Inverse operation method for lower triangle complex matrix with any order

Abstract

The invention relates to an inverse operation method for a lower triangle complex matrix with any order. The inverse operation method comprises the following steps that (1) a reciprocal obtaining unit is set, and is used for carrying out reciprocal obtaining operation on a diagonal element of an N-order matrix L, and outputting a matrix obtained after reciprocal obtaining operation is accomplished; (2) a multiplication and accumulation unit is set and is used for receiving the matrix obtained after reciprocal obtaining operation is accomplished, and multiplication and accumulation operation is carried out on the first element to the (i-1)th element in the ith row in the matrix; (3) a reciprocal multiplication obtaining unit is set and is used for receiving the accumulation result corresponding to the elements in the ith row of the matrix, reciprocal obtaining operation is carried out on the accumulation result, and then the accumulation result processed through reciprocal obtaining operation is multiplied by a diagonal element in the ith row so that a matrix element of the ith row of an inverse matrix L-1 can be obtained. In the whole process, a plurality of multiplication and accumulation units are used for carrying out parallel calculation. The inverse operation method for the lower triangle complex matrix with any order has the advantages that the inverse operation of the lower triangle complex matrix with any order can be achieved, and restriction caused by the number of operation units does not exist; only the design of a multiply-accumulator with one plural adder and one plural multiplier is adopted, hardware resources are saved, and operation efficiency is ensured through an effective parallelization mode.

Description

technical field [0001] The invention relates to a hardware structure and a realization method of matrix inversion, in particular to a triangular complex matrix inversion operation method of any order. Background technique [0002] There are many methods for matrix inversion, such as adjoint matrix method, elementary transformation method, block matrix method, Gaussian elimination method, etc. Most of the methods have problems such as complex calculation process and large storage resource requirements, and are not suitable for hardware implementation. At present, the method based on matrix factorization is mainly used in the hardware platform. There are three main methods based on matrix decomposition: LU decomposition, QR decomposition and Cholesky decomposition. Among them, although QR decomposition has a wide range of applications, the calculation process is too complicated and is not suitable for hardware implementation; although Cholesky decomposition is relatively simp...

AI Technical Summary

Problems solved by technology

At present, the most widely used hardware implementation of lower triangular matrix inversion operation is the systolic array structure, which has the advantages of high parallelism and less operation execution cycle, but the disadvantages are also obvious: the consumption of hardware resources is very large, and the required floating point The number of computing units and the order N of the matrix have a square function relationship; and the timing control is more complicated, which makes the data communication between computing units very frequent

Although it has been improved and optimized many times, the systolic array structure is still very complex, and it is difficult to achieve high-order matrix inversion

At present, there is no hardware implementation design that can effectively solve the above problems. Therefore, it is necessary to redesign and optimize the hardware implementation structure of the lower triangular matrix inversion

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