Device for decomposing characteristics of real symmetric matrix based on circular Jacobian

Abstract

The invention provides a device for decomposing the characteristics of a real symmetric matrix based on circular Jacobian, which comprises a storage module, an angle resolving module, K rotating modules and a control module, wherein the storage module is used for storing and updating the elements of an N-stage real symmetric matrix A and an orthogonal matrix Q; moreover, the storage module reads the ap, the p, the aq, the q, the ap and the q of the A according to a preset circular traversal sequence, transmits the ap, the p, the aq, the q, the ap and the q of the A to the angle resolving module, reads the left multiplication element and the right multiplication element of the A and the right multiplication element of the Q and transmits the left multiplication element and the right multiplication element of the A and the right multiplication element of the Q to the rotating modules; the angle resolving module is used for carrying out angle resolving calculation on a plurality comprising the ap, the p, the aq, the q, the ap and the q and transmitting a rotation angle to the rotating modules; the rotating modules are used for carrying out rotating calculation on the left multiplication element and the right multiplication element of the A or the right multiplication element of the Q according to the rotation angle, outputting data obtained by rotation to the storage module and updating the data; the K is the degree of parallelism; and the control module is used for controlling the data reading and updating of the storage module, the angle resolving calculation of the angle resolving module and the rotating calculation of the rotating modules. By the invention, higher operational performance is realized under a reasonable hardware resource, and the contradiction between the operational performance and the resource consumption is solved.

Description

technical field [0001] The invention relates to the technical fields of matrix calculation and integrated circuits, in particular to a cyclic Jacobian-based real symmetric matrix eigendecomposition device. Background technique [0002] The eigendecomposition of real symmetric matrices is an important matrix decomposition in linear algebra, and has important applications in signal processing, statistics and other fields. Cyclic Jacobi (Cyclic Jacobi) algorithm is a transformation method used to calculate all the eigenvalues ​​of real symmetric matrices and their corresponding eigenvectors. Its basic idea is to transform the symmetric matrix A into It is a diagonal matrix, so that all eigenvalues ​​and eigenvectors can be obtained. This method can obtain quite accurate approximate orthogonal canonical eigenvectors while calculating the eigenvalues. [0003] Using Cyclic Jacobi (Cyclic Jacobi) algorithm to implement eigendecomposition usually includes two types of implementati...

AI Technical Summary

Problems solved by technology

But its shortcomings are also very obvious. For a matrix with dimension N, it needs N 2 / 4 computing modules, so it needs to consume a lot of hardware resources in implementation

In the existing FPGA chips, it is difficult to realize the eigendecomposition of large-scale matrices

[0005] Based on the processing system of a single operation module, the existing technology usually uses an angle module and a rotation module to realize the eigendecomposition processing system. The disadvantage of this implementation method is The computing performance is relatively poor and the computing efficiency is not high

Another method is to use two CORDIC modules to realize the eigendecomposition processing system. One of the CORDIC modules is used for angle and rotation, and the other is only used for rotation to improve the efficiency of the angle calculation module. This method can adopt a certain The degree of pipeline technology has improved the computing performance of the system, but despite this, the parallelism of the system has not changed, and the computing performance is relatively low

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