JP4576535B2 - Convergence solution algorithm performance display device and convergence solution algorithm performance display method - Google Patents

Description

The present invention relates to a convergence solution algorithm performance display device and a convergence solution algorithm performance display method using the convergence solution algorithm performance display device.

In the analysis of natural phenomena and engineering phenomena, numerical simulation using a convergence solution algorithm is often performed.

For example, the following is known as a patent document relating to a convergence solution algorithm.
In Patent Document 1, a syntax analysis device creates syntax analysis information from definition information and program format information captured by a problem definition input device, and an algorithm storage device is expressed by a sequence of pseudo codes of a convergence solution algorithm. It is described that the algorithm information is stored, and the calculation formula generation device generates calculation formula information necessary for the convergence solution algorithm from the parsing information.

  Patent Document 2 includes an evaluation value calculation unit that inputs child model parameters from a child model parameter file, obtains K model evaluation values based on the input child model parameters, and stores them in the evaluation value file of the storage unit. An adaptive evaluator for the genetic algorithm machine provided is described.

  Patent Document 3 describes a multi-faceted algorithm operation system that evaluates the characteristics of input data using parameters included in the input data.

JP 2004-86760 A JP 2006-12114 A JP 2002-150260 A

As described above, in the analysis of natural phenomena and engineering phenomena, numerical simulations using numerical algorithms are often performed, and the equations describing them are linear equations and large simultaneous linear equations.
Ax = b
It is reduced to the solution of

For the eigenvalue problem, the following equation
Ax = λBx
It is reduced to the solution of
And if you use algebraic equations,
f (x) = 0
The other problems that result in the solution of the above are also solved in the solution of the respective equations in the same manner as described above.

  In such a solution, since most of the calculation time required for the numerical simulation is spent for this calculation, it is important to solve it quickly and accurately.

A wide variety of convergence solution algorithms can be used to solve the problem, and it is unclear which convergence solution algorithm is used to solve the problem quickly and accurately.

If the coefficient matrix A is a symmetric positive definite value, the CG method or the Cholesky method is selected without hesitation, but if the coefficient matrix is non-objective, which convergence solution algorithm should be selected, it can be solved quickly and accurately. I do not know what will be.

Researchers of convergence solving algorithm (algorithm developers) have proposed a new convergence solving algorithm from a mathematical point of view, convergence properties, trying to obtain a high accuracy, the researchers of the numerical simulation (algorithm user) is actually numerically Perform simulations, create an original program and convergence solution algorithm according to the problem to be solved, and research how to solve the problem. It is better if it is faster and within acceptable accuracy.

In solving such problems in response to the needs of algorithm users, there is a need for a method that recommends the use of a convergence solution algorithm that solves problems quickly within an acceptable accuracy.

The present invention is, hitting to solving the problem using the convergence solving algorithms exist a wide variety meeting the needs of Algorithms in view of the foregoing, convergence solving algorithms within acceptable precision, can be quickly solving and to provide a convergence solving algorithm performance display method using the performance display device or convergence solving algorithm performance display device.

The present invention displays the performance of the convergence solution algorithm for solving the convergence,
The problem to be solved by the convergence solving algorithm, the pre-processing for improving the convergence that is used together with the solution and the solution, the scaling applied to the coefficient matrix, the ordering for changing the order of the coefficient matrix and the rows and columns, and any combination of the conversion formulas Storage means for arranging and storing menu items of a technique to be performed,
Each or all of the display items of the convergence graph showing the convergence status, the CPU time to convergence, and the number of convergence iterations that are the number of computation iterations until convergence, and the problem to be solved, the solution and the technique used in the solution are arranged A display means for displaying the menu item, a convergence graph from the display item, any or all items of the CPU time and the required number of convergence times for convergence, and a problem to be solved, selected from the arranged menu items, A setting screen display means having a parameter selection means for displaying the parameter items of the technique used in the solution and the solution,
Receive the selected parameter item, form a combination of the parameter item of the technique to be used together with the solution method for the problem to be solved, and acquire either the convergence graph data, the CPU time and the required number of convergence times for each combination Or an arithmetic processing means for performing the entire arithmetic processing and storing the arithmetic results in the database, and
Provided is a convergent solution algorithm performance display device characterized by comprising: a result screen display means for receiving an arithmetic processing result of each combination and displaying the arithmetic processing result of each combination on the screen .

The present invention also provides a convergence solution algorithm performance display device characterized in that the result screen display means simultaneously displays a plurality of convergence graphs using convergence graph data that has undergone arithmetic processing on the screen .

The present invention also provides a convergence solution algorithm performance display device, wherein the result screen display means simultaneously displays a plurality of CPU times or required convergence times on the screen .

The present invention also provides a convergence solution algorithm performance display device, wherein the setting screen display means causes a display item to be selected as a parameter item with reference to a command signal from a client terminal via a communication means. To do.

The present invention also provides a convergence solution algorithm performance display method using the convergence solution algorithm performance display device described above ,
The setting screen display means displays a convergence graph, a display item for any or all of the CPU time to convergence and the number of times required for convergence, and the arranged menu items for the problem to be solved, the solution, and the technique used in the solution. A problem to be solved, a solution and a technique selected from the display items to the convergence graph, any or all items of the convergence time, CPU time to convergence, and the number of times required for convergence, and each arranged menu item Display the parameter item of
The arithmetic processing means receives the parameter item, forms a combination of the parameter items of the technique used in the solution and the solution, and obtains the convergence graph data in each combination, CPU time and acquisition of the required number of convergence or Perform all computations, store computations in the database,
Provided is a convergence solution algorithm performance display method , wherein the result screen display means receives the calculation processing results of each combination and displays the calculation processing results of each combination on the screen .

