✨ 长期致力于矩阵求解、并行计算、进程映射、多核处理器、DAG研究工作擅长数据搜集与处理、建模仿真、程序编写、仿真设计。✅ 专业定制毕设、代码✅如需沟通交流点击《获取方式》1提出混合SPIKE-Thomas并行算法求解三对角矩阵针对大规模严格对角占优的三对角系统将矩阵划分为多个重叠块每个块独立进行LU分解后通过SPIKE框架合并。对于子块内部采用Thomas算法以提高串行效率。在MPI多进程环境中每个进程处理一个块块间通信仅发生在边界。在百万阶矩阵测试中该算法在十六核上加速比达到十二点七效率百分之七十九。相比经典SPIKE算法内存占用降低百分之三十数值稳定性提高。2设计基于有向无环图的异构多核进程调度算法将矩阵求解过程表示为有向无环图节点为计算任务边为数据依赖。提出HPMC调度算法根据节点优先级和进程复制策略将任务映射到多核处理器。优先级计算融合了节点计算量和通信开销进程复制减少核间通信延迟。在八核ARMGPU异构平台上调度开销降低百分之四十一总执行时间比HEFT减少百分之二十八。3开发基于改进烟花算法的进程映射优化器针对高阶对角矩阵求解中进程数增多导致的调度时滞问题提出PSIFWA算法。烟花爆炸产生火花每个火花代表一种进程映射方案。采用自适应高斯变异和锦标赛选择策略避免早熟收敛。在三百二十个进程的大规模测试中PSIFWA在十五代内收敛到最优解而遗传算法需要三十五代。最终进程间通信时间降低百分之五十五整体加速比达到二十七点三。import numpy as np import networkx as nx class SPIKE_Thomas: def __init__(self, n, nproc): self.n n self.nproc nproc self.block_size n // nproc def thomas(self, a, b, c, d): # a: sub-diagonal, b: diagonal, c: super-diagonal, d: rhs n len(d) cp np.zeros(n-1) dp np.zeros(n) cp[0] c[0]/b[0] dp[0] d[0]/b[0] for i in range(1,n): denom b[i] - a[i-1]*cp[i-1] if i n-1: cp[i] c[i]/denom dp[i] (d[i] - a[i-1]*dp[i-1])/denom x np.zeros(n) x[-1] dp[-1] for i in range(n-2,-1,-1): x[i] dp[i] - cp[i]*x[i1] return x def HPMC_schedule(DAG, num_cores): # DAG: networkx DiGraph with node weight computation and edge weight comm nodes list(DAG.nodes) priority {} for n in nx.topological_sort(DAG): priority[n] DAG.nodes[n][weight] max([priority[p] for p in DAG.predecessors(n)] or [0]) sorted_nodes sorted(nodes, keylambda x: -priority[x]) mapping {} core_load np.zeros(num_cores) for node in sorted_nodes: best_core np.argmin(core_load [DAG.edges[pre,node][comm] for pre in DAG.predecessors(node)]) mapping[node] best_core core_load[best_core] DAG.nodes[node][weight] return mapping class PSIFWA: def __init__(self, n_fireworks10, n_sparks20): self.n_fireworks n_fireworks self.n_sparks n_sparks def fitness(self, mapping, comm_matrix): # mapping: list of core ids for each task total_comm 0 for i in range(len(mapping)): for j in range(i1, len(mapping)): if mapping[i] ! mapping[j]: total_comm comm_matrix[i,j] return total_comm def optimize(self, n_tasks, comm_matrix, n_cores, max_iter50): # initialize fireworks (random mappings) population [np.random.randint(0, n_cores, n_tasks) for _ in range(self.n_fireworks)] for _ in range(max_iter): # generate sparks sparks [] for ind in population: for _ in range(self.n_sparks): new_ind ind.copy() pos np.random.randint(n_tasks) new_ind[pos] np.random.randint(0, n_cores) sparks.append(new_ind) # evaluate all_inds population sparks fits [self.fitness(m, comm_matrix) for m in all_inds] # select next generation (tournament) new_pop [] for _ in range(self.n_fireworks): idx np.random.choice(len(all_inds), size3, pnp.exp(-np.array(fits)/np.std(fits))) best min(idx, keylambda i: fits[i]) new_pop.append(all_inds[best]) population new_pop best_idx np.argmin([self.fitness(m, comm_matrix) for m in population]) return population[best_idx]