基于GPU的多层次并行QR分解算法研究

QR分解作为一个基本计算模块,广泛应用在图像处理、信号处理、通信工程等众多领域.传统的并行QR分解算法只能挖掘计算过程中的数据级并行.在分析快速Givens Rotation分解特征的基础上,提出了一种多层次并行算法,能够同时挖掘计算过程中的任务级并行和数据级并行,非常适合于以图形处理器(GPU)为代表的大规模并行处理器.同时,采用GPU的并行QR分解算法可以作为基本运算模块被GPU平台上的众多应用程序直接调用.实验结果显示,与CPU平台上使用OpenMP实现的算法相比,基于GPU的多层次并行算法能够获得5倍以上的性能提升,而调用QR分解模块的奇异值分解(SVD)应用可以获得3倍以上的性能提升.     

一种改进的二维局部均值分解算法

针对二维局部均值分解(BLMD)对图像进行多尺度分解时,计算过程费时,模态混叠现象严重的问题,提出一种快速自适应二维局部均值分解算法(FABLMD)。算法首先通过图像极值点信息计算顺序统计滤波器(OSF)窗口大小;然后利用OSF求图像上下包络曲面,进而得到包络估计函数和局部均值函数;最后在新的筛分终止条件下经过有限次迭代,快速将图像分解成一系列尺度不同的分量图像。仿真结果表明,改进算法计算速度更快,模态混叠现象得到有效抑制,对图像中不同频率成分的分解能力和效率都要优于BLMD。     

利用蚁群算法实现基于MP的信号稀疏分解

信号的稀疏表示在信号处理的许多方面有着重要的应用,但稀疏分解计算量十分巨大,难以产业化应用。利用蚁群算法实现快速寻找MatchingPursuit(MP)过程每一步的最优原子,大大提高了信号稀疏分解的速度,算法的有效性为实验结果所证实。     

采用图分解的特征识别算法研究

CAD/CAE模型转换,其关键在于如何将模型分解为最简单元,这些单元往往具有相近的网格划分属性,可以方便估计计算误差和计算时间。基于此提出了基于图分解的特征识别算法,对属性邻接图进行分解,根据分解后的属性邻接图中的连通分量生成体特征。该算法不再局限于特征类型,只要合理控制顶点的可分解性判断就可以得到期望的模型分解结果;同时该算法可以获得体特征,使得可以在特征这一粒度上进行特征删除和替换,以方便地完成模型的简化。     

大数据环境下基于概率矩阵分解的个性化推荐

概率矩阵分解是近几年广泛应用的协同过滤推荐方法。针对如何利用矩阵分解技术提高推荐质量以及在大数据环境下如何突破计算时间、计算资源瓶颈等问题进行研究,提出了Improved Probabilistic Matrix Factorization(IPMF)融入邻居信息的概率矩阵分解算法,并且提出了parallel-IPMF (p-IPMF)算法来解决融入邻居信息后计算复杂度高和难以并行化等问题。 在MapReduce并行计算框架下将p-IPMF算法加以实现,并在真实数据集上进行验证。实验结果表明,所提算法能有效提高推荐质量并缩短计算时间。     

嵌入式DSP系统中SDF模型的层次化存储优化方法

在同步数据流模型(SDF)描述的嵌入式数字信号处理(DSP)系统中,计算体单一出现调度(SAS)算法对于存在反馈环和数据密集处理的应用不可解或内存优化效果很差.文中提出了将SAS和Non-SAS类型调度算法相结合的层次化的存储优化方法,定义了数据密集分量和强连通分量来描述环和数据密集处理结构,并依据数据优先消耗原则设计了启发式的Non-SAS调度算法对分量进行存储优化.该方法适用于任意SDF模型,并有良好的存储优化效果.实验结果证明了其有效性.     

一种新的图像稀疏分解快速算法

图像的稀疏表示特别适合于图像的处理，而求得图像稀疏表示的图像稀疏分解的计算量十分巨大。利用基于Matching Pursuit(MP)方法实现的图像稀疏分解算法，采用遗传算法快速寻找MP过程中每一步分解的最佳原子。根据寻找最佳原子的遗传算法的内在特点，提出了一种优化的快速算法。算法的有效性为实验结果所证实。     

基于环Zn上圆锥曲线的ElGamal数字签名方案

首先介绍了剩余类环Zn上圆锥曲线Cn(a,b)的基本性质,给出了基于环Zn上圆锥曲线的ElGamal数字签名方案及其数值模拟.该方案综合利用了大数分解的困难性和有限群上计算离散对数问题的困难性,从而增强了该数字签名方案的安全性.由于在Cn(a,b)上明文的嵌入,阶的运算以及点的运算都比较容易,且通过引进标准二进制计算群元素的整数倍的算法,使该方案具有运算速度快,更易于实现等优点.     