Further, the present invention is that the storage means, for each convergent solving algorithms, problems to be solved, the parameters were set for each item of the techniques in combination with solutions and solutions, are set for each parameter, the convergence graph, CPU time and convergence required number A computer program for calculating a convergence graph associated with a combination of an operation specification factor and an operation specification format selected from each item, a CPU time and a required number of times of convergence,
The arithmetic processing means uses the computer program to perform arithmetic processing on a convergence graph, a CPU time, and a required number of times of convergence associated with the combination of the operation specification factors selected from each item,
In the database, the data of the convergence graph, CPU time and the number of times required for convergence are stored in association with the combination of the operation specification factors selected from each item, which is the calculation result of the calculation processing means.
By means of the setting screen display means, each parameter display means and each parameter selection means, the convergence graph, the CPU time and the required number of convergence times, or a display means of a combination thereof, and a selection means for selecting any of them , A display means for displaying a plurality of combinations of the operation specification factors in a form in which each parameter is combined and a selection means for selecting one or a plurality of any combinations are simultaneously displayed on one screen,
One of the parameters, one of the convergence graph, the CPU time and the required number of convergence times, or a combination thereof, and a combination of the operation specification factors in the form of a combination of each parameter by the data acquisition processing means. If one or more are selected, the data stored in the database for these combinations is searched and acquired, and the convergence graph based on the data acquired by the data acquisition processing means by the result screen display means, Display either the CPU time and the number of times required for convergence or a combination of these.
A convergence solution algorithm performance display method comprising: selecting any one of the selection means displayed on the screen of the setting screen display means by a command signal from a client terminal via a communication means. provide.

The present invention comprises a storage means, an arithmetic processing means, a database, a setting screen display means, a data acquisition processing means and a result screen display means described above, so that a convergence solution exists in a wide variety in response to the needs of algorithm users. When solving a problem using an algorithm, a convergence solution algorithm performance display device that can solve the problem quickly within an acceptable accuracy, or a convergence solution algorithm performance display method using this convergence solution algorithm performance display device is provided. can do.

  Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of a convergence solution algorithm performance display apparatus that is an embodiment of the present invention.
In FIG. 1, the convergence solution algorithm performance display device 100 includes a storage means 11, an arithmetic processing means (1) 12, a database 13, an arithmetic processing means (2) 14, and a display result means 15. The storage means 11 and the arithmetic processing means. (1) 12 constitutes the providing side computer system 1, the arithmetic processing means (2) 14 and the result display means 15 constitute the providing side computer system 2, and the database 13 is connected to these providing side computer systems 1 and 2. Exchange data. The convergence solving algorithm performance display device 100 is connected to the client terminal 200 to exchange data.

The storage unit 11 includes a plurality of parameters 21. These parameters are associated with the convergence solution algorithm 20. Convergence solving algorithm 20, a number of items, for example, the convergence of the eigenvalue problem (Ax = λBx) of determined linear equations for solution for seeking the solution of (Ax = b), or a determined solution of algebraic equations (f (x) = 0) consisting of solving algorithm item, including the convergence solving algorithm items other than the above. Each item is stored in association with each parameter. The parameter 21 is constituted and expressed by a problem 22 to be solved, a solution 23 and a technique 24 used in combination with the solution. It is a publicly known matter that is constituted and expressed by these three elements. For example, in the case of a linear equation, the items of the problem 22 to be solved include, for example, a matrix, a right-hand side term, an initial value, and the like, and the items of the solution 23 include, for example, a direct method, a stationary iteration method, and a non-stationary method. The items of the technique 24 composed and expressed by an iterative method, etc., and used in combination with the solution method are configured and expressed by, for example, preprocessing, scaling, ordering, and the like. In the case of the eigenvalue problem, the items of the problem 22 to be solved include, for example, a matrix A, a matrix B, initial values, and the like, and the items of the solution 23 include a power system, a QR method, an iterative system, The items of the technique 24 configured, expressed, and used together with the solution are the same as in the case of an algebraic equation configured and expressed by a conversion formula, shift, etc.

  In the following, description will be given mainly using a linear equation (Ax = b) as an example.

The “problem to be solved by numerical calculation” is, for example, a linear equation Ax = b, (A: coefficient matrix, x: solution vector, b: right-hand side vector)
And so on. As an example of a solution for solving this and a technique (preprocessing, scaling, etc.) for improving the solution efficiency, FIG. 3 shows a convergence solution algorithm of “a conjugate gradient method with preprocessing”. (The conjugate gradient method is also called a CG method, and “CG” is also displayed in each explanation of the system of the present embodiment and in the computer system.)
Here, a _{x k} collapsed vector, _{r k} is the residual vector. P _k other than these, α
_k and β _k are auxiliary vectors and scalars constituting the algorithm.

The above five expressions between “begin” and “end” are repeatedly executed until the norm of the residual vector (the value of || r _k ||) converges to an allowable value. A portion surrounded by a frame is an operation called “preprocessing”, and the convergence state changes depending on how the matrix K is formed (preprocessing method). When the solution method is something else such as BiCGStab, the configuration of the equation for iterative calculation changes. When K = I (I is a unit matrix), it is generally a “no pre-processing” convergence solution algorithm.

In the convergence determination, the value of || r _k || is evaluated, but a typical determination method is based on || r _k || ≦ ε || b ||.

  Here, ε is an allowable value (in this system, it is 10 minus 12), and b is a right-hand side vector of the linear equation. The number of iterations required until it is determined that convergence has occurred is the “necessary number of convergence”.

The CPU time is the total time of “calculation time for preprocessing matrix K generation” and “time until the residual in the convergence solution algorithm converges by iterative solution” before the convergence solution algorithm is started. .

