JP4576536B2 - Performance comparison display device and performance display comparison system for convergent solution algorithm - Google Patents

Description

The present invention relates to a convergence solution algorithm performance comparison display device, a convergence solution algorithm performance comparison display device , a performance display comparison system, and a convergence solution algorithm performance comparison display method.

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

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 asymmetric, it can be solved quickly and accurately by selecting which convergence solution algorithm. I do not know.

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 study how to solve the problem.

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.

In view of this point, the present inventor previously solved the problem quickly by using the convergence solution algorithm that exists in a variety of ways in response to the needs of the algorithm user. convergence solving algorithm performance comparison display device or the focus solving algorithm performance comparison display method using the convergence solving algorithm performance comparison display device can have filed a patent application to provide.

The present invention further convergence solving algorithms capable of displaying the result by performing a performance comparison for the purpose of using the convergence solving algorithms of interest hitting the performance comparison display of the above convergence solving algorithm performance comparison display or / Another object of the invention is to provide a convergent solution finding algorithm performance comparison display method using the convergence solving algorithm performance comparison display device.
[Means for solving problems]

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,
Display means for displaying any or all of the display items of the CPU time to convergence and the number of times of convergence that is the number of iterations of computation until convergence, the problem to be solved, the solution method, and each arranged menu item of the technique used in the solution method And any or all of the CPU time and the required number of times of convergence from the display items, and the problem item to be solved, the solution method, and the parameter item of the technique used in the solution method selected from each of the arranged menu items. A setting screen display means comprising a parameter selection means,
Receiving the selected parameter item, forming a solution for the problem to be solved and a combination of techniques used in the solution, and performing any or all of the calculation processing to obtain the CPU time and the required number of convergence times for each combination An arithmetic processing means for performing arithmetic processing of a relative determination value by comparing the processed values and storing the arithmetic result in a database; and
Receiving the calculation result of the relative judgment value of each combination, and displaying the calculation result of each combination on the screen,
XY formed by both parameter items on the XY coordinate axis in which the parameter items of the problem to be solved on the Y axis and the respective parameter items of the technique used in the solution and the solution method are set on the X axis Result screen display means for displaying the performance comparison result for the CPU time or the required number of convergence times for the problem to be solved at the coordinate position on the screen with the relative judgment value obtained by the arithmetic processing,
A convergence solving algorithm performance display device characterized by comprising:

Further, according to the present invention, whether the arithmetic processing means is within a range of a reference value of a true residual norm set by the acquired CPU time or the required number of convergence times before the arithmetic processing of the relative determination value . A convergence solving algorithm performance comparison display device characterized in that it is determined whether or not it is out of range.

Further, the present invention is the result screen displaying means, on a screen, a by the X-Y coordinates of the relative determination value to be displayed on the position result corresponds to a determination value to be displayed in different colors for each said position A characteristic convergence solving algorithm performance comparison display device is provided.

Further, the present invention is the result screen displaying means, a combination of CPU time and convergence required number on the screen, convergence solving algorithm performance comparison and displaying a relative judgment values obtained by the arithmetic processing A display device is provided.

Further, the present invention is the result screen displaying means, the convergence solving algorithm performance comparison display grouped according to claim you to view the CPU time or converge required number for each techniques for solving each and combination on the screen provide.

Further, the present invention provides the convergence solution algorithm performance display device, and
Consists of a client terminal connected via a communication means to the convergence solution algorithm performance display device,
The client terminal is selectable via the communication means for the selection means displayed on the screen of the setting screen display means of the convergence solution algorithm performance display device, and the result screen display means of the client terminal Displaying the performance comparison result of the performance comparison for the CPU time or the required number of convergence times displayed on the result screen display means of the solution solving algorithm performance display device
A convergent solution algorithm performance display system is provided.

Further, the present invention provides a convergence solution algorithm performance display method by the convergence solution algorithm performance display device,
Arithmetic processing means receives the selected parameter item, forms a combination of a solution for the problem to be solved and a technique used in the solution, and obtains the CPU time and the required number of convergence times of each combination or all of the arithmetic processing , Perform a relative decision value calculation process by comparing the calculated values, store the calculation result in the database,
The result screen display means receives the calculation processing result of the relative determination value in each combination, and displays the calculation processing of each combination,
XY formed by both parameter items on the XY coordinate axis in which the parameter items of the problem to be solved on the Y axis and the respective parameter items of the technique used in the solution and the solution method are set on the X axis Display the performance comparison result of the CPU time or the required number of convergence times for the problem to be solved at the coordinate position on the screen with the relative judgment value obtained by the above arithmetic processing.
Providing convergence solving algorithm performance comparison display method comprising.

Further, according to the present invention, the arithmetic processing means is within a range of a reference value of a true residual norm set for the acquired CPU time or the required number of convergences before the arithmetic processing of the relative determination value. A convergent solution algorithm performance comparison display method is characterized in that it is determined whether or not it is out of range.

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. hitting to solving the problem by using an algorithm, within acceptable precision, performance comparison convergence solving algorithm of the target, relative determination convergence solving algorithm performance comparison display device capable of performing, or comparative convergence solving algorithm performance A convergence solution algorithm performance comparison display method using a display device can be provided.

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

FIG. 1 is a block diagram showing a configuration of a convergence solution algorithm performance comparison display apparatus according to an embodiment of the present invention.

