Advanced Programming Guide

More documents

Recommendations

Info

5 Numerical <strong>Programming</strong>in MapleFloating-Point CalculationsThe focus of this chapter is on how to perform floating-point calculationsin Maple. You can select from the following:• Software floating-point calculations of arbitrary precision – other thanspeed, independent of your computer• Hardware floating-point arithematic – precision determined by thearchitecture of your computer, but offers exceptional speedIn This Chapter• Basics of the evalf Command• Hardware Floating-Point Numbers• Foating-Point Models in Maple• Extending the evalf Command• Using the Matlab PackageWhy Use Numerical ComputationsRepresentation and manipulation of expressions in symbolic mode, interms of variables, functions, and exact constants, is a powerful feature ofthe Maple system. Practical scientific computation also demands floatingpointcalculations which represent quantities by approximate numericalvalues.Typically, numerical computations are used for one of three reasons.193
194 • Chapter 5: Numerical <strong>Programming</strong> in Maple1. Not all problems have analytical or symbolic solutions. For example,there are many forms of partial differential equations, but only a smallsubset have known closed-form solutions. Despite this, it is usuallypossible to find numerical solutions.2. The analytic solution that Maple returns to a problem may be verylarge or complex. To understand the behavior of these expressions,compute a floating-point approximation.3. In some cases, it is wasteful to compute an exact answer. Computingan analytic solution is not necessary if only an approximation isneeded. For example, to plot a solution, an approximation accurateto the resolution of the plotting device is sufficient.5.1 The Basics of evalfThe evalf command is the primary tool in Maple for performing floatingpointcalculations. It causes Maple to evaluate in software floating-pointmode. The Maple software floating-point arithmetic has an n-digit machinefloating-point model as its basis, but allows computations at arbitraryprecision. The environment variable Digits, which has an initialsetting of 10, determines the default number of digits for calculations.> evalf(Pi);3.141592654You can alter the number of digits either by changing the value ofDigits, or by specifying the number as an index to evalf. Note thatwhen you specify the number of digits as an index to evalf, the default,Digits, remains unchanged.> Digits := 20:> evalf(Pi);3.1415926535897932385> evalf[200](Pi);
Page 1 and 2:
command the brilliance of a thousan
Page 3 and 4:
ii•Waterloo Maple Inc.57 Erb Stre
Page 6 and 7:
Contents • v3.6 Interfaces and Im
Page 8 and 9:
Contents • viiPlotting Gears . .
Page 10 and 11:
Contents • ixForeign Data . . . .
Page 12 and 13:
1 Introduction1.1 Purpose of This B
Page 14 and 15:
2 Procedures, Variables,and Extendi
Page 16 and 17:
2.1 Nested Procedures • 5procedur
Page 18 and 19:
2.1 Nested Procedures • 7> A[j] :
Page 20 and 21:
2.1 Nested Procedures • 9> quicks
Page 22 and 23:
2.1 Nested Procedures • 11> U :=
Page 24 and 25:
2.2 Procedures That Return Procedur
Page 26 and 27:
2.2 Procedures That Return Procedur
Page 28 and 29:
2.3 Local Variables and Invoking Pr
Page 30 and 31:
assign(another_a = a);> eqn;2.3 Loc
Page 32 and 33:
[ seq( s[j][c[j]], j=1..2 ) ];2.3 L
