High-performance matrix operation acceleration method and system based on parallel computing

Abstract

This invention discloses a high-performance matrix operation acceleration method and system based on parallel computing, relating to the field of matrix operation technology. The method includes: multi-scale matrix decomposition: performing multi-scale decomposition on the matrix to be processed to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; parallel computing task allocation: distributing the sub-matrices of different scales obtained by decomposition to multiple parallel processing sub-units. This invention divides the matrix to be processed into sub-matrices of different resolutions through multi-scale decomposition, and combines parallel computing technology to distribute the sub-matrices to multiple parallel processing sub-units for simultaneous processing. At the same time, a cross-scale information transmission mechanism is designed to allow coarse and fine-scale sub-matrices to iterate collaboratively. The coarse-scale sub-matrices adopt an improved block Krylov subspace method and matrix preconditioning technology, while the fine-scale sub-matrices introduce an adaptive step-size conjugate gradient algorithm and establish inter-scale constraint relationships to achieve bidirectional feedback.

Description

Technical Field

[0001] This invention relates to the field of matrix operation technology, specifically to a high-performance matrix operation acceleration method and system based on parallel computing. Background Technology

[0002] In today's era of rapid technological development, many fields such as scientific computing, engineering simulation, and data analysis have increasingly stringent requirements for computing technology. As a core supporting technology in these fields, matrix operations are becoming increasingly important. With the explosive growth of data scale and the continuous increase in problem complexity, traditional matrix operation methods face enormous challenges when dealing with large-scale matrices, and new technologies are urgently needed to improve the performance and efficiency of matrix operations.

[0003] Traditional iterative algorithms for matrix operations have gradually revealed numerous serious shortcomings when faced with large-scale complex problems. On the one hand, their convergence speed is extremely slow; when processing large-scale matrices, a large number of iterations are often required to achieve acceptable accuracy. This not only significantly increases computation time but also leads to inefficient use of computing resources, failing to meet the demands of applications with high real-time requirements. On the other hand, traditional algorithms are prone to getting trapped in local optima and struggle to find the global optimum, thus affecting the accuracy and reliability of the results. Although the introduction of parallel computing technology has brought new opportunities to improve the efficiency of matrix operations by distributing computational tasks across multiple processing subunits... Parallel execution reduces computation time to some extent. However, existing parallel computing methods have overly simplistic strategies for processing submatrices when handling matrix operations, lacking flexibility and specificity. Submatrices at different scales have different characteristics and computational requirements, but existing methods fail to fully consider these differences, resulting in a lack of effective collaboration mechanisms between submatrices at different scales. This lack of collaboration hinders information exchange between processing units during parallel computing, making it impossible to fully utilize the inherent connections between submatrices at different scales. Consequently, it limits further improvements in overall computational efficiency and accuracy, making it difficult to meet the urgent need for high-performance matrix operations in large-scale computing scenarios. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a high-performance matrix operation acceleration method and system based on parallel computing. It can decompose a matrix into sub-matrices of different resolutions through multi-scale decomposition, design a cross-scale information transfer mechanism to achieve collaborative iteration of coarse and fine-scale sub-matrices. The coarse-scale sub-matrices adopt an improved block Krylov subspace method and matrix preconditioning technology, while the fine-scale sub-matrices introduce an adaptive step-size conjugate gradient algorithm and establish inter-scale constraint relationships to achieve bidirectional feedback. Finally, the final calculation result is obtained through result fusion, realizing efficient matrix operations and effectively improving computational efficiency and accuracy.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: On one hand, a high-performance matrix operation acceleration method based on parallel computing, the method comprising:

[0006] Multiscale matrix decomposition: The matrix to be processed is decomposed into multiple scales to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices;

[0007] Parallel computing task allocation: The sub-matrices of different scales obtained from the decomposition are allocated to multiple parallel processing sub-units. Each processing sub-unit is responsible for processing at least one sub-matrix. During the allocation process, load balancing is performed based on the size and complexity of the sub-matrix and the performance of the processing sub-unit.

