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Expressions for k from 0 to D – 1 , where N is the size of the specified array and D is the size of the DCT. If only one argument is given, then D is set to equal the next power of two larger than N . If a second argument is given, then its value is the order of the DCT, and the size of the DCT is . If a third argument is given, then it specifies the scaling factors according to the following table: The default, if a third argument is not given, is “Normalized.” The IDCT function is similar, and can also take one, two, or three arguments. The formula in this case is 3.8 Fixed Point Numbers xn skX ( 2n + 1)k. (5) k π = ⎛ ------⎞ ∑ cos ⎝ 2D⎠ Ptolemy II includes a preliminary fixed point data type. We represent a fixed point value in the expression language using the following format: fix(value, totalBits, integerBits) Thus, a fixed point value of 5.375 that uses 8 bit precision of which 4 bits are used to represent the (signed) integer part can be represented as: fix(5.375, 8, 4) TABLE 3: Normalization options for the DCT function Name Third argument Normalization Normalized 0 Unnormalized 1 Orthonormal 2 N – 1 Xk sk xn ( 2n + 1)k π = ⎛ ------ ⎞ ∑ cos ⎝ 2D⎠ N – 1 k = 0 n = 0 s k s k s k s k 1/ 2; k = 0 1 ; otherwise 2 order The value can also be a matrix of doubles. The values are rounded, yielding the nearest value representable with the specified precision. If the value to represent is out of range, then it is saturated, meaning that the maximum or minimum fixed point value is returned, depending on the sign of the specified 114 Ptolemy II = = = ⎧ ⎨ ⎩ 1 ⎧ ⎪ ⎨ ⎪ ⎩ 1/ D; k = 0 2/D ; otherwise (4)
Expressions value. For example, fix(5.375, 8, 3) will yield 3.968758, the maximum value possible with the (8/3) precision. In addition to the fix() function, the expression language offers a quantize() function. The arguments are the same as those of the fix() function, but the return type is a DoubleToken or DoubleMatrixToken instead of a FixToken or FixMatrixToken. This function can therefore be used to quantize double-precision values without ever explicitly working with the fixed-point representation. To make the FixToken accessible within the expression language, the following functions are available: To create a single FixPoint Token using the expression language: fix(5.34, 10, 4) This will create a FixToken. In this case, we try to fit the number 5.34 into a 10 bit representation with 4 bits used in the integer part. This may lead to quantization errors. By default the round quantizer is used. To create a Matrix with FixPoint values using the expression language: fix([ -.040609, -.001628, .17853 ], 10, 2) This will create a FixMatrixToken with 1 row and 3 columns, in which each element is a FixPoint value with precision(10/2). The resulting FixMatrixToken will try to fit each element of the given double matrix into a 10 bit representation with 2 bits used for the integer part. By default the round quantizer is used. To create a single DoubleToken, which is the quantized version of the double value given, using the expression language: quantize(5.34, 10, 4) This will create a DoubleToken. The resulting DoubleToken contains the double value obtained by fitting the number 5.34 into a 10 bit representation with 4 bits used in the integer part. This may lead to quantization errors. By default the round quantizer is used. To create a Matrix with doubles quantized to a particular precision using the expression language: quantize([ -.040609, -.001628, .17853 ], 10, 2) This will create a DoubleMatrixToken with 1 row and 3 columns. The elements of the token are obtained by fitting the given matrix elements into a 10 bit representation with 2 bits used for the integer part. Instead of being a fixed point value, the values are converted back to their double representation and by default the round quantizer is used. 3.9 Units Ptolemy II supports units systems, which are built on top of the expression language. Units systems allow parameter values to be expressed with units, such as “1.0 * cm”, which is equal to “0.01 * meters”. These are expressed this way (with the * for multiplication) because “cm” and “meters” are actually variables that become in scope when a units system icon is dragged in to a model. A few simple units systems are provided (mainly as examples) in the utilities library. Heterogeneous Concurrent Modeling and Design 115
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PTOLEMY II HETEROGENEOUS CONCURRENT
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VOLUME 1 INTRODUCTION TO PTOLEMY II
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Volume 1 Contents Introduction to P
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2.10.3. Constructing Modal Models 8
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7. MoML 191 7.1. Introduction 191 7
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1 Introduction Author: Edward A. Le
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Introduction heterochronous dataflo
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Introduction A major emphasis in Pt
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Introduction determine when actors
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Introduction provides levels of vis
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Introduction is a guard, and the se
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Introduction well. All of these are
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Introduction clients to update thei
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Introduction will be supplied with
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Introduction 1.3.12 Synchronous Dat
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Introduction FIGURE 1.10. Refinemen
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Introduction occlusions due to terr
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Introduction tion. The overall arch
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Introduction kernel.attributes This
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Introduction 1.5.2 Overview of Key
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Introduction Actor interfaces are k
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Heterogeneous Concurrent Modeling a
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Introduction actor actor.gui data.e
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Introduction cient, scalable, and u
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Introduction 1.5.8 Future Capabilit
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Introduction Appendix A: UML — Un
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Introduction grams, the only constr
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2 Using Vergil Authors: Edward A. L
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Using Vergil 2.2.2 Executing a Pre-
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Using Vergil The Lorenz attractor m
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Using Vergil The Continuous-Time (C
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Using Vergil box in figure 2.11. En
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Using Vergil Don’t panic! Excepti
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Using Vergil tions are a normal par