Page 34 and 35:
2.3 Local Variables and Invoking Pr
Page 36 and 37:
2.4 Interactive Input • 25Improve
Page 38 and 39:
2.4 Interactive Input • 27> reads
Page 40 and 41:
2.5 Extending Maple • 29The parse
Page 42 and 43:
2.5 Extending Maple • 31> ‘type
Page 44 and 45:
2.5 Extending Maple • 33The follo
Page 46 and 47:
2.5 Extending Maple • 3556 IIn th
Page 48 and 49:
2.5 Extending Maple • 37Extending
Page 50 and 51:
2.5 Extending Maple • 39The useri
Page 52 and 53:
3 Programming withModulesProcedures
Page 54 and 55:
• 43> gentemp := proc()> count :=
Page 56 and 57:
3.1 Syntax and Semantics3.1 Syntax
Page 58 and 59:
3.1 Syntax and Semantics • 47name
Page 60 and 61:
3.1 Syntax and Semantics • 49> He
Page 62 and 63:
3.1 Syntax and Semantics • 51mode
Page 64 and 65:
3.1 Syntax and Semantics • 53The
Page 66 and 67:
3.1 Syntax and Semantics • 55true
Page 68 and 69:
3.1 Syntax and Semantics • 57modu
Page 70 and 71:
3.1 Syntax and Semantics • 59> m
Page 72 and 73:
This is achieved by the double assi
Page 74 and 75:
3.1 Syntax and Semantics • 63This
Page 76 and 77:
3.1 Syntax and Semantics • 65With
Page 78 and 79:
3.1 Syntax and Semantics • 67> wh
Page 80 and 81:
SpecFuncs := module()> export F; #
Page 82 and 83:
3.2 Records • 71b> evalb( % = b )
Page 84 and 85:
3.3 Packages • 73Packages in the
Page 86 and 87:
3.3 Packages • 751 −1 + 1 21k x
Page 88 and 89:
3.3 Packages • 77> "new types ‘
Page 90 and 91:
3.3 Packages • 79definition. This
Page 92 and 93:
3.3 Packages • 81true> member( 10
Page 94 and 95:
3.3 Packages • 83The display show
Page 96 and 97:
3.3 Packages • 85> end module:How
Page 98 and 99:
3.3 Packages • 87From the output
Page 100 and 101:
3.3 Packages • 89The final output
Page 102 and 103:
3.3 Packages • 91shape-specific f
Page 104 and 105:
3.3 Packages • 93The area Procedu
Page 106 and 107:
"but got %1", shape> end if;>> # Ex
Page 108 and 109:
3.4 The use Statement • 97> circl
Page 110 and 111:
3.4 The use Statement • 99use sta
Page 112 and 113:
3.4 The use Statement • 101C++),
Page 114 and 115:
3.5 Modeling Objects3.5 Modeling Ob
Page 116 and 117:
3.5 Modeling Objects • 10514 πFo
Page 118 and 119:
3.5 Modeling Objects • 107> nitem
Page 120 and 121:
3.5 Modeling Objects • 109> for i
Page 122 and 123:
3.5 Modeling Objects • 111> lengt
Page 124 and 125:
3.6 Interfaces and Implementations
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
(−2790 T 6 − 77814+ 1943715124T
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155: 3.6 Interfaces and Implementations
Page 166 and 167: 4 Input and OutputAlthough Maple is
Page 168 and 169: 4.1 A Tutorial Example • 157Openi
Page 170 and 171: 4.1 A Tutorial Example • 159xy :=
Page 172 and 173: Buffered Files:4.2 File Types and M
Page 174 and 175: 4.3 File Descriptors versus File Na
Page 176 and 177: f := fopen("testFile.txt",WRITE):>
Page 178 and 179: 4.5 Input Commands • 167iostatus(
Page 180 and 181: 4.5 Input Commands • 169otherwise
Page 182 and 183: 4.5 Input Commands • 171y The nex
Page 184 and 185: 4.5 Input Commands • 173various c
Page 186 and 187: 4.5 Input Commands • 175Example T
Page 188 and 189: 4.6 Output Commands • 177One-Dime
Page 190 and 191: 4.6 Output Commands • 179the appr
Page 192 and 193: 4.6 Output Commands • 181Writing
Page 194 and 195: 4.6 Output Commands • 183z format
Page 196 and 197: 4.6 Output Commands • 185• If n
