JP2004086760A - Numerical calculation program generation system, numerical calculation program generation method, and numerical calculation program generation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To realize a numerical calculation program generation system capable of efficiently expanding a generated numerical calculation algorithm. <P>SOLUTION: A syntax analysis device 20 prepares syntax analysis information 21 based on definition information 11 taken in by a problem definition input device 10 and program format information 12. An algorithm storage device 40 stores the algorithm information 41 expressed by the ordering row of the pseudo codes of the numerical calculation algorithm. A format template program storage device 50 stores format template program information 51 for the pseudo codes, a calculation generating device 60 generates calculation expression information 61 necessary for the numerical calculation program based on the syntax analysis information 21, and a program generating control device 30 generates a generation program 70 based on the syntax analysis information 21, algorithm information 41, format template program information 51, and calculation expression information 61. <P>COPYRIGHT: (C)2004,JPO

Description

[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a numerical calculation program generation system, a numerical calculation program generation method, and a numerical calculation program generation program, and particularly to a computer architecture that has easy scalability of a numerical calculation algorithm that can be generated, and that the generated program corresponds to The present invention relates to a numerical calculation program generation system, a numerical calculation program generation method, and a numerical calculation program generation program having flexibility.
[0002]
[Prior art]
In conventional numerical calculation program generation systems, from the input information that expresses PDEs etc. in text, the calculation formulas necessary for the numerical calculation program of PDEs created on a computer according to a mathematical method are prepared in advance. Numerical calculation programs have been generated or interpreted by embedding them in a fixed format template program or interpreting them in an interpreted manner (for example, Patent Documents 1 and 2).
[0003]
Examples of such software include software in the United States, ELLPACK, PDE / PROTRAN, and the like.
[0004]
[Patent Document 1]
JP-A-6-180644
[Patent Document 2]
JP-A-6-59868
[0005]
[Problems to be solved by the invention]
The first problem is that it takes time and effort to add a newly generated calculation algorithm to the numerical calculation program generation system.
[0006]
The reason is that in the conventional numerical calculation program generation method, calculation formula parts created on a computer in accordance with a mathematical procedure can be filled in a prepared hole program without considering the detailed structure of the algorithm. Because it only generates. In a program generation method that does not consider the internal structure of a generated program, only the difference in the coefficients of the equations appearing in an input partial differential equation or the like can be handled.
[0007]
Therefore, in order to increase the number of calculation algorithms to be generated, it is necessary to prepare a new template program to be used for generating an artificial program, which requires much labor.
[0008]
The second problem is that it is troublesome to expand the numerical calculation program generation system when increasing the computer architecture, matrix data structure, etc., which are the targets of the program generated by the numerical calculation program generation system.
[0009]
The reason is that, similarly to the first problem, in a fill-in-the-blank program generation method that does not consider a change in the data structure of a generated program, even if the mathematical calculation algorithm is the same, the conventional program generation method does not. This is because it is necessary to prepare a new template of the program to be used for filling in the generation of the program. For example, if a program generation function for a parallel computer is added to a program generation system for a scalar computer, the mathematical calculation algorithm is the same, but the data structure handled by the program to be generated is different. A fill-in-the-blank program generation method could not cope.
[0010]
An object of the present invention is to realize a numerical calculation program generation system capable of efficiently expanding a numerical calculation algorithm that can be generated by the numerical calculation program generation system.
[0011]
Another object of the present invention is to make it possible to generate a numerical calculation program in accordance with a plurality of program formats such as a difference in computer architecture and matrix structure from information of one mathematical numerical calculation algorithm, and to generate a numerical calculation program. It is to facilitate the expansion of the system.
[0012]
[Means for Solving the Problems]
A first numerical calculation program generation system according to the present invention inputs problem definition information and program format information relating to a numerical calculation algorithm from a first storage device, and generates a numerical calculation algorithm of a numerical calculation program to be generated in a sequence of pseudo codes. By generating a program from the representation, a sequence of pseudo codes corresponding to the new numerical calculation algorithm is created using the already defined pseudo code, and the numerical calculation algorithm generated by the numerical calculation program generation system is created. And a means for generating a numerical calculation program in the second storage device.
[0013]
A second numerical calculation program generation system according to the present invention is the first numerical calculation program generation system, and corresponds to each pseudo code in accordance with designation of program format information input to the first storage device. Means for generating, in the second storage device, a numerical calculation program of a combination of a plurality of program format information from the same sequence of pseudo-codes by selecting template program information for each style and generating a numerical calculation program It is characterized by.
[0014]
A third numerical calculation program generation system according to the present invention is the second numerical calculation program generation system, wherein a problem is determined based on syntax analysis information generated from the problem definition information input to the first input device. For each numerical calculation algorithm specified by the definition information, the ordered set data of the pseudo code expressing the algorithm is called from the algorithm information stored in the third storage device. In accordance with the format specified by the program format information, the style-specific template program information for generating a program corresponding to each pseudo code is called from the fourth storage device, and all the pseudo codes are stored in the fifth storage device. Generates program parts for each numerical algorithm along with the calculation formula information to be Characterized in that it comprises means for generating a beam in the second storage device.
[0015]
According to a first numerical calculation program generation method of the present invention, problem definition information and program format information relating to a numerical calculation algorithm are input from a first storage device, and a numerical calculation algorithm of a numerical calculation program to be generated is represented by a pseudo code sequence. By generating a program from the representation, a sequence of pseudo codes corresponding to the new numerical calculation algorithm is created using the already defined pseudo code, and the numerical calculation algorithm generated by the numerical calculation program generation system is created. And a step of generating a numerical calculation program in the second storage device.
[0016]
A second numerical calculation program generation method according to the present invention is the first numerical calculation program generation method, and corresponds to each pseudo code in accordance with designation of program format information input to the first storage device. Generating a numerical calculation program by selecting template-specific template program information to generate a numerical calculation program of a combination of a plurality of program format information from the same pseudo-code sequence in the second storage device. It is characterized by.
