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Spark-based distributed matrix inversion parallel operation method

A dense matrix and computing method technology, applied in complex mathematical operations, concurrent instruction execution, computing, etc., can solve the problems of large matrix, unfriendly users, fault tolerance, poor scalability, etc., achieve good fault tolerance, improve computing Efficiency, Quantity Reduction Effect

Inactive Publication Date: 2016-03-02
NANJING UNIV
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Problems solved by technology

The two main problems addressed by the present invention are: the existing matrix scale is very large, and the traditional single computer serial operation method is not feasible; the existing distributed matrix parallelization scheme has poor fault tolerance and scalability, and is not convenient friendly

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  • Spark-based distributed matrix inversion parallel operation method
  • Spark-based distributed matrix inversion parallel operation method
  • Spark-based distributed matrix inversion parallel operation method

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Embodiment Construction

[0019] like figure 1 As shown, the implementation of the present invention is to convert the distributed row matrix in the distributed file system into a distributed block matrix, run the LU decomposition parallelization algorithm of the distributed block matrix, and then perform the distributed update in the decomposition result The triangular matrix and the distributed lower triangular matrix respectively run the inversion parallelization algorithm to find their inverse matrix, and then use the permutation matrix obtained by the original LU decomposition and the obtained inverse matrix of the two triangular matrices to run distributed matrix multiplication, The final result is obtained, which is the inverse matrix of the original input matrix.

[0020] The complete process of the present invention includes three parts: LU decomposition of distributed dense matrix, inversion of distributed triangular matrix (namely upper triangular matrix and lower triangular matrix as claime...

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Abstract

The invention discloses a Spark-based distributed matrix inversion parallel operation method. The method comprises the following steps: carrying out parallel LU decomposition operation on an input matrix in an iteration process; taking a distributed upper triangular matrix and a distributed lower triangular matrix obtained through the LU composition as basis so as to the inverse matrixes of the distributed upper triangular matrix and the distributed lower triangular matrix by using a recursive algorithm; and finally taking a permutation matrix and the inverse matrixes of the triangular matrixes obtained in the above two steps as basis so as to implement distributed matrix multiplication to obtain the inverse matrix of any original input matrix. According to the method, the dense matrixes with large dimensionalities can be processed, and relatively high operation efficiency as well as relatively good fault tolerance and expandability can be obtained.

Description

technical field [0001] The present invention relates to the technical field of linear algebra (LinearAlgebra) operation, in particular to a distributed parallel computing method based on the one-stop big data processing platform Spark's distributed dense matrix inversion operation. Background technique [0002] With the advent of the era of big data, the amount of data has grown explosively. The scale of data that people need to calculate and analyze is getting larger and larger, and the requirements for operating efficiency and accuracy are getting higher and higher. In many fields such as scientific computing, data mining, and machine learning, the solution to many problems can be abstracted into a series of operations centered on matrix operations. However, as an intermediate calculation step in common complex data calculation and analysis tasks, the inversion operation of large-scale matrices is a very time-consuming process. One of the main reasons is that the calculati...

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Application Information

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IPC IPC(8): G06F17/16G06F9/38G06F17/30
CPCG06F9/3818G06F16/182G06F17/16
Inventor 黄宜华顾荣高兴坤
Owner NANJING UNIV
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