In this paper, we analyze how to calculate the matrix transposition in continuous flow by using a memory or group of memories. The proposed approach studies this problem for specific conditions such as square and non-square matrices, use of limited access memories and use of several memories in parallel. Contrary to previous approaches, which are based on specific cases or examples, the proposed approach derives the fundamental theory involved in the problem of matrix transposition in a continuous flow. This allows for obtaining the exact equations for the read and write addresses of the memories and other control signals in the circuits. Furthermore, the cases that involve non-square matrices, which have not been studied in detail in the literature, are analyzed in depth in this paper. Experimental results show that the proposed approach is capable of transposing matrices of 8192 × 8192 32-bit data received in series at a rate of 200 mega samples per second, which doubles the throughput of previous approaches.

中文翻译：

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使用存储器的连续流矩阵转置


在本文中，我们分析如何使用一个存储器或一组存储器来计算连续流中的矩阵转置。所提出的方法针对特定条件（例如方阵和非方阵、有限访问存储器的使用以及并行使用多个存储器）研究该问题。与之前基于具体案例或示例的方法相反，所提出的方法导出了连续流中矩阵转置问题所涉及的基本理论。这允许获得存储器的读取和写入地址以及电路中的其他控制信号的精确方程。此外，本文还对文献中尚未详细研究的涉及非方阵的情况进行了深入分析。实验结果表明，所提出的方法能够以每秒 200 兆样本的速率对串行接收的 8192 × 8192 32 位数据矩阵进行转置，这使之前方法的吞吐量增加了一倍。