Object-Oriented Programming and Laboratory of Simulation Development

Transcription

1 Object-Oriented Programming and Laboratory of Simulation Development Marco Valente LEM, Pisa and University of L Aquila January, 2008

2 Outline Goal: show major features of LSD and their methodological motivations

3 Outline Goal: show major features of LSD and their methodological motivations Definition of a simulation model: a normal form

4 Outline Goal: show major features of LSD and their methodological motivations Definition of a simulation model: a normal form LSD definition of simulation models

5 Outline Goal: show major features of LSD and their methodological motivations Definition of a simulation model: a normal form LSD definition of simulation models Presentation of LSD examples

6 Outline Goal: show major features of LSD and their methodological motivations Definition of a simulation model: a normal form LSD definition of simulation models Presentation of LSD examples Methodological remarks

7 Outline Goal: show major features of LSD and their methodological motivations Definition of a simulation model: a normal form LSD definition of simulation models Presentation of LSD examples Methodological remarks Technical comments

8 Definition of simulation models A simulation models is defined independently from the medium containing it. A model must theoretically generate the same results using any programming language.

9 Definition of simulation models A simulation models is defined independently from the medium containing it. A model must theoretically generate the same results using any programming language. Simulation run: sequence(s) of values across simulation time steps. {X 1, X 2,..., X t,..., X T }

10 Definition of simulation models A simulation models is defined independently from the medium containing it. A model must theoretically generate the same results using any programming language. Simulation run: sequence(s) of values across simulation time steps. {X 1, X 2,..., X t,..., X T } Simulation model: generic definition of how X t is computed: X t = f(x t k, Y t,α)

11 Definition of simulation models Notice that we choose to refer to time driven simulation models, as opposed to event driven models. The two styles of modelling are equivalent, since one can be turned into the other.

12 Definition of simulation models The following definition of a simulation is meant to satisfy two requirements: 1 Univocal. There must not be ambiguity, leaving room for implementations potentially generating different results. 2 User friendly. It must be as close as possible to (one of) the way(s) people usually refer to models in natural languages.

13 Definition of simulation models The elements required in a simulations models must be chosen within the following classes: 1 Variables. Symbols associated to a single value at each time step, computed according to a specified equation.

14 Definition of simulation models The elements required in a simulations models must be chosen within the following classes: 1 Variables. Symbols associated to a single value at each time step, computed according to a specified equation. 2 Parameters. Symbols associated to values not changing of their own accord.

15 Definition of simulation models The elements required in a simulations models must be chosen within the following classes: 1 Variables. Symbols associated to a single value at each time step, computed according to a specified equation. 2 Parameters. Symbols associated to values not changing of their own accord. 3 Functions. Symbols providing values computed by an equation on request by other equations (independently from the time).

16 Definition of simulation models The elements required in a simulations models must be chosen within the following classes: 1 Variables. Symbols associated to a single value at each time step, computed according to a specified equation. 2 Parameters. Symbols associated to values not changing of their own accord. 3 Functions. Symbols providing values computed by an equation on request by other equations (independently from the time). 4 Objects. A structure to generate multiple copies of the elements above.

17 Definition of simulation models A simulation model needs to specify also the initialization, values required to start a simulation run: Variables. If a variable is used with a lag, it is necessary to provide the past values used at the earlier steps of a run.

18 Definition of simulation models A simulation model needs to specify also the initialization, values required to start a simulation run: Variables. If a variable is used with a lag, it is necessary to provide the past values used at the earlier steps of a run. Parameters. Values for the model s constants.

19 Definition of simulation models A simulation model needs to specify also the initialization, values required to start a simulation run: Variables. If a variable is used with a lag, it is necessary to provide the past values used at the earlier steps of a run. Parameters. Values for the model s constants. Functions. If the function s values are used with a delay, it is necessary to provide earliest values.