[0008] Submatrix collaborative iterative processing: A cross-scale information transfer mechanism is designed. Each parallel processing subunit adopts an appropriate iterative strategy for the assigned submatrix to perform collaborative processing, and the inter-scale constraint relationship is realized by establishing a solution space mapping function.

[0009] Result fusion: The sub-matrix results obtained from each parallel processing sub-unit are fused. The fusion process combines the sub-matrix results according to the inverse process of multi-scale decomposition to obtain the final operation result of the matrix to be processed.

[0010] Furthermore, in the matrix multi-scale decomposition step, wavelet basis functions are selected from a preset wavelet basis function library or a multi-resolution analysis method is adopted based on the characteristics of the matrix to be processed. The number of decomposition layers and the scale parameters for dividing different scale ranges are set according to the matrix size and computational accuracy requirements. According to the set method and parameters, a coarse-scale sub-matrix that retains low-frequency features is generated by filtering and downsampling, and a fine-scale sub-matrix that retains high-frequency detail features is generated by filtering and upsampling, so that each sub-matrix reflects the characteristics of the original matrix at the corresponding scale.

[0011] Furthermore, in the parallel computing task allocation step, the size, proportion of non-zero elements, and complexity of the submatrix are extracted. The floating-point operations per second, memory capacity, and cache size of each parallel processing subunit are monitored in real time. Based on the submatrix characteristics and the performance of the processing subunit, a dynamic allocation strategy based on task complexity is adopted. The submatrix is ​​mapped to different parallel processing subunits through a load balancing algorithm, and each processing subunit processes at least one submatrix.

[0012] Furthermore, in the parallel computing task allocation step, a load balancing algorithm is used to map the submatrix to different parallel processing subunits. The algorithm formula is as follows: ,in For the first The amount of tasks allocated to each parallel processing subunit The number of sub-matrices allocated to this processing sub-unit. For the first The complexity coefficient of each submatrix For the first The processing subunit for the first The processing capability adaptation coefficient of each submatrix.

[0013] Furthermore, in the submatrix collaborative iterative processing step, cross-scale information transmission is achieved through shared memory or a message passing interface. For coarse-scale submatrices, an improved block Krylov subspace method is used, combined with matrix preconditioning techniques. Specifically, based on the traditional block Krylov subspace method, the number of dimensions of the subspace is increased to improve the approximation of the matrix features by the subspace. The matrix preconditioning technique uses incomplete LU decomposition preprocessing to decompose the original matrix into incomplete lower triangular and upper triangular matrices, thereby reducing the condition number of the matrix. The iterative process follows the formula... ,in For the coarse-scaled submatrix at the th The solution vector of the nth iteration. For the coarse-scaled submatrix The solution vector of the nth iteration. The iteration step size coefficients of the coarse-scaled submatrix are... For the first Improved block Krylov subspace operator for the next iteration solution It is the preconditioning matrix for the coarse-scaled submatrix.

[0014] Furthermore, in the submatrix collaborative iterative processing step, for the fine-scale submatrix, an adaptive step-size conjugate gradient algorithm is introduced to monitor the norm change of the local residual in real time, adjust the iteration step size and convergence criterion according to a preset threshold, use the solution range determined by the coarse-scale submatrix as the initial value and fine-tune it according to its own characteristics, and the iterative process satisfies the formula ,in For the fine-scale submatrix at the th The solution vector of the nth iteration. For the first The solution vector of the nth iteration. For the first Local residuals of the next iteration The adaptive step size function, It is the conjugate gradient operator.

[0015] Furthermore, in the submatrix collaborative iterative processing step, the inter-scale constraint relationship is realized by establishing a solution space mapping function, satisfying the cross-scale constraint formula. ,in For scale feedback coefficients, For the fine-scale solution The coarse-scale reference solution obtained by mapping is used to generate fine-scale physical constraint boundaries through interpolation. The fine-scale solution is then fed back to the coarse-scale model through filtering.

