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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Network operator matrix ： ウィキペディア英語版 Network operator matrix Network operator matrix (NOM) is a representation of mathematical expressions in computer memory. NOM is a new approach to the problem of automatic search of mathematical equations. The researcher defines the sets of operations, variables and parameters.〔Diveyev A.I., Sofronova E.A. Application of network operator method for synthesis of optimal structure and parameters of automatic control system. ''Proceedings of 17-th IFAC World Congress'', Seoul, Korea 05 – 12 July 2008〕 The computer program generates a number of mathematical equations that satisfy given restrictions. Then the optimization algorithm finds the structure of appropriate mathematical expression and its parameters. Network operator is a directed graph that corresponds to some mathematical expressions. Every source nodes of the graph are variables or constants of mathematical expression, inner nodes correspond to binary operations and edges correspond to unary operations. The calculation’s result of mathematical expression is kept in the last sink node.〔(【引用サイトリンク】url=http://www.network-operator.com/papers.php )〕 ==Example== Consider the following mathematical expression The graph for Expression (), is presented in Fig. 1. On the edges we place unary operations $\backslash rho\_1(z)=\; z\; \backslash ,\; ;$ $\backslash rho\_3(z)=\; -z\; \backslash ,;$ $\backslash rho\_6(n)\; =$ \begin \varepsilon\!^, & \textz>\ln \varepsilon \!\\ e^z, & \text \end ; $\backslash rho\_(z)=\; \backslash sin\; z\; \backslash ,;$ In the inner and sink nodes we place binary operations $\backslash chi\_0(z\text{'},z\text{'}\text{'})=\; z\text{'}+z\text{'}\text{'}\; \backslash ,\; ;$ $\backslash chi\_1(z\text{'},z\text{'}\text{'})=\; z\text{'}\; \backslash times\; z\text{'}\text{'}\; \backslash ,\; ;$ Expression 1 can be presented in the PC memory as a NOM : $\backslash Psi\; =\; \backslash begin$ 0 & 0 & 0 & 1 & 1 & 0 & 0 & 12 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 3 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 6 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end Any mathematical expression can be presented as a network operator matrix.〔A.I. Diveev, E.A. Sofronova The synthesis of optimal control system by the network operator method ''IFAC Workshop on Control Applications and Optimization, CAO’09'', 6–8 May, University of Jyväskylä, Agora, Finland.〕〔Diveev A.I., Sofronova E.A. Numerical method of network operator for multi-objective synthesis of optimal control system, ''Proceedings of 7-th International Conference on Control and Automation (ICCA’09)'', Christchurch, New Zealand, December 9–11, 2009.〕〔Diveev A.I. A multiobjective synthesis of optimal control system by the network operator method. ''Proceedings of international conference «Optimization and applications» (OPTIMA 2009)'', Petrovac, Montenegro, September 21–25, 2009〕〔(【引用サイトリンク】url=http://www.intechopen.com/books/bio-inspired-computational-algorithms-and-their-applications/the-network-operator-method-for-search-of-the-most-suitable-mathematical-equation )〕 To calculate the mathematical expression by the network operator matrix the node vector is used. Each component of node vector corresponds to the nodes of the network operator graph. Initially each component is equal to the argument for the given node or the unit element of binary operation. For addition and multiplication the number of operation equals its unit element. For addition it is 0, for multiplication it is 1. The node vector for the given example $\backslash mathbf=(q\_1\backslash \; x\_2\backslash \; 0\backslash \; 1\backslash \; 0\backslash \; 1\backslash \; 0)^T$ The calculation by matrix $\backslash Psi$ is performed for nonzero nondaigonal elements $\backslash psi\_\backslash neq\; 0$ by $z\_j=\backslash chi\_\}(z\_i))$ Follow the rows of the matrix. For the Row 1 we have $\backslash psi\_=1$, that is $i=1$, $j=4$, $\backslash psi\_=\backslash psi\_=0$. Take arguments from $\backslash mathbf=(q\_1\backslash \; x\_2\backslash \; 0\backslash \; 1\backslash \; 0\backslash \; 1\backslash \; 0)^T$ $z\_1=x\_1$, $z\_4=0$ then $z\_4=\backslash chi\_\}(z\_1))=\backslash chi\_0(z\_4,\backslash rho\_1(z\_1))=0+x\_1=x\_1$ Further in Row 1 we have $\backslash psi\_=1$ $z\_5=\backslash chi\_\}(z\_1))=\backslash chi\_1(z\_5,\backslash rho\_1(z\_1))=1\backslash times\; x\_1=x\_1$ $\backslash psi\_=12$ $z\_8=\backslash chi\_\}(z\_1))=\backslash chi\_0(z\_8,\backslash rho\_(z\_1))=0+\backslash sin\; x\_1=\backslash sin\; x\_1$. As a result after Row 1 we have $\backslash mathbf=(q\_1\backslash \; x\_2\backslash \; x\_1\backslash \; x\_1\backslash \; 0\backslash \; 1\backslash \; \backslash sin\; x\_1)^T$. For the Row 2 we have $\backslash psi\_=1$ $z\_5=\backslash chi\_\}(z\_2))=\backslash chi\_1(z\_5,\backslash rho\_(z\_1))=x\_1q\_1$ then follow the rows $\backslash psi\_=3$ $z\_6=\backslash chi\_\}(z\_3))=\backslash chi\_0(z\_6,\backslash rho\_(z\_3))=0+(-x\_2)=-x\_2$ $\backslash psi\_=1$ $z\_8=\backslash chi\_\}(z\_4))=\backslash chi\_0(z\_8,\backslash rho\_(z\_4))=\backslash sin\; x\_1+x\_1$ $\backslash psi\_=1$ $z\_7=\backslash chi\_\}(z\_5))=\backslash chi\_1(z\_7,\backslash rho\_(z\_5))=1x\_1q\_1=x\_1q\_1$ $\backslash psi\_=6$ $z\_7=\backslash chi\_\}(z\_6))=\backslash chi\_1(z\_7,\backslash rho\_(z\_6))=x\_1q\_1e^$ $\backslash psi\_=1$ $z\_8=\backslash chi\_\}(z\_7))=\backslash chi\_0(z\_8,\backslash rho\_(z\_7))=\backslash sin\; x\_1+x\_1+x\_1q\_1e^$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Network operator matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.