20 Definition of simulation models A simulation model needs to specify also the initialization, values required to start a simulation run: Variables. If a variable is used with a lag, it is necessary to provide the past values used at the earlier steps of a run. Parameters. Values for the model s constants. Functions. If the function s values are used with a delay, it is necessary to provide earliest values. Objects. Number of copies of each object, each containing a single copy of the elements contained.

21 Definition of simulation models A simulation model needs to specify also the initialization, values required to start a simulation run: Variables. If a variable is used with a lag, it is necessary to provide the past values used at the earlier steps of a run. Parameters. Values for the model s constants. Functions. If the function s values are used with a delay, it is necessary to provide earliest values. Objects. Number of copies of each object, each containing a single copy of the elements contained. Simulation settings. Parameters determining the external environment (e.g. last time step, random number generators, statistics to collect, etc.).

22 Definition of simulation models Note that the objects form the structure of the model. Object-based representations are equivalent to a matrix-based representation. Vectorbased Object-based Object 1 Object 2... Object N X X 1 X 2... X N Y Y 1 Y 2... Y N α α 1 α 2... α N

23 Definition of simulation models Note that the objects form the structure of the model. Object-based representations are equivalent to a matrix-based representation. Vectorbased Object-based Object 1 Object 2... Object N X X 1 X 2... X N Y Y 1 Y 2... Y N α α 1 α 2... α N Object-based representations are also far more flexible, easily expressing, for example, the equivalent of nested matrices and matrices with different number of rows in each column.

24 Definition of simulation models Let s give some terminology: Model structure: the set of objects and the elements there contained. Possibly, objects may form a hierarchical structure: Market containing Firms, each containing Department, etc.

25 Definition of simulation models Let s give some terminology: Model structure: the set of objects and the elements there contained. Possibly, objects may form a hierarchical structure: Market containing Firms, each containing Department, etc. Model configuration: the model structure enriched with the number of objects and the initial values for the elements requiring them. Includes also sim. settings.

26 Definition of simulation models Let s give some terminology: Model structure: the set of objects and the elements there contained. Possibly, objects may form a hierarchical structure: Market containing Firms, each containing Department, etc. Model configuration: the model structure enriched with the number of objects and the initial values for the elements requiring them. Includes also sim. settings. Model s equations: equations computing the values for variables and functions, expressed in a generic way: operations to be executed to compute the value for the i th copy of the element at time t.

27 LSD goals LSD s aims is to allow users to provide only a simulation model s configuration and equations and to generate automatically any further code required for a professional simulation program.

28 LSD goals LSD s aims is to allow users to provide only a simulation model s configuration and equations and to generate automatically any further code required for a professional simulation program. LSD users define independently the different parts of the model, and the system assembles them in a program generating fast and flexible simulation runs, or detailed error messages.

29 LSD goals LSD s aims is to allow users to provide only a simulation model s configuration and equations and to generate automatically any further code required for a professional simulation program. LSD users define independently the different parts of the model, and the system assembles them in a program generating fast and flexible simulation runs, or detailed error messages. Crucially, LSD considers the development of a model as a gradual process. Its modular structure allows easily to revise an existing model.

30 LSD s equations major features Coding a LSD models can be done only by writing the code for the model s equations. The closest metaphor to a LSD model is a system of discrete equations, one for each variable.

31 LSD s equations major features Coding a LSD models can be done only by writing the code for the model s equations. The closest metaphor to a LSD model is a system of discrete equations, one for each variable. The equations of a LSD models are defined as independent chunks of code, with references to the model made only via the labels of required elements.

32 LSD s equations major features Coding a LSD models can be done only by writing the code for the model s equations. The closest metaphor to a LSD model is a system of discrete equations, one for each variable. The equations of a LSD models are defined as independent chunks of code, with references to the model made only via the labels of required elements. At run time the Lsd Simulation Manager re-arranges the equations calling them as necessary to perform the necessary computation.

33 LSD s equations major features LSD is endowed with an automatic scheduling. The modeller needs not to consider when a particular equation is executed within a time step. The LSM automatically (and constantly) re-arranges the order as implied by the equations. For example, consider the following model : X t = F X (Y t ) Y t = F Y (X t 1 ) The system interprets the equations so that Y must be updated before X. Changing order of execution entails simply to change the number of lags within the equations code.

