Hermitian matrix parallel characteristic decomposition method for electromagnetic reconnaissance system

Abstract

The invention relates to the technical field of electromagnetic reconnaissance, and particularly discloses a Hermitian matrix parallel characteristic decomposition method for an electromagnetic reconnaissance system, and the method comprises the steps: constructing a 2N-order real symmetric matrix S based on a real part and an imaginary part of an N-order Hermitian matrix of the electromagnetic reconnaissance system; performing M times of iterative computation on the 2N-order real symmetric matrix S and the feature vector matrix R based on the scheduling rule matrix T to obtain a corresponding real symmetric matrix S 'and a feature vector matrix R'; and finally, on the basis of elements of the matrix S'and the matrix R ', obtaining eigenvalues of the N-order Hermitian matrix and eigenvectors corresponding to the eigenvalues. According to the method, the complex matrix is converted into the real matrix for processing, the scheduling rule matrix T is designed for iterative calculation, and the method has high decomposition precision. The same processing method can be adopted to perform characteristic decomposition on the Hermitian matrix of odd or even dimensions, and the method can be suitable for any processing system supporting parallel computing and is wide in application range.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic reconnaissance technology, and in particular to a Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system. Background Art

[0002] The Hermitian matrix is ​​a key matrix in the complex field, which is widely used in mathematics, physics and engineering. In the engineering field, the complex signal column vector is often used. and its conjugate transpose Multiply to get the covariance matrix , that is, the Hermitian matrix. Eigendecomposition yields multiple eigenvalues ​​and their corresponding eigenvectors, which have specific physical meanings in different fields. For example, in structural mechanics, eigenvalues ​​represent natural frequencies, while eigenvectors represent mode shapes. In electromagnetic reconnaissance systems, large eigenvalues ​​represent signal power, while small eigenvalues ​​represent noise power. The QR method is a commonly used eigendecomposition algorithm in engineering, but its implementation is complex and difficult to parallelize. The Jacobi eigendecomposition method offers advantages such as high accuracy, good parallelism, and strong stability, but is only applicable to real symmetric matrices.

[0003] The invention patent No. 201810120721.4, "Method for Implementing Hermitian Matrix Decomposition Using FPGA," provides a method for implementing the eigendecomposition of Hermitian matrices on FPGA. Different processing methods are required for Hermitian matrices of odd and even dimensions, and there is no unified algorithm for the eigendecomposition of Hermitian matrices of arbitrary dimensions. Summary of the Invention

[0004] The present invention provides a Hermitian matrix parallel eigendecomposition method for electromagnetic reconnaissance systems, which solves the technical problem that the current Jacobi parallel eigendecomposition method mainly targets real matrices, or requires separate processing of odd-dimensional and even-dimensional Hermitian matrices, and there is no unified algorithm applicable to the eigendecomposition of Hermitian matrices of arbitrary dimensions.

[0005] To solve the above technical problems, the present invention provides a Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system, comprising the steps of: S1. Obtain the N-channel complex signal vector of the electromagnetic reconnaissance system and construct the N-order Hermitian matrix ; S2. Extract N-order Hermitian matrix The real and imaginary parts of are obtained to obtain an N-order real matrix A and an N-order imaginary matrix B; a 2N-order real symmetric matrix S is constructed based on matrices A and B; S3, generate The scheduling rule matrix T is composed of 2N elements from 1 to 2N arranged in a different order, and the elements in the first column are all 1; S4. After performing M iterations on the 2N-order real symmetric matrix S and the eigenvector matrix R based on the scheduling rule matrix T, the corresponding real symmetric matrix S' and the eigenvector matrix R' are obtained; S5. Based on the elements of matrix S' and matrix R', get the N-order Hermitian matrix The eigenvalues ​​and the eigenvectors corresponding to each eigenvalue.

[0006] Furthermore, in step S2, the matrix S is constructed as: .

