A high -dimensional interpolation compression storage and calculation method

A technology for compressing storage and computing methods, applied in computing, instruments, database indexing, etc., can solve the problems of lack of efficient solution methods for interpolation, and achieve the effects of saving storage costs, good universality, and improving efficiency

Active Publication Date: 2022-05-24
BEIJING AEROSPACE AUTOMATIC CONTROL RES INST
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  • Description
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Problems solved by technology

Higher dimensional interpolation lacks general and efficient solution methods

Method used

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  • A high -dimensional interpolation compression storage and calculation method
  • A high -dimensional interpolation compression storage and calculation method
  • A high -dimensional interpolation compression storage and calculation method

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0088] Embodiment 1: take a 4-dimensional interpolation as an example to illustrate

[0089] Problem Definition:

[0090] Defining a 4-dimensional ordered interpolation table is defined as follows:

[0091]

[0092]

[0093] Set the interpolation independent variable to be interpolated as: {a=12, b=15, c=45, d=55}, and calculate the interpolation result.

[0094] According to the method of the present invention, the solution is as follows:

[0095] 1. Establish a deep storage tree of interpolation data, as shown below figure 1 shown

[0096] 2. Create a value range data storage table, as shown in the following table

[0097]

[0098]

[0099]

[0100] 3. Build a dynamic interpolation binary tree from the root to the leaves, as attached figure 2 shown.

[0101] 4. From the leaves to the roots, after solving the interpolation results in the dynamic interpolation binary tree, as attached image 3 shown.

[0102] 5. Take the interpolation result domain valu...

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Abstract

The invention discloses a compressed storage and calculation method for high-dimensional interpolation, which first recursively builds a deep storage tree of interpolation independent variables according to the interpolation independent variables of each dimension in the interpolation table, and is used for searching interpolation intervals of each dimension. Then construct a dynamic interpolation binary tree according to the interpolation independent variable, convert the interpolation calculation process into a graph operation on the tree, and finally obtain the result. The storage tree structure of the multi-dimensional interpolation table greatly reduces the storage overhead of repeated data; the establishment of the dynamic interpolation binary tree unifies the interpolation process of the linear interpolation space and the nonlinear interpolation space, simplifies the calculation, and helps chip-level implementation to greatly improve the high-speed The efficiency of dimensional interpolation calculation; combined with the method of tree type and binary search, it avoids the time overhead of linear sequential search for interpolation coordinate vectors by traditional methods, and improves the search efficiency from linear to exponential. This advantage will become more obvious as the order of magnitude of the problem dimension increases.

Description

technical field [0001] The invention relates to a compressed storage and calculation method for high-dimensional interpolation, which is a unified high-dimensional interpolation calculation technical framework and mainly solves the problems of large storage capacity and long time-consuming caused by the high-dimensional interpolation operation. Background technique [0002] Functions are a common tool when describing mathematical or physical spaces. However, in many cases, the form of function description cannot solve the function value, and even more often, the space cannot be described by elementary functions, so the space can only be expressed numerically by means of sampling and other methods, by means of point models. In such cases, interpolation is often used. [0003] At present, the most used interpolation is one-dimensional linear interpolation, two-dimensional bilinear interpolation, etc., which can obtain interpolation results according to a fixed formula. Highe...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F16/22G06F16/2455
CPCG06F16/2246G06F16/2264G06F16/2282G06F16/24566
Inventor 高飞苏平吴浩孙建祥薛玥曹芳芳梁中兴彭汉章王琦徐自衡王冲杨威钱景周韶楠
Owner BEIJING AEROSPACE AUTOMATIC CONTROL RES INST
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