34 LSD s equations major features In general a model contains many copies of each element, say many Market s may contain each many Firm s etc. In a simulation run it must be ensured that each copy of a variable makes use of the correct copies of the elements required in its equations. As, for example, Q i = f(k i, p j ).

35 LSD s equations major features In general a model contains many copies of each element, say many Market s may contain each many Firm s etc. In a simulation run it must be ensured that each copy of a variable makes use of the correct copies of the elements required in its equations. As, for example, Q i = f(k i, p j ). LSD is an object-based language, and therefore it is impossible (besides impractical) to use indexes. By default, LSD finds on its own the correct copy of the elements to use in an equation, using a automatic tagging system to retrieve required elements.

36 LSD s equations major features Note that both features make completely effortless the modification of a model, the extension adding new elements, and the re-use of its parts.

37 LSD s equations major features Note that both features make completely effortless the modification of a model, the extension adding new elements, and the re-use of its parts. In practice, a LSD model is made of individual modules (the equations) which are related only by the labels of the elements required for the computation.

38 LSD s equations major features The language for expressing the equations can be considered as composed by multiple layers.

39 LSD s equations major features The language for expressing the equations can be considered as composed by multiple layers. Lacking any specific indication the system makes use of the internal scheduler and retriever. This system covers most of the cases and makes the code extremely simple and readable.

40 LSD s equations major features The language for expressing the equations can be considered as composed by multiple layers. Lacking any specific indication the system makes use of the internal scheduler and retriever. This system covers most of the cases and makes the code extremely simple and readable. A second layer entails the use of specific LSD commands overruling the default behaviour to express frequently used operations. E.g. pick at random one of the elements in this set.

41 LSD s equations major features The language for expressing the equations can be considered as composed by multiple layers. Lacking any specific indication the system makes use of the internal scheduler and retriever. This system covers most of the cases and makes the code extremely simple and readable. A second layer entails the use of specific LSD commands overruling the default behaviour to express frequently used operations. E.g. pick at random one of the elements in this set. Finally, LSD is built on standard C++ so that any command or external library compatible with GNU C++ can be used within the model.

42 LSD technical components LSD is distributed with a companion program called Lsd Model Manager which performs the following tasks: 1 Organize the projects and manage the required files.

43 LSD technical components LSD is distributed with a companion program called Lsd Model Manager which performs the following tasks: 1 Organize the projects and manage the required files. 2 Assist in the writing of the equations.

44 LSD technical components LSD is distributed with a companion program called Lsd Model Manager which performs the following tasks: 1 Organize the projects and manage the required files. 2 Assist in the writing of the equations. 3 Manage the compilation process.

45 LSD technical components LSD is distributed with a companion program called Lsd Model Manager which performs the following tasks: 1 Organize the projects and manage the required files. 2 Assist in the writing of the equations. 3 Manage the compilation process. 4 Provide indications on grammar errors in the equations code.

46 LSD technical components Lsd Model Manager - LMM Model Equation file "fun_mymodel.cpp" Fix errors Failure Grammar Error Messages Lsd system code src\lsdmain.cpp src\object.cpp... src\variable.cpp Compilation Success

47 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations.

48 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations. 2 Run single or multiple simulations.

49 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations. 2 Run single or multiple simulations. 3 Analyse the results, at run-time and at the end of the simulation.

50 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations. 2 Run single or multiple simulations. 3 Analyse the results, at run-time and at the end of the simulation. 4 Investigate the model state before, during or after a run.

51 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations. 2 Run single or multiple simulations. 3 Analyse the results, at run-time and at the end of the simulation. 4 Investigate the model state before, during or after a run. 5 Catch and report on errors at run time, keeping data produced until the stop.