[0007] Furthermore, in step S3, the arrangement rule of the 1st to Nth rows of the matrix T is: All elements in the first column are 1; Starting from the first digit of "2, 4, 6, ..., 2N, 2N-1, 2N-3, 2N-5, ..., 5, 3", slide rightward with a sliding window of length N to obtain N groups of data, and fill them sequentially into the even columns from the first row to the Nth row of the matrix T; Starting from the last digit of "3, 5, ..., 2N-1, 2N, 2N-2, ..., 4", slide leftward with a sliding window of length N to obtain N-1 groups of data, and fill them sequentially into the even columns from row N+1 to row 2N-1 of matrix T; Starting from the last digit of "2N-2, 2N-4, ..., 4, 2, 3, 5, ..., 2N-3, 2N-1", slide leftward with a sliding window of length N-1 to obtain N-1 groups of data, and fill them sequentially into the first row to the Nth row and the remaining odd columns of the matrix T; Starting from the first digit of "2N-3, 2N-5, ..., 3, 2, 4, ..., 2N-2", slide rightward with a sliding window of length N-1 to obtain N-1 groups of data, and sequentially fill them into the N+1th row to the 2N-1th row and the remaining odd columns of the matrix T.

[0008] Furthermore, step S4 specifically includes the steps of: S41, assign the 2N×2N identity matrix I to the matrix R and set the number of iterations to an initial value of 0; S42. Determine whether the number of iterations is less than M. If so, add 1 to the number of iterations and initialize the number of iterations to 0 before proceeding to the next step. If not, output the current matrices S and R as the final real symmetric matrix S' and eigenvector matrix R'. S43, determine whether the number of iteration steps is less than 2N-1, if not, return to the previous step; if so, execute steps S44 to S46; S44, assigning the identity matrix I to the matrix W; S45. Update the element values ​​of the corresponding row and column indexes in the matrix W according to the row and column indexes of the elements in the current row of the scheduling rule matrix T and the 2N-order real symmetric matrix S; S46. Update matrices S and R based on the updated matrix W, and then return to step S43.

[0009] Furthermore, step S45 specifically includes the following steps: S451, calculate the rotation angle cosine value c(j) and the rotation angle sine value s(j) of the row corresponding to the current iteration step according to the matrix S and the matrix T, ; S452, based on 、 、 Update the matrix W OK List, OK List, OK List, OK Elements of a column.

[0010] Furthermore, in step S451, 、 Calculated by the following formula: , , , , in, Indicates the cotangent value of 2 times the rotation angle, Representation matrix middle OK The element value of Represents a symbolic function.

[0011] Furthermore, in step S46, the matrix is ​​updated and matrix , the superscript H indicates the conjugate transpose.

[0012] Furthermore, step S5 specifically includes the steps of: S51. Arrange the diagonal elements of the real symmetric matrix S' in ascending order, and record the sorted odd index sequence: index(1), index(3), ..., index(2N-1); S52, the elements corresponding to the odd numbers 1, 3, ..., 2N-1 after the diagonal elements of the matrix S' are arranged in ascending order are the elements of the matrix The eigenvalues ​​of in ascending order; S53, according to the sorted odd index sequence, the matrix The corresponding columns of the matrix UV are taken out, the first N rows of the matrix UV are taken to form the matrix U, and the last N rows are taken to form the matrix V. Then the matrix The columns of are the eigenvectors corresponding to the eigenvalues ​​in ascending order.

[0013] The Hermitian matrix parallel eigendecomposition method for the electromagnetic reconnaissance system provided by the present invention is based on the N-order Hermitian matrix of the electromagnetic reconnaissance system. The real and imaginary parts of the 2N-order real symmetric matrix S are constructed; and based on the scheduling rule matrix T, the 2N-order real symmetric matrix S and the eigenvector matrix R are iterated M times to obtain the corresponding real symmetric matrix S' and eigenvector matrix R'; finally, based on the elements of the matrix S' and the matrix R', the N-order Hermitian matrix is ​​obtained The present invention converts complex matrices into real matrices for processing and designs a scheduling rule matrix T for iterative calculations, achieving high decomposition accuracy (eigenvalues ​​can be accurate to 13 decimal places). The same processing method can be used for eigendecomposition of Hermitian matrices of odd or even dimensions, and is applicable to any processing system that supports parallel computing, thus having a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Flowchart of a Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system provided by an embodiment of the present invention; Figure 2 This is a flowchart of iteratively generating matrices S' and R' provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The following describes the embodiments of the present invention in detail with reference to the accompanying drawings. The embodiments are provided for illustrative purposes only and are not to be construed as limiting the present invention. The accompanying drawings are provided for reference and illustration only and do not constitute a limitation on the scope of protection of the present invention. Many changes may be made to the present invention without departing from the spirit and scope of the present invention.

