大型基因组亲缘矩阵求逆算法的优化研究

基因组选择常用的评估方法GBLUP和ssGBLUP都涉及到基因组亲缘矩阵的求逆，而大规模矩阵求逆运算非常耗时。本研究以提高大型基因组亲缘矩阵求逆运算的效率为目的。本研究通过真实数据和模拟数据构建基因组亲缘矩阵，引入Intel MKL矩阵函数，以减少迭代次数（方法1）和重复分块（方法2）两种方式改良分块迭代求逆算法，编程实现算法并在台式电脑和服务器上测试计算时间。结果表明，利用方法1计算4 000×4 000的基因组亲缘矩阵逆矩阵时，与MKL库函数的加速比为0.898。而16 000×16 000矩阵的计算速度为MKL库函数的1.006倍。利用方法2计算4 000×4 000矩阵的运算速度是MKL库函数的1.084倍；而在更大型的128 000×128 000基因组亲缘矩阵求逆运算时，该方法与MKL直接求逆函数的加速比为1.805倍。相比于MKL直接求逆函数，改进后的两种方法在效率上有一定程度的提升。

Optimization Study of Inverse Algorithm of Large Genomic Relationship Matrix

Both GBLUP and ssGBLUP methods involved in the inversion of genomic relationship matrices in genomic selection, and large-scale matrix inversion operations were time-consuming. The purpose of this study was to improve the efficiency of the inverse operation of large genomic relationship matrix. The genomic relationship matrix from real data and simulated data was constructed, and the Intel MKL matrix function was introduced, and the efficiency of matrix inversion was improved by reducing the number of iterations (method 1) and repeating the block (method 2), programming to implement algorithms and test computing time on desktop computers and servers. The results showed that the acceleration ratio of the direct inversion function with the MKL was 0.898 when calculating the genomic relationship matrix of 4 000×4 000 using method 1. The calculation speed of 16 000×16 000 was 1.006 times more than that of the inversion function in MKL; The calculation speed of method 2 in the 4 000×4 000 genomic relationship matrix was 1.084 times more than that of the MKL inversion function; For larger 128 000×128 000 matrix inversion operations, the acceleration ratio of this method was 1.805 times more than that of the inversion function in MKL. Compared with MKL direct inversion function, the improved two methods have higher efficiency.