[0016] Furthermore, in the result fusion step, the sub-matrix results obtained from each parallel processing sub-unit are fused. A multi-scale reconstruction algorithm is used to weight and combine the results of each sub-matrix according to the inverse process of multi-scale decomposition. Specifically, the results of the fine-scale sub-matrix are upsampled and filtered, and then superimposed with the results of the coarse-scale sub-matrix according to the set weight coefficients to obtain the preliminary fusion result. The final fusion result satisfies the formula... ,in The final matrix operation result, For the first The result of iterative processing of the submatrices For the first The fusion weight coefficients corresponding to the submatrix results It is the number of all submatrices.

[0017] On the other hand, a high-performance matrix operation acceleration system based on parallel computing, the system comprising:

[0018] Matrix multi-scale decomposition module: used to decompose the matrix to be processed into multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices;

[0019] Task allocation module: used to distribute the submatrices of different scales obtained from the decomposition to multiple parallel processing subunits, and to balance the load based on the size and complexity of the submatrices and the performance of the processing subunits.

[0020] Cross-scale information transfer module: used to realize information transfer between coarse-scale and fine-scale submatrices, and establish inter-scale constraint relationships, so that the coarse-scale solution provides physical constraints for the fine-scale, and the fine-scale solution feeds back to correct the coarse-scale model;

[0021] The result fusion module is used to fuse the sub-matrix results obtained from each parallel processing sub-unit to obtain the final calculation result of the matrix to be processed.

[0022] Compared with existing technologies, this high-performance matrix operation acceleration method and system based on parallel computing has the following advantages:

[0023] I. This invention divides the matrix to be processed into sub-matrices of different resolutions through multi-scale decomposition. Combined with parallel computing technology, the sub-matrices are distributed to multiple parallel processing sub-units for simultaneous processing. At the same time, a cross-scale information transfer mechanism is designed to allow coarse and fine-scale sub-matrices to iterate collaboratively. The coarse-scale sub-matrices adopt an improved block Krylov subspace method and matrix preconditioning technology, while the fine-scale sub-matrices introduce an adaptive step-size conjugate gradient algorithm and establish inter-scale constraint relationships to achieve bidirectional feedback. This comprehensive processing method optimizes the matrix operation strategy, gives full play to the advantages of parallel computing, significantly improves the synergy and processing efficiency of matrix operations, and can obtain operation results more quickly.

[0024] Second, by introducing an adaptive step-size conjugate gradient algorithm, this invention can dynamically adjust the iteration parameters according to the changes in local residuals, better capture the detailed features of the matrix, and through the constraint relationship between scales, the coarse-scale solution provides physical constraints for the fine-scale solution, and the fine-scale solution feeds back to correct the coarse-scale model, making the final result fusion more accurate, enhancing the adaptability of the entire calculation process to matrices of different sizes and complexities, and effectively improving the calculation accuracy.

[0025] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0027] Figure 1 A flowchart of a high-performance matrix operation acceleration method based on parallel computing;

[0028] Figure 2 This is a block diagram of a high-performance matrix operation acceleration system based on parallel computing. Detailed Implementation

[0029] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0030] Example 1

[0031] In large-scale sparse matrix operations in the field of scientific computing, such as Figure 1As shown, a multi-scale matrix decomposition is first performed. Based on the element distribution pattern and sparsity of the large sparse matrix, a wavelet decomposition method is selected. Suitable wavelet basis functions are chosen from a pre-set wavelet basis function library. According to the size of the matrix and the accuracy requirements of scientific computing, the number of decomposition layers is set to 4, and corresponding scale parameters are defined. Each scale corresponds to a specific resolution. According to the set decomposition method and parameters, the large sparse matrix is ​​decomposed. Coarse-scale sub-matrices are generated through filtering and downsampling operations, and fine-scale sub-matrices are generated through filtering and upsampling operations. Each sub-matrix reflects the characteristics of the original matrix at the corresponding scale. The coarse-scale sub-matrix retains the low-frequency features of the original matrix, while the fine-scale sub-matrix retains the high-frequency detail features.

