Advanced Programming Guide

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5.5 Using the Matlab Package • 213Now you can properly evaluate MyFcn with numeric as well as symbolicarguments.> MyFcn(x);x − sin(x)x 3> MyFcn(0.099999999);0.1665833531735> MyFcn(0.1);0.1665833531700Section 2.5 describes how to extend many other Maple commands.5.5 Using the Matlab PackageAnother way to accomplish numerical computations in Maple is to usethe Matlab package, which provides access to several MATLAB R built-infunctions. Note: You must have a copy of MATLAB properly installed onyour computer. The mathematical functions provided are:• chol: Cholesky factorization• defined: test whether variable exists• det: determinant• dimensions: compute dimensions of matrix• eig: eigenvalues and eigenvectors• evalM: evaluate expression• fft: discrete Fourier transforms• getvar: get numeric array or matrix• inv: matrix inverse
214 • Chapter 5: Numerical <strong>Programming</strong> in Maple• lu: LU decomposition• ode45: solve ordinary differential equation• qr: QR orthogonal-triangular decomposition• size: compute size of matrix• square: determine whether matrix is square• transpose: matrix transpositionSome support and utility commands are provided. MATLAB convertsall Maple structures to its representation of hardware floating-point arraysbefore it performs any computations. The results are usually Arrays withdata type float[8] (that is, hardware float entries). For more information,refer to ?Array and ?Matrix.For more information on all these commands and the Matlab packagein general, refer to the online help for ?Matlab. To learn howto start the MATLAB application from your Maple session, refer to?Matlab[openlink].5.6 ConclusionWith numerical techniques, you can solve equations which are otherwiseunsolvable, investigate the properties of complicated solutions, andquickly obtain numerical estimates.Symbolic calculations give precise representations, but in some casescan be expensive to compute even with a tool as powerful as Maple. Atthe other extreme, hardware floating-point arithmetic allows you fast computationdirectly from Maple. This involves, however, limited accuracy.Software floating-point offers a balance. As well as sometimes being muchfaster than symbolic calculations, you also have the option to control theprecision of your calculations, thus exerting control over errors.Software floating-point calculations and representations mimic theIEEE 754 standard representation closely, except for the great advantageof arbitrary precision. The similarity with this popular standardallows you to readily apply accumulation of error and numerical analysisprinciples contained in numerous texts and papers.
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command the brilliance of a thousan
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ii•Waterloo Maple Inc.57 Erb Stre
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Contents • v3.6 Interfaces and Im
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Contents • viiPlotting Gears . .
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Contents • ixForeign Data . . . .
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1 Introduction1.1 Purpose of This B
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2 Procedures, Variables,and Extendi
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2.1 Nested Procedures • 5procedur
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2.1 Nested Procedures • 7> A[j] :
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2.1 Nested Procedures • 9> quicks
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2.1 Nested Procedures • 11> U :=
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2.2 Procedures That Return Procedur
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2.2 Procedures That Return Procedur
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2.3 Local Variables and Invoking Pr
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assign(another_a = a);> eqn;2.3 Loc
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[ seq( s[j][c[j]], j=1..2 ) ];2.3 L
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2.3 Local Variables and Invoking Pr
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2.4 Interactive Input • 25Improve
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2.4 Interactive Input • 27> reads
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2.5 Extending Maple • 29The parse
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2.5 Extending Maple • 31> ‘type
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2.5 Extending Maple • 33The follo
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2.5 Extending Maple • 3556 IIn th
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2.5 Extending Maple • 37Extending
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2.5 Extending Maple • 39The useri
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3 Programming withModulesProcedures
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• 43> gentemp := proc()> count :=
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3.1 Syntax and Semantics3.1 Syntax
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3.1 Syntax and Semantics • 47name
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3.1 Syntax and Semantics • 49> He
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3.1 Syntax and Semantics • 51mode
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3.1 Syntax and Semantics • 53The
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3.1 Syntax and Semantics • 55true
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3.1 Syntax and Semantics • 57modu
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3.1 Syntax and Semantics • 59> m
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This is achieved by the double assi
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3.1 Syntax and Semantics • 63This
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3.1 Syntax and Semantics • 65With
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3.1 Syntax and Semantics • 67> wh
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SpecFuncs := module()> export F; #
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3.2 Records • 71b> evalb( % = b )
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3.3 Packages • 73Packages in the
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3.3 Packages • 751 −1 + 1 21k x
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3.3 Packages • 77> "new types ‘
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3.3 Packages • 79definition. This
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3.3 Packages • 81true> member( 10
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3.3 Packages • 83The display show
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3.3 Packages • 85> end module:How
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3.3 Packages • 87From the output
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3.3 Packages • 89The final output
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3.3 Packages • 91shape-specific f
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3.3 Packages • 93The area Procedu
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"but got %1", shape> end if;>> # Ex
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3.4 The use Statement • 97> circl
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3.4 The use Statement • 99use sta
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3.4 The use Statement • 101C++),
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3.5 Modeling Objects3.5 Modeling Ob
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3.5 Modeling Objects • 10514 πFo
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3.5 Modeling Objects • 107> nitem
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3.5 Modeling Objects • 109> for i
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3.5 Modeling Objects • 111> lengt
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3.6 Interfaces and Implementations
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(−2790 T 6 − 77814+ 1943715124T
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4 Input and OutputAlthough Maple is
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4.1 A Tutorial Example • 157Openi
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4.1 A Tutorial Example • 159xy :=
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Buffered Files:4.2 File Types and M
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Page 198 and 199: 4.6 Output Commands • 187> writed
Page 200 and 201: 4.7 Conversion Commands • 189Conv
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Page 204 and 205: 5 Numerical Programmingin MapleFloa
Page 206 and 207: 5.1 The Basics of evalf • 1953.14
Page 208 and 209: 5.2 Hardware Floating-Point Numbers
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Page 220 and 221: 5.4 Extending the evalf Command •
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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
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6.6 Vector Field Plots • 263> mak
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6.6 Vector Field Plots • 265> vec
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6.7 Generating Grids of Points •
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A := array(1..2, 1..2):> evalgrid(
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6.8 Animation • 271The gridpoints
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6.8 Animation • 2731.00.500. 0. 2
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6.8 Animation • 275> partsum := p
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6.8 Animation • 277Demonstrating
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plot3d( p, -3..3, -3..3, color=q );
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6.9 Programming with Color • 2811
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6.9 Programming with Color • 283>
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6.9 Programming with Color • 2851
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chessplot3d( sin(x)*sin(y), x=-Pi..
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7 Advanced ConnectivityIn This Chap
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7.1 Code Generation • 291Many opt
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7.2 Using Compiled Code in Maple
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char * concat( char* a, char *b ){c
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myAdd = to_maple_integer( kv, r )EN
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to_maple_char( kv, c )to_maple_comp
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7.3 System Integrity • 337by anot
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Table 7.3 Wrapper Compound TypesMap
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AInternal Representationand Manipul
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A.1 Internal Organization • 343wi
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A.2 Internal Representations of Dat
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Type Specification or TestA.2 Inter
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Length: 3 or moreA.2 Internal Repre
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A.3 The Use of Hashing in Maple •
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Index%, 174&, 31accuracy, 193, 195,
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Index • 375SAVE, 362SERIES, 363SE
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Index • 377defining numeric, 210n
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Index • 379name, 357name table, 3
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Index • 381statements, 174strings
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Waterloo Maple Inc.57 Erb Street We
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