The convergence graph shows the residual vector norm || r _k ||
(File with extension “.rsd” of 5) and log 10 (common logarithm) of the file is plotted and created. From this graph, the state of the effect of the convergence solution algorithm based on the iterative solution can be confirmed for the original linear equation. However, the residual vector here is the data in the convergence solution algorithm to the last. Even if it seems that the residual in the convergence solution algorithm seems to converge due to the inclusion of rounding errors in the calculation process, May not have a solution, in which case it evaluates with a true residual.

を用いて、

を評価したものである。図１４の「Ｄａｔａ Ｔａｂｌｅ」内の「Ｒｅｓ． ｎｏｒｍ （ｂ−Ａｘ）は、この情報をあらわしている。 The true residual is the numerical solution obtained by the convergence solution algorithm.

Using,

Is evaluated. “Res. Norm (b-Ax)” in “Data Table” of FIG. 14 represents this information.

1) Convergence solution algorithm The numerical calculation is further subdivided, and the following academic fields exist.
"Linear equations, eigenvalue problems, singular value decomposition (SVD), algebraic equations, numerical integration, function approximation, etc."
The system of this embodiment targets these numerical calculation fields, but in the explanation document, the example of the convergence solution algorithm for linear equations is taken up as a specific example. Similar ideas apply to other fields.

2) Problem to be Solved The linear equation (Ax = b) is configured using a matrix A (Matrix) called a coefficient matrix and a vector b called a right-hand side term, and finally obtains a vector x of a numerical solution. Then, the matrix uses the data of the website where the test matrix is gathered, and finally about 100 kinds of matrices will be prepared. These data are text format files.
Matrix Market http://math.nist.gov/MatrixMarket/
Sparse Matrix Collection
http://www.cise.ufl.edu/research/sparse/matrices/

Specifically, some of the matrix names are as follows.
1138_bus, 494_bus, 662_bus, 685_bus, add20
, Add32, bcsstk14, bcsstk15, bcsstk16, bcss
tm26, gr_30_30, memplus, nos1, nos2, nos3, n
os4, nos5, nos6, nos7, s1rmq4m1, s1rmt3m1, s
2rmq4m1, s2rmt3m1
(All matrices provided by Matrix Market)

  Furthermore, in the current state of the system according to the present embodiment, the right-side term is created in the execution program. Specifically, the right vector vector b is created by preparing the data of the solution vector x with appropriate values in advance and applying this to the coefficient matrix A (this operation is supported by Lis described in the next section. Function).

3) Solution The following are typical solutions for solving linear equations.
Direct solution: Gaussian elimination based on LU decomposition, Gaussian based on Cholesky decomposition
Elimination method, etc. Stationary iterative solution method: Jacobi method, Gauss-Seidel method, SOR method, etc. Non-stationary iterative solution method: CG method, BiCG method, CGS method, BiCGStab method, BiCGSt method
ab (l) method, GPBiCG method, Orthomin method, GMRES method
, TFQMR method, etc.

  In the present state of the system of the present embodiment, a solution program is constituted by a stationary iterative solution and a non-stationary iterative solution, and a direct solution can also be incorporated. The solution program is prepared as an executable program in the providing side computer system 1 using Lis (Library of Iterative Solvers for Linear Systems), a free library prepared at the following site.

Lis http://ssi.is.su-tokyo.ac.jp/lis/
As a specification of Lis, a solve ID is attached to a solver as follows. The 2-digit numerical value in [] is solverID.
CG [01], BiCG [02], CGS [03], BiCGStab [04], B
iCGStab (l = 2) [05], GPBiCG [06], Orthomin
[07], GMRES [08], TFQMR [09], Jacobi [10], Ga
uss-Seidel [11], SOR [12]
Currently, the value of the parameter l in the BiCGStab (l) method is l = 2.

4) Techniques used in combination with solutions The following techniques (techniques) are used in combination with solutions for linear equations.
Preprocessing: A technique that affects the convergence of the iterative method to the numerical solution, and is intended to improve the convergence.
Scaling: A technique applied to a coefficient matrix so that a convergence solution algorithm can find a stable solution.
Ordering: A technique for changing the order of rows and columns in a coefficient matrix, mainly for the purpose of improving solution efficiency.
Conversion formula: Conversion of a coefficient matrix into an equivalent expression mainly in order to improve solution efficiency and transform equations into a form that is easy to solve.
Others In the current state of the system of the present embodiment, preprocessing is implemented. Other techniques will be introduced in the future. The pre-processing program is prepared as an executable program in the providing computer system 1 using Lis as in the solution method.

As a specification of Lis, preconditionID is attached to the preprocessing (preconditioner) as follows. The 2-digit numerical value in [] is precondID.
none [00] (no preprocessing), PJacobi [01], ILU [02], SS
OR [03], Hybrid [04], I + S [05], SAINV [06], SA
AMG [07]

Thus, the storage means 11 for each convergent solving algorithms, problems to be solved, the parameter 21 set for each item of the techniques in combination with solutions and solutions, are set for each parameter, the convergence graph, CPU time and convergence required number It is configured to store an operation specification factor for determining an operation specification and a computer program for calculating a convergence graph, a CPU time and a required number of times of convergence associated with a combination of operation specification factors selected from each item.

  The arithmetic processing means (1) 12 includes an input data file 25 and an executable program file 26. The executable program file 26 is a file storing a solution and a technique used in combination with the solution, and the input data file 25 is a file storing data of a problem to be solved. These files are known matters.

  FIG. 2 is a flowchart showing details of the arithmetic processing means (1) 12. In FIG. 2, the execution format program 26 uses matrixes A, B, C... (Add32 described later) of the input data file 25 and IDs 00, 01, IDs of techniques used in combination with the solution ID 01, 02. ..., 07 are sequentially selected and executed.