[0017]
A third numerical calculation program generating method according to the present invention is the second numerical calculation program generating method, wherein a problem is solved based on syntax analysis information generated from the problem definition information input to the first input device. For each numerical calculation algorithm specified by the definition information, the ordered set data of the pseudo code expressing the algorithm is called from the algorithm information stored in the third storage device. In accordance with the format specified by the program format information, the style-specific template program information for generating a program corresponding to each pseudo code is called from the fourth storage device, and all the pseudo codes are stored in the fifth storage device. Generates program parts for each numerical calculation algorithm along with the calculation formula information to be Characterized in that it comprises a step of generating the second storage device.
[0018]
A first numerical calculation program generation program according to the present invention inputs problem definition information and program format information relating to a numerical calculation algorithm from a first storage device, and generates a numerical calculation algorithm of a numerical calculation program to be generated in a pseudo code sequence. By generating a program from the representation, a sequence of pseudo codes corresponding to the new numerical calculation algorithm is created using the already defined pseudo code, and the numerical calculation algorithm generated by the numerical calculation program generation system is created. And causing the computer to execute a procedure for generating a numerical calculation program in the second storage device.
[0019]
A second numerical calculation program generation program according to the present invention is the first numerical calculation program generation program, and corresponds to each pseudo code in accordance with the specification of the program format information input to the first storage device. By selecting the style-specific template program information and generating a numerical calculation program, the computer is provided with a procedure for generating a numerical calculation program of a combination of a plurality of program format information in the second storage device from the same pseudo code sequence. It is characterized by being executed.
[0020]
A third numerical calculation program generation program according to the present invention is the second numerical calculation program generation program, wherein a problem is calculated based on syntax analysis information generated from the problem definition information input to the first input device. For each numerical calculation algorithm specified by the definition information, the ordered set data of the pseudo code expressing the algorithm is called from the algorithm information stored in the third storage device. In accordance with the format specified by the program format information, the style-specific template program information for generating a program corresponding to each pseudo code is called from the fourth storage device, and all the pseudo codes are stored in the fifth storage device. Generates program parts for each numerical calculation algorithm along with the Characterized in that to execute a procedure for generating grams in the second storage device to the computer.
[0021]
BEST MODE FOR CARRYING OUT THE INVENTION
Next, a first embodiment of the present invention will be described in detail with reference to the drawings.
[0022]
FIG. 1 is a block diagram showing a configuration of the first exemplary embodiment of the present invention.
[0023]
Referring to FIG. 1, a first embodiment of the present invention includes a problem definition input device 10 including a keyboard and an external storage device, and a syntax analysis device 20 that operates under program control and generates syntax analysis information 21. A program generation control device 30 for controlling program generation based on the syntax analysis information 21, an algorithm storage device 40 including a memory or the like for storing algorithm information 41 representing a numerical calculation algorithm in pseudo code, Separately, the style-specific template program storage device 50 including a memory for storing the style-specific template program information 51, which is the template program information corresponding to the pseudo code, and the partial differential equation given by the problem definition information 11 are discretized. Calculations that become the data of individual numerical calculation programs, such as obtained calculation formulas A calculation formula generation apparatus 60 for generating comprises a generator 70 which is generated in the storage device.
[0024]
The problem definition input device 10, the algorithm storage device 40, and the style-specific template program storage device 50 may be one storage device. Further, the syntax analysis device 20, the program generation control device 30, and the calculation expression generation device 60 may be one information processing device.
[0025]
The problem definition input device 10 stores problem definition information 11 and program format information 12 given by a user. The problem definition information 11 is data composed of a mathematical algorithm such as designation of an algorithm appearing in numerical calculation, parameters associated with the algorithm, and a calculation formula. Algorithms represented by such data include interpolation as a substitution process, solving for a linear partial differential equation, Newton's method for a nonlinear equation, and calling a visualization library. Generally, the problem definition information 11 is a set of a plurality of numerical calculation algorithms. The program format information 12 includes a programming language name used for a program to be generated, an identification name for specifying how to handle data representation in a generated numerical calculation program, a matrix, particularly a data representation format name of a sparse matrix, a linear solver and visualization. This is attribute information such as the name of a program, which is necessary when a numerical calculation algorithm is actually implemented in a programming language.
[0026]
The syntax analysis device 20 creates syntax analysis information 21 for processing by the program generation control device 30 from the problem definition information 11 and the program format information 12 and provides the syntax analysis information 21 to the program generation control device 30.
[0027]
The algorithm storage device 40 stores the algorithm information 41 represented by an ordered set of pseudo codes. Pseudocode is an algorithm step that appears when implementing an abstract numerical algorithm in a programming language and is subdivided by factors in a specific program style.
[0028]
For each pseudo code used in the algorithm information 41, template program information for generating a program for each style is stored in the style-specific template program storage device 50 as style-specific template program information 51. Each pseudo code can include a plurality of template program information for generating a program for each format. Examples of these formats include a programming language format, a program structure / data representation format, a matrix structure format, and a library call format.
[0029]
The calculation formula generation device 60 is started from the program generation control device 30 and creates calculation formulas and variable name lists necessary for generating a numerical calculation program corresponding to each numerical calculation algorithm by data processing such as numerical formula processing. It is supplied to the program generation control device 30 as formula information 61. The calculation formula information 61 is a calculation formula serving as an attribute of an individual algorithm, such as a variable list appearing in the algorithm, a function form of coordinate transformation, a calculation formula at a numerical integration point, and the like. The calculation formula generation device 60 is not necessarily required depending on the program to be generated.
[0030]
Based on the syntax analysis information 21 analyzed by the syntax analysis device 20, the program generation control device 30 determines, for each of the numerical calculation algorithms specified in the problem definition information 11, the order of the pseudo code expressing that algorithm. The set data is called from the algorithm information 41, and further, the style-specific template program information 51 for generating a program corresponding to each pseudo code is called in accordance with the style specified by the program format information 12 for each pseudo code, and the necessary In this case, a program component of each numerical calculation algorithm is generated together with the calculation formula information 61. This operation is performed for all the pseudo codes constituting the specified algorithm. The generation program 70 is generated by performing the above processing for all the numerical calculation algorithms specified by the problem definition information 11 and the program format information 12.
[0031]
Next, the operation of the first exemplary embodiment of the present invention will be described with reference to the drawings.
[0032]
FIG. 2 is an explanatory diagram showing a specific example of problem definition information 11 describing a numerical calculation problem using a finite element method of a user and program format information 12.