[0016] The embodiment of the present invention first provides a Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system, such as Figure 1 As shown in the flowchart, the following steps are included: S1. Obtain the N-channel complex signal vector of the electromagnetic reconnaissance system and construct the N-order Hermitian matrix ; S2. Extract N-order Hermitian matrix The real and imaginary parts of are obtained to obtain an N-order real matrix A and an N-order imaginary matrix B; a 2N-order real symmetric matrix S is constructed based on matrices A and B; S3, generate The scheduling rule matrix T is composed of 2N elements from 1 to 2N arranged in a different order, and the elements in the first column are all 1; S4. After performing M iterations on the 2N-order real symmetric matrix S and the eigenvector matrix R based on the scheduling rule matrix T, the corresponding real symmetric matrix S' and the eigenvector matrix R' are obtained; S5. Based on the elements of matrix S' and matrix R', get the N-order Hermitian matrix The eigenvalues ​​and the eigenvectors corresponding to each eigenvalue.

[0017] This method constructs the scheduling rule matrix T and performs M iterations on the real symmetric matrix S and the identity matrix R (each iteration has steps, with 2N elements processed in parallel in each step), the obtained eigenvalues ​​and eigenvectors have high accuracy, high calculation speed, short processing time and strong stability.

[0018] The following describes each step in more detail.

[0019] (1) Step S1: Construct an N-order Hermitian matrix

[0020] Taking the 8-channel electromagnetic reconnaissance system as an example, the complex signals of each channel are obtained to form a complex signal vector ,by Get the 8th order Hermitian matrix , Columns 1-2, 3-4, 5-6, and 7-8 are shown in Table 1, Table 2, Table 3, and Table 4, respectively.

[0021] Table 1: Matrix 1~2 columns

[0022] Table 2: Matrix 3~4 columns

[0023] Table 3: Matrix 5~6 columns

[0024] Table 4: Matrix 7~8 columns

[0025] Columns 1 to 4 and columns 5 to 8 of the N-order real part matrix A corresponding to Tables 1 to 4 are shown in Tables 5 and 6 below, respectively.

[0026] Table 5: Columns 1 to 4 of Matrix A

[0027] Table 6: Columns 5 to 8 of Matrix A

[0028] (2) Step S2: Based on the N-order Hermitian matrix Construct a 2N-order real symmetric matrix S

[0029] Columns 1 to 4 and columns 5 to 8 of the N-order imaginary part matrix B corresponding to Tables 1 to 4 are shown in Tables 7 and 8 below, respectively.

[0030] Table 7: Columns 1 to 4 of Matrix B

[0031] Table 8: Columns 5 to 8 of Matrix B

[0032] In this embodiment, the 2N-order real symmetric matrix S is constructed as: .

[0033] The 1st to 4th columns, 5th to 8th columns, 9th to 12th columns, and 13th to 16th columns of the 16th-order real symmetric matrix S constructed based on Tables 5 to 8 are shown in Tables 9, 10, 11, and 12, respectively.

[0034] Table 9: Columns 1 to 4 of matrix S

[0035] Table 10: Columns 5 to 8 of matrix S

[0036] Table 11: Columns 9 to 12 of matrix S

[0037] Table 12: Columns 13 to 16 of matrix S

[0038] (3) Step S3: Generate The scheduling rule matrix T

[0039] The number of rows in the scheduling rule matrix T is 2N-1, and the number of columns is 2N, which means that each iteration has 2N-1 steps, and each step processes 2N elements in parallel. The row and column indices of the elements processed by the eigendecomposition process are respectively, that is, every two elements in each row correspond to one eigenvalue. Each row of the matrix T is composed of 2N elements from 1 to 2N arranged in a different order.

