Fundamentals of matrix computations

说明：  cuda矩阵乘法 通过GPU并行运算实现乘法的加速(cuda GPU parallel matrix multiplication operation by the accelerated realization of multiplication)

交错网格声波方程交错网格有限差分地震波场计算波场正演模拟。 (The CalCulation of the SeismiC Wave一 fieldwith Staggered-grid Finite difference Sheme )

自己编写的求可达矩阵，层次划分 代码.使用时，替换已有矩阵，即可运算！ (I have written for reachability matrix, the level of classified code. Use, replace the existing matrix, computing can be!)

二层地质模型波场模拟,用有限差分进行波场的模拟,充分利用多波多分量地震记录，以及各向异性方面的独特信息，可有效地减少 纵波勘探的多解性，定量地描述裂缝储层，改善某些纵波资料成像不好地区的构造 成像。这样可获得比纵波分辨率高的多波剖面，从而有利于研究小幅度构造、断层、 裂缝裂隙等复杂地质现象，对油气勘探与开发具有现实意义和实用价值(Two-layer geological model wave field simulation, using finite difference wave field simulation to make full use of multi-wave multi-component seismic records, and the anisotropy of the unique information can be effective in reducing the P-wave exploration, multi-solution and quantitatively describe the crack reservoir to improve the poor image of some P-wave data area structure imaging. This availability of higher resolution than the longitudinal wave of multi-wave profile, thus contributing to the small amplitude structures, faults, cracks, fissures and other complex geological phenomena, for oil and gas exploration and development of practical significance and practical value)

基于abaqus umat的修正的M-C子程序，《ABAQUS在隧道与地下工程中的应用》-陈卫忠，版权归作者所有(Based on the modified MC abaqus umat subroutine, " ABAQUS in the tunnel and underground engineering" - Chen Weizhong, copyright of all)

Description 设a[0…n-1]是一个包含n个数的数组，若在i<j的情况下，有a[i]>a[j]，则称(i, j)为a数组的一个逆序对（inversion）。 比如 <2,3,8,6,1> 有5个逆序对。请采用类似“合并排序算法”的分治思路以O(nlogn)的效率来实现逆序对的统计。 一个n个元素序列的逆序对个数由三部分构成： （1）它的左半部分逆序对的个数，（2）加上右半部分逆序对的个数，（3）再加上左半部分元素大于右半部分元素的数量。 其中前两部分（1）和（2）由递归来实现。要保证算法最后效率O(nlogn)，第三部分（3）应该如何实现？ 此题请勿采用O(n^2)的简单枚举算法来实现。 并思考如下问题： （1）怎样的数组含有最多的逆序对？最多的又是多少个呢？ （2）插入排序的运行时间和数组中逆序对的个数有关系吗？什么关系？ 输入格式 第一行：n，表示接下来要输入n个元素，n不超过10000。 第二行：n个元素序列。 输出格式 逆序对的个数。 输入样例 5 2 3 8 6 1 输出样例 5(Set a[0... N-1] is a n array containing n numbers. If there is a [i] > a [j] i n the case of I < j, then (i, j) is a n inversion pair of a array. For example, <2,3,8,6,1> has five reverse pairs. Please use the idea of "merge sorting algorithm" to achieve the statistics of inverse pairs with O (nlogn) efficiency. The number of inverse pairs of a sequence of n elements consists of three parts: (1) The number of reverse pairs in the left half, (2) the number of reverse pairs in the right half, (3) the number of elements in the left half is greater than that in the right half. The first two parts (1) and (2) are implemented by recursion. To ensure the final efficiency of the algorithm O (nlogn), how should the third part (3) be implemented? Do not use O (n ^ 2) simple enumeration algorithm to solve this problem.)

基于干扰矩阵的重置和导向矢量估计的数字波束形成，程序经过优化，可运行，里面包含了一个矩阵求积分的子程序，可参考(Reset based on interference matrix and steering vector estimation of digital beamforming, the program has been optimized to run, which contains a matrix integral subroutines, refer to)

无网格法移动最小二乘近似（MLS）型函数计算子程序 (Meshless method moving least square approximation (MLS) type function calculation subroutine)

频域二维卷积算法，通过在频域用fft计算，加速了卷积的实现过程(Frequency domain of two-dimensional convolution algorithm, by calculating the frequency domain using fft and accelerate the realization of the convolution process)

用三元组表为结构，实现稀疏矩阵的加法并输出。(Achieve sparse matrix addition)