[0033]
Referring to FIG. 2, processing relating to three numerical calculation algorithms, ie, substitution processing involving interpolation at 204, solution processing of a linear partial differential equation at 205, and visualization processing at 206 are expressed as specifications relating to the algorithm of the problem definition information 11. .
[0034]
S201 and S202 are the problem definition information 11 on variables used for problem description. In S201, the variable u is specified to be interpolated by the interpolation function name T1, and in S202, the variable rho is specified to have a value at the integration point of the numerical integration method defined by tet3.
[0035]
S203 is an example of the specification of the program format information 12, in which the program format of the finite element method with a format name of feelfem90 is specified as the program format.
[0036]
In this example, FORTRAN 90 is specified as a programming language, and a field called feelfem 90 is specified as a data expression / program format of the finite element method. Within the specification of the linear partial differential equation S205, the specification of an unknown variable and a test function symbol S205a, the specification of a numerical integration method of a region S205b, the specification of a linear solver S205c, the specification of a variational equation S205d, and the specification of a Dirichlet-type boundary condition S205e , The designation S205f of the Neumann-type boundary condition is described. The designation of the solver in S205c belongs to the program format information 12.
[0037]
FIG. 3 is an explanatory diagram illustrating an example of the problem definition information 11.
[0038]
FIG. 4 is an explanatory diagram illustrating an example of the problem definition information 11.
[0039]
FIG. 5 is a flowchart showing the basic operation of the program generation control device 30.
[0040]
Referring to FIG. 5, the text data of the problem definition information 11 input to the problem definition input device 10 is supplied to the syntax analysis device 20. The syntax analysis device 20 supplies the problem definition information 11 and the syntax analysis information 21 of the program format information 12 to the program generation control device 30. The program generation control device 30 extracts data on each numerical calculation algorithm from the syntax analysis information 21 (step A01 in FIG. 5). The program generation control device 30 generates a numerical calculation program component corresponding to the extracted numerical calculation algorithm (step A02 in FIG. 5). The generation of the individual numerical calculation algorithm program parts is repeated for all the numerical calculation algorithms described in the problem definition information 11 and the program format information 12 (step A03 in FIG. 5). Next, the numerical calculation algorithm program parts generated in step A02 are connected to generate a complete generation program 70 (step A04 in FIG. 5).
[0041]
FIG. 6 is a flowchart showing details of step A02 in FIG.
[0042]
For one numerical calculation algorithm (hereinafter referred to as a numerical calculation algorithm to be processed) extracted in step A01 in FIG. 5, a necessary calculation formula created by the calculation formula generation device 60, a calculation formula such as a variable name list, etc. The information 61 is extracted (step B01 in FIG. 6). The algorithm information 41 represented by the ordered set of the corresponding pseudo code for the numerical calculation algorithm to be processed is extracted from the algorithm storage device 40 (step B02 in FIG. 6).
[0043]
Pseudocodes are sequentially extracted one by one from the ordered set of pseudocodes representing the numerical calculation algorithms extracted from the algorithm information 41 (step B03 in FIG. 6).
Next, from the pseudo code extracted in step B03 and the program format information 12 specified in the pseudo code of the syntax analysis information 21, the corresponding format-specific template program information 51 is extracted from the format-specific template program storage device 50 ( (Step B04 in FIG. 6).
[0044]
Based on the extracted style-specific template program information 51 and calculation formula information 61, a portion corresponding to the extracted pseudo code is generated (step B05 in FIG. 6). The process is repeated for all pseudo codes representing the calculation algorithm to be processed (step B06 in FIG. 6).
[0045]
In this way, the generation of a program corresponding to each numerical calculation algorithm stored in the form of an ordered set of pseudo codes is performed for each pseudo code constituting the algorithm by using program format information 12 specified by user input information. Is generated from the style-specific template program information 51 of the program format specified for the pseudo code and the calculation formula information 61 independent of the program format.
[0046]
For this reason, when newly increasing the numerical calculation algorithm to be generated, the pseudo code constituting the algorithm information 41 already registered in the system is reused, and the pseudo code order of the newly increased numerical calculation algorithm is changed. A set expression can be constructed. In this case, it is not necessary to newly extend the system with respect to the portion of the pseudo code that has been reused, so that it is possible to increase the number of new numerical calculation algorithms with little effort.
[0047]
Further, when the system attempts to add a program generation function using a new program format to a numerical calculation algorithm that already has a program generation function, the system expansion work includes pseudo code related to the program format to be newly added. Only by individually adding style-specific template program information 51 corresponding to the pseudo code.
[0048]
Therefore, it is possible to generate a numerical calculation program having attributes of a plurality of program formats for one numerical calculation algorithm with a small amount of trouble, and it is easy to expand and manage the system.
[0049]
Next, a first embodiment of the present invention will be described with reference to the drawings.
[0050]
In the first embodiment, a keyboard is used as the problem definition input device 10, a personal computer is used as the syntax analysis device 20, the program generation control device 30, and the calculation formula generation device 60, an algorithm storage device 40, and a template program storage device 50 for each style. As a magnetic disk drive.
[0051]
The personal computer has a central processing unit that performs logical processing as a syntax analysis device 20, a program generation control device 30, and a calculation formula generation device 60, and each magnetic disk storage device has algorithm information. 41, and template program information 51 for each style.
[0052]
In the first embodiment, a numerical calculation method of a linear partial differential equation by the finite element method is used as an example of the generation program 70 to be generated. At this time, the unknown function is approximated by a linear combination of certain interpolation functions, and a numerical solution is obtained as a variational problem. At this time, the problem definition information 11 includes the shape of the interpolation function used for approximation, the numerical integration method for dealing with variational problems, and the boundary conditions of Dirichlet type and Neumann type. These are mathematical things that do not depend on a particular implementation. The input information necessary for performing other specific implementation is called program format information 12.
[0053]
FIG. 2 is an explanatory diagram showing an example of the problem definition information 11 and the program format information 12.
[0054]
FIG. 3 is an explanatory diagram showing an example of the problem definition information 11 and the program format information 12.
[0055]
FIG. 4 is an explanatory diagram showing an example of the problem definition information 11 and the program format information 12.