52 LSD technical components On success LMM generates an executable called LSD Model Program embodying the equations of the model and offering every operation concerning the model: 1 Define, save and load model configurations. 2 Run single or multiple simulations. 3 Analyse the results, at run-time and at the end of the simulation. 4 Investigate the model state before, during or after a run. 5 Catch and report on errors at run time, keeping data produced until the stop. 6 Document a model with its own interfaces, or exporting reports in HTML or Latex format

53 LSD technical components Lsd Model Program Define and Save Load Help Model Configuration - Model Structure (Objects, Variables and Parameters) - Initial values - Sim. settings - Running options Run Simulation Create Report Success Model Report User-friendly hypertextual documentation Failure Logical Error Messages Saved data series - Analysis of Results - Export data - Export graphs

54 LSD usage Using existing configurations Analysing results Setting initial values Setting the number of objects Defining model s element Debugging models Multiple runs Help pages Documentation

55 Examples: Random walk A random walk model may be implemented with the following equations: X t RandomEvent t = X t 1 + RandomEvent t = UNIFORM(minX, maxx) Different model structures can be used to exploit the equations above

56 Example: Replicator Dynamics A discrete version of this model may be apparently be expressed as: Num i t ( ) = Numt 1 i 1 + α fitnessi AvFitness t AvFitness t AvFitness t = N i=1 fitnessi Num i t N j=1 Numj t

57 Example: Replicator Dynamics A discrete version of this model may be apparently be expressed as: Num i t ( ) = Numt 1 i 1 + α fitnessi AvFitness t AvFitness t AvFitness t = N i=1 fitnessi Num i t N j=1 Numj t... but it cannot work

58 Example: Replicator Dynamics The logical error must be fixed inserting a lag in the equations Num i t ( ) = Numt 1 i 1 + α fitnessi AvFitness t AvFitness t AvFitness t = N i=1 fitnessi Num i t-1 N j=1 Numj t-1

59 Example: Smallwood and Conlisk, 1979 The model represents consumers using a product that can break down with a given probability. If the product breaks down, a new one is purchased randomly with probabilities proportional to market shares. Prob(i) = msα i j msα j Varying the parameter α we can observe a large variety of results.

60 Using simulations Simulation programs can be used for many purposes. Simulation models for research, particularly in social sciences can (should?) be used for answering questions like: How did phenomena like Ω emerged from a system like Σ?

61 Using simulations Simulation programs can be used for many purposes. Simulation models for research, particularly in social sciences can (should?) be used for answering questions like: How did phenomena like Ω emerged from a system like Σ? For a simulation model to be useful for research, we need therefore to ensure that the phenomenon under study is represented in the simulation results. However, this is not sufficient. We need also to explain how the simulated phenomenon was generated from our assumptions, the equations and configuration of the model.

62 Using simulations A consequence of this approach is that mere representation of a phenomenon, replicating somewhat realistic empirical evidence, may not be necessary, and in any case is not sufficient.

63 Using simulations A consequence of this approach is that mere representation of a phenomenon, replicating somewhat realistic empirical evidence, may not be necessary, and in any case is not sufficient. Empirical evidence on social phenomena is necessarily approximated, scarce, and ever changing. Even a perfect fitting of existing data does not ensure that the same, or even similar events, will ever occur again.

64 Using simulations A consequence of this approach is that mere representation of a phenomenon, replicating somewhat realistic empirical evidence, may not be necessary, and in any case is not sufficient. Empirical evidence on social phenomena is necessarily approximated, scarce, and ever changing. Even a perfect fitting of existing data does not ensure that the same, or even similar events, will ever occur again. Researchers need to focus on invariances, reliable regularities, that simply do not exist empirically as data sets. Even when some robust quantitative facts can be found, they are so vague and high level that many generating mechanisms may be devised.

65 Using simulations Many invariances exists in social phenomena, but they can be perceived not as quantitative data, but as forces, tendencies pressing toward predictable directions.

66 Using simulations Many invariances exists in social phenomena, but they can be perceived not as quantitative data, but as forces, tendencies pressing toward predictable directions. Therefore, the goal of a research project in systems like economic ones consists mainly in identifying some of the forces acting on the system, discarding the possibility to generate a replica.

