JP2003248674A - Function value interpolation method, device, and program, and recording medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a function value interpolation method, a device, and a program capable of interpolating a function value of a function defined in a three-dimensional space at high speed and to provide a recording medium. <P>SOLUTION: This function value interpolating method interpolates the value of the function mapping from a point in the three-dimensional space to a point in a one-dimensional space. This method is provided with a calculation result retaining step calculating a coefficient for interpolating a partial space of the three-dimensional space and retaining the calculated result and interpolation calculating means interpolating the function value of an arbitrary point in the three-dimensional space using the calculation result. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a function value interpolation, and more particularly to a function value interpolation method, a function value interpolation device, a function value interpolation program and a recording medium in a function from a three-dimensional space to a one-dimensional space.

[0002]

2. Description of the Related Art The calculation processing speed of a computer is increasing year by year, and it is said that the calculation processing speed of the present personal computer is comparable to the calculation processing speed of a super computer 10 years ago. However, when performing scientific and technological calculations using a computer, the amount of calculation and the amount of data to be handled by the computer are increasing with the increase in the computational processing speed of the computer, and therefore it takes time even if the computer is used. There is.

As an example of such a time-consuming process, there is a process of observing a spectrum of light transmitted through a gas and calculating a function for obtaining an absorption coefficient required for radiative transfer calculation for obtaining a component concentration in the gas. This absorption coefficient is a coefficient obtained from a domain defined by the space of air temperature × atmospheric pressure × wave number (reciprocal of wavelength), and the change in atmospheric pressure × temperature is smooth, but the change in the wave number direction is abrupt. In such a case, in order to shorten the time, the domain of the function is discretized, the function values at the discretized points are obtained in advance, and the function values previously obtained at points other than the discretized points are obtained. A method is often used in which the function value at that point is obtained by interpolation using.

[0004]

However, the above method is not always appropriate in all cases. For example, if the domain of the above function is limited to atmospheric pressure x atmospheric temperature of a set of points consisting of atmospheric temperature x atmospheric pressure x wave number, since the change in the function value is smooth, it is possible to interpolate from discrete points. , The change in the function value with respect to the change in the wave number direction is large, and the number of points to be discretized for interpolation becomes unrealistic for a computer to handle, and interpolation from the discretized points is practically impossible. It may be possible.

In view of the above problems, the present invention provides a function value interpolation method, a function value interpolation device, a function value interpolation program and a recording medium for rapidly interpolating the function value of a function defined in a three-dimensional space. The purpose is to do.

[0006]

According to a first aspect of the present invention, there is provided a function value interpolation method for interpolating a range of a function mapping from a point in a three-dimensional space to a point in a one-dimensional space using a computer. A calculation result holding step of calculating a value range for a subspace of the three-dimensional space and holding the calculated calculation result, and an interpolation calculation for interpolating a function value of an arbitrary point in the three-dimensional space using the calculation result And stages.

According to the first aspect, by holding the calculated result, it becomes possible to interpolate the values for other arbitrary points at high speed.

According to a second aspect of the present invention, the calculation result holding step does not hold the calculation result when all the calculation results for the points of the subspace are equal to or less than a constant value that does not affect the calculation accuracy. Characterize.

According to the second aspect, when the calculation result is equal to or less than a certain value that does not affect the calculation accuracy, the result is not held, so that the waste of computer resources can be prevented.

The invention according to claim 3 is characterized in that, in the calculation result holding step, the calculation result is held as a plurality of files.

According to the third aspect, it is possible to reuse by holding it as a non-volatile file.

According to a fourth aspect of the present invention, the file is a file in which the calculation result for a point on a straight line parallel to the coordinate axis to be interpolated in the three-dimensional space is recorded in the unit of the straight line. It is characterized by

According to the fourth aspect, when the function value is smooth in the plane direction perpendicular to the specific coordinate axis, only the file in which the value relating to the coordinate axis direction is recorded needs to be held, so that the file size is reduced. Can be reduced.

According to a fifth aspect of the present invention, in the interpolation calculation step, the result read from the file is reused for another interpolation calculation.

According to the fifth aspect, by reusing the data, it does not take time to read it again, so that the processing can be performed at high speed.

According to a sixth aspect of the present invention, in the interpolation calculation step, information regarding the points in the three-dimensional space is input in advance according to the frequency of performing the interpolation calculation for the points in the three-dimensional space. To do.

According to the sixth aspect, since the information is input in advance according to the frequency, it does not take time to input the information at a high frequency, so that the processing can be performed at high speed.

According to a seventh aspect of the present invention, there is provided an interpolating device for interpolating a range of a function mapping from a point in a three-dimensional space to a point in a one-dimensional space by using a computer. It has a calculation result holding means for calculating a value range and holding the calculated calculation result, and an interpolation calculation means for interpolating a function value of an arbitrary point in the three-dimensional space using the calculation result. To do.

