only:

After entering the "RUN" mode, we iirmedtately get the prompt "INPUT N-NO. OF DATA". Since there are 4 points, enter the number 4. In response to the prompt "ENTER POINT 1", the values 1.1 and 50 are entered . We are then

Sx.Y^

SY^ 5 N

— b=

SXi SY.

_ 2

SXi sx.

S Xi2 S Xi

S Xi E N

This is the least-squares method. The approach can be appl^^ to fit data to the curve y=be‘^ in the following manner: take the log of

proipted;' TINIER POINT 2", and the values 2.9 and 43 are input, and so on. The answer is printed out, i.e. ,

"THELINE WHICH FITS THE DATA IS:

Y=5.3011G18*x + 55.716711 "

lO REM L5T5QC'

REM i_ER;5T SOURRE FIT TO 30 REM R LINE FOR N E^RTR >.'3 DIM Xi 100:1 36 DIM F ( 100 :i

4-0 PRINT "INPUT N-ND. HF OCTC” 50 INPUT N 55 CL 5

60 PRINT "INPUT PflTP;=. HF naTO-

10 REM L5T50X

b-95'r "SOURRE FIT TO 30 R^M B*c/.P i:fl^x:i FOP N DIM Xi:i00i ”

36 DIM F I 100 -I

TmI-? N-NO. of Di:

INPUT N 55 ULS

P0 PRINT "INPUT DaTD<^ ,-,cr r.,-

70	FOR K=1 TO N	70	FOR	K=1 TO
75	INPUT .>:. 1 K '1		I NR	JT >: 1 K 1
60	INPUT FiKi	U0	I NR	UT F ( K 1
50 100	NEXT K LET SUMi=0	62 SF	CLS LET	F iK) =LN
110	LET SUM2=0	50	HEX	T K
120	LET 5UM3=0	100	LET	SUM 1=0
130	LET SUM4.=0	110	LET	SUM 2 =0
14-0	FOP. L=1 TO N	120	LET
150	LET SUMl =SUM1+X IL)	130	i-ET	SUM 4=0
160	LET SUM2=SUM2 + X' (L'! *>:' I'L'!	14-0	FOR	L = i TO
170	LET SUM:3=5UM:3 + F iL'i	l50	LET	SUM! =Fi 1
160	LET 5UM4.=5UM4- + X 'L' +F n't	160	LET	SUM2 = 5U
150	Nt:XT L	170	LET	5UM3=5U
200	LET D = 1 •' f N*5UM2-:5.UMl-^;=ii iMii	160	LET	Si iMm. =:=,.■ 1
2X0	LET A0= i 5UM2*5UM3-SUMl-»-:=iUM4	150	NEX	r L
*D 220	LET PI = I -5UM1-»5UM3 + N5UM4.:!	2 00 210	LET LET	D = 1 y H * A0= iSUh

5 PRINT "THE LINE UHICH F DRTR 15:"

? PRINT "■

5 PRINT "Y= ";R1 ;“•»>; + " :

) STOP

230 PRINT HE DRTR IS 2^0 PRINT £ w’ 0 P‘ K X N"^

’ ; H X ■ ‘ X

260 STOP

Cl D=l/ (N^SUfiS-SUf-li-^^a !H- ET R0= ! SUM2'»5UM3-SUMl-^:5i.

P'i' Hi= -SUM1*5UM3+N*5UMj

PINT "THE EXP WHICH FiTi

; EXP ( R0 ) ; " *E')

PROGRAM

EDUCATION

• NEW FOR TIMEX/SINCLAIR 10(X)/ZX81 16K.

Dual Purpose Academic Programs

• Challenging. Self-Pacing ... Tailored to Specific Interests and Abilities.

• Software Written In Basic ... Easily Understood ... Not a Bit of Machine Code.

Full Documentation Package

□ RISING SUN . $14«

Tour Japan, facts, geography (12-Adult)

□ LONG DIVISION TUTORIAL. .$12“

A dedicated tutor ... not flash cards (8-10)

□ AREAS OF CONCERN . $13“

Areas, perimeters, discovery, fun (10-13)

□ THANKS MR. NEWTON .... $13“

Laws of motion, serious graphics (16-Adult)

□ VINS FRANCAIS . $14“

French wine guide (Adult)

(CT residents add 7.5% sates tax; Outside USA add 15%)

~~| I All software on high quality

t cassettes and is replacement

- - guaranteed.

— - To order, send check or

V _ money order to:

— C _ tag software

I I \WJI \ P.O. BOX 688

RADIO SHACK COMPUTERS

AX DISCOUMX PRICES

» FULL RADIO SHACK UARRANTY

* PURE RADIO SHACK EQUIPHENT •MAIL ORDER DISCOUNT PRICES

* FREE SOFTWARE WITH EACH COMPUTER SOLD » FREE BOOK 'HOW TO GET RICH WITH YOUR

MICROCflHPUrER* WITH EACH COMPUTER SOLO

• W SALES TAX ON OUT OF STATE SALES

• FULL LINE OF PROOUaS

pBOEMMai

NAUGATUCK, CT 06770

TIMEX/SINCLAIR 1000/ZX81 TRADEMARK TIMEX SINCLAIR