In FIG. 1, the convergence solution algorithm performance comparison 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, and includes the storage means 11 and the arithmetic processing. Means (1) 12 constitutes the providing side computer system 1, arithmetic processing means (2) 14 and result display means 15 constitute the providing side computer system 2 (indicated by numeral 30), and the database 13 is provided by these providing sides. Connected to computer systems 1 and 2 to exchange data. The convergent solution algorithm performance comparison 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 inherent problems (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) Includes numerical algorithm algorithm items other than the above, consisting of solution algorithm items. Each item is stored in association with each parameter. The parameter 21 is constituted and represented 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 steady iteration method, and a steady iteration method. The items of the technique 24 configured, expressed, and used in combination with the solution are configured and expressed as 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 finding efficiency, a convergence solution algorithm of “a conjugate gradient method with preprocessing” is shown in FIG. (The conjugate gradient method is also called a CG method, and “CG” is also displayed in each description 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 , α _k , and β _k other than these 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 || 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. .

In the convergence graph, the norm of the residual vector || r _k || was stored in the data file (file with the extension “.rsd” in FIGS. 6 and 7) at each iteration, and its log 10 (common logarithm) was taken. Plot things. 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 such cases, evaluate with the true residual norm.

を用いて、

を評価したものである。図２０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 norm is the numerical solution obtained by the convergence solution algorithm.

Using,

Is evaluated. “Res. Norm” in “Data Table” of FIG.
(B-Ax) 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.
In the system according to the present embodiment, the matrix uses test site data obtained by collecting test matrices, and finally, about 100 types of matrices are planned to 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, bcsstm26, gr_30_30, memplus, nos1, nos2, nos3, nos4, nos5, nos4, nos5, nos4
(All are provided at 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 method: Gaussian elimination method based on LU decomposition, Gaussian elimination method based on Cholesky decomposition, etc. Stationary iterative solution method: Jacobi method, Gauss-Seidel method, SOR method, etc. Nonstationary iterative solution method: CG method, BiCG method, CGS method , BiCGStab method, BiCGStab (l) method, GPBiCG method, Orthomin method, GMRES method, TFQMR method, etc. In the present state of the system of this embodiment, a solution program is composed of a steady iterative solution method and a non-stationary iterative solution method. 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], BiCGStab (l = 2) [05], GPBiCG [06], TFQMR [07], Orthomin [08], GMRES [09], Jacobi [10], Gauss-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], SSOR [03], Hybrid [04], I + S [05], SAINV [06], SAAMG [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 block diagram showing a part of the details of the convergence solution algorithm performance comparison display device 100 and the client terminal 200. In FIG. 2, parameter item selection in the parameter 53 is assumed to be parameter item selection (method 1) 53A, parameter item selection (method 2) 53B, and parameter item selection (method 3) 53C. More parameter items may be set.

  The result screen display means 4 includes a result screen display (method 1) 54A and a result screen display corresponding to the parameter item selection (method 1) 53A, parameter item selection (method 2) 53B and parameter item selection (method 3) 53C. (Method 2) 54B and result screen display (Method 3) 54C can be performed.

In parameter item selection (method 1) 53A, for example, 1) setting of display item 2) problem to be solved 3) solution 4) technique used in combination with solution 5) tolerance for true residual norm is selected and set.

Correspondingly, in the result screen display (method 1) 54A showing the contents of the result screen display means 54, for example, 1) convergence graph 2) CPU time 3) required number of convergences 4) true residual norm value is displayed. .

In parameter item selection (method 2) 53B, for example, 1) a problem to be solved 2) an allowable value for the true residual norm is selected and set.

Correspondingly, in the result screen display (method 2) 54B, for example, 1) Convergence solving algorithm 2) Comparison items (CPU time, number of times required for convergence)
3) True residual norm 4) The relative judgment result of 3) is displayed.

In parameter item selection (method 3) 53C, for example, 1) Items for grouping (solution method, combined technique)
2) Items to be compared 3) Tolerance for true norm 4) The nature of the problem to be solved is selected and set.

Correspondingly, in the result screen display (method 3), for example, 1) convergence solution algorithm 2) problem to be solved 3) relative determination result of comparison item 4) set parameter value is displayed.

The database 13 includes a database (1) 13A and a database (2) 13B. The database (1) 13A is a parameter,
1) Convergence graph 2) CPU time 3) Number of times required for convergence 4) True residual norm value is stored in association with each other.

Database (2) 13B is a parameter
1) Nature of problem (1)
2) Nature of the problem (2)
3) Nature of the problem (3)
Are stored in association with each other.

  The providing-side computer system 2 includes calculation processing means (2A) 14A, calculation processing means (2B) 14B, and result screen display means 54A.

The arithmetic processing means (2B) 14A performs determination on the comparison item, rearrangement based on the result, and other calculations.
Creating a database 1, Web site that contains the performance test problem of convergence solving algorithm (for example, MatrixMarket [http://math.nist.gov/MatrixMarket/], University of Florida Sparse Matrix Collection, [http: / /www.cise.ufl.edu/research/sparse/matrices/], Sparse matrix test problems http://users.tkk.fi/~kouhia/sparse.html
In the apparatus of this example, data of Matrix Market is used. ) Is transferred along with the data file of the test questions (characteristics such as matrix size, representative features, spectral characteristics such as eigenvalues, etc.).

  The former is used as an “input data file” of the providing computer system 1. The latter information is formed into a text data file using awk, which is a basic tool of UNIX (registered trademark), and is called a database (2) 13B.

