Dense Matrix LU Factorization With Balanced Submatrix Workloads
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Solution Overview
Problem
Existing matrix factorization methods for dense matrices suffer from imbalanced process load due to large block granularity, leading to reduced overall calculation efficiency in matrix multiplication.
Innovation Solution
A data processing method involving combined LU factorization and row switching operations is applied, dividing dense matrices into smaller submatrices for efficient matrix multiplication, ensuring balanced process load and improved overall factorization efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the dense matrix is divided into blocks at a large granularity to increase the amount of data for matrix multiplication, then matrix multiplication calculation efficiency is improved, but process load becomes imbalanced
Solution Approach 1:
The patent divides the dense matrix into multiple submatrices arranged in an M*M grid, where each submatrix can be independently processed. This fine-grained segmentation allows better distribution of calculation tasks across multiple processes, achieving balanced process load while maintaining efficient matrix multiplication through combined LU factorization and row switching operations on the segmented submatrices.
2Ease of operation
If the dense matrix is divided into blocks at a small granularity to balance process load, then process load balance is improved, but matrix multiplication calculation efficiency decreases
Solution Approach 1:
The patent combines LU factorization and row switching operations into a unified computational framework that operates on multiple submatrices simultaneously. This merging of operations allows the system to maintain small block granularity for load balance while achieving efficient matrix multiplication through the combined computational approach, resolving the efficiency loss that would normally result from fine-grained division.
Data Source
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AI summary
A data processing method and apparatus, and a related device are provided. LU factorization calculation is performed on to-be-processed data of an application, that is, a dense matrix; for a to-be-factorized matrix that needs to be factorized in each iteration process, LU factorization is performed on R columns of submatrices; and matrix multiplication calculation at a dimension of a product of R and a submatrix dimension is performed. The dimension of matrix multiplication calculation is large, and efficient matrix multiplication calculation can be implemented. In this way, the dense matrix can be divided into submatrices at a small granularity, to ensure high matrix multiplication calculation efficiency while implementing balanced process load, so as to improve overall matrix factorization calculation efficiency.