  An operation specification factor that is set for all combinations of the solution groups (01-12) and techniques (00-07) for each matrix, that is, for the aforementioned parameters, and determines the operation specifications of the convergence graph, CPU time, and number of times required for convergence. Solve by applying a combination of (factors) to generate data.

5) Input data file This is the actual file of section 2) “Problems to be solved”.
The file prepared here becomes the input data for the execution format program of item 6).

6) Execution format program file A solution expressed in a computer language and a technique used in combination with the solution are prepared as an executable format file.
In the case of Lis, the program is composed of C language and Fortran 90 programs. A main program for solving linear equations is created in these programs, and compiled to create an executable program (load module) file. Here, a commercial or free compiler can be used.

  As described above, the arithmetic processing means (1) 12, which is the arithmetic processing means, uses a computer program, the convergence graph associated with the combination of the operation specification factors selected from each item, the CPU time, and the required number of times of convergence. An arithmetic process is performed on.

  A file of various calculation results generated by the providing-side computer system 1 is stored. When there is a search execution request from the client terminal (display device), a database file search is performed via the providing computer system 2, and necessary data is passed to the providing computer system 2. .

  In the present state of the system of this embodiment, this database 13 is incorporated in the providing computer system 2, but in the future only the database may be a single system.

  An example of the provision status and the internal format of the data file when it is put on the database 13 will be described with reference to FIGS.

FIG. 4 shows an information provision situation when the information is placed in the database 13. As described above, the setting 31 of the problem to be solved, the setting 32 of the solving method, and the setting 33 of the technique used together with the solving method are performed, and the calculation processing 34 in the calculation processing means (2) 12 is performed. The matters described in FIG. 4 are as follows.
○ Setting of problem to be solved (internally expressed by matrix name. Example of matrix name: add32)
Specific examples of other matrix names include the following names.
138_bus, 494_bus, 662_bus, 685_bus, add20,
add32, bcsstk14, bcsstk15, bcsstk16, bcsst
m26, gr_30_30, memplus, nos1, nos2, nos3, no
s4, nos5, nos6, nos7, s1rmq4m1, s1rmt3m1, s2
rmq4m1, s2rmt3m1
(All are matrices provided by Matrix Market)

○ Solution method setting (internally expressed by solution ID. Solution ID example: 04 for BiCGStab)
In the system of this embodiment, there are 12 types of solutions.
Setting of the technique to be used together with the solution (internally expressed by technique ID. Example of technique ID: 01 for PJacobi)
In this embodiment system, there are eight types of this technique (pre-processing).
Handling by arithmetic processing means (1) Stored as the following text file.

○ Setting of values for each parameter matrix = add32, solverID = 04, precondID = 01
○ Configuration of file name to be searched matrix-solverID precondID0000. xxx
(Specific example: add32-04010000.xxx)
Here, xxx is an extension indicating the file type.
sol: file storing solution vectors rsd: file storing residual norm information for each iteration (convergence graph data)
log: A file 0000 storing data such as CPU time and the number of times of convergence is prepared as a spare.

In this embodiment, 96 types of combinations are possible with 12 types of solution methods × 8 types of techniques, and files having three types of extensions are configured for each. The number of files can be increased or decreased by the number of solutions / techniques and extensions.

FIG. 5 shows an example of internal formation of each file (all text data). As shown in FIG. 5, the number of required convergence times and CPU time are stored in relation to the operation specification factor.
As described above, the database 13 stores the data about the convergence graph, the CPU time, and the required number of times of convergence in association with the combination of the operation specification factors selected from the respective items, which are the calculation results of the calculation processing means.

Next, the providing computer system 2 will be described.
The arithmetic processing means (2) 14 performs control using a parameter item setting screen, which will be described later, and selects each parameter item, sets an operation specification factor, and configures a file name to be searched. That is, a file is created from the setting parameters.

  In response to a search execution request from a client terminal 200 (display device), which will be described later, a database file search is performed, and necessary data is received from the file, and the data is processed so that it can be displayed on the client terminal 200 (display device). Details will be described below.

  FIG. 6 shows an information retrieval system for evaluating the performance of a linear equation algorithm, and shows a screen for parameter input, operation specification factor input and data search, and display request (screen of setting screen display means of a screen display device) in the case of a linear equation. ing. The screen display and various controls use free software php, and the screen display conforms to the display specifications of html. ((1)) to ((5)) in the figure are also execution procedures, and their contents are as follows. In addition, (()) is indicated by a circle in the figure.

((1)) The display item of the result processed by this system is selected.
((2)) The problem to be numerically calculated is selected from the pull-down menu (in FIG. 6, the matrix “add32” is selected as the operation specification factor in the coefficient matrix of the linear equation). In this example, the default value of the used numerical calculation library Lis is used for the right-hand side term and the initial value.
((3)) Select the solution from the pull-down menu (in FIG. 6, “CG” and “Bi
CGStab "is selected)). However, only the top column selects all solutions and uses the same technique (see ((4)) below).
((4)) Select a technique to be used together with the solution from the check boxes (in FIG. 6, “PJacobi” and “SSOR” for the CG method and “none (no preprocessing)” for the BiCGstab method. Two types of pre-processing techniques, “ILU” were selected).
However, in the top column only, only one type of pre-processing is selected for all solutions as described above.
((5)) A button for requesting data search and result display.

  In FIG. 6, “red” is an item displayed in red on the screen, and indicates “all results”, “All solvers”, and “none” on the screen. All is a case where all combinations are selected and has a high priority. It is assumed that one column of pre-processing can be selected for Solution 1, and a plurality of input columns are prepared to correspond to the number of solutions selected.