About database (2) 13B:
The “problem to be solved” in the database (2) 13B indicates a “matrix” in the case of a linear equation. Here, the nature 1 and nature 2 of the problem refer to the “size” of the matrix, “representative characteristics of the matrix (symmetric, asymmetric, positive definite, etc.)”, “conditional number”, and the like.
In the database (2) 13B, the name of the problem to be solved (matrix name) is used as a key to associate the properties of the matrix.

Regarding the arithmetic processing means (2B) 14B:
The “allowable value of true residual norm for convergence” set on the input screen shown in FIG. 8 is stored in the parameter “criterion” and received by the arithmetic processing means (2B) 14B.
The algorithm to be compared and determined for the true residual norm is the selected algorithm in the case of Method 1 in FIG. 2, and in the case of Methods 2 and 3, all the algorithms (12 kinds of solution methods) are used. And combinations of all eight types of preprocessing).

1) For Method 1:
The parameter passed from the client terminal (display device) is analyzed using the function of the free software php.
All the parameters set in the input screen of FIG. 8 and the values stored in them are stored in the parameter passing handler array (which is a php operation specification, which is publicly known). Each parameter and variable value is received from an array (explained here by the array name “POST”).
As the display format, a value is stored in the parameter “SEL” (SEL = POST [SEL]).
The matrix name is stored in the parameter “matrix” (matrix = POST [matrix])
As the solution name, the solution ID is stored in the parameter “solverID” (array format) (same).
For the technique name, the technique ID is stored in the parameter “precondID” (array format) (similarly).
The allowable value is stored in the parameter “criterion” (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 ( Analysis of (number of array elements) (4) Receiving value of parameter “criterion” (5) Receiving value of parameter “SEL” and control according to the value.

At this time, if the true residual norm is equal to or less than the criterion, it is determined to have converged, and if the value is larger than the criterion, it is determined to be apparently converged, and the following correspondence is made.
Situation Value to be set for parameter "stat" Parameter "col_stat"
No convergence conv. No apparent convergence no conv. Msg_col (yellow)
Maximum number of iterations mat.itr. war_col (red)
Breakdown brk.dwn war_col (red)
When creating the html of the data table display, the background color of the corresponding line (colored by the function of html) is displayed in the color “col_stat” according to the above situation. A display output example is as shown in FIG.

2) For Method 2:
The parameter input method is as shown in FIG. 9 or FIG. 10 (specifying a matrix name) to be described later. Processing is performed on data of all algorithms (a combination of 12 types of solutions and all 8 types of pre-processing) for one selected matrix. The correspondence between the solution ID, the preprocessing ID, and the algorithm name is performed by “loop_solpre”.

The "true log norm value" and the "criterion" value are compared and determined with the data in the file with the ".log" extension. At this time, if the true residual norm is equal to or less than the criterion, it is determined to have converged, and if the value is larger than the criterion, it is determined to be apparently converged, and the following correspondence is made.
Situation Value to be set for parameter "stat" Parameter "col_stat"
No convergence conv. No apparent convergence no conv. Msg_col (yellow)
Maximum number of iterations mat.itr. war_col (red)
Breakdown brk.dwn war_col (red)
A set of data to be displayed (sequential number, algorithm, number of times of convergence, CPU time, true residual norm value, solution status information, col_stat) is stored in an array (INFO_dat).

Depending on the comparison item (value of sort_key) for the array INFO_dat, the CPU time is sorted in ascending order according to one of the required convergence times (use of the function of php).
After sorting, assign the value of the comparison item of the first record to the parameter “TheFastest” for the records whose col_stat value is NULL (converged), and the relative evaluation index of the comparison items for the subsequent records (Currently “TheFastest ÷ value of comparison item”) is calculated, and the first decimal place is substituted for the parameter “Rat”.
When creating the html of the data table display, the background color of the corresponding row (colored with the function of html) is displayed in the color “col_stat” according to the above-described solution situation. A display output example is as shown in FIG.
For those that have converged, use gnuplot to draw a bar graph of the comparison item data.

3) Method 3:
The parameter input method is as shown in FIG. 10 (when no matrix name is specified).
A matrix name list is acquired from the database (1) 13A. The following processing is performed on the data of all algorithms (a combination of 12 types of solutions and all 8 types of preprocessing) for each matrix.
A set of data to be displayed (record number, algorithm name, number of convergence times, CPU time, norm of true residual, solution status information, col_stat) is displayed in an array (INFO_dat). Store.
Copy the array INFO_dat to create INFO_datO.
“INFO_dat” is sorted in ascending order according to the comparison item (value of sort_key) in ascending order by either of the required convergence times (using a function of php). Then, from the beginning of the record in ascending order, the value of the comparison item of the first record satisfying the condition of INFO_dat [i] [alg] (the solution status, i is the record number) = conv. Is substituted into [TheFastest].

FIG. 3 is a flowchart showing details of the arithmetic processing means (1) 12. 3, the execution format program 26 uses the matrixes A, B, C... (1138_bus 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.

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

5) 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 the computer program to determine the convergence graph, CPU time, and required number of times of convergence associated with the combination of the operation specification factors selected from each item. Perform arithmetic processing.

In FIG. 3, a file of various calculation results generated by the providing computer system 1 (12) is stored in the database (1) 13A. Further, when transmitted from a site 41 that contains the performance test convergence problems solving algorithm provider computer system 1 (12) the performance of the convergence solving algorithm, the providing computer system 1 (12) is organized in file transfers and information The performance test problem of the convergence solution algorithm organized by performing 42 is stored in the database (2) 13B. Further, when a search execution request is received from the client terminal (display device) 200, a file search of the database 13 is performed via the providing computer system 2 (30), and necessary data is obtained from the file search. Passed to 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.