[0040] As a preferred embodiment, the arrangement rule of the 1st to Nth rows of the matrix T is: All elements in the first column are 1; Starting from the first digit of "2, 4, 6, ..., 2N, 2N-1, 2N-3, 2N-5, ..., 5, 3", slide rightward with a sliding window of length N to obtain N groups of data, and fill them sequentially into the even columns from the first row to the Nth row of the matrix T; Starting from the last digit of "3, 5, ..., 2N-1, 2N, 2N-2, ..., 4", slide leftward with a sliding window of length N to obtain N-1 groups of data, and fill them sequentially into the even columns from row N+1 to row 2N-1 of matrix T; Starting from the last digit of "2N-2, 2N-4, ..., 4, 2, 3, 5, ..., 2N-3, 2N-1", slide leftward with a sliding window of length N-1 to obtain N-1 groups of data, and fill them sequentially into the first row to the Nth row and the remaining odd columns of the matrix T; Starting from the first digit of "2N-3, 2N-5, ..., 3, 2, 4, ..., 2N-2", slide rightward with a sliding window of length N-1 to obtain N-1 groups of data, and sequentially fill them into the N+1th row to the 2N-1th row and the remaining odd columns of the matrix T.

[0041] Taking N=8 as an example, the matrix T generated according to the above rules is shown in Table 13 below.

[0042] Table 13: Matrix T

[0043] (4) Step S4: Iterative calculation based on the scheduling rule matrix T

[0044] Figure 2 This is a flowchart of iterative calculation in step S4. Figure 2 As shown, the iterative calculation specifically includes the following steps: S41. Assign the identity matrix I (2N×2N dimensions) to the matrix R and set the number of iterations (clean_num) to an initial value of 0; S42. Determine whether the number of iterations (clean_num) is less than M. If so, add 1 to the number of iterations and initialize the number of iteration steps (step_num) to 0 before proceeding to the next step. If not, output the current matrices S and R as the final real symmetric matrix S' and eigenvector matrix R'. S43, determine whether the number of iteration steps (step_num) is less than 2N-1, if not, return to the previous step; if so, execute steps S44 to S436; S44, assigning the identity matrix I to the matrix W; S45. Update the element values ​​of the corresponding row and column indexes in the matrix W according to the row and column indexes of the elements in the current row of the scheduling rule matrix T and the 2N-order real symmetric matrix S; S46. Update matrices S and R based on the updated matrix W, and then return to step S43.

[0045] Step S45 specifically includes the following steps: S451, calculate the row corresponding to the current iteration step according to the matrix S and the matrix T i The cosine value of the rotation angle c(j) and the sine value of the rotation angle s(j) ( ): , , , , in, Representation matrix middle OK The element value of represents the symbolic function, Indicates the cotangent value of 2 times the rotation angle; S452, update matrix W OK List, OK List, OK List, OK The elements of the columns are 、 、 、 :

[0046]

[0047]

[0048] .

[0049] In step S46, the matrix is ​​updated and matrix , the superscript H indicates the conjugate transpose.

[0050] Continuing with the example of the previous steps, after 10 parallel iterative calculations are performed based on the scheduling rule matrix T, the iterated matrices S' and R' are obtained. Columns 1 to 4, columns 5 to 8, columns 9 to 12, and columns 13 to 16 of the matrix S' are shown in Tables 14, 15, 16, and 17, respectively. Columns 1 to 4, columns 5 to 8, columns 9 to 12, and columns 13 to 16 of the matrix R' are shown in Tables 18, 19, 20, and 21, respectively.

[0051] Table 14: Columns 1 to 4 of the matrix S'

[0052] Table 15: Columns 5 to 8 of the matrix S'

[0053] Table 16: Columns 9 to 12 of the matrix S'

[0054] Table 17: Columns 13 to 16 of the matrix S'

[0055] Table 18: Columns 1 to 4 of matrix R'

[0056] Table 19: Columns 5 to 8 of matrix R'

[0057] Table 20: Columns 9 to 12 of matrix R'

[0058] Table 21: Columns 13 to 16 of matrix R'

[0059] (5) Step S5: Obtain eigenvalues ​​and eigenvectors

[0060] Step S5 specifically includes the following steps: S51. Arrange the diagonal elements of the real symmetric matrix S' in ascending order, and record the sorted odd index sequence: index(1), index(3), ..., index(2N-1); S52, the elements corresponding to the odd numbers 1, 3, ..., 2N-1 after the diagonal elements of the matrix S' are arranged in ascending order are the elements of the matrix The eigenvalues ​​of in ascending order; S53, according to the sorted odd index sequence, the matrix The corresponding columns of the matrix UV are taken out, the first N rows of the matrix UV are taken to form the matrix U, and the last N rows are taken to form the matrix V. Then the matrix The columns of are the eigenvectors corresponding to the eigenvalues ​​in ascending order.