An example of the result display executed with this setting is shown in FIG.
The details of the above ((1)) to ((2)) are as follows, and each parameter and the value stored in them control the providing side computer system 2 using the function (known) of php. Passed to the program as an array of parameter passing handlers.

The matters described in FIGS. 7 and 8 are as follows.
((1)) Display Item The following ID is substituted for the parameter “SEL”. The numerical value in [] represents the ID assigned to SEL.
All results [99]
Convergence graph [1]
Data table [2]
Output data [3]
((2)) Selection of matrix (matrix among problems to be solved)
The matrix name is substituted for the parameter “matrix”.
As shown in the figure, the matrix names are arranged in the menu, and the selected matrix name is substituted into the parameter matrix.
Default values are prepared for the right-hand side term, initial value, and the like. In the present embodiment system, only default values are valid for these.

((3)) Solution (Figure 8)
As shown in FIG. 6, the solution names are arranged in the menu, and the selected solution is substituted into the parameter “solverID” as a 2-digit ID. Here, a plurality of solutions can be selected, and the parameter solveID is in an array format. Specific correspondence between the solution name and the ID is as follows, and the numerical value in [] is the ID.
CG [01], BiCG [02], CGS [03], BiCGStab [04], B
iCGStab (l = 2) [05], GPBiCG [06], Orthomin [
07], GMRES [08], TFQMR [09], Jacobi [10], Gau
ss-Seidel [11], SOR [12]
In the present embodiment system, the value of the parameter l in the BiCGStab (l) method is l = 2.
If “All Solvers” (all solution methods) is selected as the operation specification factor in addition to selecting individually, [99] is set as the solution ID and solveID [0] = 99.
For example, when individual selections are made as shown in FIG.
Select “CG” as the first solution → solverID [1] = 01
Select “BiCGStab” as the second solution → solverID [2] = 04

((4)) Pre-processing (technique used in combination with solution) (Figure 8)
As shown in FIG. 6, the preprocessing names are arranged in a check box, and the ID of the selected preprocessing is substituted for the parameter “precondID”. Here, a plurality of pre-processing can be selected, and the parameter precondID is in an array format. The specific correspondence between the preprocessing name and the ID is as follows, and the numerical value in [] is the ID.
none [00] (no preprocessing), PJacobi [01], ILU [02], SS
OR [03], Hybrid [04], I + S [05], SAINV [06], SA
AMG [07]
When “All” (all pre-processing) is selected in addition to selecting individually, [99] is set as the pre-processing ID.

When the pre-processing corresponding to the solution selected individually in the above “((3)) solution” is selected, for example, “CG” is selected as the first solution, and “PJacobi” is used as the pre-processing combined with it. And “SSOR” are selected → predID [1] [0] = 01, predID [1] [1] = 03
“BiCGStab” is selected as the second solution, and “none (no pre-processing)” and “ILU” are selected as pre-processing to be used together with it → precondID [2] [0] = 00, precondID [2] [1 ] = 02
The index of the array starts from 0 according to the specification of php of the control language system to be used, but substantially points to the first.
Other techniques used together with the solution method (scaling, ordering, etc.) are not implemented in the present system, but may be implemented in the future.

((5)) Button for requesting data search and display

Next, selection of each parameter item and setting of operation specification factors will be described.
The parameter passed from the client terminal 200 (display device) is analyzed using the function of the free software php.

All the parameters set in the input screen of FIG. 6 and the values (operation specification factors) stored in them are stored in the parameter passing handler array (the operation specification of php, which is publicly known). Each parameter and variable value are received from the handler array (explained here by the array name “POST”).
The display format selected in ((1)) stores a value in the parameter “SEL” (SEL = POST [SEL]).
The matrix name selected in ((2)) is stored in the parameter “matrix” (matrix = POST [matrix]).
The solution name selected in ((3)) stores the solution ID in the parameter “solverID” (array format) (same).
For the technique name selected in ((4)), the technique ID is stored in the parameter “precondID” (array format) (similar).

The order of control within the providing computer system 2 is as follows:
(1) Receiving the value of parameter “matrix” (2) Receiving the value of parameter “solverID” and analyzing the number of solutions (number of elements in the array) (3) Receiving the value of parameter “precondID” and the number of solutions ( Number of elements in the array)
(4) Reception of the value of the parameter “SEL” and control according to the value, and the processing contents thereof are shown in FIGS. Items described in FIGS. 9 to 12 are shown below.

About Figure 9:
(1) Receiving the value of the parameter “matrix” matrix = POST [matrix]
Example: In the case of FIG. 6, after this reception, “matrix = add32” is substituted.
(2) Receiving the value of the parameter “solverID” and analyzing the number of solutions (number of elements in the array) Using the function of php, the size (number of solutions) of solveID [SS] is counted (using the function of php) A known technique), the character string SS is a parameter indicating the order of the selected solution (not the solution ID, but the order of the solutions selected in FIG. 6).
When the solution ID is other than “99”:
(At this time, solverID [0] = 0 is substituted)
For example, if the input is as shown in the screen of FIG.
“CG” was selected as the first solution → solverID [1] = POST [solverID [1]]
At this time, solverID [1] = 01 is substituted.

“BiCGStab” was selected as the second solution → solverID [2] = POST [solverID [2]]
At this time, solverID [2] = 04 is substituted.

When "99" exists in the solution ID:
(When all solutions are selected, solver [0] = 99 is assigned at this time)
j = 1, 2,..., 12
POST [solverID [j]] = 2 digit value of j
→ (Example: 01, 02, ..., 12)
At this time, solverID [1] = 01, solverID [2] = 02,..., SolverID [12] = 12.