[0056]
Referring to FIG. 2, the calculation processing involving the numerical calculation algorithm relates to substitution processing involving interpolation (S204 in FIG. 2), processing relating to solution of a linear partial differential equation (S205 in FIG. 2), and processing relating to visualization processing (FIG. 2 S206). Is specified. Other descriptions other than the program format information 12 (S203, S205c in FIG. 2) belong to the problem definition information 11.
[0057]
In S201, it is specified that the variable u is a function variable to be interpolated by an interpolation function having the name T1. In S202, it is specified that the variable rho is a function variable having a value at each integration point of the numerical integration method defined by the name tet3. In S203, a program style named feelfem90 is designated as the program style information 12. In this example, FORTRAN 90 is designated as a programming language, and a field called feelfem 90 is designated as a data expression / program format of the finite element method.
[0058]
S205 is the problem definition information 11 of the linear partial differential equation. In S205a, the solve specifies a partial differential equation problem, a symbol representing an unknown variable is designated as u, and a symbol representing a test function is designated as tu. In S205b, it is specified that the numerical integration method used when solving this partial differential equation is the numerical integration method defined by the name tet3.
[0059]
In S205c, it is specified that a solver defined by the name amg is used as a solver for solving a system of linear equations appearing by discretization. In step S205c, the program format information 12 implicitly specifies the type of the solver library to be used and the data structure of the matrix of the simultaneous linear equations dependent on the type. In S205d, the variational problem form of the linear partial differential equation is specified in the form of integral. The term specified by integral (integrated function) is the area integral term, and the element stiffness matrix and the calculation formula information 61 of the element load vector are specified. The term specified by bintegral (the integrand) is a boundary integral term, and calculation formula information 61 on the Neumann-type boundary condition is specified. In S205e, u = 1000 which is the calculation formula information 61 of the Dirichlet type boundary condition and the names ab and bc of the boundaries imposing the condition are specified.
[0060]
In S205f, g = u-100, which is the calculation formula information 61 of the Neumann-type boundary condition, and the name eg of the boundary imposing this condition are specified. In S206, it is specified to output a contour diagram for the function amount u * 100.
[0061]
Referring to FIG. 3, the interpolation function relating to the interpolation method T1 used in S201 is a name T1, an element shape tetra (tetrahedron), and coordinates in the reference element and the interpolation function are represented by r, s, t polynomials. Is specified in the set. Further, another interpolation method T2 is specified following T1.
[0062]
Referring to FIG. 4, information on the name tet3 of the numerical integration method used in S202 is designated as a set of a numerical integration point and its weight in the reference element.
[0063]
These pieces of input information are analyzed by the syntax analysis device 20, and syntax analysis information 21 is created.
[0064]
FIG. 7 is an explanatory diagram showing an example of the syntax analysis information 21 for FIGS. 2, 3, and 4.
[0065]
701 is the basic program format information 12 specified by the ProgramModel statement in S203. Reference numerals 711, 712, 721, and 722 are created from the input information of FIGS. 3 and 4 and S201 and S202, respectively, and are used as mathematical attribute information of discretization when generating a numerical calculation program. Each of 711a and 712a stores an internal expression of a mathematical expression information list such as coordinates and mathematical expressions in FIGS.
[0066]
S204, S205, and S206 of the schema block in FIG. 2 are input information specifying independent numerical calculation processing, and the respective pieces of syntax analysis information 730, 740, and 750 are collected for each calculation processing unit. Each calculation processing unit includes one or more numerical calculation algorithms.
[0067]
For simplicity, the numerical solution processing of the linear partial differential equation by the finite element method in S205 will be referred to as a solve block. In view of the numerical calculation algorithm in the first embodiment, this solve block is composed of four numerical calculation algorithms, that is, three sub-processes and a process of controlling a solve block that controls the sub-processes. . The numerical calculation algorithm of the first sub-process is a process of calculating an element stiffness matrix and an element load vector of the finite element method and adding them to the entire matrix and the entire load vector, and corresponds to 745 of the parsing information 21. The second sub-processing is a numerical calculation algorithm for processing Neumann-type boundary conditions, and corresponds to 746 of the parsing information 21. The third sub-processing is a numerical calculation algorithm for processing Dirichlet-type boundary conditions, and corresponds to 747 of the parsing information 21. The process of controlling the solve block is generated from 740 of the syntax analysis information 21.
[0068]
In accordance with the flowchart of FIG. 5, the program generation control device 30 extracts the list of the type information of the numerical calculation algorithm 731, 741, 745 a, 746 a, 747 a, and 751 from the syntax analysis information 21 and sequentially generates the components of the numerical calculation program. I do. The generation processing of the numerical calculation program corresponding to the individual numerical calculation algorithm is executed by the program generation control device 30 according to the flowchart of FIG.
[0069]
Here, as an example for explaining the processing of the flowchart of FIG. 6 in detail, a numerical calculation algorithm of the processing related to the control of the above solve block will be described.
[0070]
The numerical calculation algorithm, which is the processing method of the first embodiment, is represented by a sequence of pseudo codes, and the process of generating template-specific information 51 for each pseudo code to generate a program is performed by the other three numerical calculation algorithms. The same can be applied to
[0071]
Prior to describing the operation of the flowchart in FIG. 6, an example of a mounting method of the numerical calculation algorithm related to the control of the solve block in the first embodiment using the algorithm information 41 will be specifically described.
[0072]
FIG. 8 is a flowchart showing the contents of a numerical calculation algorithm relating to control of the solve block in S205.
[0073]
The algorithm relating to the control of the solve block is an abstract one that does not depend on a program style such as a programming language to be implemented or a computer architecture.
[0074]
Referring to FIG. 8, a data structure of a sparse matrix appearing by discretizing a differential equation is obtained from the connection relationship between elements and nodes and the degrees of freedom at each node (step D01 in FIG. 8). The element stiffness matrix and element load vector calculated for each element are added to the array storing the entire matrix allocated to the memory with the structure determined by D01 (step D02 in FIG. 8). The contribution from the evaluation amount of the boundary integral defined by the Neumann-type boundary condition is added to the overall matrix (step D03 in FIG. 8).