[0061] Continuing with the above example, when N=8, the diagonal elements of the matrix S' obtained in step S51 are sorted in ascending order as index(1), index(3), ..., index(15). The elements corresponding to the odd numbers 1, 3, ..., 15 are the elements of the matrix The eigenvalues ​​of are arranged in ascending order, as shown in Table 22.

[0062] Table 22: Characteristic values

[0063] Take the corresponding columns of matrix R' to form matrix UV, take the first 8 rows of matrix UV to form matrix U, and the last 8 rows to form matrix V, and get matrix ,matrix The columns of are the eigenvectors corresponding to the eigenvalues ​​in ascending order. Columns 1~2, 3~4, 5~6, and 7~8 are shown in Table 23, Table 24, Table 25, and Table 26 respectively.

[0064] Table 23: Matrix 1~2 columns

[0065] Table 24: Matrix 3~4 columns

[0066] Table 25: Matrix 5~6 columns

[0067] Table 26: Matrix 7~8 columns

[0068] Use Matlab function eig() to transform the matrix Perform eigendecomposition and arrange the eigenvalues ​​in ascending order as shown in Table 27. Based on Tables 22 and 27, the absolute errors of the eigenvalues ​​can be calculated as shown in Table 28. Table 28 shows that using this method to perform parallel eigendecomposition on the Hermitian matrix, the eigenvalue accuracy can be accurate to 13 decimal places.

[0069] Table 27: Eigenvalues ​​in ascending order obtained using Matlab function

[0070] Table 28: Eigenvalue Absolute Error

[0071] It should be noted that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present invention can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solution of the present invention can be achieved. This embodiment is not limited here.

[0072] The embodiments described herein can be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.

[0073] Computer programs for implementing the methods of the present invention can be written in any combination of one or more programming languages ​​and stored in a computer-readable storage medium. These computer programs can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that when the computer program is executed by the processor, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The computer program can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0074] Computer-readable storage media can be tangible media that can contain or store a computer program for use with an instruction execution system, device or equipment or used in combination with an instruction execution system, device or equipment. Computer-readable storage media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, computer-readable storage media can be a machine-readable signal medium. More specific examples of machine-readable storage media can include electrical connections based on one or more lines, portable computer disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), optical fibers, compact disc read-only memories (CD ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0075] It should also be noted that this method is also applicable to other fields of mathematics, physics and engineering.

[0076] In summary, the Hermitian matrix parallel eigendecomposition method for the electromagnetic reconnaissance system provided by the embodiment of the present invention is based on the N-order Hermitian matrix of the electromagnetic reconnaissance system. The real and imaginary parts of the 2N-order real symmetric matrix S are constructed; and based on the scheduling rule matrix T, the 2N-order real symmetric matrix S and the eigenvector matrix R are iterated M times to obtain the corresponding real symmetric matrix S' and eigenvector matrix R'; finally, based on the elements of the matrix S' and the matrix R', the N-order Hermitian matrix is ​​obtained The present invention converts complex matrices into real matrices for processing and designs a scheduling rule matrix T for iterative calculations, achieving high decomposition accuracy (eigenvalues ​​can be accurate to 13 decimal places). The same processing method can be used for eigendecomposition of Hermitian matrices of odd or even dimensions, and is applicable to any processing system that supports parallel computing, thus having a wide range of applications.

[0077] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A Hermitian matrix parallel eigendecomposition method for electromagnetic reconnaissance systems, characterized in that: include: S1. Obtain the N-channel complex signal vector of the electromagnetic reconnaissance system and construct the N-order Hermitian matrix ; S2. Extract N-order Hermitian matrix The real and imaginary parts of are obtained to obtain an N-order real matrix A and an N-order imaginary matrix B; a 2N-order real symmetric matrix S is constructed based on matrices A and B; S3, generate The scheduling rule matrix T is composed of 2N elements from 1 to 2N arranged in a different order, and the elements in the first column are all 1; S4. After performing M iterations on the 2N-order real symmetric matrix S and the eigenvector matrix R based on the scheduling rule matrix T, the corresponding real symmetric matrix S' and the eigenvector matrix R' are obtained; S5. Based on the elements of matrix S' and matrix R', get the N-order Hermitian matrix The eigenvalues ​​and the eigenvectors corresponding to each eigenvalue.

2. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 1, characterized in that: In step S2, the matrix S is constructed as: .

3. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 1, characterized in that: In step S3, the arrangement rule of the first to Nth rows of the matrix T is: All elements in the first column are 1; Starting from the first digit of "2, 4, 6, ..., 2N, 2N-1, 2N-3, 2N-5, ..., 5, 3", slide rightward with a sliding window of length N to obtain N groups of data, and fill them sequentially into the even columns from the first row to the Nth row of the matrix T; Starting from the last digit of "3, 5, ..., 2N-1, 2N, 2N-2, ..., 4", slide leftward with a sliding window of length N to obtain N-1 groups of data, and fill them sequentially into the even columns from row N+1 to row 2N-1 of matrix T; Starting from the last digit of "2N-2, 2N-4, ..., 4, 2, 3, 5, ..., 2N-3, 2N-1", slide leftward with a sliding window of length N-1 to obtain N-1 groups of data, and fill them sequentially into the first row to the Nth row and the remaining odd columns of the matrix T; Starting from the first digit of "2N-3, 2N-5, ..., 3, 2, 4, ..., 2N-2", slide rightward with a sliding window of length N-1 to obtain N-1 groups of data, and sequentially fill them into the remaining odd columns from row N+1 to row 2N-1 of matrix T.

4. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to any one of claims 1 to 3, characterized in that: Step S4 specifically includes the following steps: S41, assign the 2N×2N identity matrix I to the matrix R and set the number of iterations to an initial value of 0; S42. Determine whether the number of iterations is less than M. If so, add 1 to the number of iterations and initialize the number of iterations to 0 before proceeding to the next step. If not, output the current matrices S and R as the final real symmetric matrix S' and eigenvector matrix R'. S43, determine whether the number of iteration steps is less than 2N-1, if not, return to the previous step; if so, execute steps S44 to S46; S44, assigning the identity matrix I to the matrix W; S45. Update the element values ​​of the corresponding row and column indexes in the matrix W according to the row and column indexes of the elements in the current row of the scheduling rule matrix T and the 2N-order real symmetric matrix S; S46. Update matrices S and R based on the updated matrix W, and then return to step S43.

5. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 4, characterized in that: Step S45 specifically includes the following steps: S451, calculate the rotation angle cosine value c(j) and the rotation angle sine value s(j) of the row corresponding to the current iteration step according to the matrix S and the matrix T, ; S452, based on 、 、 Update W OK List, OK List, OK List, OK Elements of a column.

6. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 5, characterized in that: In step S451, 、 Calculated by the following formula: ， ， ， ， in, Indicates the cotangent value of 2 times the rotation angle, Representation matrix middle OK The element value of Represents a symbolic function.

7. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 6, characterized in that: In step S452, the matrix W OK List, OK List, OK List, OK The elements of the columns are updated as 、 、 、 .

8. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to claim 6, characterized in that: In step S46, the matrix is ​​updated and matrix , the superscript H indicates the conjugate transpose.

9. The Hermitian matrix parallel eigendecomposition method for an electromagnetic reconnaissance system according to any one of claims 5 to 8, characterized in that: Step S5 specifically includes the following steps: S51. Arrange the diagonal elements of the real symmetric matrix S' in ascending order, and record the sorted odd index sequence: index(1), index(3), ..., index(2N-1); S52, the elements corresponding to the odd numbers 1, 3, ..., 2N-1 after the diagonal elements of the matrix S' are arranged in ascending order are the elements of the matrix The eigenvalues ​​of in ascending order; S53, according to the sorted odd index sequence, the matrix The corresponding columns of the matrix UV are taken out, the first N rows of the matrix UV are taken to form the matrix U, and the last N rows are taken to form the matrix V. Then the matrix The columns of are the eigenvectors corresponding to the eigenvalues ​​in ascending order.

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