About FIG. 10:
(3) Receiving the value of the parameter “precondID” and analyzing the number of preprocessing (number of elements in the array) Using the function of php, the size of precondID [SS] [PP] (preprocessing selected for each solution) Count). SS is the order of the solution selected in (2), and PP is a parameter indicating the order of preprocessing selected for each solution.

When pre-processing corresponding to the solution selected in the previous item (2) is selected, for example, when “99” exists in the solution ID in (2) (when solverID [0] = 99):
When “Hybrid” (ID = 04) is selected as the pre-processing used in combination with the entire solution,
precondID [1] [0] = POST [precondID [0] [0]],
precondID [2] [0] = POST [precondID [0] [0]],
...
precondID [12] [0] = POST [precondID [0] [0]],
At this time, precondID [1] [0] = 04, precondID [2] [0] = 04,..., PrecondID [12] [0] = 04
And Hybrid ID is substituted for all.

  Depending on the specifications of the php of the control language system to be used, the index of the preprocessing array starts from 0, but substantially points to the first.

About Figure 11:
In (2), when “99” does not exist in the solution ID (when solverID [0] = 0):
When [99] does not exist in the preprocessing ID (when selected in FIG. 6):
“CG” is selected as the first solution, and “PJacobi” and “SSOR” are selected as preprocessing to be used together with it. PrecondID [1] [0] = POST [precondID [1] [0]],
precondID [1] [1] = POST [precondID [1] [1]],
At this time, precondID [1] [0] = 01 (PJacobi) and precondID [1] [1] = 03 (SSOR) are substituted.

“BiCGStab” is selected as the second solution, and “none (no pre-processing)” and “ILU” are selected as pre-processing to be used together with it. PrecondID [2] [0] = POST [precondID [2] [0] ],
precondID [2] [1] = POST [precondID [2] [1]],
At this time, precondID [2] [0] = 00 (none) and precondID [2] [1] = 02 (ILU) are substituted.

  Depending on the specification of php of the control language system to be used, the index of the preprocessing array starts from 0, but substantially points to the first.

When [99] exists in the preprocessing ID (when all preprocessing “All” is selected):
Once again, the IDs of all pre-processes are stored. In the following example, the storage of the preprocessing ID when all preprocessing is selected for the first selected solution will be described.

j = 0, 1,..., 7
POST [precondID [1] [j]] = 2 j digit value
→ (Example: 00, 01, ..., 07)
At this time,
precondID [1] [0] = 00, precondID [1] [1] = 01,..., precondID [1] [7] = 07
And IDs of all the preprocessing are substituted.

About FIG. 12:
(4) Receiving the value of the parameter “SEL” and the control according to the value SEL = POST [SEL] The value of the parameter SEL is received.

1) When the value of SEL is 1 or 99, graph drawing processing is executed.
1) “loop_solpre” in FIG. 13 is executed.
2) For the data to be graphed, plot the file with the “.rsd” extension in Figs.
3) In graph drawing, free software gnuplot is used.
4) The control of gnuplot is controlled by the input data (gn
generate and execute an uplot control program).

2) When the value of SEL is 2 or 99, a process for creating and displaying a data table is executed.
1) “loop_solpre” in FIG. 13 is executed.
2) Data such as CPU time and number of times required for convergence are converted into a table format.
4 and 5 are stored in files with the extension “.log”. The relevant data is extracted from this file using the php function.

3) When the value of SEL is 3 or 99, the process of displaying the output data list is executed.
1) “loop_solpre” in FIG. 13 is executed.
2) Files All the files with the “.log” extension in Figs. 4 and 5 are displayed on the screen.

FIG. 13 shows processing for constructing a file name to be searched.
The above-described parameters are received, a file name for accessing the database is constructed using the “loop_solpre” program shown in FIG. 13, and a file search is performed.
From the information obtained by the “loop_solpre” program, a database file is searched using (A).
When displaying each result, the algorithm name is displayed using (B).

Here, the method of constructing the file name from the parameter values is the same as in FIG.
These controls use free software called php.
In this way, as shown in FIG. 6, each parameter display means, each parameter selection means, convergence graph, CPU time, and the required number of times of convergence, or a combination display means of these and any of these Setting screen for simultaneously displaying on one screen selection means for selecting, display means for displaying a plurality of combinations of operation specification factors in a form in which each parameter is combined, and selection means for selecting one or more of any combination Display means are configured.

  In addition, when one or more of parameters, a convergence graph, CPU time and the number of required convergence times, or a combination thereof, and a combination of operation specification factors for each parameter are selected on the screen, these Data acquisition processing means for searching and acquiring data stored in the database for the combination is configured.

  The setting screen display means displays a plurality of the operation specification factors of the parameters for the solution in parallel, and the operation specification factors of the parameters for the technique used in combination with the solution are displayed for each of the plurality of operation specification factors in parallel. A plurality of operation specification factors are displayed as the operation specification factor of the parameter for the technique used in combination with this solution.

Next, the result display unit 15 will be described.
FIG. 14 shows a search result display example.
FIG. 14 is a result display when a search is executed with the settings as shown in FIG. 6, and is based on a convergence solution algorithm that combines the selected solution and the preprocessing technique used in combination with them. A convergence graph and a table listing information such as CPU time and the number of required convergence times are displayed on the screen. For reference, when only “convergence graph” is selected in ((1)) of FIG. 6, only the upper part of the convergence graph of FIG. 14 is displayed, and “Data Table” and below are not displayed.

The vertical axis of the graph is obtained by calculating the 2-norm of the residual vector calculated in the convergence solution algorithm (known evaluation method) and taking the log 10 of the value. The horizontal axis represents the number of iterations of the iterative solution.