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Using Vergil 2.4 Hierarchy Ptolemy
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Using Vergil Then using these ports
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Page 75 and 76: Using Vergil pan window, it is easy
Page 77 and 78: Using Vergil FIGURE 2.33. The pan w
Page 79 and 80: Using Vergil we have modified the c
Page 81 and 82: Using Vergil model, simply copy (or
Page 83 and 84: Using Vergil A key issue is to deci
Page 85 and 86: Using Vergil instances. This proble
Page 87 and 88: Using Vergil quick tour for more de
Page 89 and 90: Using Vergil uses the index in the
Page 91 and 92: Using Vergil AddSubtract actor, and
Page 93 and 94: Using Vergil If you look inside the
Page 95 and 96: Using Vergil If you look inside the
Page 97 and 98: Using Vergil transition (or right c
Page 99 and 100: Using Vergil Once you have created
Page 101 and 102: Using Vergil The grid is turned off
Page 103 and 104: Authors: Edward A. Lee Xiaojun Liu
Page 105 and 106: Expressions classes to create a gen
Page 107 and 108: Expressions The % operation is a mo
Page 109 and 110: Expressions attribute, which includ
Page 111 and 112: Expressions 3.3.5 State Machines Ex
Page 113 and 114: Expressions whose value is an array
Page 115 and 116: Expressions from it. For instance,
Page 117 and 118: Expressions defined. For example, >
Page 119 and 120: Expressions length is given by the
Page 121 and 122: Expressions Thus, for example, you
Page 123: Expressions number. With one additi
Page 127 and 128: Expressions In the example in figur
Page 129 and 130: Expressions A.2 Basic Mathematical
Page 131 and 132: Expressions A.3 Matrix, Array, and
Page 133 and 134: Expressions A.5 Signal Processing F
Page 135 and 136: Expressions TABLE 8: Functions perf
Page 137 and 138: 4 Actor Libraries Authors: Elaine C
Page 139 and 140: Actor Libraries properly in the CT
Page 141 and 142: Actor Libraries ing that multiple c
Page 143 and 144: Actor Libraries TypedAtomicActor «
Page 145 and 146: Actor Libraries SequenceScope (exte
Page 147 and 148: Actor Libraries UnsignedByteArrayTo
Page 149 and 150: Actor Libraries MobileFunction (ext
Page 151 and 152: Actor Libraries LogicFunction (exte
Page 153 and 154: Actor Libraries Sleep (extends Tran
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Page 157 and 158: Actor Libraries Integrator: Integra
Page 159 and 160: Actor Libraries Figure 4.4 shows th
Page 161 and 162: 5 Designing Actors Authors: Christo
Page 163 and 164: Designing Actors /** Javadoc commen
Page 165 and 166: Designing Actors although with most
Page 167 and 168: Designing Actors import ptolemy.act
Page 169 and 170: Designing Actors makes such actors
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Designing Actors To get data polymo
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Designing Actors public class Seque
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Designing Actors be used in domains
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Designing Actors alComm actor. Beca
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Designing Actors attribute has valu
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Designing Actors import ptolemy.act
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6 Coding Style Authors: Christopher
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Coding Style /* One line descriptio
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Coding Style Copyright (c) 2004 The
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Coding Style @version $Id: NamedObj
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Coding Style } We use instead the i
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Coding Style * @exception MyExcepti
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Coding Style + "it does not impleme
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Authors: Edward A. Lee Steve Neuend
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MoML cutes it forever, until you hi
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MoML A second difference between ou
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MoML
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MoML 7.3.3 Names and Classes Most M
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MoML Here, the element named
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MoML implement. 7.3.7 Doc Element S
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MoML It is also sometimes necess
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MoML then there will be a link t
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MoML found. For example, if the cla
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MoML it cannot collide with the nam
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MoML The rendering of the icon is d
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MoML 7.4.5 Deleting Entities, Relat
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MoML This unlinks a port from the s
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MoML model. The EntityLibrary class
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MoML Suppose that using incremental
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MoML Generate a sine wave.
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MoML
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MoML Number of iterations in
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MoML -P- The f
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MoML -P- The phase,
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8 Custom Applets Authors: Edward A.
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Custom Applets html code, see the J
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Custom Applets public class Tutoria
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Custom Applets then the result of
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Custom Applets 8.3.5 Using Model Pa
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Custom Applets ptolemy/domains/doma
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References [1] G. Agha, Actors: A M
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[33] S. A. Edwards, “The Specific
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[67] E. Kohler, The Click Modular R
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[95] J. Liu, X. Liu, T. J. Koo, B.
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[132]W. R. Sutherland, "The on-Line
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Glossary abstract syntax ..........
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Ptolemy II ........................
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Index Symbols - in UML 41 # in UML
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coin flips 142 Color class 173 colo
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entity in XML 198 EntityLibrary cla
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Director class 159 inverse FFT 124
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CompositeEntity class 206 nextPower
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safety 34 SampleDelay actor 78, 138
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type constraint 155 type constraint
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