[0075]
Processing is performed for the degree of freedom whose value is specified by the directory condition (step D04 in FIG. 8). Solve the constructed system of linear equations with a solver. In step D06, post-processing such as dividing the selected solution into physical quantities is performed (step D05 in FIG. 8).
[0076]
Each step of the abstract algorithm represented by the flowchart of FIG. 8 is divided into small steps subdivided according to the dependence on the level of the program style, and each divided step is referred to as one pseudo code. Then, the numerical calculation algorithm for which the program is to be generated is represented by a list formed by a sequence of pseudo codes.
[0077]
FIG. 9 is a pseudo-code level flowchart illustrating an example of the decomposition of the flowchart of FIG. 8 into pseudo code.
[0078]
Prior to the description of FIG. 9, the pseudo code will be described with a specific example. When each step of the abstract algorithm as shown in FIG. 8 is actually implemented in a computer language, the program style must be determined for various levels in order to determine the actual implementation.
[0079]
For example, a programming language of a computer to be used and various data structures. In the first embodiment, the first level of the programming language used in the generated numerical calculation program, such as FORTRAN77 or C ++, the ProgramModel relating to the data structure handled by the generated numerical calculation program and its expression, as the level of this program style class. A second level to be called, a third level to deal with the representation of a data structure in particular of a matrix component storage format among data structures, and a fourth level to deal with a difference in a method of calling a general library routine such as a solver for solving simultaneous linear equations. Consider the above four levels.
[0080]
At this time, it should be noted that the fourth level depends on the third level, the third level also depends on the second level, and the second level also depends on the first level. We focus on the hierarchical structure of this program style, and hereafter it is called the implementation level. An actual implementation is possible with the program style specified for each of these four levels.
[0081]
Explaining with a specific example, the process of “allocating an array for storing a sparse matrix from the calculation of the degrees of freedom” in step D01 in FIG. 8 includes the level of the second program style of “calculating the degrees of freedom” and It can be divided into a third program style level of "allocating an array for storing a sparse matrix". When divided in this way, the generation processing of the numerical calculation program for step D01 can be subdivided into a part dependent on the second level and a part dependent on the third level. The subdivided program generation processing is determined by the individual program format specified at that level. The minimum processing unit of program generation, which is subdivided according to the level of the program style, is the pseudo code referred to in the present invention. Also, in the present invention, units that are structural components of the program source code, such as "declare a subroutine" or "declare a variable", which is a statement of a program, are also separated for each level of the program style. Is treated as pseudo code.
[0082]
Although the division of the algorithm steps into pseudo code is arbitrary, it is effective to separate the pseudo algorithm code by separating the steps of the abstract algorithm that depend on the lowest possible program style. Because, for example, in the case of the linear solver, if the fourth-level of calling the solver and the third-level matrix storage method are completely separated by pseudo code, the solver using the same matrix storage method can be used. This is because, in the case of replacement, the change of the numerical calculation program to be generated is localized only in the pseudo code for the fourth level.
[0083]
In the first embodiment, a description will be given of a case where the level is divided into four levels, but the same applies even if the number of levels changes. For example, since the input / output data file format such as mesh data is independent of the numerical calculation algorithm, it is possible to add this level to five levels. In this case, it is easy to create a system that generates programs with different file input / output methods.
[0084]
Referring to FIG. 9, the pseudo code expression of the algorithm in FIG. 8 is composed of 15 steps E01 to E15. It is important that the pseudo code steps E01 to E15 divided according to the program style level do not depend on the specific specification of the program style. Next, this step will be described. Hereinafter, as a term, a module of a program generated corresponding to steps E01 to E15 is referred to as a solve subroutine.
[0085]
Step E01 is pseudo code corresponding to creating a source file for writing a solve subroutine in which the algorithm of FIG. 8 is realized. Step E02 is a pseudo code corresponding to generating a header part of a solve subroutine, such as a declaration procedure statement.
[0086]
Step E03 is pseudo code corresponding to generating a declaration statement such as a constant determined before execution of a problem-dependent parameter or the like. Step E04 is pseudo code corresponding to declaring a local variable used in the solve subroutine. Step E05 is pseudo code corresponding to the initialization of variables in the solve subroutine.
[0087]
Step E06 is a pseudo code corresponding to calculating the degrees of freedom and equation numbers of unknown variables necessary for determining the matrix structure. Step E07 is a pseudo code corresponding to preparing the data of the boundary condition. Step E08 is a pseudo code corresponding to allocating a memory for storing a matrix or a vector required for the process of the solve subroutine. Step E09 is a pseudo code corresponding to calling the calculation of the element matrix / element weight and the processing of assembling the element matrix by the numerical solution of the differential equation by the finite element method.
[0088]
Step E10 is pseudo code corresponding to calling a subroutine for processing the Neumann-type boundary condition. Step E11 is pseudo code corresponding to calling a subroutine for processing a Dirichlet-type boundary condition. Step E12 is pseudo code corresponding to calling a solver library that solves a simultaneous linear equation selected by discretizing the differential equation. Step E13 is pseudo code corresponding to calling the post-processing after calling the solver library. Step E14 is a pseudo code corresponding to performing processing for ending the solve subroutine. Step E15 is a pseudo code corresponding to closing the file in which the solve subroutine has been written.
[0089]
FIG. 10 is an explanatory diagram showing an example of a method for realizing the algorithm information 41 of FIG. 1 in which each pseudo code of FIG. 9 is a C ++ virtual function, and the flowchart of FIG. 9 is implemented as a function procedure for sequentially calling them.
[0090]
Although it is implemented as a function procedure in FIG. 10, it can be represented by list data and handled by interpretive processing.
[0091]
The flowchart of FIG. 9 is expressed by a member function NormalLinearProblem of the class SolveScheme. Referring to FIG. 10, the pseudo code sequence representing the flowchart of FIG. 9 is realized as a virtual function call procedure 1001 in the NormalLinearProblem function.
[0092]
The list of call functions 1001 corresponds to the steps E01 to E15 in FIG. 9 on a one-to-one basis. In other words, E01 represents RouteInitialize (solvePtr), and E02 represents RouteHeader (solvePtr) in the order of RouteTerminate (solvePtr) of E15, and the steps corresponding to the 15 pseudo codes in FIG.