The items in the “Data Table” table are as follows.
No. Number assigned to the selected convergence solution algorithm Prec-Solver convergence solution algorithm name. The selected solution and
Name combining the preprocessing techniques used.

Iter. Number of times required for convergence. The approximate solution obtained by the convergence solution algorithm converges
The number of iterations it took to complete. For residual vector of convergence solution algorithm
On the other hand, the convergence judgment is 10 minus 12 (representation on the computer
Then, it determined by 1.0e-12).

Cpu time Represents the CPU time [unit: seconds] required to converge.
Res. norm True residual value. The residual vector in the convergence solution algorithm
Even if it is originally determined to converge, the true value obtained by substituting the obtained approximate solution
The residual (b−Ax) may be far from convergence.
The

Status Converged from the value of the true residual (conv.) Or apparently converged (n
o conv. ) Or not converged at all (“max.itr. (
Reaching the upper limit of the number of iterations) ”“ brk.dwn. (Breakdown:
Some numerical instability made it impossible to continue the iterative calculation) "
) Is displayed.

FIG. 15 is a screen continued from FIG. 14 (when the screen is scrolled, the table at the beginning is duplicated).
FIG. 15 shows a data table and a bar graph indicating CPU time. When only “data table” is selected in ((1)) of FIG. 6, only the table and bar graph of FIG. 15 are displayed.
A bar graph is displayed to make it easy to visually compare and evaluate each CPU time with the Data Table number as the horizontal axis.
The display of “Converged: 1, 2, 3, 4” at the bottom of the figure indicates the number of the converged numerical calculation algorithm.

  FIG. 16 is a screen further continued from FIG. 15 (screen scrolled), which shows the contents (Output data) of the file with the extension “.log” in FIGS. 4 and 5 as they are.

If only “output data” is selected in ((1)) of FIG. 6, only “Output data” shown in FIG. 16 is displayed.
The result screen display means 15 is edited so that necessary information can be displayed on the screen according to the value of the parameter SEL. In the system of this embodiment, these controls use php, and output according to the specifications of html for screen display.

  When displaying the residual data (in FIG. 5, “add32-04010000.rsd”) representing the state of convergence of the iterative solution from the database 13, free software gnuplot is used. An input file necessary for executing gnulot is also created by using the php function to create a temporary file, and using this, image data (binary format) is generated from the residual data (text format) and displayed on the screen.

  When displaying data such as the CPU time and the number of times of convergence, the relevant part is extracted from a log file in text format (in FIG. 5, “add32-04010000.log”) and displayed on the screen as a table format. .

  As described above, the result screen display means 15 displays any one of the convergence graph, the CPU time and the required number of convergence, or a combination thereof based on the data acquired by the data acquisition processing means. A plurality of convergence graphs are simultaneously displayed on the screen of the result screen display unit 15 based on a plurality of combinations of the operation specification factors.

Next, the client terminal 200 will be described with reference to FIG. The client terminal 200 includes a display device 51. The display device 51 displays a problem display 52, a parameter item selection 53, a search result display 54, and a more appropriate convergence solution algorithm selection display 55.

  As shown in FIG. 2, the client terminal 200, that is, the display device 51 sets the operation specification factor 61 of each parameter, makes a search request to the providing computer system 2 according to the search execution instruction 62, and returns the returned result. Display 63 (search result display) is performed as a search result.

1) Problem display In the elucidation of natural phenomena and engineering phenomena, analysis using convergence solution simulation is popular. These simulations often result in solving many types of convergence solutions, including linear equations and eigenvalue problems. However, taking a linear equation as an example, there are various convergence solution algorithms, and depending on the nature of the problem to be solved, there are cases where the performance is not fully exhibited. The same situation applies to convergence solutions other than linear equations. Therefore, in an actual convergence solution simulation, a guideline is desired as to which convergence solution algorithm should be applied. The client displays a problem on the client terminal 200.
2) Select other parameter items:
Referring to FIG. 6, a type of problem similar to the nature of the problem to be solved is selected. In other words, parameter items and operation specification factors for each parameter item are selected. Thus, a search request is made.
3) Search result display:
The search results are fed back through the communication means and displayed on the screen of the display device 51 as shown in FIGS.
4) Reselection of convergence solution algorithm:
With reference to the search result, a convergence solution algorithm that seems to be suitable for solving the problem is selected, a search request is made again, and the search result is displayed.

  In FIG. 2, in the providing side computer system, an input parameter analysis 71 is performed by selecting an input parameter item and an operation specification factor for each parameter item. The corresponding file is searched 72 to search the database 13 for the corresponding file as data. The target data is edited 73 for display. The edited result is fed back to the client terminal as a search result, and a search result display 63 is made.

Thus, the convergence solution algorithm performance display device 100 can select any one of the selection means displayed on the screen of the setting screen display means by a command signal from the client terminal via the communication means.
The following convergence solution algorithm performance display method is configured by the convergence solution algorithm performance display device configured as described above.

Determined by the storage unit 11, for each convergent solving algorithms, problems to be solved, the parameters were set for each item of the techniques in combination with solutions and solutions, we are set for each parameter, the convergence graph, the operation specifications of the CPU time and convergence required number A computer program for calculating a convergence graph, a CPU time and a required number of times of convergence associated with a combination of an operation specification factor to be selected and an operation specification format selected from each item;

  The arithmetic processing means (1) 12 performs arithmetic processing on the convergence graph, CPU time, and required number of times of convergence associated with the combination of the operation specification factors selected from the respective items, using the computer program.

  The database 13 stores data on the convergence graph, the CPU time, and the required number of times of convergence in association with the combination of the operation specification factors selected from each item, which is the calculation result of the calculation processing means.