According to the seventh aspect, by holding the calculated result, it becomes possible to interpolate the values for other arbitrary points at high speed.

The recording medium for recording this program is a recording medium such as a CD-ROM, a flexible disk or a magneto-optical disk (MO) for recording information optically, electrically or magnetically, ROM, flash. Various types of recording media such as a semiconductor memory that electrically records information such as a memory can be used.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows the configuration of the high-speed interpolation system according to the embodiment of the present invention. In FIG. 1, a plurality of distributed processing computers 10a, 10b, 10n and a workstation 1 are shown.
2 and a high speed switch 11 connecting them are shown. The workstation 12 is the distributed processing computer 10.
a, 10b, 10n are managed. Further, the distributed processing computer 10 is equipped with a large capacity hard disk and a memory.

FIG. 2 shows a block diagram of an embodiment of the distributed processing computer 10. The distributed processing computer 10 shown in FIG. 2 has a drive device 23, a recording medium 24, an auxiliary storage device 25, and a memory device 21 which are connected to each other by a bus B.
And an arithmetic processing unit 27 and an interface unit 29.

The interface device 29 is an interface for connecting the distributed processing computer 10 to a network, and is composed of, for example, a network card.

The auxiliary storage device 25 stores programs, and also stores necessary files and data. The memory device 21 stores programs and data. The arithmetic processing unit 27 executes processing according to the program read and stored in the memory unit 26.

FIG. 3 is a block diagram of an embodiment of the system of the workstation 12. The computer system of FIG. 3 has an input device 31, a display device 32, a drive device 33, a recording medium 34, an auxiliary storage device 35, a memory device 36, which are connected to each other by a bus B.
It is configured to include an arithmetic processing unit 37 and an interface unit 38.

Further, in the case of performing the processing at a higher speed, it is possible to further speed up the processing by connecting a plurality of distributed processing computers 10 with a high-speed switch and performing the processing with each other.

Next, the function calculated by the high speed interpolation system will be described. The function is a mapping from a three-dimensional space having a domain of the three-dimensional space of (x, y, z) to a one-dimensional space. In this function, the change of the function value in the (x, y) space is smooth and can be interpolated from relatively few discrete points, but the change in the z direction is extremely small and cannot be interpolated from discrete points.

Next, the interpolation method will be described. The interpolation method is a two-dimensional cubic B-spline in the (x, y) plane. The interpolation value V is calculated by the following formula.

[0030]

[Equation 1] This equation will be described with reference to FIG. Figure 4 shows xy in the z-axis direction
It is a figure which shows a mode that the grid point was provided on several planes parallel to a plane. Black circles on the grid points are points for which calculation is performed in advance, and white circles are interpolation target points (x, y). The black circles on the grid points calculated in advance are secured as a numerical table described later.

In Equation 1, the subscript a is an integer having a value of 1 to l, and the subscript b is an integer having a value of 1 to m. The sequence ξ _a represents discrete point coordinates in the x-axis direction, and ζ _b represents discrete point coordinates in the y-axis direction. Further, in this case, the point (x, y) is ξ _a ≦ x <ξ _{a + 1} and ζ _b ≦ y <ζ _{b + 1 as shown} in FIG. And N _i (x: ξ _a ) is a b-spline coefficient calculated from the relationship with the discrete point coordinate ξ _a, and N _i (y: ζ _b ) is calculated from the relationship with the discrete point coordinate ζ _b It is a b-spline coefficient. Note that N _i (x: ξ _a ) is obtained by the following formula.

[0032]

[Equation 2] Similarly, N _i (y: ζ _b ) can be obtained by replacing x with y and ξ with ζ in the above equation.

Next, the data structure of the above numerical table will be described with reference to FIG. The number table is recorded in a file, and the number table file is composed of k attribute files which are sequential organization files and an interpolation coefficient file which is a fixed record length direct organization file attached to the attribute files. Of these, the attribute file will be described first with reference to FIG. FIG. 6 is a table showing the record items of the attribute file, and is composed of columns of items, contents and remarks. As shown in FIG. 6, the attribute file has “coordinate range” as an item. The coordinate range indicates the range of the three-dimensional space to which this attribute file corresponds as a numerical table. And
In the case of the table of FIG. 6, the x-axis range is xs ≦ x ≦ xe, the y-axis range is ys ≦ y ≦ ye, and the z-axis range is zs ≦ z ≦ ze.
Is. Next, the item “division number of discrete points” represents the division number obtained by dividing the “coordinate range” at discrete points, 1 is the number of ξ, and m is the number of ζ. There is.
The z-axis direction is the number of divisions at a predetermined interval as will be described later, and in this case, it is n. The next two items "x
The “direction discrete point coordinates” and the “y direction discrete point coordinates” represent the above ξ and ζ. Moreover, the z-axis direction is divided at a predetermined interval Δz.