[0093]
Next, the operation of the program generation control device 30 will be described in more detail with reference to the drawings.
[0094]
FIG. 11 is an explanatory diagram showing the contents of the numerical calculation algorithm processing function table.
[0095]
In the above example, the table of 740 of FIG. 7 is selected from the syntax analysis information 21 of FIG. 7, and the process of step A02 of FIG. 5, that is, steps B01 to B06 of FIG. 6 is started. In step B01, the appearance variable table 742 is passed to the calculation formula generation device 60 from SOLVE of the calculation process type information 741, and the calculation formula information 61 is generated. In the case of the numerical calculation algorithm for control of the solve block, the list 742 of the calculation formula information 61 becomes the calculation formula information 61 as it is. The generation of the calculation formula information 61 by mathematical processing or the like is necessary when generating a numerical calculation program corresponding to the ASSEMBLE numerical calculation algorithm of 745 of the syntax analysis information 21, but is not relevant to the essence of the present invention. This calculation formula generation processing is described in, for example, “Japanese Patent Application Laid-Open No. 06-180644”.
[0096]
The processing of step B02 in FIG. 6 is executed by referring to the numerical calculation algorithm processing function table (FIG. 11) from the calculation processing type information of 741 and calling the corresponding numerical calculation algorithm processing function. In the case of the control algorithm of the Solve block, SolveScheme :: NormalLinearProblem is called from the processing type name SOLVE. The process of sequentially extracting the pseudo code in step B03 is realized by sequentially executing the execution statement 1001 of SolveScheme :: NormalLinearProblem. That is, the algorithm expression by the pseudo code corresponds to a list of 1001 calling functions.
[0097]
In the first embodiment, the realization method of step B04 and step B05 in FIG. 6 is based on the virtual function of C ++ and the mechanism of polymorphism.
[0098]
First, the configuration of the implementation of a virtual function and its real function, which is the premise of polymorphism, will be described with reference to the drawings.
[0099]
FIG. 12 is an explanatory diagram showing the contents of the pseudo code / program format level dependency table.
[0100]
FIG. 13 is an explanatory diagram showing virtual functions corresponding to grouping of levels in the program format.
[0101]
FIG. 14 is an explanatory diagram showing the contents of the dependency relationship table between program style levels.
[0102]
FIG. 15 is an explanatory diagram showing the classification of the substantive functions.
[0103]
FIG. 16 is an explanatory diagram showing an implementation example regarding the C ++ class declaration of the first embodiment.
[0104]
FIG. 17 is an explanatory diagram showing an implementation example of the template program information for each style.
[0105]
Each function 1001 called in the function NormalLinearProblem of FIG. 10 is declared as a virtual function of the class SolveScheme. These virtual functions are grouped as pseudo code into four program styles (Language, ProgramModel, MatrixModel, Library) as shown in the pseudo code / program style existence table shown in FIG. As in the virtual function grouping shown in FIG. 13, one group of the real functions is implemented as one class.
[0106]
The designation of the program format in the input example of FIG. 2 is performed by specifying a solver library named amg at the level of the program format of the fourth library in FIG. 2S205c, and specifying a program name of feelf90 at the level of the second program format in FIG. Two program styles are explicitly specified. Since the third-level matrix structure and the first-level programming language level are determined from the fourth and second levels, respectively, the matrix structure is obtained from the dependency table between the program style levels shown in FIG. Has been determined as a program format, and Fortran 90 has been determined as a programming language format.
[0107]
From this, in the specific example of FIG. 2, the real functions corresponding to the virtual functions are, as shown in FIG. 15, class Fortran 90 (FIG. 15G01), class field90 (FIG. 15G02), class CRS (FIG. 15G03), and class amg (FIG. 15G02). 15G04) are implemented in the four classes.
[0108]
From the above configuration, the mechanism of step B04 in FIG. 6 can be realized. FIG. 16 shows this. Although the function procedure 1001 in FIG. 10 is declared as a virtual function in the class SolveScheme, the corresponding substantial function is implemented in the classes L1, L2, L3, and L4 declared as templates by the public declaration in FIG. 16H01. It becomes possible to do. By specifying the combination of L1, L2, L3, and L4, it is possible to select a substantial function from the program format information 12. For example, FIG. 15 and FIG. 16H03 show the specified examples of FIG. 2, and L1, L2, L3, and L4 of the template declaration are designated as Fortran 90, feelfem90, CRS, and amg, respectively. The selection process in step B04 is realized.
[0109]
In the first embodiment, as described above, the “format-specific template program information 51 corresponding to the pseudo code” in step B04 in FIG. 6 is the entity corresponding to the virtual function grouped for each class declared for each level of the program format. It is stored in the form of a function execution statement. Specifically, this is a C ++ executable statement as shown in FIG. The list in FIG. 17J01 is template program information corresponding to step E08 in FIG. 9 that is called when the CRS format is designated as the matrix format program format. As described above, in the first embodiment, the style-specific template program information 51 is realized in the form of a C ++ printf statement.
[0110]
The processing of steps B02 to B06 in FIG. 6 is shown in the lists of FIGS. That is, the process of extracting the algorithm information 41 by the pseudo code from the algorithm storage device 40 in step B02 in FIG. 6 corresponds to FIG. 16H04. When the NormalLinearProblem function in FIG. 16H04 is executed, 1001 in FIG. 10 is executed, so that the process of sequentially extracting the pseudo code in step B03 in FIG. 6 can be realized. The process of extracting the template program information for each format 51 from the program format information 12 in step B04 in FIG. 6 is realized by the polymorphism mechanism of the virtual function in C ++ in FIG. In the process of generating the portion corresponding to the numerical calculation program in step B05 in FIG. 6, the actual functions of each virtual function (J01, J02, etc. in FIG. 17) are executed, and the portion of the generation program 70 is sequentially written to a disk device or the like by a printf statement. Thus, the generation of the generation program 70 is realized.
[0111]
FIG. 18 is an example of the generation program 70 output according to the above procedure. As shown in FIG. 18, when the function NormalLinearProblem of FIG. 10 corresponding to the pseudo code is called and the virtual functions of 1001 are sequentially executed, the real function shown in FIG. 15 is designated by the polymorphism mechanism. The source files of the generation program 70 are generated by sequentially calling the components of the program in a file or the like according to the program format.