基于GPU的稀疏矩阵Cholesky分解

稀疏矩阵Cholesky分解是求解大规模稀疏线性方程组的核心算法,也是求解过程中最耗时的部分.近年来,一系列并行算法通过图形处理器(GPU)获得了显著的加速比,然而,由于访存的不规则性以及任务间的大量数据依赖关系,稀疏矩阵Cholesky分解算法在GPU上的计算效率很低.文中实现了一种新的基于GPU的稀疏矩阵Cholesky分解算法.在数据组织方面,改进了稀疏矩阵超节点数据结构,通过超节点合并和分块控制计算粒度;在计算调度方面,将稀疏矩阵Cholesky分解过程映射为一系列的数据块任务,并设计了相应的任务生成与调度算法,在满足数据依赖性的前提下提高任务的并行性.实验结果表明,该算法能够显著提高稀疏矩阵Cholesky分解算法在GPU上的实现效率,在单个GPU上获得了相对4核CPU平台2.69~3.88倍的加速比.     

基于值分解的多智能体深度强化学习综述

基于值分解的多智能体深度强化学习是众多多智能体深度强化学习算法中的一类,也是多智能体深度强化学习领域的一个研究热点。它利用某种约束将多智能体系统的联合动作值函数分解为个体动作值函数的某种特定组合,能够有效解决多智能体系统中的环境非稳定性和动作空间指数爆炸等问题。文中首先说明了进行值函数分解的原因;其次,介绍了多智能体深度强化学习的基本理论;接着根据是否引入其他机制以及引入机制的不同将基于值分解的多智能体深度强化学习算法分为3类：简单因子分解型、基于IGM(个体-全局-最大)原则型以及基于注意力机制型;然后按分类重点介绍了几种典型算法并对算法的优缺点进行对比分析;最后简要阐述了所提算法的应用和发展前景。     

Reconstruction of edges in digital building models

Traditionally, the geometry of building components or rooms is either described by their boundary or it is defined by constructive solid models. Modeling tools are available which are based on the principle of constructing building components and of composing a building by adding building components step by step. However, topological relations are relevant besides the shape of components and rooms. These topological relationships are not necessarily explicit information in boundary representation or constructive solid models. As a consequence, they must be computed. At present time, there exists to the best knowledge of the author only a single approach in this subject area that is able to reconstruct topological relations including their geometry. The objects which need to be considered are building components, built-in components and rooms. The challenge is to calculate the three relevant aspects of geometry in digital building models completely and in an efficient way. These three relevant aspects are clashes, voids and contact faces. The existing approach to calculate these aspects is based on space partitioning concepts. Space partitioning concepts store neighboring relations explicitly. The approach presented in this paper is also based on space partitioning. One basic and novel consideration of the approach presented in this paper is to execute the reconstruction procedure in a mesh. The mesh itself is not refined anymore at a certain point during the calculations to avoid uncontrollable refinements. The second basic and novel consideration is the way of avoiding topological inconsistencies. Integer values are chosen for coordinates, and a specific algorithm is presented that guarantees that topological inconsistencies cannot occur. The research presented in this paper addresses the first step on the way to compute clashes, voids and contact faces. This is the reconstruction of edges. This paper presents the theory and a pilot implementation for the reconstruction of straight edges. Examples show the benefits of the approach presented. Open questions are discussed.     

基于Delaunay四面体剖分的网格分割算法

为了构建有意义曲面分片,提出一种基于Delaunay四面体剖分的网格分割算法.首先根据Delaunay四面体剖分得到多边形网格内部的四面体,求出每个面上反映网格内部信息的Delaunay体距离;然后对Delaunay体距离进行平滑处理,再对网格上面的Delaunay体距离进行聚类,用高斯混合模型对Delaunay体距离作柱状图的拟合,利用期望最大化算法来快速求得拟合结果;最后结合图切分技术,同时考虑聚类的结果、分割区域的边界平滑和视觉认知中的最小规则,得到最终的网格分割结果.实验结果表明,采用文中算法可以有效地实现有意义的网格分割.     

Offsetting operations on non-manifold topological models

This paper describes non-manifold offsetting operations that add or remove a uniform thickness from a given non-manifold topological model. The mathematical definitions and properties of the non-manifold offsetting operations are investigated first, and then an offset algorithm based on the definitions is proposed and implemented using the non-manifold Euler operators proposed in this paper. In this algorithm, the offset elements of minimal size for the vertices, edges and faces of a given non-manifold model are generated first. Then, they are united into a single body using the non-manifold Boolean operations. In order to reduce computation time and numerical errors, the intersections between the offset elements are calculated considering the origins of the topological entities during union. Finally, all topological entities that are within the offset distance are detected and removed in turn. In addition to the original offset algorithm based on mathematical definitions, some variant offset algorithms, called sheet thickening and solid shelling, are proposed and implemented for more practical and efficient solid modeling of thin-walled plastic or sheet metal parts. In virtue of the proposed non-manifold offset operation and its variations, different offsetting operations for wireframes, sheets and solids can be integrated into one and applied to a wide range of applications with a great potential usefulness.     

