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Compression storage and calculation method for high-dimensional interpolation

A technology for compressing storage and computing methods, applied in computing, special data processing applications, instruments, etc., to solve problems such as the lack of efficient solution methods for interpolation

Active Publication Date: 2020-01-10
BEIJING AEROSPACE AUTOMATIC CONTROL RES INST
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Problems solved by technology

Higher dimensional interpolation lacks general and efficient solution methods

Method used

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  • Compression storage and calculation method for high-dimensional interpolation
  • Compression storage and calculation method for high-dimensional interpolation
  • Compression storage and calculation method for high-dimensional interpolation

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Embodiment 1

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

[0089] Problem definition:

[0090] The definition of a 4-dimensional ordered interpolation table is defined as follows:

[0091]

[0092]

[0093] Suppose the interpolation independent variable to be interpolated is: {a=12, b=15, c=45, d=55}, find the interpolation result.

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

[0095] 1. Establish a deep storage tree for interpolation data, as attached below figure 1 Shown

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

[0097]

[0098]

[0099]

[0100] 3. Establish dynamic interpolation binary tree from root to leaf, 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 value of the tree root as the final 4-...

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Abstract

The invention discloses a compression storage and calculation method for high-dimensional interpolation. The compression storage and calculation method comprises the following steps: recursively constructing a deep storage tree of an interpolation independent variable according to the interpolation independent variable of each dimension of an interpolation table for searching an interpolation interval of each dimension, constructing a dynamic interpolation binary tree according to the interpolation independent variable, converting an interpolation calculation process into graph operation on the tree, and finally obtaining a result. The storage tree structure of the multi-dimensional interpolation table greatly compresses the storage overhead of repeated data; and the establishment of the dynamic interpolation binary tree unifies the interpolation process of a linear interpolation space and a nonlinear interpolation space, simplifies the calculation, and is helpful for chip-level implementation to greatly improve the efficiency of high-dimensional interpolation calculation. A tree type and binary search method is combined, so that the time expenditure of performing linear sequentialsearch on interpolation coordinate vectors in a traditional method is avoided, and the search efficiency is improved from a linear level to an exponential level. Along with the increase of the orderof magnitudes of problem dimensions, the advantages are more obvious.

Description

Technical field [0001] The invention relates to a compression 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 time-consuming caused by the high-dimensional interpolation calculation process. Background technique [0002] When describing mathematical or physical space, functions are a common tool. But 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. Therefore, the space can only be expressed numerically by means of sampling and the point model. In this case, interpolation is very common. [0003] At present, the most commonly used interpolation is one-dimensional linear interpolation, two-dimensional bilinear interpolation, etc., which can obtain interpolation results according to a fixed formula. Higher-dimensiona...

Claims

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Application Information

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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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