[0032] Next, parallel computing tasks are allocated, and features such as the size, proportion of non-zero elements, and complexity of each submatrix obtained from the decomposition are extracted. Simultaneously, performance metrics such as the number of floating-point operations per second, memory capacity, and cache size of the multiple parallel processing subunits used are monitored in real time. Based on the extracted submatrix features and the monitored processing subunit performance, a dynamic allocation strategy based on task complexity is adopted. A load balancing algorithm maps the submatrix to different parallel processing subunits, ensuring that each processing subunit processes at least one submatrix, and that the load across all processing subunits remains balanced, with the workload allocated to each processing subunit meeting the requirements. .

[0033] Then, submatrix collaborative iterative processing is performed, with cross-scale information transfer achieved through shared memory or message passing interfaces. For the allocated coarse-scale submatrix, the processing unit adopts an improved block Krylov subspace method, which improves computational stability by expanding the subspace dimension. Simultaneously, combined with matrix preconditioning techniques, incomplete LU decomposition preprocessing is used to process the coarse-scale submatrix. The iterative process follows... For the fine-scale submatrix, an adaptive step-size conjugate gradient algorithm is introduced into the processing sub-units to monitor the norm change of the local residuals in real time. The iteration step size and convergence criterion are dynamically adjusted according to a preset threshold. The solution range determined by the coarse-scale submatrix is ​​used as the initial value, and appropriate fine-tuning is performed according to the characteristics of the fine-scale submatrix itself. The iteration process satisfies During the iteration process, inter-scale constraints are established through a solution space mapping function. The coarse-scale solution generates fine-scale physical constraint boundaries through interpolation, and the fine-scale solution is filtered and fed back to the coarse-scale model, achieving coordinated iteration of the coarse-scale and fine-scale sub-matrices. This constraint relationship satisfies... .

[0034] Finally, the results are fused. Reconstruction parameters are set, and the fusion weight coefficients are determined based on the scale resolution of each sub-matrix. Sub-matrices with higher resolution have larger fusion weight coefficients. A multi-scale reconstruction algorithm is used, weighting and combining the processing results of each sub-matrix according to the inverse process of multi-scale decomposition. First, the results of the fine-scale sub-matrix are upsampled and filtered, then superimposed with the results of the coarse-scale sub-matrix according to the set weight coefficients to obtain the preliminary fusion result. The final fusion result satisfies... ,in This represents the number of all submatrices. Post-processing operations such as outlier removal and smoothing are performed on the initial fusion result to obtain the final computation result of this large sparse matrix.

[0035] Example 2

[0036] In high-dimensional dense matrix operation scenarios in the field of engineering simulation, the high-performance matrix operation acceleration method and system based on parallel computing of the present invention are applied.

[0037] First, a matrix multi-scale decomposition step is performed. Based on the size of the high-dimensional dense matrix and the accuracy requirements of the engineering simulation, a multi-resolution analysis method is selected, the number of decomposition layers is set to 3, and corresponding scale parameters are defined. Each scale corresponds to a specific resolution. According to the set multi-resolution analysis method and parameters, the high-dimensional dense matrix is ​​decomposed. Coarse-scale sub-matrices are generated through filtering and downsampling, and fine-scale sub-matrices are generated through filtering and upsampling. Each sub-matrix reflects the characteristics of the original matrix at the corresponding scale.

[0038] Next, parallel computing tasks are allocated. Features such as the size, proportion of non-zero elements, and complexity of each sub-matrix are extracted. Simultaneously, the performance metrics of the parallel processing units used are monitored in real time. Based on these sub-matrix features and the performance of the processing units, a dynamic allocation strategy based on task complexity is adopted. A load balancing algorithm is used to rationally distribute the sub-matrixes to different parallel processing units, such as... Figure 2 As shown, this ensures that each processing subunit processes at least one submatrix, thereby achieving load balancing among the processing subunits.

