CSC4700-Monte Carlo Methods скачать в хорошем качестве

CSC4700-Monte Carlo Methods

This lecture introduces Monte Carlo methods in scientific computing, focusing on their implementation in C++. Also, the students will learn to generate pseudo-random numbers using C++ libraries, create histograms to visualize data distributions, and apply Monte Carlo methods to estimate mathematical values like the average length of lines in a unit square and the value of π. The lecture also delves into parallelizing Monte Carlo simulations using HPX, addressing challenges like race conditions and cache contention. [00:00:00] - Intro [00:00:19] - Monte Carlo Method Introduction [00:01:44] - Generating Random Numbers [00:04:14] - Simple Random Number Sequences [00:05:11] - Generating Numbers in Ranges [00:06:07] - C++ Random Number Facilities [00:07:16] - Seeding and Reproducibility [00:08:43] - Using random_device and Mersenne Twister [00:11:04] - Thread Safety and Random Number Generation Summary [00:11:18] - Histogram Implementation Introduction [00:11:39] - What is a Histogram? [00:13:23] - Histogram Data Members and Initialization [00:15:38] - Adding Values to Histogram [00:17:00] - C++ Constructors and Initialization Details [00:18:36] - Adding and Normalizing Histogram Data [00:21:19] - Using Standard Algorithms for Normalization [00:24:46] - Using the Histogram Class in Practice [00:25:38] - Plotting Libraries and matplotlib-cpp in C++ [00:28:31] - Applying Monte Carlo Simulations [00:29:45] - Monte Carlo Example: Line in a Unit Square [00:32:41] - Assessing Accuracy and Error Rates [00:33:51] - Monte Carlo Example: Dice Probability [00:37:09] - Running the Simulation and Interpreting Results [00:38:23] - Monte Carlo Example: Estimating Pi [00:41:11] - Observations on Iterations and Empirical Results [00:41:55] - Parallelization Concepts and Prerequisites [00:44:29] - Embarrassingly Parallel Problems [00:46:55] - Coding Parallelization in HPX [00:49:14] - Results and Issues with Initial Parallelization [00:51:23] - Race Conditions: Examples and Explanation [00:53:30] - Synchronization and Mutual Exclusion [00:56:42] - Applying Mutex Knowledge to Code [00:57:38] - Performance and Problems with Mutex-Based Solution [00:59:06] - Introducing Atomic Variables [01:00:56] - Issues with Atomic Approach and Cache Contention [01:01:47] - Efficient Solution: One Counter per Thread [01:05:16] - Memory Impact and Speedup Tradeoffs [01:05:50] - Upcoming Assignment and Birthday Problem Preview [01:06:52] - Course Project Option [01:08:59] - Project Discussion and Examination