FIG. 5 is a diagram for explaining a flowchart of the embodiment of the present invention described above. In FIG. 5, for the convergence solution algorithm, parameters including comparison items are set on the screen (S1). A true residual norm reference value is set on the screen (S2). It is determined whether the true residual norm value is within the range of the true residual norm reference value (S3), and the numerical algorithm list is rearranged on the screen in the order of the numerical algorithms within the range ( S4). Performance data for comparison items is output for each numerical algorithm or for the convergence solution algorithms in the upper list (these are called target convergence solution algorithms) (S5). Performance comparison between the performance, i.e. to calculate the relative comparison values for the convergence solving algorithm object performs relative determination by relative comparison of the performance of the convergence solving algorithm of the target (relative determination value) (S6). Finally, the target convergence solution algorithm is color-coded on the screen corresponding to the relative comparison and the relative comparison value (S7). In the method 1 in FIG. 2, the processing flow from S1 to S3 described above corresponds. Method 2 corresponds to the processing flow from S1 to S6 described above. In the method 3, all the processing flows from S1 to S7 described above are applicable.

The steps shown in FIG. 5 will be described in detail below.
An example of the provision status and the internal format of the data file when being placed in the database 13 will be described with reference to FIGS.

  FIG. 6 shows an information provision situation when the information is put on the database 13A. As described above, the setting 31 of the problem to be solved, the setting 32 of the solution, and the setting 33 of the technique used together with the solution are performed, and the calculation process 34 in the calculation processing means (1) 12 is performed. The matters described in FIG. 6 are as follows.

○ Problem to be solved 31 (internally expressed by matrix name. Example of matrix name: 1138_bus)
Specific examples of other matrix names include the following names.
1138_bus, 494_bus, 662_bus, 685_bus, add20, add32, bcsstk14, bcsstk15, bcsstk16, bcsstm26, gr_30_30, memplus, nos1, nos2, nos3, nos4, nos5, nos6
(All are provided at Matrix Market)

○ Solution setting 32
(Represented internally by solution ID. Example of solution ID: 04 for BiCGStab)
In the system of this embodiment, there are 12 types of solutions.
Setting a technique to be used with the solution 33
(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.

○ Handling in the arithmetic processing means (1) 34
○ Setting of values for each parameter matrix = 1138_bus, solver ID = 04, precondID = 01
○ Configuration of file name to be searched matrix-solverID precondID0000. xxx
(Specific example: 1138_bus-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 example, there are 12 kinds of solution methods x 8 kinds of techniques, and 96 combinations are possible, 3 for each.
A file with a different type of extension is configured. The number of files can be increased or decreased by the number of solutions / techniques and extensions.
FIG. 7 shows an example of internal formation of each file (all text data). As shown in FIG.
The number of times required for convergence, CPU time, solution status, and norm value of true residual are stored in association with the operation specification factor.
As described above, the database 13A includes a convergence graph, a CPU time and a required number of convergence times, a solution situation, and a true residual in association with the combination of the operation specification factors selected from the respective items, which are calculation results of the calculation processing means. Data on the norm value of is stored.

Next, the provider computer system 2 (30) will be described.
The arithmetic processing means (2A) 14A performs control using a parameter item setting screen, which will be described later, and selects each parameter item, sets operation specification factors, and configures a file name to be searched. That is, the file name is created from the setting parameter.
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.

8 and 9 each show an information retrieval system for linear equation algorithm performance evaluation, FIG. 8 shows an input screen based on the parameter item selection (method 1) shown in FIG. 2, and FIG. 9 shows the parameter item selection shown in FIG. The input screen based on (Method 2) is shown. It represents a parameter input, an operation specification factor input and data search, a calculation result accuracy determination, and a display request screen (screen of a setting screen display means of a screen display device) in the case of a linear equation. The screen display and various controls use free software php, and the screen display conforms to the display specification of html.
In FIG. 8, the circle items are selected or set.

A double circle item is a column for setting an allowable value of the true residual norm in convergence. The content of the result output in FIG. 22 differs depending on the setting of this value.
This double-circled item indicates an allowable value for “true residual norm”. Even if the norm of the residual used in the algorithm has converged, it has converged when the true residual norm obtained by substituting the solution obtained at that time into the original linear equation is evaluated. In many cases, it is determined that there is no.
The value specified here is assigned to the parameter “criterion”.

9 is different from FIG. 8 in that a circle is selected. When this item is checked, a list of results is displayed in ascending order of the item to be compared ("CPU time" or "Convergence required number of times") for all algorithm combinations (currently 96 solutions with 12 solutions x 8 preprocessing). To do.
In this figure, “CPU time” is set in ascending order (early order). The other is arranged in ascending order of “the number of times required for convergence” (the order of convergence in a smaller number of times).
In the screen display control, there are the following two types of options.
"All results (convergence graph data table output table)
Or [Sort in ascending order of [CPU time. Convergence count] (selection menu)]
If neither is selected, the default is “all results”.

1) When “all results” is selected (FIG. 8):
19 to 21 are displayed (more specifically, among “all results”, the items “convergence graph” in FIG. 19, “data table” in FIG. 20, and “output data” in FIG. 21 are individually selected. By setting the “allowable value of true residual norm for convergence” in FIG. 8, the data table display compares the norm value of the true residual vector as shown in FIG. (Accuracy judgment of calculation result) and “convergence converged” and “apparent convergence” are discriminated.