The next item, interpolation coefficient storage address information 39, is interpolation coefficient c (z _k ) (k = 1,2, _k ) corresponding to a grid point (ξ _i , ζ _j ) on the (x, y) plane. .., n), which can be obtained using the interpolation coefficient file 40. The interpolation coefficient storage address information 39, as shown in FIG.
The abscissa is i-th, the ordinate is j-th, and k is a file in which c (z _k ) is stored at an address determined from the divided file numbers. The interpolation coefficient file 40 is
When the interpolation coefficient corresponding to each grid point on the (x, y) plane is recorded in one record and all the interpolation coefficients recorded in that record are equal to or less than a certain value that does not affect the calculation accuracy. , Do not make a record for that grid point. By doing so, it is possible to reduce the number of records to be read when executing the interpolation process, and it is possible to speed up the interpolation process.

When operating the data recorded in these files, the data is expanded on the memory. In this case, a memory interpolation coefficient storage address information area,
An interpolation coefficient reference index area and an interpolation coefficient storage area are provided on the memory. These will be described with reference to FIG.
First of all, indx (4,4,
In describing (k), the interpolation coefficient is stored.
Explain c (:, :). c (i, j) is the interpolation coefficient storage area 28, and i, which is the first subscript of c (i, j), is a number in the z direction and takes a value from 1 to the record length. The second subscript j is the storage number of the interpolation coefficient storage area.

Further, this c (i, j) stores interpolation coefficients corresponding to 4 × 4 discrete points surrounding the interpolation target point (x, y). Therefore, the interpolation coefficient reference index area indx (4,4,
k) stores the second subscript in c (i, j). Also, the third
The subscript k corresponds to the file number.

Next, the back reference table jikc (4, s) 26 will be described. This reverse citation table 26 has a grid number i,
Memory interpolation coefficient address information ad2 (i, j, k) 2 from j, k
4 is a table for obtaining an interpolation coefficient using 4. It also has a reference counter. This reference counter is c
This is a counter used when all of the area (i, j) is used up and overwritten. The area where the reference counter is positive and minimum is the oldest memory area, and therefore writing is performed again from that area.

Next, for (x _i , y _i ) i = 1,2, .., no, the function value f (x _i , y _i , z _j ) (j = 1,2, .., n , i = 1,2, .., no) will be described with reference to FIG. The calculation result is stored in v (lw, i) (lw = 1 to n, i = 1 to no).

In step S1, the interpolation coefficient reference counter i
Let c be 0. This counter is a counter used in the above-mentioned back-citation table 26. Next step S2
Then, the attribute file is input and the interpolation coefficient file is input in advance. This is stored in the pre-input area of the interpolation coefficient storage area 28. In the next step S3, the above equation 2
Calculate. K in step S4 is a loop counter that moves in the subscript range in the z direction. And in this case, the loop counter k moves from ls to le. In the next step S5, 0 is substituted for v (i, k) within the moving range of k.
Next, in step S6, the loop counter is normalized. In the next step S7, if the memory interpolation coefficient address information described above is positive, the interpolation coefficient has been stored, so the flow proceeds to step S9. In step S9, the value stored in the memory interpolation coefficient address information is substituted into the variable ip.

Returning to the branching process of step S7, if the memory interpolating coefficient address information is 0 or less, the step of retrieving a free area or an overwriting area of the interpolation coefficient storing area to newly store the information is a step. It is performed in S8. In this process, the reference counter mentioned earlier is used.
In this step S8, a process of searching for the ip having the fourth reference counter in the reverse citation table 26 that is 0 or more and has the smallest ip between 1 and 16 is performed. And
When ip is searched, the interpolation coefficient reference counter ic is first incremented. Then, the lattice numbers corresponding to x, y, and z of the reverse citation table 26 are stored, and ip is substituted in the memory interpolation coefficient address information 24. Next step S10
Then, it is input to the interpolation coefficient storage area, and its record number is input to the interpolation coefficient storage address information. In the next step S12, ip is assigned to the interpolation coefficient reference index area. Then, in step S13, the loop counter ix is incremented, and if the value is a + 2 or less, the process of step S6 is performed again. If it is larger than a + 2, the loop counter iy is incremented in step S15, and if the value is less than b + 2, the process of step S6 is performed again. If it is larger than b + 2,
In the next step S17 and step S18 of FIG. 10, ix2, iy
1 is substituted for 2 and the loop counter is initialized.
Then, in step S19, ls is substituted into the loop counter l that counts the number of calculations in step S20.
In step S20, the function value, which is the main purpose, is calculated. In the next step S21, the loop counter 1 is incremented and its value is compared with le in the next step S22.
If l is less than or equal to le, the process of step S20 is performed again. If 1 is larger than le, the loop counter iy2 is incremented in the next step S23, and iy2 and 4 are compared in step S24. If iy2 is 4 or less, the process of step S19 is performed again. If iy2 is larger than 4, ix2 is incremented in the next step S25. In the next step S26, ix2 and ix are compared. ix2 is 4
If the following is true, the process of step S18 is performed again.
If ix2 is larger than 4, the loop counter k is incremented in the next step S27. If k is less than or equal to le, the process of step S5 of FIG. 9 is performed again. If k is larger than le, the loop counter i is incremented in the next step S29. In the next step S30, if i is less than or equal to the number of interpolation target points, the process proceeds to step S4 of FIG. 7 again, and if i is greater than the number of interpolation target points, calculation is performed for all the interpolation target points. It's finished.