67 Using simulations Initial State Transformation Final State Reality Real entities Aggregative explanations Temporal explanations Real entities Abstraction Validation Model Aggregative explanations Temporal explanations Symbols Symbols

68 Using simulations Simulations can therefore be used to replicate and investigate the effects on partial systems of a sub-set of the forces existing on the real world. Though replication of empirical may be a tool in the investigation, it is not a paramount yardstick for evaluation of model effectiveness. Another protocol needs to be used.

69 Hunting for explanations Consider research as the attempt to test and improve explanations: A µ B where µ is an explanatory mechanism and A and B two states of the world.

70 Hunting for explanations Explanations can be considered a form of knowledge, and scientific research as the attempt to increase scientific knowledge. There are only three ways to improve knowledge, meant as explanations.

71 Properties A µ B Knowledge refinement: An existing explanation, proved correct on a number of cases, may accommodate a counter example by refining the definition of states where it applies or the explanatory mechanism, or both. A µ B

72 Properties A µ B Knowledge refinement: An existing explanation, proved correct on a number of cases, may accommodate a counter example by refining the definition of states where it applies or the explanatory mechanism, or both. A µ B µ ; A B with A = A A and B = B B

73 Properties A µ B Knowledge deepening: Knowledge is never ultimately specified. You can always request a further specification of how µ is actually working, investigating intermediate steps and their explanations, potentially diving into search of infinitely small details: A µ B

74 Properties A µ B Knowledge deepening: Knowledge is never ultimately specified. You can always request a further specification of how µ is actually working, investigating intermediate steps and their explanations, potentially diving into search of infinitely small details: A µ A µ B

75 Properties A µ B Knowledge extensions: Knowledge can be extended to form chains of causes, or explanations, in which the final state of an explanation is used as the initial state of the next: A µ B

76 Properties A µ B Knowledge extensions: Knowledge can be extended to form chains of causes, or explanations, in which the final state of an explanation is used as the initial state of the next: µ 1 A 1 A µ B µ 1 B +1

77 Properties of knowledge as A µ B Though the explanatory mechanism can take any form, there are only three conceptual classes of components of explanations:

78 Properties of knowledge as A µ B Though the explanatory mechanism can take any form, there are only three conceptual classes of components of explanations: Temporal/Tranformational: the explanation consists in the passing of time during which the elements comprising the state of the world A can be expected to produce B.

79 Properties of knowledge as A µ B Though the explanatory mechanism can take any form, there are only three conceptual classes of components of explanations: Temporal/Tranformational: the explanation consists in the passing of time during which the elements comprising the state of the world A can be expected to produce B. Aggregative: elements at a certain level of aggregation explain the properties of elements at a different levels.

80 Properties of knowledge as A µ B Though the explanatory mechanism can take any form, there are only three conceptual classes of components of explanations: Temporal/Tranformational: the explanation consists in the passing of time during which the elements comprising the state of the world A can be expected to produce B. Aggregative: elements at a certain level of aggregation explain the properties of elements at a different levels. Logical inferences: inferential rules, look-up tables, or any explicit coding system allow to associate one entity or event to another. Most relevant explanations in the real world are a combination of explanations from all classes, though they need to be logically kept distinct.

81 Explanations and simulations Simulation models can implement any conceivable form of explanation. In this sense, they can reproduce any mechanism we may have in mind, provided it is consistent.

82 Explanations and simulations Simulation models can implement any conceivable form of explanation. In this sense, they can reproduce any mechanism we may have in mind, provided it is consistent. The most interesting use of simulations is when the system we wrote A generates as result a system resembling some of the real world aspects B. The goal is to find out how our system generates the result.

83 Explanations and simulations Simulation models can implement any conceivable form of explanation. In this sense, they can reproduce any mechanism we may have in mind, provided it is consistent. The most interesting use of simulations is when the system we wrote A generates as result a system resembling some of the real world aspects B. The goal is to find out how our system generates the result. A research project should consist in identifying a problem and finding a good explanation for it.