2) When “Sort in ascending order of [CPU time. Convergence required number]” is selected (FIG. 9):
2-1) When sorting in ascending order of CPU time:
FIG. 23 is displayed.
2-2) When sorting in ascending order of convergence required:
The display is the same as in FIG.

FIG. 10 is an input screen based on “parameter item selection (method 3)” in FIG.
In FIG. 9, information for each matrix is displayed. Here, combinations of a plurality of matrices and all solution algorithms are listed using color visualization information based on the relative evaluation index (Rat.) Of the comparison item. To display.

  A circled area is an input item from the selection menu. The contents of the choices of each input item are expressed in units of “solution group” in the selection of the first priority sorting item (first priority grouping item) and the result display, or in the unit of “preprocessing group” Select whether to display with. A comparison item (“CPU time” or “required number of times of convergence”) is selected or a matrix name is selected.

  In FIG. 8, “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.

One example of the result display executed with this setting is shown in FIG.
The matters described in FIGS. 11 and 12 are as follows. The parameters and the values stored in them are passed as an array of parameter passing handlers to a program that controls the providing computer system 2 using the php function (known).

((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 12)
As shown in FIG. 8, 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], BiCGStab (l = 2) [05], GPBiCG [06], TFQMR [07], Orthomin [08], GMRES [09], Jacobi [10], Gauss-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” is selected as the operation specification factor in addition to selecting individually, [99] is set as the solution ID, and solverID [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) (Fig. 12)
As shown in FIG. 8, 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], SSOR [03], Hybrid [04], I + S [05], SAINV [06], SAAMG [07]
If “All” (all pre-processing) is selected in addition to selecting individually, [99] is set as the ID of the pre-processing.

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 factor 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. 8 and the values (operation specification factor) stored in them are stored in the parameter passing handler array (the operation specification of php, 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 provider computer system 2 (30) 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 are shown in FIG. 13 to FIG. Items described in FIGS. 13 to 17 are as follows.

About FIG. 13:
(1) Receiving the value of the parameter “matrix” matrix = POST [matrix]
Example: In the case of FIG. 8, after this reception, “matrix = 1138_bus” is substituted.
(2) Receiving the value of the parameter “solverID” and analyzing the number of solution methods (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. 8).

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 Figure 14:
(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 preprocessing corresponding to the solution selected in the previous item (2) is selected, for example, in (2), when “99” exists in the solution ID (when solverID [0] = 99) (in FIG. 8) When selected):
When “ILU” (ID = 02) 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] = 02, precondID [2] [0] = 02,..., PrecondID [12] [0] = 02.
And the ID of the ILU 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 15:
In (2), when “99” does not exist in the solution ID (when solverID [0] = 0):
When [99] does not exist in the preprocessing ID:
“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.
(4) Receiving value of parameter “SEL” and control according to the value SEL = POST [SEL] The value of parameter SEL is received.

The following 1) to 3) is Method 1.
1) When the value of SEL is 1 or 99, graph drawing processing is executed.
2) When the value of SEL is 2 or 99, the data table is created and displayed. 3) When the value of SEL is 3 or 99, the process of displaying the output data list is executed.
4) When the value of SEL is 90, search result display (method 2) is executed.

  The following 1) to 5) describe the method 2. In the method 1, the same method is used for the value substitution to the parameter “col_stat” and the screen display according to the convergence state.

1) Corresponding solution algorithm names are constructed from all solution IDs (01 to 12) and all preprocessing IDs (00 to 07), and file names for extracting data are also constructed as shown in FIG. The file to be used is a file having a “.log” extension in FIG. 7), and the following information is set every time each file name is configured. In this process, sequential numbers (numbers each time the solution ID and preprocessing ID increase) are assigned.
The “CPU time”, “number of convergence times”, “true norm value of true residual” and parameter “criterion” in the file with the “.log” extension in FIG. 7 were compared and evaluated (same as method 1). Set as shown in the table below according to the results and information on the “solution status”.
Situation Value to be set for parameter "stat" Parameter "col_stat"
No convergence conv. No apparent convergence no conv. Msg_col (yellow)
Maximum number of iterations mat.itr. War_col (red)
Breakdown brk.dwn.war_col (red)
These, the algorithm name (precondNMsolverNM) and the sequential number (num_sel) are also stored in the array.
INFO_dat [num_sel] [num] = num_sel
INFO_dat [num_sel] [alg] = precondNMsolverNM
INFO_dat [num_sel] [itr] = number of required convergence times
INFO_dat [num_sel] [cpu] = extracted CPU time
INFO_dat [num_sel] [rsd] = extracted true residual norm
INFO_dat [num_sel] [sta] = extracted solution status
INFO_dat [num_sel] [col] = col_stat
2) Depending on the comparison item (value of sort_key) for the array “INFO_dat” obtained in 1),
Sort in ascending order (using php function) by either CPU time or number of convergence times.
3) After sorting, assign the value of the comparison item of the first record to the parameter “TheFastest” for records with a col_stat value of NULL (converged), and compare the comparison item relative to the subsequent records. An evaluation index (currently “The Fastest / comparison item value”) is calculated, and the first decimal place is substituted for the parameter “Rat”.
4) The data table of FIG. 24 is displayed in html for each value of Rat. At this time, the background color of the corresponding row is displayed in the color “col_stat”.
5) For those that have converged, draw a bar graph of the comparison item data using gnuplot.
(5) Receipt of parameter “SEL” value and control according to the value
The value of the parameter SEL is received as SEL = POST [SEL].

