本文選題：奇異值分解 + 現(xiàn)場可編程邏輯門陣列　； 參考：《北京交通大學》2017年碩士論文

【摘要】：奇異值分解(singular value decomposition)是數(shù)值計算學科中的一個重要組成,并且在諸如無線通信領域的大規(guī)模MIMO、圖像處理領域的特征提取及主成分分析、機器學習領域的數(shù)據(jù)壓縮、詞義索引和大數(shù)據(jù)領域的數(shù)據(jù)相關性分析中都發(fā)揮著至關重要的作用。奇異值分解算法是計算復雜度相對較高的矩陣分解算法,而且隨著數(shù)據(jù)處理規(guī)模的不斷增加,無論在通信方向的大規(guī)模MIMO中,還是對于矩陣維度及數(shù)據(jù)量都更加龐大的圖像及數(shù)據(jù)挖掘等研究與應用場景中,對于奇異值分解的運算速度都有越來越高的需求,因此對矩陣奇異值分解的加速方案實現(xiàn)具有很高的研究與應用價值。本文重點研究了基于單邊Jacobi方法的矩陣奇異值分解,該算法具有相對精度高、分解速度快的特點,是一種非常適合并行化和大規(guī)模矩陣計算的一種旋轉(zhuǎn)運算方法。對于Jacobi算法而言,旋轉(zhuǎn)變換和列對排序?qū)Ψ纸獾乃俣扔袥Q定性作用,本文對不同的矩陣列對索引方式進行了研究,并將兩種序列生成方式,循環(huán)序列和指環(huán)序列應用到硬件設計當中。其中指環(huán)序列的列對排序方式,不僅利于并行化實現(xiàn),而且可以得到有序排列奇異值矩陣,并對算法的收斂速度也有積極的促進作用。針對實時性、低延遲需求,本文提出了基于片上存儲的循環(huán)序列單邊Jacobi變換算法硬件架構,其性能相比于相同算法的MATLAB方案和GPU方案有很明顯加速效果,保持了相當?shù)臄?shù)值精度。在此基礎上,設計實現(xiàn)了一種基于片上存儲以及指環(huán)序列方式的并行化硬件加速方案,相比于循環(huán)序列方式,實測加速比達到2.95倍。其次,針對大規(guī)模、高吞吐率的圖像處理以及數(shù)據(jù)挖掘等應用場景,為解決片內(nèi)存儲容量與硬件設計復雜的問題,提出了基于片外存儲器和指環(huán)序列的單邊Jacobi算法的并行架構設計,并且基于性能與資源的關系,提出了其在并行化硬件設計上性能與資源的平衡策略。
[Abstract]:Singular value decomposition (singular value decomposition) is an important component of numerical computing, and it plays an important role in large scale MIMO in the field of wireless communications, feature extraction and principal component analysis in the field of image processing, data compression in machine learning, word meaning index and data correlation analysis in large data fields. The singular value decomposition algorithm is a matrix decomposition algorithm with relatively high computational complexity, and as the scale of data processing is increasing, the singular values are in the large-scale MIMO of the communication direction, or in the research and application scenarios, such as the matrix dimension and the data mining, which are more large in the matrix dimension and the data amount. The computing speed of decomposition is higher and higher, so the acceleration scheme of matrix singular value decomposition has high research and application value. This paper focuses on the singular value decomposition of matrix based on single side Jacobi method. This algorithm has the characteristics of high relative precision and fast decomposition speed, which is very suitable for parallelization and large scale. A rotation operation method of scale matrix calculation. For Jacobi algorithm, the rotation transformation and column pair sorting have a decisive effect on the speed of decomposition. In this paper, the index mode of different matrix columns is studied, and two kinds of sequence generation, cyclic sequence and ring sequence are applied to the hardware design. The sequence method is not only conducive to parallel implementation, but also can get an orderly array of singular value matrices, and it also has a positive effect on the convergence speed of the algorithm. In view of real time and low delay demand, this paper proposes a hardware architecture of the single side Jacobi transform algorithm based on the memory on chip. Its performance is compared to the same algorithm. The MATLAB scheme and the GPU scheme have obvious acceleration effect and maintain a considerable numerical accuracy. On this basis, a parallel hardware acceleration scheme based on the on-chip storage and the ring sequence is designed and implemented. Compared with the cyclic sequence, the measured acceleration ratio is 2.95 times. Secondly, for large-scale, high throughput images. In order to solve the problem of complex memory storage capacity and hardware design, the parallel architecture design of single side Jacobi algorithm based on external memory and ring sequence is proposed. Based on the relationship between performance and resources, the balance strategy of performance and resources in the design of parallel hard pieces is proposed.
【學位授予單位】：北京交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TP301.6;TN791

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