知识图谱划分算法研究综述

知识图谱是人工智能的重要基石,因其包含丰富的图结构和属性信息而受到广泛关注.知识图谱可以精确语义描述现实世界中的各种实体及其联系,其中顶点表示实体,边表示实体间的联系.知识图谱划分是大规模知识图谱分布式处理的首要工作,对知识图谱分布式存储、查询、推理和挖掘起基础支撑作用.随着知识图谱数据规模及分布式处理需求的不断增长,...     

Face coloring in unstructured CFD codes

We propose an algorithm for preventing race conditions in the evaluation of the surface integral contributions in edge-based CFD solvers by coloring the faces (or edges) of the computational mesh. We use a partitioning algorithm that separates the edges of triangular elements into three groups, the faces of quadrilateral and tetrahedral elements into four groups, and the faces of hexahedral elements into six groups. Our method is also applicable to hybrid meshes. We then extend this partitioning to adaptively refined, nonconforming meshes. We use the coloring to reduce code memory requirements by eliminating buffering. The coloring is also used to renumber and reorder elemental data to optimize reading and writing to memory, thus reducing access latencies and accelerating computations.     

Surface reconstruction by multiaxial triangulation

Outlines for reconstructing object surfaces are traditionally drawn from sequential images in parallel planes. The method presented here instead supports complex object topologies by drawing contours from multiaxial image planes. Multiaxial triangulation of an object in a given data volume involves four steps. First, the user generates contours interactively by selecting sample planes inside the data volume, then drawing object contours from the image corresponding to this sample plane. Our algorithm for multiaxial triangulation then processes these contours to verify consistency within and between sample planes. Second, it uses the sample planes containing the contours to partition the data volume into a divided volume. The contours are partitioned against the plane boundaries, and the contour parts (chains) are associated with faces, edges, and vertices in the divided volume. Third, these chains are joined into closed loops in the divided volume. Fourth, the loops are triangulated patchwise to create the surface model     

Graph-based extraction of two-connected morphological features from boundary representations

In this paper a feature extraction technique to isolate two-connected features from a boundary model is discussed. The technique involves identification of faces with multiple edge loops and faces sharing multiple edges as candidates for entrance faces of such features. It is observed that the two-connected features constitute tri connected components in the edge-face graphs of the boundary models. Heuristics are used to enhance an algorithm to decompose the edge-face graph of a boundary representation into its triconnected components. Pros and cons of this method are compared with the classic graph theoretic algorithm used to obtain triconnected components from a graph.     

Edge-based identification of DP-features on free-form solids

Numerous applications in mechanical CAD/CAM need robust algorithms for the identification of protrusion and depression features (DP-features) on geometric models with free-form (B-spline) surfaces. This paper reports a partitioning algorithm that first identifies the boundary edges of DP-features and then creates a surface patch to cover the depressions or isolate the protrusions. The novelty of the method lies in the use of tangent continuity between edge segments to identify DP-feature boundaries that cross multiple faces and geometries.     

An algorithm for the medial axis transform of 3D polyhedral solids

The medial axis transform (MAT) is a representation of an object which has been shown to be useful in design, interrogation, animation, finite element mesh generation, performance analysis, manufacturing simulation, path planning and tolerance specification. In this paper, an algorithm for determining the MAT is developed for general 3D polyhedral solids of arbitrary genus without cavities, with nonconvex vertices and edges. The algorithm is based on a classification scheme which relates different pieces of the medial axis (MA) to one another, even in the presence of degenerate MA points. Vertices of the MA are connected to one another by tracing along adjacent edges, and finally the faces of the axis are found by traversing closed loops of vertices and edges. Representation of the MA and its associated radius function is addressed, and pseudocode for the algorithm is given along with recommended optimizations. A connectivity theorem is proven to show the completeness of the algorithm. Complexity estimates and stability analysis for the algorithms are presented. Finally, examples illustrate the computational properties of the algorithm for convex and nonconvex 3D polyhedral solids with polyhedral holes     

有限元并行计算自动分区方法的优化

针对集群系统下动力学问题的大规模显式有限元并行计算的特点,在对多层次谱二分分区方法各个阶段的算法进行分析和试验的基础上,对其相关阶段的分区策略和算法进行了优化和调整,提出了一种多层次谱二分优化分区方法,并应用该方法对不同几何类型的有限元模型进行了分区测试,得到了满意的结果．与多层次谱二分分区方法相比,多层次谱二分优化分区方法的分区效果和分区效率都得到了明显改善．