1) When the value of SEL is 1 or 99, graph drawing processing is executed.
1) The following “loop_solpre” is executed.
2) For data to be graphed, a file with the extension “.rsd” in FIG. 7 is plotted.
3) Use gnuplot of free software for graph drawing.
4) The control of gnuplot generates and executes input data (gnuplot control program) to gnuplot with this program.
2) When the value of SEL is 2 or 99, a process for creating and displaying a data table is executed.
1) The following “loop_solpre” is executed.
2) Data such as CPU time and required number of convergence are displayed in a table format. These data are stored in a file with a “.log” extension in FIG. The corresponding data is extracted from this file using the function of php.
3) The result of comparing and evaluating the “norm value of true residual” and the parameter “criterion” in the file with the “.log” extension in FIG. If the value is larger than the criterion, it is determined to be an apparent convergence.) And the following table is set according to the information of the “solution status”.
Situation Value to be set for parameter "stat" Parameter "col_stat"
No convergence conv. No apparent convergence no conv. Msg_col (yellow)
Maximum number of iterations mat.itr. War_col (red)
Breakdown brk.dwn.war_col (red)
4) When creating the html of the data table display, the background color of the corresponding row is displayed in the color “col_stat” according to the above situation.

3) When the value of SEL is 3 or 99, the process of displaying the output data list is executed.
1) The following “loop_solpre” is executed.
2) All the files with the extension “.log” in FIG. 7 are displayed on the screen.
3) When the value of SEL is 90, search result display (method 2) is executed.

FIG. 18 shows a process for constructing a file name to be searched.
The above parameters are received, a file name for accessing the database is constructed using the “loop_solpre” program shown in FIG. 18, 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. 8, each parameter display means and each parameter selection means, a convergence graph, CPU time, and the required number of times of convergence, or a display means of a combination of these, and any one of these are displayed. 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.
19 and 20 show search result display examples. FIG. 20 is a screen continued from FIG. 19 (screen scrolled).
FIG. 19 is a result display when a search is executed with the settings as shown in FIG. 8, and a convergence graph based on a convergence solution algorithm combining the selected solution and the preprocessing technique used in combination with the selected solution is displayed on the screen. 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.
In FIG. 20, a table listing information such as the CPU time and the required number of times of convergence is displayed on the screen.

The items in the “Data Table” table are as follows.
No. Number assigned to the selected solution algorithm Prec-Solver convergence solution algorithm name. The selected solution and use it together
Name combining preprocessing techniques.
Iter. Number of times required for convergence. Until the approximate solution obtained by the convergence solution algorithm converges
The number of iterations taken. For the norm of the residual vector of the solution algorithm
The convergence judgment is 10 to the power of minus 12 (1.0 on the computer expression).
It was determined in e-12).
CPU time Indicates the CPU time [unit: seconds] required to converge.
Res. norm True residual value. Based on the residual vector in the solution algorithm
Even if it is determined to be a bundle, the true residual (
b-Ax) may be far from convergence.
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.
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, 4, 6” at the bottom of the figure indicates the number of the convergence solution algorithm.

  FIG. 21 is a screen (after scrolling the screen) continued from FIG. 20, and the contents (Output data) of the file with the extension “.log” in FIGS. 6 and 7 are displayed as they are.

  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. 7, “1138_bus−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 corresponding part is extracted from the log file in text format (in FIG. 7, “1138_bus-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.

FIG. 22 shows the convergence algorithm in FIG. 5 where parameters including comparison items are set on the screen (S1), the reference value of the true residual norm is set (S2), and the true residual norm is set. The situation where determination (S4) is performed as to whether the value is within the range of the true residual norm reference value is shown.

  As shown in FIG. 22, if the true residual norm is 1.0e-08 (the value set in FIG. 8) or less, it is determined as “conv. If the true residual norm is less than the allowable value, it will be judged as “no conv. (Apparent convergence)” and displayed in yellow. Otherwise, it will be displayed in red. To do. This example indicates that “max.itr. (Maximum number of iterations)” has been reached.

FIG. 23 rearranges the list of numerical algorithms based on the result determined in step S3 in FIG. 5 (S4), and outputs performance data for comparison items for the target convergence solution algorithm (S5). An example is shown in which the performance of the target convergence solution algorithm is relatively determined by relative comparison and the relative comparison value (relative determination value) of the target convergence solution algorithm is calculated (S6). In this example, finally, corresponding to the relative comparison and the relative comparison value, the target convergence solution algorithm is color-coded (white, yellow, red) on the screen in the same manner as described above.

The items in the table are almost the same as the items shown in FIG. 22, but an item “Rat.” (Ratio ratio) is added as an index for relative determination. Currently, Rat. Is defined as “Rat. = (Value of first comparison item) ÷ (value of comparison item of target convergence solution algorithm)”. In the case of the example of FIG. 9 (sorting in ascending order of CPU time), “Rat. = (Fastest CPU time) ÷ (CPU time of target convergence solution algorithm)”. The calculated values can be displayed in different colors as described above.

  FIG. 24 shows an output result when the “solution” is selected as the first priority item in FIG. 10 and “symmetric” is selected as the matrix type. In FIG. 24, the setting contents are as follows.

