A short summary of this paper. Download Download PDF. Translate PDF. The simplification process on rational matrices consists of simplifying each entry represented by a rational function. We follow the classic approach of dividing the numerator and denominator polynomials by their common GCD polynomial, and provide the activity diagram in UML for this process.
A rational matrix representation as the quotient of a polynomial matrix and a polynomial is also discussed here and illustrated via activity diagrams.
Also, a class diagram giving the links between the class of rational matrices and the classes of rational functions and polynomials is obtained. Introduction Rational polynomial matrix is the matrix consisting of entries being rational func- tions polynomials. Therefore, rational matrices are the generalization of polyno- mial ones.
These are a mathematical tool often used for dynamical systems. Fur- thermore, polynomial matrices can be used for advanced controller design and in some signal processing applications. Matrix decompositions are often considered in many applications, such as finding matrix inverses and generalized inverses [2].
Decomposition of a polynomial matrix is frequently observed to evaluate polynomial generalized inverses, as explained in [3, 5]. Also, some well-known polynomial algorithms of computer algebra are provided in [11].
The Unified Modeling Language UML is a graphical language for visualizing, specifying and constructing classes of software intensive systems [1]. Received September 21, OOA is a discovery process which clarifies and documents the requirements of a system and focuses on understanding the problem domain. Significantly, it discov- ers and documents the key problem domain classes, concerned with developing an object-oriented model of the problem domain.
The identified objects reflect the entities that are associated with the problem to be solved. It creates abstractions and mechanisms necessary to meet behavioral requirements determined during analysis.
Therefore, OOD provides an object- oriented model of a software system to implement the identified requirements. Notice that in UML a class as the structural element represents a description of a set of objects that share the same attributes, operations and relations. Classes are usually graphically rendered as rectangles often including class names, attributes and operations. Interface is a collection of operations that specifies a service of a class. It describes the externally visible behavior of a class and defines a set of operations but not their implementations.
Usually, interfaces are graphically represented as a circle with a name below. Use Case is the structural element that provides the description of a sequence of actions that a system performs to deliver an observable result to a particular actor and is used to structure the behavioral elements in a model. Use Cases are graphically depicted as ellipses drawn with a solid line.
The most famous concept of UML is the diagram. Diagrams are graph rep- resentations of a set of elements and relationships with the nodes being elements and the edges being relationships. They are the projections of systems and can visualize a system from various perspectives. UML is characterized by nine major diagrams: 1 class; 2 object; 3 use case; 4 sequence; 5 collaboration; 6 statechart; 7 activity; 8 component; 9 deployment.
Many algorithms involving the processing of rational matrices and their sim- plifications were introduced. Therefore, the simplification procedure is performed on the entries of rational matrices L and D, 2 which are obtained. Two methods for the computation of AT,S inverses of a given polynomial matrix A are derived in [6, 7]. Notice that, in order to apply Algorithm 3. Example 1. Our main motivation is to demonstrate the simplification procedures used on rational matrices in the above mentioned algorithms.
This demonstration is due to the diagrams in UML, which will later provide a good basis for the implementa- tions. Also, a goal is to identify the role of each UML diagram use cases, statecharts and activity diagrams in the performance process under an object-oriented per- spective. The final objective is to obtain a set of annotated UML diagrams that should be the input to create a performance model in terms of some performance modeling paradigm.
Our goal is to use UML to develop a model of the class of rational matrices. The benefits of applying UML on such complex class types are numerous. Notice that UML provides views for development and deployment, and it is process-indepen- dent. UML is highly suitable for use with the processes that are iterative and incre- mental. Therefore, the class of rational matrices and methods for rational matrix manipulations can be modeled in UML.
Also, UML provides an expressive, visual modeling language for developing meaningful models. The rest of the paper is organized as follows. In the second section a class dia- gram of the class of rational matrices is provided, also illustrating the correlations with the classes of rational functions and polynomials.
In the third section the use-case diagram is depicted showing the position of the simplification procedures in the algorithm evaluation. Some activity diagrams are given in the fourth sec- tion determining some simplification procedures for rational matrices. Illustrative examples are provided in the fifth section in order to demonstrate simplification techniques.
Class diagrams The most widely used diagram of UML is the class diagram. It is used to model the static design view of a system and to specify the structure, interfaces and relationships between classes that underlie the system architecture.
Class diagram stands as the primary diagram for generating codes from UML models. The purpose of a class diagram is to depict the classes within a model. In an object oriented application, classes have attributes member variables , operations member functions and relations with other classes.
The newly added components that are added with this release must be configured with Rational License Key Servers. The components are:. Click the Fix List link in the table of contents above to review a list of the problems solved in this release. Download Description Table of Contents Sections Description This section provides an overview on what is new in this release with a description of any new functions or enhancements when applicable.
This section provides information related to the impact of this release to allow you to assess how your environment may be affected. This section provides important information to review prior to the installation of this release. This section provides the direct link to obtain the download package for installation in your environment.
This section provides the installation instructions necessary to apply this release into your environment. This section contains a link to the known problems open defects identified at the time of this release. Supporting Documentation Document Description Click to review the detailed system requirements information for a complete list of hardware requirements, supported operating systems, prerequisites and optional supported software, with component-level details and operating system restrictions.
Click to review a complete list of the defects APARs resolved in this release including a list of resolved defects for the entire version family. Internet Explorer does not render the server administration and reporting tool properly in Compatibility View. Fix Central This release is also available to download from Fix Central. How critical is this fix? It contains new features as well as fixes for client-reported and internally found defects.
Problems Solved Click the Fix List link in the table of contents above to review a list of the problems solved in this release. Double-byte characters that are used as a host name to add a license server in Rational License Key Server Administration and Reporting Tool does not identify the server.
The server status is displayed as unreachable in the tool. The installation log of Rational License Key Server Administration and Reporting Tool package shows error messages after the package is installed.
0コメント