[0112]
The numerical solution of partial differential equations is mainly solved by solving simultaneous linear equations. Generally, the matrix that appears in this calculation is a sparse matrix with a large dimension, so it is necessary to store the matrix efficiently.However, the properties of the PDE, the architecture of the computer that performs the calculation, or the linear solver that solves simultaneous linear equations There is a difference in the effective way of storing the matrix. Therefore, it is industrially useful for a numerical calculation program generation system to generate a calculation program corresponding to the data structure of a newly devised matrix.
[0113]
The processing unit of program generation according to the first embodiment of the present invention is subdivided into basic units for each program format in the implementation, and each is expressed as one pseudo code. In other words, only for the pseudo code related to the matrix structure level, if a new matrix structure format, that is, template program information corresponding to the new program format is prepared, the numerical calculation program generation system corresponding to the new matrix structure can be provided. Can be extended.
[0114]
FIG. 19 is an explanatory diagram showing a method of extending template program information.
[0115]
Referring to FIG. 19, in addition to the CRS format, style-specific template program information, which is a Skyline format program format, is added to the pseudo code of FIG. 9E08 belonging to the third matrix structure level. If this operation is performed on the remaining pseudo code diagrams 9E09, E10, and E11 belonging to the third matrix structure level, the pseudo code diagrams 9E01, E05, E15 belonging to the first programming language level, and the second ProgramModel Pseudo-code belonging to level 9 The change of the numerical calculation program generation system relating to E02, E03, E04, E06, E07, E13, E14 is unnecessary, and by calling the function SolveScheme :: NormalLinearProblem, the matrix structure for the input information S205c of FIG. Can generate the generation program 70 in the Skyline format, which facilitates expansion of the numerical calculation program generation system. Specifically, it is only necessary to add J02 to J01 in FIG.
[0116]
Although the extension related to the matrix structure level has been described above, the same applies to the programming language level, the ProgramModel level, and the library level. When the program format is extended, a numerical calculation program is generated by adding a minimum necessary as in the first embodiment. System expansion is realized.
[0117]
In the present invention, a numerical calculation program corresponding to a certain numerical calculation algorithm is generated from control information consisting of a sequence of pseudo codes. When adding a function of generating a numerical calculation program corresponding to a new numerical calculation algorithm to the numerical calculation program generation system of this method, it is possible to add the numerical calculation algorithm by using already implemented pseudo code. As an example, using a function of generating a numerical calculation program of a control algorithm for linear partial differential equations (FIG. 9), a numerical calculation program of a control algorithm for numerically solving a nonlinear partial differential equation using the Newton method is generated. A case where a function is added will be described.
[0118]
FIG. 20 is an explanatory diagram showing that a sequence of pseudo codes dealing with a non-linear problem is expressed using pseudo codes of a linear problem.
[0119]
When a nonlinear equation is solved by the Newton method, a solution is obtained by linearizing the equation and repeatedly solving a linear problem. What is needed when extending the flow chart of the control program for the linear problem shown in FIG. 9 to the nonlinear problem is to insert control regarding the initialization and the loop of the nonlinear problem between FIGS. 9E08 and 9E09, Only the post-processing of the solver of FIG. 9E13 is changed to the post-processing of the solver in the case of the nonlinear problem, and the processing of the remaining FIGS. 9E01 to E08, E10 to E12, and E14 to E15 may be exactly the same. That is, as shown in FIG. 20, a pseudo code (K01, K02 in FIG. 20) specific to a nonlinear problem may be newly prepared, and a program component generation function corresponding thereto may be added.
[0120]
In this way, by reusing the existing pseudo code, it is possible to expand the numerical calculation algorithm that can be handled by the program generation system only by adding the necessary pseudo code, and it is easy to add the algorithm that can be handled by the numerical calculation program generation system It can be carried out. In this embodiment, the case of the finite element method has been described. However, a program generation system can be created by a similar method using the difference method or the finite volume method.
[0121]
Next, a second embodiment of the present invention will be described in detail with reference to the drawings.
[0122]
The second embodiment of the present invention is a method including the steps of each processing of the first embodiment of the present invention (for example, the steps of FIGS. 5, 6, 8, and 9).
[0123]
Next, a third embodiment of the present invention will be described in detail with reference to the drawings.
[0124]
According to the third embodiment of the present invention, each processing step (for example, each step of FIG. 5, FIG. 6, FIG. 8, and FIG. 9) of the second embodiment of the present invention is performed by a computer (for example, syntax analysis). This is a program to be executed by the device 20, the calculation formula generation device 60, and the program generation control device 30).
[0125]
【The invention's effect】
The first effect is that it is easy to add a function of generating a numerical calculation program having a new program format to a numerical calculation program generation system of a numerical calculation algorithm that has already been implemented.
[0126]
The reason is that the generation of a numerical calculation program corresponding to a certain numerical calculation algorithm is controlled by a sequence of pseudo codes, but when a new program form is added, only the pseudo code to which the program form is related is added. This is because it is only necessary to add the corresponding template program information. That is, the control structure of the numerical calculation program reflecting the mathematical algorithm of the pseudo code sequence can be used as it is without depending on the individual program style.
[0127]
Further, the addition of the program format is useful for constructing a program generation system in that the additional necessity is localized only in the relevant pseudo code.
[0128]
The second effect is that it is easy to add a numerical calculation algorithm that can generate a program.
[0129]
The reason is that the generation of the numerical calculation program corresponding to the numerical calculation algorithm is represented by the pseudo code sequence considering the implementation level. This is because the pseudo code already defined can be reused when making it.
[Brief description of the drawings]
FIG. 1 is a block diagram showing a configuration of a first exemplary embodiment of the present invention.
FIG. 2 is an explanatory diagram showing a specific example of problem definition information describing a numerical calculation problem using a finite element method of a user and program format information.
FIG. 3 is an explanatory diagram showing data relating to an interpolation method T1.
FIG. 4 is an explanatory diagram showing a part of data relating to a numerical integration method tet3.
FIG. 5 is a flowchart showing a basic operation of the program generation control device.