First priority sort item: “Solution”
Display result sorted in ascending order: “CPU time”
Tolerance for true residual norm: “1.0e-08”
Matrix type: “Symmetric matrix”
The combination of ID and name is displayed for the solution and preprocessing.
It is a horizontal axis of the list, and the ID of the solution is displayed on the top and the ID of the preprocessing is displayed on the bottom.

Assuming that “Solution” is grouped with the first priority in FIG.
Solver: 01 01 01 01… 01 02 02 02 02… 02 03 ……… 12
Precond .: 00 01 02 03… 07 00 01 02 03… 07 01 ……… 07
After all, they are grouped for each solution. The same display is displayed again at the bottom of the table.

  The vertical axis of the list shows a list of matrix names of the specified type. Here, for the matrix type, information is collected from the database 13B of FIGS.

  From the representative characteristics of each matrix, “Size V.” (matrix size in the row direction) and “Cond.Num.” (Condition number of the matrix) are displayed. Both of these collect information from the database 13B of FIGS.

  The performance of all algorithms for each matrix is arranged in the horizontal direction (for each matrix) as a relative determination value of the comparison item (CPU time in this figure). The relative judgment value here is a value obtained by multiplying the above-mentioned “Rat.” By 10 (for convenience of display, it is multiplied by 10 to eliminate redundant characters such as a decimal point). In FIG. 23, the comparison items are arranged in ascending order in the vertical direction, but here they are arranged in the horizontal direction in the order of the algorithm IDs (particularly as set in FIG. 10).

  For items corresponding to “conv.” In FIG. 23, relative judgment values are described, and for all other items, only “*” (asterisk) is displayed. For items other than "conv.", Only "no conv." Is displayed with a period, and "." (Period) is used for other "max.itr." And "brk.dwn." Is displayed.

Also, the colors are classified according to the numerical value of the relative judgment value (Rat). The description of the color coding is as described above.
In the color-coded information according to the relative determination value, the score (score) is 0 for white and 10 for black. For 1 to 9 in the meantime, gradation is from light yellow to dark red.

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. 3, the client terminal 200, that is, the display device 51 sets the operation specification factor 61 of each parameter, and makes a search / comparison request according to a search or comparison execution instruction 62 to the providing computer system 2 (30). And the returned result is displayed 63 (search result display) as a result of search or comparison.

1) Display of problems Analysis using numerical simulations is popular in elucidating natural and engineering phenomena. These simulations often result in solving many types of numerical problems, 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 numerical calculations other than linear equations. Therefore, in actual numerical calculation simulation, we want a guideline on which convergence solution algorithm should be applied. The client displays a problem on the client terminal 200.

2) Parameter item selection:
Referring to FIG. 8, a problem type 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. That is, here, the parameter selection of the method 1 and method 2 described above is performed. In FIG. 10, settings are made to obtain a list of all algorithm results for multiple problems (matrix). That is, the parameter item of method 3 is selected. Here, when the “matrix selection” field is selected (when it is not left blank), method 2 is performed.

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. That is, here, the search results corresponding to the parameter item selection of the method (1), method (2), and method (3) described above are displayed.

4) Selection of convergence solution algorithm:
Here, the performance with respect to a convergence solution algorithm is compared and a relative determination is performed.
Using the search results as a reference, select a convergence solution algorithm that seems suitable for solving your problem, make a search request again, and display the search results.

  In FIG. 3, in the providing side computer system 2 (30), an input parameter analysis 71 is performed by selecting an input parameter item and an operation specification factor for each parameter item, and the corresponding file is searched 72 and the corresponding file is stored in the database 13. The search is received and provided as data, and 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 or comparison result display 63 is displayed.

Thus, the convergence solution algorithm performance comparison display device 100 can select any one of the selection means displayed on the screen of the setting screen display means by the command signal from the client terminal via the communication means.

As described above, the convergent solution algorithm performance comparison display device can be composed of the following elements.

For each convergence solution algorithm, the problem to be solved, the parameter set for each item of the solution and the technique used in combination with the solution, the operation specification factor that is set for each parameter and determines the operation specification of the comparison item, and the item selected from each item Store a computer program that performs operations on comparison items associated with combinations of behavioral specification factors.
The computer program is used to perform arithmetic processing on comparison items associated with the combination of the operation specification factors selected from the items.
Storing the data about the comparison item in association with the combination of the operation specification factors selected from the items, which is the calculation result of the calculation processing means.
Each parameter display means, each parameter selection means, comparison item display means, selection means for selecting any of them, and 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 are simultaneously displayed on one screen.
On the screen, when one or more of the parameters, one of the comparison items, or a combination thereof, and one or more of the combinations of the operation specification factors in a combination form are selected, the database for these combinations is selected. Search and retrieve the data stored in.
Relative comparison is performed for any of the comparison items or a combination thereof based on the data acquired by the data acquisition processing means, and relative comparison is made with performance comparison for a plurality of numerical algorithms.
Display performance comparison results.
Prior to the relative comparison, the performance comparison processing means determines whether the set value is within a range of a reference value of a set true residual norm or not.
The result of the relative evaluation is displayed in different colors on the screen of the result screen display means.