84 Technical aspects Simulation programs must permit users not only to generate the results efficiently and observe them. Crucially, it must allow to understand the generative mechanism, since this is the only type of results we may gain.

85 Technical aspects Simulation programs must permit users not only to generate the results efficiently and observe them. Crucially, it must allow to understand the generative mechanism, since this is the only type of results we may gain. However, programming languages are not designed for inspecting their internal working, and separate the role of programmer and of user, hiding its own internal working for obvious reasons of efficiency and security.

86 Technical aspects Languages tend to show an inverse relation between simplicity of use and power. LSD breaks this trade-off by offering C++ power accessible by means of a natural way to represent models.

87 Technical aspects Languages tend to show an inverse relation between simplicity of use and power. LSD breaks this trade-off by offering C++ power accessible by means of a natural way to represent models. Crucially, LSD generates automatically all the interfaces to access the state of the model at any stage and detail required to fully generate and understand the mechanisms produced.

88 People say that... In the following we list some of the most frequently points raised in the debate on the use of simulations, and report on the answers derived by the approach proposed above.

89 People say that... Sim. models produce all and only whatever you code into them.

90 People say that... Sim. models produce all and only whatever you code into them. True, but computers help to understand exactly the implications of the assumptions. Think, for example, of models of weather forecasting. The basic physics is trivial, but the aggregate effect is impossible to derive by analytical means, and computers help to fill the gap between the hypotheses (e.g. basic physics) and their implications (forecasting).

91 People say that... Random models/models with many parameters must be adequately tested for the robustness of results.

92 People say that... Random models/models with many parameters must be adequately tested for the robustness of results. False. Robustness in respect of randomness or initial conditions are relevant to assess universal properties of systems. OSD systems, as real economic systems, may potentially assume a huge number of states, but almost all of them will never be realized. We need to explain phenomena, and possibly the most relevant ones are the very rare. Simulation models can frequently be understood by studying the exceptions, as much as doctors understand how the human body works by studying sick patients.

93 People say that... Better one theorem than a hundred simulations.

94 People say that... Better one theorem than a hundred simulations. True. Mathematics is a wonder of compactness, representing many (infinite) cases by one single line of symbols. Moreover, mathematical representations allow to deduce many non-obvious properties. However, non-linear aggregations and dynamics are poorly managed by mathematical tools, while computers can easily do both: simulations can replicate (though inelegantly) results embodied in theorems, but, in general, theorems cannot contain the knowledge provided by models.

95 People say that... Your model does not consider X, which is relevant for phenomenon Y.

96 People say that... Your model does not consider X, which is relevant for phenomenon Y. True. Any model is necessarily limited and partial. Models for open systems in particular neglect aspects that, by definition, are relevant for every phenomenon. A model must be always considered under strong ceteris paribus conditions, and the explanations produced are conditional to other explanations reinforcing or hindering the ones considered.

97 People say that... Programming simulations is difficult, don t want to waste my time learning how to program.

98 People say that... Programming simulations is difficult, don t want to waste my time learning how to program. False. Writing programs is difficult, writing simulations model is not, at least if you adopt a cautious approach. Most of simulation models code is made of trivial, IF-THEN-ELSE statements and simple arithmetic operations. Arranging the model s code in a computer program is very difficult, particularly because you need sophisticated interfaces to investigate model s behaviour. However, endowing a model with the necessary interfaces is a technical problem, that technicians can help to solve.

99 People say that... Are your results confirmed empirical observations?

100 People say that... Are your results confirmed empirical observations? Futile. Data replication is useless without understanding their meaning. And having such knowledge you don t need to replicate any data. Worse, there are always a large number of different ways to replicate a data set, only some of which may make sense.

101 People say that... Then, for you empirical analysis is useless...

102 People say that... Then, for you empirical analysis is useless... False. Statistical analysis, descriptive or inferential, provides the crucial information on what is going on in such complex entities like economic system. We need constantly to take into account that quantitative measures are a very fuzzy shadow of the systems that produced them.