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Less-Numerical Algorithms in Software Development pdf417 2d barcode in Software Less-Numerical Algorithms




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22. Less-Numerical Algorithms use software barcode pdf417 printing touse pdf417 for software Office Excel 5.*i/499.; exp(-0.

5*x1[i]); e pdf417 2d barcode for None xp(-0.5*SQR(x1[i])); exp(-0.5*sqrt(5.

-x1[i])); cos(0.062957*i); sin(0.088141*i); Instantiate a page.

Instantiate a plot on the page. Position is speci ed in pt (72 pt = 1 in, or 28 pt = 1 cm)..

PSpage pg("d:\\nr3\\newchap20 \\myplot.ps"); PSplot plot1(pg,100.,500.

,100.,500.); plot1.

setlimits(0.,5.,0.

,1.); plot1.frame(); plot1.

autoscales(); plot1.xlabel("abscissa"); plot1.ylabel("ordinate"); plot1.

lineplot(x1,y1); plot1.setdash("2 4"); plot1.lineplot(x1,y2); plot1.

setdash("6 2 4 2"); plot1.lineplot(x1,y3); plot1.setdash(""); plot1.

pointsymbol(1.,exp(-0.5),72,16.

); plot1.pointsymbol(2.,exp(-1.

),108,12.); plot1.pointsymbol(2.

,exp(-2.),115,12.); plot1.

label("dingbat 72",1.1,exp(-0.5)); plot1.

label("dingbat 108",2.1,exp(-1.)); plot1.

label("dingbat 115",2.1,exp(-2.)); PSplot plot2(pg,325.

,475.,325.,475.

); plot2.clear(); plot2.setlimits(-1.

2,1.2,-1.2,1.

2); plot2.frame(); plot2.scales(1.

,0.5,1.,0.

5); plot2.lineplot(x2,y4); pg.close(); pg.

display(); }. Unsets dash. Instantiate a second plot. Erase what s underneath it. Pop up a window displaying the plot le. The general idea is that a PS page object (pg in the example above) represents a whole sheet of paper, or window on the screen. It can contain one or more PSplot objects. In the above example there are two: plot1 and plot2.

PSplot objects can be separate on the page, or overlapping. Each has its own x; y coordinate system, its own x- and y-axis labels, and so forth. With no more explanation than this, you should be able to nd a program line above that corresponds to each feature in the gure.

The last line makes the plot pop up on our screen. Point symbols are referenced by their character number in the Zapf Dingbats font, which is built into PostScript. If you want to see all the possible symbols, a Web search for LaTeX Postscript Dingbats will turn up several charts.

Or, just write a program to plot them all. (Hint: There are possibly useful symbols from 33 to 126, and from 161 to 254.) A Webnote [3] gives the complete source code for the PSpage and PSplot objects, which is only about 150 lines long.

In the course of writing this book, our personal version of the code expanded to about 450 lines. This is an order of magnitude or two less than the standard packages that are available in open source code, GNUPLOT, for example [4]. It is a question of trading off capability (theirs much greater) for ease of modifying the source code (you be the judge).

. 22.2 Diagnosing Machine Parameters If you choose to go down this road, you ll soon want to learn more of PostScript as a language. A good reference is [5]..

CITED REFERENCES AND FURTHER pdf417 2d barcode for None READING: Adobe Systems, Inc. 1999, PostScript Language Reference, 3rd ed. (Reading, MA: AddisonWesley).

[1] Ghostscript and GSview 2007+, at http://www.cs.wisc.

edu/~ghost/.[2] Numerical Recipes Software 2007, Code for PSpage and PSplot, Numerical Recipes Webnote No. 26, at http://www.

nr.com/webnotes 26 [3] GNUPLOT 2007+, at http://www.gnuplot.

info.[4] McGilton, H., and Campione, M.

1992, PostScript by Example (Reading, MA: Addison-Wesley).[5]. 22.2 Diagnosing Machine Parameters A convenient ction is that a Software PDF417 computer s oating-point arithmetic is accurate enough. If you believe this ction, then numerical analysis becomes a very clean subject. Roundoff error disappears, and many nite algorithms are exact.

Only manageable truncation error ( 1.1) stands between you and a perfect calculation. Sounds rather naive, doesn t it Yes, it is naive.

Notwithstanding, we have adopted this ction throughout most of this book. To do a good job of answering the question of how roundoff error propagates, or can be bounded, for every algorithm that we have discussed would be impractical. In fact, it would not be possible: Rigorous analysis of many practical algorithms has never been made, by us or anyone.

Almost all processors today share the same oating-point data representation, namely that speci ed in IEEE Standard 754-1985 [1], and therefore the same strengths and weaknesses as regards roundoff error. But this was not always so! The history of computing is full of machines with strange oating-point representations by modern standards. Many early computers had 36-bit words, typically partitioned as a sign bit, 8 bits of exponent, and 27 bits of mantissa.

The in uential IBM 7090/7094 series was of this type. The legendary CDC 6600 and 7600 machines, designed by Seymour Cray, had 60-bit words (sign, 11-bit exponent, 48-bit mantissa). A particularly odd design was the IBM STRETCH, whose 64 bits were allocated to an exponent ag bit, 10 exponent bits, the exponent sign, a 48-bit mantissa, its sign, and three ag bits.

The exponent ag bit was used to signal over ow or under ow, while the other ag bits could be set by the user to indicate anything! So let us all be grateful for IEEE 754. Likewise, almost all numerical computing today is done in double precision, that is, in 64-bit words, what C++ de nes as double and we denote as Doub. This, also, was not always so.

It has happened (one might argue) because the availability of memory has increased even more rapidly than the appetite for it in numerical computation. Many programmers born before 1960 still feel a small frisson when they type double instead of float. Indeed, the vast majority of routines in this book will work just ne, for the vast majority of applications, with merely float precision.

In most cases, the use of double simply serves to reinforce an erroneous belief in the above convenient ction. .
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