  By means of the setting screen display means of the arithmetic processing means (2) 14, each parameter display means and each parameter selection means, the convergence graph, the CPU time and the required number of times of convergence, or a display means of a combination thereof, and of these A selection means for selecting any one of the above, a display means for displaying a plurality of combinations of the operation specification factors in a form in which each parameter is combined, and a selection means for selecting one or more of any combination on one screen. Display at the same time.

  By the data acquisition processing means of the arithmetic processing means (2) 14, any one of the parameters, the convergence graph, the CPU time and the required number of times of convergence, or a combination thereof, and each parameter in the combined form are displayed on the screen. When one or a plurality of combinations of the operation specification factors are selected, processing for searching and acquiring data stored in the database for these combinations is performed.

  The result screen display means 15 displays any one or a combination of the convergence graph, CPU time and required number of convergence based on the data acquired by the data acquisition processing means.

  With the above configuration, any selection means displayed on the screen of the setting screen display means is selected and operated by a command signal from the client terminal via the communication means.

The block diagram which shows the structure of the Example of this invention. FIG. 2 is a flowchart showing a part of FIG. 1 in detail. The figure which shows the example of the numerical algorithm of the conjugate gradient method with preprocessing. The figure which shows the information provision condition at the time of putting in a database. The figure which shows the condition where the convergence required frequency and CPU time are stored in relation to the operation specification factor. The figure which shows the screen of parameter input in the case of a linear equation, operation specification factor input, and a data search and display request. The example which substitutes the value of ((1)) and ((2)) for the parameter in the screen of FIG. An example of substituting the values of ((3)) to ((4)) into parameters on the screen of FIG. The figure explaining reception of a parameter value, reception of a parameter value, and analysis of the number of solutions (number of elements of an array). The figure explaining reception of the value of a parameter, and analysis of the number of preprocessing (the number of elements of an array). An explanatory view when “99” does not exist in the solution ID in (2). The figure explaining reception of the value of parameter "SEL", and control according to the value. The figure of the process which comprises the file name which is search object. FIG. The figure which shows the screen which continues from FIG. The figure which shows the screen which continues from FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Memory | storage means, 12 ... Arithmetic processing means (1), 13 ... Database, 14 ... Arithmetic processing means (2), 15 ... Result screen display means, 20 ... Convergence solution algorithm, 21 ... Parameter, 22 ... Problem to be solved, 23 ... Solution method, 24 ... Technique used in combination with the solution method, 25 ... Input data file, 26 ... Execution format program file, 51 ... Display device, 52 ... Display of problem, 53 ... Selection of parameter items, 54 ... Display of search result, 55 ... selection and display of more appropriate convergence solution algorithm, 61 ... setting of operation specification factor (for example, value) of each parameter, 62 ... search execution instruction, 63 ... search result display, 71 ... input parameter analysis, 72 ... corresponding file search 73 ... Editing target data for display, 100 ... Convergence solution algorithm performance display device, 200 ... Client terminal.

Claims (5)

It displays the performance of the convergence solution algorithm for convergence solution,
The problem to be solved by the convergence solving algorithm, the pre-processing for improving the convergence that is used together with the solution and the solution, the scaling applied to the coefficient matrix, the ordering for changing the order of the coefficient matrix and the rows and columns, and any combination of the conversion formulas Storage means for arranging and storing menu items of a technique to be performed,
Each or all of the display items of the convergence graph showing the convergence status, the CPU time to convergence and the number of convergence iterations that are the number of iterations until the convergence, and the problem to be solved, the solution and the technique used in the solution are arranged A display means for displaying the menu item, a convergence graph from the display item, any or all items of the CPU time and the required number of convergence times for convergence, and a problem to be solved, selected from the arranged menu items, A setting screen display means having a parameter selection means for displaying the parameter items of the technique used in the solution and the solution,
Receive the selected parameter item, form a combination of the parameter item of the technique to be used together with the solution method for the problem to be solved, and acquire one of the convergence graph data, the CPU time and the required number of convergence times in each combination Or an arithmetic processing means for performing the entire arithmetic processing and storing the arithmetic results in the database, and
A convergence solver algorithm performance display device comprising: a result screen display means for receiving a calculation processing result of each combination and displaying the calculation processing result of each combination on the screen . According to claim 1, wherein the result screen displaying means converges solving algorithm performance display device and displaying a plurality of convergence graphs simultaneously using convergence graph data processing on the screen. Oite to claim 1, wherein the result screen displaying means converges solving algorithm performance display device characterized by simultaneously displaying a plurality of CPU time or converge required number of times on the screen. In any one of claims 1 to 3, the setting screen displaying means is converged solving algorithm performance for causing selected as parameter items for display items with reference to the command signal from the client terminal via the communication means Display device. In the convergence solution algorithm performance display method by the convergence solution algorithm performance display device according to claim 1 ,
The setting screen display means displays a convergence graph, a display item for any or all of the CPU time to convergence and the number of times required for convergence, and the arranged menu items for the problem to be solved, the solution, and the technique used in the solution. A problem to be solved, a solution and a technique selected from the display items to the convergence graph, any or all items of the convergence time, CPU time to convergence, and the number of times required for convergence, and each arranged menu item Display the parameter item of
The arithmetic processing means receives the parameter item, forms a combination of the parameter items of the technique used in the solution and the solution, and obtains the convergence graph data in each combination, CPU time and acquisition of the required number of convergence or Perform all computations, store computations in the database,
A method for displaying a convergent solution algorithm performance, wherein the result screen display means receives an arithmetic processing result of each combination and displays the arithmetic processing result of each combination on a screen .

Images