The block diagram which shows the structure of the Example of this invention. The figure which shows the one part detail of FIG. The flowchart figure of FIG. The figure which shows the example of the numerical algorithm of the conjugate gradient method with preprocessing. The figure which shows the flow of the Example of this invention. 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 input screen figure based on the parameter item selection (method 1) of FIG. The input screen figure based on the parameter item selection (method 2) of FIG. FIG. 2 is an input screen diagram based on the parameter item selection of FIG. 1 (mainly method 3. If a matrix name is specified, it also functions as method 2). The figure which shows the example substituted to a parameter on the screen of FIGS. The figure which shows the example substituted to a parameter on the screen of FIGS. 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). Explanatory drawing when "99" does not exist in solution ID. The figure explaining reception of the value of parameter "SEL", and control according to the value. (Part 1) The figure explaining reception of the value of parameter "SEL", and control according to the value. (Part 2) 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. The figure which shows the determination result by the method 1. The figure which shows the relative determination result by the method 2. The figure which shows an output result by the method 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Memory | storage means, 12 ... Arithmetic processing means (1), 13 ... Database, 13A ... Database (1), 13B ... Database (2), 14 ... Arithmetic processing means (2), 14A ... Arithmetic processing means (2A), 14B ... arithmetic processing means (2B), 15 ... result screen display means, 20 ... convergence solution algorithm, 21 ... parameter, 22 ... problem to be solved, 23 ... solution, 24 ... technique used in combination with the solution, 25 ... input data file, 26 ... Execution format program file, 51 ... Display device, 52 ... Problem display, 53 ... Parameter item selection, 54 ... Search result display, 55 ... Selection / display of more appropriate convergence solution algorithm, 61 ... Operation of each parameter Specification factor (for example, value) setting, 62 ... Search execution instruction, 63 ... Search result display, 71 ... Input parameter analysis, 72 ... Applicable file Search, edited for display 73 ... target data, 100 ... convergence solving algorithm performance comparison display device, 200 ... client terminal.

Claims (8)

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,
Display means for displaying any or all of the display items of the CPU time to convergence and the number of times of convergence that is the number of iterations of computation until convergence, the problem to be solved, the solution method, and each arranged menu item of the technique used in the solution method And any or all of the CPU time and the required number of times of convergence from the display items, and the problem item to be solved, the solution method, and the parameter item of the technique used in the solution method selected from each of the arranged menu items. A setting screen display means comprising a parameter selection means,
Receiving the selected parameter item, forming a solution for the problem to be solved and a combination of techniques used in the solution, and performing any or all of the calculation processing to obtain the CPU time and the required number of convergence times for each combination An arithmetic processing means for performing arithmetic processing of a relative determination value by comparing the processed values and storing the arithmetic result in a database; and
Receiving the calculation result of the relative judgment value of each combination, and displaying the calculation result of each combination on the screen,
XY formed by both parameter items on the XY coordinate axis in which the parameter items of the problem to be solved on the Y axis and the respective parameter items of the technique used in the solution and the solution method are set on the X axis Result screen display means for displaying the performance comparison result for the CPU time or the required number of convergence times for the problem to be solved at the coordinate position on the screen with the relative judgment value obtained by the arithmetic processing,
A convergence solving algorithm performance display device characterized by comprising: 2. The calculation processing unit according to claim 1, wherein the arithmetic processing means is within a range of a reference value of a true residual norm set by the acquired CPU time or the required number of convergences before the calculation processing of the relative determination value . A convergence solving algorithm performance comparison display device characterized by determining whether or not it is out of range. 3. The result screen display means according to claim 1, wherein the result of the relative determination value displayed at the XY coordinate position is displayed on the screen in a color-coded manner for each position corresponding to the determination value. Convergent solution algorithm performance comparison display device characterized by that. 4. The result screen display means according to claim 1, wherein the result screen display means displays a relative judgment value obtained by the calculation process on the screen in a combination of a CPU time and a required number of times of convergence. Convergence solution algorithm performance comparison display device. According to claim 1, wherein the result screen displaying means, converges solving algorithm performance comparison display device grouped characterized you to view the CPU time or converge required number for each techniques for solving each and combination on the screen. A convergence solving algorithm performance display device according to claim 1, and
Consists of a client terminal connected via a communication means to the convergence solution algorithm performance display device,
The client terminal is selectable via the communication means for the selection means displayed on the screen of the setting screen display means of the convergence solution algorithm performance display device, and the result screen display means of the client terminal Displaying the performance comparison result of the performance comparison for the CPU time or the required number of convergence times displayed on the result screen display means of the solution solving algorithm performance display device
Convergent solution algorithm performance display system characterized by In the convergence solution algorithm performance display method by the convergence solution algorithm performance display device according to claim 1,
Arithmetic processing means receives the selected parameter item, forms a combination of a solution for the problem to be solved and a technique used in the solution, and obtains the CPU time and the required number of convergence times of each combination or all of the arithmetic processing , Perform a relative decision value calculation process by comparing the calculated values, store the calculation result in the database,
The result screen display means receives the calculation processing result of the relative determination value in each combination, and displays the calculation processing of each combination,
XY formed by both parameter items on the XY coordinate axis in which the parameter items of the problem to be solved on the Y axis and the respective parameter items of the technique used in the solution and the solution method are set on the X axis Display the performance comparison result of the CPU time or the required number of convergence times for the problem to be solved at the coordinate position on the screen with the relative judgment value obtained by the above arithmetic processing.
Convergence solving algorithm performance comparison display method comprising. In Claim 7, The said arithmetic processing means exists in the range of the reference value of the true residual norm set about the acquired CPU time or the convergence required number before the said calculation process of the relative determination value. Or a convergent solution algorithm performance comparison display method characterized by determining whether or not it is out of range.

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