"矩阵实验报告：三对角、下三角和稀疏矩阵转置操作"

The purpose of this experiment is to create and manipulate different types of matrices, including lower triangular matrices and sparse matrices. The experiment took place at Shandong University's School of Software on October 25th, 2018, using a laptop running Windows 10 and Visual Studio 2017. The experiment consisted of three main parts. First, a lower triangular matrix class was created using the store and retrieve methods, implemented in a column-mapping manner. The store method allowed for the insertion of values into the lower triangular matrix, while the retrieve method allowed for the retrieval of specific elements from the matrix. Secondly, a tridiagonal matrix class was created, also using the store and retrieve methods in a column-mapping manner. This class allowed for the creation and manipulation of tridiagonal matrices, with the store method enabling the insertion of values and the retrieve method facilitating the retrieval of specific elements. Finally, a sparse matrix class was created, utilizing the row-major order to map the sparse matrix to a one-dimensional array. This class also implemented methods for transposing the sparse matrix and performing addition operations on two sparse matrices. The experiment was conducted with the aim of gaining a better understanding of matrix structures and their manipulation. The implementation of these different types of matrices provided a hands-on opportunity to work with various data structures and algorithms, contributing to a deeper understanding of their practical applications. Overall, the experiment was successful in achieving its objectives, providing valuable insight into the creation and manipulation of different types of matrices. Additionally, it allowed for practical experience in working with data structures and algorithms, furthering the understanding of their real-world significance.