[0039] Then, the process enters the submatrix collaborative iterative processing stage. Cross-scale information transfer is achieved through shared memory. A shared memory region is set up, and each parallel processing subunit can read and write to this region. The relevant units for cross-scale information transfer ensure the consistency and timeliness of data transmission. For coarse-scale submatrices, the processing subunit adopts an improved block Krylov subspace method to expand the subspace dimension to improve computational stability. At the same time, combined with matrix preconditioning techniques, incomplete LU decomposition is used to preprocess the coarse-scale submatrix. For fine-scale submatrices, the processing subunit introduces an adaptive step-size conjugate gradient algorithm to dynamically adjust the iteration step size and convergence criterion according to the norm change of the local residual. The solution range determined by the coarse-scale submatrix is ​​used as the initial value, and fine-tuning is performed according to the characteristics of the fine-scale submatrix itself to establish inter-scale constraint relationships. Through the solution space mapping function, the coarse-scale solution is interpolated to generate the fine-scale physical constraint boundary. The fine-scale solution is filtered and fed back to the coarse-scale model to achieve collaborative iteration between the two.

[0040] Finally, the results are fused. Reconstruction parameters are set, and the fusion weight coefficients are set according to the scale resolution of the sub-matrices. A multi-scale reconstruction algorithm is adopted, and the processing results of each sub-matrix are weighted and combined according to the inverse process of multi-scale decomposition. First, the results of the fine-scale sub-matrix are upsampled and filtered, and then superimposed with the results of the coarse-scale sub-matrix according to the set weight coefficients to obtain the preliminary fusion result. The preliminary fusion result is then post-processed to obtain the final calculation result of the high-dimensional dense matrix, which meets the needs of engineering simulation.

[0041] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A high-performance matrix operation acceleration method based on parallel computing, characterized in that, The method includes the following specific steps: Multiscale matrix decomposition: The matrix to be processed is decomposed into multiple scales to obtain multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Parallel computing task allocation: The sub-matrices of different scales obtained from the decomposition are allocated to multiple parallel processing sub-units. Each processing sub-unit is responsible for processing at least one sub-matrix. During the allocation process, load balancing is performed based on the size and complexity of the sub-matrix and the performance of the processing sub-unit. Submatrix Collaborative Iterative Processing: A cross-scale information transfer mechanism is designed. Each parallel processing subunit adopts an appropriate iterative strategy for its assigned submatrix and performs collaborative processing. For coarse-scale submatrices, an improved block Krylov subspace method is used, combined with matrix preconditioning techniques. Specifically, based on the traditional block Krylov subspace method, the dimension of the subspace is increased to improve the approximation of the matrix features. The matrix preconditioning technique uses incomplete LU decomposition preprocessing to decompose the original matrix into incomplete lower triangular and upper triangular matrices, thereby reducing the condition number of the matrix. The iterative process follows the formula... ,in For the coarse-scaled submatrix at the th The solution vector of the nth iteration. For the coarse-scaled submatrix The solution vector of the nth iteration. The iteration step size coefficients of the coarse-scaled submatrix are... For the first Improved block Krylov subspace operator for the next iteration solution For the coarse-scale submatrix, a preconditioning matrix is ​​used. For the fine-scale submatrix, an adaptive step-size conjugate gradient algorithm is introduced to monitor the norm change of local residuals in real time. The iteration step size and convergence criterion are adjusted according to a preset threshold. The solution range determined by the coarse-scale submatrix is ​​used as the initial value and fine-tuned according to its own characteristics. The iteration process satisfies the formula... ,in For the fine-scale submatrix at the th The solution vector of the nth iteration. For the first The solution vector of the nth iteration. For the first Local residuals of the next iteration The adaptive step size function, It is a conjugate gradient operator, and the inter-scale constraint relationship is realized by establishing a solution space mapping function; Result fusion: The sub-matrix results obtained from each parallel processing sub-unit are fused. The fusion process combines the sub-matrix results according to the inverse process of multi-scale decomposition to obtain the final operation result of the matrix to be processed.

2. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that, In the matrix multi-scale decomposition step, wavelet basis functions are selected from a preset wavelet basis function library or a multi-resolution analysis method is adopted based on the characteristics of the matrix to be processed. The number of decomposition layers and the scale parameters for dividing different scale ranges are set according to the matrix size and computational accuracy requirements. According to the set method and parameters, a coarse-scale sub-matrix that retains low-frequency features is generated by filtering and downsampling, and a fine-scale sub-matrix that retains high-frequency detail features is generated by filtering and upsampling, so that each sub-matrix reflects the characteristics of the original matrix at the corresponding scale.

3. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that, In the parallel computing task allocation step, the size, proportion of non-zero elements, and complexity of the submatrix are extracted. The floating-point operations per second, memory capacity, and cache size of each parallel processing subunit are monitored in real time. Based on the submatrix characteristics and the performance of the processing subunit, a dynamic allocation strategy based on task complexity is adopted. The submatrix is ​​mapped to different parallel processing subunits through a load balancing algorithm, and each processing subunit processes at least one submatrix.

4. The high-performance matrix operation acceleration method based on parallel computing according to claim 3, characterized in that, In the parallel computing task allocation step, a load balancing algorithm maps the submatrix to different parallel processing subunits. The algorithm formula is as follows: ,in For the first The amount of tasks allocated to each parallel processing subunit The number of sub-matrices allocated to this processing sub-unit. For the first The complexity coefficient of each submatrix For the first The processing subunit for the first The processing capability adaptation coefficient of each submatrix.

5. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that, In the submatrix collaborative iterative processing step, the inter-scale constraint relationship is realized by establishing a solution space mapping function, satisfying the cross-scale constraint formula. ,in For scale feedback coefficients, For the fine-scale solution The coarse-scale reference solution obtained by mapping is used to generate fine-scale physical constraint boundaries through interpolation. The fine-scale solution is then fed back to the coarse-scale model through filtering.

6. The high-performance matrix operation acceleration method based on parallel computing according to claim 1, characterized in that, In the result fusion step, the sub-matrix results obtained from each parallel processing sub-unit are fused. A multi-scale reconstruction algorithm is used to weight and combine the sub-matrix results according to the inverse process of multi-scale decomposition. Specifically, the results of the fine-scale sub-matrix are upsampled and filtered, and then superimposed with the results of the coarse-scale sub-matrix according to the set weight coefficients to obtain the preliminary fusion result. The final fusion result satisfies the formula... ,in The final matrix operation result, For the first The result of iterative processing of the submatrices For the first The fusion weight coefficients corresponding to the submatrix results It is the number of all submatrices.

7. A high-performance matrix operation acceleration system based on parallel computing, the system being applicable to the high-performance matrix operation acceleration method based on parallel computing as described in any one of claims 1-6, characterized in that, The system includes: Matrix multi-scale decomposition module: used to decompose the matrix to be processed into multiple sub-matrices at different resolutions, including coarse-scale sub-matrices and fine-scale sub-matrices; Task allocation module: used to distribute the submatrices of different scales obtained from the decomposition to multiple parallel processing subunits, and to balance the load based on the size and complexity of the submatrices and the performance of the processing subunits. Cross-scale information transfer module: used to realize information transfer between coarse-scale and fine-scale submatrices, and establish inter-scale constraint relationships, so that the coarse-scale solution provides physical constraints for the fine-scale, and the fine-scale solution feeds back to correct the coarse-scale model; The result fusion module is used to fuse the sub-matrix results obtained from each parallel processing sub-unit to obtain the final calculation result of the matrix to be processed.

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