Page 198 and 199: 4.6 Output Commands • 187> writed
Page 200 and 201: 4.7 Conversion Commands • 189Conv
Page 202 and 203: 4.8 Notes to C Programmers • 191(
Page 206 and 207: 5.1 The Basics of evalf • 1953.14
Page 208 and 209: 5.2 Hardware Floating-Point Numbers
Page 212 and 213: iterate(f, df, x0, N);> end proc:Us
Page 216 and 217: 5.3 Floating-Point Models in Maple
Page 218 and 219: 5.3 Floating-Point Models in Maple
Page 220 and 221: 5.4 Extending the evalf Command •
Page 222 and 223: 5.4 Extending the evalf Command •
Page 224 and 225: 5.5 Using the Matlab Package • 21
Page 226 and 227: 6 Programming with MapleGraphicsMap
Page 228 and 229: 6.1 Basic Plot Functions • 217If
Page 230 and 231: 6.2 Programming with Plotting Libra
Page 236 and 237: 6.3 Maple Plotting Data Structures
Page 242 and 243: PLOT( CURVES( points ) );6.3 Maple
Page 246 and 247: 6.4 Programming with Plot Data Stru
Page 254 and 255:
6.5 Programming with the plottools
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
6.6 Vector Field Plots • 257Examp
Page 270 and 271:
6.6 Vector Field Plots • 259> end
Page 272 and 273:
6.6 Vector Field Plots • 261input
Page 274 and 275:
6.6 Vector Field Plots • 263> mak
Page 276 and 277:
6.6 Vector Field Plots • 265> vec
Page 278 and 279:
6.7 Generating Grids of Points •
Page 280 and 281:
A := array(1..2, 1..2):> evalgrid(
Page 282 and 283:
6.8 Animation • 271The gridpoints
Page 284 and 285:
6.8 Animation • 2731.00.500. 0. 2
Page 286 and 287:
6.8 Animation • 275> partsum := p
Page 288 and 289:
6.8 Animation • 277Demonstrating
Page 290 and 291:
plot3d( p, -3..3, -3..3, color=q );
Page 292 and 293:
6.9 Programming with Color • 2811
Page 294 and 295:
6.9 Programming with Color • 283>
Page 296 and 297:
6.9 Programming with Color • 2851
Page 298 and 299:
chessplot3d( sin(x)*sin(y), x=-Pi..
Page 300 and 301:
7 Advanced ConnectivityIn This Chap
Page 302 and 303:
7.1 Code Generation • 291Many opt
Page 304 and 305:
7.2 Using Compiled Code in Maple
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 316 and 317:
Page 318 and 319:
Page 320 and 321:
Page 322 and 323:
Page 324 and 325:
char * concat( char* a, char *b ){c
Page 326 and 327:
Page 328 and 329:
Page 330 and 331:
myAdd = to_maple_integer( kv, r )EN
Page 332 and 333:
Page 334 and 335:
to_maple_char( kv, c )to_maple_comp
Page 336 and 337:
Page 338 and 339:
Page 340 and 341:
Page 342 and 343:
Page 344 and 345:
Page 346 and 347:
Page 348 and 349:
7.3 System Integrity • 337by anot
Page 350 and 351:
Table 7.3 Wrapper Compound TypesMap
Page 352 and 353:
AInternal Representationand Manipul
Page 354 and 355:
A.1 Internal Organization • 343wi
Page 356 and 357:
A.2 Internal Representations of Dat
Page 358 and 359:
Type Specification or TestA.2 Inter
Page 360 and 361:
Page 362 and 363:
Length: 3 or moreA.2 Internal Repre
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Page 376 and 377:
Page 378 and 379:
A.3 The Use of Hashing in Maple •
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Index%, 174&, 31accuracy, 193, 195,
Page 386 and 387:
Index • 375SAVE, 362SERIES, 363SE
Page 388 and 389:
Index • 377defining numeric, 210n
Page 390 and 391:
Index • 379name, 357name table, 3
Page 392 and 393:
Index • 381statements, 174strings
Page 394:
Waterloo Maple Inc.57 Erb Street We
show all

Advanced Programming Guide

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?