[0041]

As described above, the function value interpolation method for rapidly interpolating the function value of the function defined in the three-dimensional space,
A function value interpolating device can be provided.

[Brief description of drawings]

FIG. 1 is an overall configuration diagram of a high-speed interpolation system according to an embodiment of the present invention.

FIG. 2 is a hardware block diagram of a distributed processing computer.

FIG. 3 is a hardware block diagram of a workstation.

FIG. 4 is a diagram showing a number table registration point and an interpolation target point.

FIG. 5 is a diagram showing a structure of a number table file.

FIG. 6 is a diagram showing the contents of a number table file structure.

FIG. 7 is a diagram showing a relationship between interpolation coefficient storage address information and an interpolation coefficient file.

FIG. 8 is a diagram showing a memory data structure.

FIG. 9 is a flowchart showing a high-speed interpolation procedure (No. 1)
Is.

FIG. 10 is a flowchart (part 2) showing the high-speed interpolation procedure.

[Explanation of symbols]

10a, 10b, 10n ... Distributed processing device 11 ... High-speed switch 12 ... workstation 21 ... Memory device 22 ... Interpolation coefficient reference index area 23 ... Drive device 24 ... Memory interpolation coefficient address information 25 ... Auxiliary storage device 26 ... Backquote table 27 ... Arithmetic processing device 28 ... Interpolation coefficient storage area 29 ... Interface device 31 ... Input device 32 ... Display device 33 ... Drive device 35 ... Auxiliary storage device 36 ... Memory device 37 ... Arithmetic processing device 38 ... Interface device 39 ... Interpolation coefficient storage address information 40 ... Interpolation coefficient file

Claims (9)

[Claims] 1. A function value interpolation method for interpolating a value of a function mapping from a point of a three-dimensional space to a point of a one-dimensional space by using a computer, for interpolating a subspace of the three-dimensional space. And a calculation result holding step of holding the calculated calculation result, and an interpolation calculation step of interpolating a function value of an arbitrary point in the three-dimensional space using the calculation result. Function value interpolation method. 2. The calculation result holding step does not hold the calculation result when all the calculation results for the points of the subspace are equal to or less than a constant value that does not affect the calculation accuracy. Function value interpolation method described. 3. The function value interpolation method according to claim 1, wherein the calculation result holding step holds the calculation results as a plurality of files. 4. The file is in the three-dimensional space,
2. The function value interpolation method according to claim 1, wherein the file is a file in which calculation results for points on a straight line parallel to the coordinate axis to be interpolated are recorded in units of the straight lines. 5. The function value interpolation method according to claim 3, wherein in the interpolation calculation step, a result read from the file is reused for another interpolation calculation. 6. The method according to claim 1, wherein the interpolation calculation step inputs in advance information about the points in the three-dimensional space according to the frequency of performing the interpolation calculation for the points in the three-dimensional space. Function value interpolation method. 7. A function value interpolation device for interpolating a value of a function mapping from a point in a three-dimensional space to a point in a one-dimensional space by using a computer, for interpolating a subspace of the three-dimensional space. And a calculation result holding unit that holds the calculated calculation result, and an interpolation calculation unit that interpolates a function value at an arbitrary point in the three-dimensional space using the calculation result. Function value interpolator 8. A calculation result holding procedure for causing a computer to calculate a coefficient for interpolating a subspace of a three-dimensional space, and holding the calculated calculation result; A function value interpolation program for executing an interpolation calculation procedure for interpolating a function value at an arbitrary point in space. 9. A calculation result holding procedure for causing a computer to calculate a coefficient for interpolating a subspace of the three-dimensional space and holding the calculated calculation result, and using the calculation result, the three-dimensional A computer-readable recording medium recording a function value interpolation program for executing an interpolation calculation procedure for interpolating a function value at an arbitrary point in space.