FIG. 6 is a flowchart showing details of step A02 in FIG. 5;
FIG. 7 is an explanatory diagram showing an example of syntax analysis information for FIGS. 2, 3, and 4;
FIG. 8 is a flowchart showing the contents of a numerical calculation algorithm relating to control of a solve block.
9 is a pseudo-code level flowchart illustrating an example of decomposition of the flowchart of FIG. 8 into pseudo code.
FIG. 10 is an explanatory diagram showing an example of a method for implementing the algorithm information of FIG. 1 implementing the flowchart of FIG. 9;
FIG. 11 is an explanatory diagram showing the contents of a numerical calculation algorithm processing function table.
FIG. 12 is an explanatory diagram showing the contents of a pseudo code / program format level dependency table.
FIG. 13 is an explanatory diagram showing virtual functions corresponding to grouping of levels in a program format.
FIG. 14 is an explanatory diagram showing the contents of a dependency relationship table between program style levels.
FIG. 15 is an explanatory diagram showing a classification of an entity function.
FIG. 16 is an explanatory diagram showing an implementation example regarding a C ++ class declaration in the first embodiment.
FIG. 17 is an explanatory diagram showing an implementation example of template program information for each style.
FIG. 18 is an explanatory diagram illustrating an example of a generation program.
FIG. 19 is an explanatory diagram showing a method of extending template program information.
FIG. 20 is an explanatory diagram showing that a sequence of pseudo codes dealing with a nonlinear problem is expressed using pseudo codes of a linear problem.
[Explanation of symbols]
10 Problem definition input device
11 Problem definition information
12 Program form information
20 syntax analyzer
21 Parsing information
30 Program generation control device
40 Algorithm storage device
41 Algorithm Information
50 Template program storage device by style
51 Template program information by style
60 Calculation formula generator
61 Calculation formula information
70 generation program

Claims (9)

The problem definition information and program format information relating to the numerical calculation algorithm are input from the first storage device, and the numerical calculation algorithm of the numerical calculation program to be generated is generated by expressing the numerical calculation algorithm in a sequence of pseudo-codes. A pseudo-code sequence corresponding to a new numerical calculation algorithm is created using the pseudo-code that has been set, the numerical calculation algorithm generated by the numerical calculation program generation system is increased, and the numerical calculation program is generated in the second storage device. A numerical calculation program generation system, comprising: By selecting the style-specific template program information corresponding to each pseudo code and generating a numerical calculation program in accordance with the specification of the program format information input to the first storage device, a plurality of sequence codes of the same pseudo code are generated. 2. The numerical calculation program generation system according to claim 1, further comprising means for generating a numerical calculation program of the combination of the program format information in the second storage device. Based on syntax analysis information generated from the problem definition information input to the first input device, for each of the numerical calculation algorithms specified in the problem definition information, a pseudo code expressing the algorithm is provided. An ordered set data is called from the algorithm information stored in the third storage device, and further, a format-specific template for generating a program corresponding to each pseudo code in accordance with the format specified by the program format information for each pseudo code The program information is called from the fourth storage device, and program parts of each numerical calculation algorithm are generated together with the calculation formula information stored in the fifth storage device for all the pseudo codes, and the numerical calculation program is stored in the second storage device. 3. A computer program according to claim 2, further comprising means for generating a numerical calculation program. Stem. The problem definition information and program format information relating to the numerical calculation algorithm are input from the first storage device, and the numerical calculation algorithm of the numerical calculation program to be generated is generated by expressing the numerical calculation algorithm in a sequence of pseudo-codes. A pseudo-code sequence corresponding to a new numerical calculation algorithm is created using the pseudo-code that has been set, the numerical calculation algorithm generated by the numerical calculation program generation system is increased, and the numerical calculation program is generated in the second storage device. A method for generating a numerical calculation program, comprising the steps of: By selecting the style-specific template program information corresponding to each pseudo code and generating a numerical calculation program in accordance with the specification of the program format information input to the first storage device, a plurality of sequence codes of the same pseudo code are generated. 5. The method according to claim 4, further comprising the step of generating a numerical calculation program of the combination of the program format information in the second storage device. Based on syntax analysis information generated from the problem definition information input to the first input device, for each of the numerical calculation algorithms specified in the problem definition information, a pseudo code expressing the algorithm is provided. An ordered set data is called from the algorithm information stored in the third storage device, and further, a format-specific template for generating a program corresponding to each pseudo code in accordance with the format specified by the program format information for each pseudo code The program information is called from the fourth storage device, and program parts of each numerical calculation algorithm are generated together with the calculation formula information stored in the fifth storage device for all the pseudo codes, and the numerical calculation program is stored in the second storage device. 6. The method according to claim 5, further comprising a step of generating the numerical calculation program in the apparatus. . The problem definition information and program format information relating to the numerical calculation algorithm are input from the first storage device, and the numerical calculation algorithm of the numerical calculation program to be generated is generated by expressing the numerical calculation algorithm in a sequence of pseudo-codes. A pseudo-code sequence corresponding to a new numerical calculation algorithm is created using the pseudo-code that has been set, the numerical calculation algorithm generated by the numerical calculation program generation system is increased, and the numerical calculation program is generated in the second storage device. A program for generating a numerical calculation program, which causes a computer to execute a procedure for performing the calculation. By selecting the style-specific template program information corresponding to each pseudo code and generating a numerical calculation program in accordance with the specification of the program format information input to the first storage device, a plurality of sequence codes of the same pseudo code are generated. 8. The computer program according to claim 7, wherein the computer is caused to execute a procedure for generating a numerical calculation program of the combination of the program format information in the second storage device. Based on syntax analysis information generated from the problem definition information input to the first input device, for each of the numerical calculation algorithms specified in the problem definition information, a pseudo code expressing the algorithm is provided. An ordered set data is called from the algorithm information stored in the third storage device, and further, a format-specific template for generating a program corresponding to each pseudo code in accordance with the format specified by the program format information for each pseudo code The program information is called from the fourth storage device, and program parts of each numerical calculation algorithm are generated together with the calculation formula information stored in the fifth storage device for all the pseudo codes, and the numerical calculation program is stored in the second storage device. 9. The numerical value according to claim 8, wherein the computer is caused to execute a procedure for generating the data. Calculation program generation program.

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