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CPS615-Linear Programming and Whirlwind Full Matrix Discussion

This lecture covers two distinct areas.

Firstly a short discussion of LInear Programming -- what type of problems its used for, what the equations look like and basic issues in the difficult use of parallel processing

Then we give an abbreviated discussion of Full Matrix algorithms covering The types of applications that use them Matrix Multiplication including Cannon's algorithm in detail Use of MPI primitives including communicator groups Performance Analysis

CPS615Master96                   Master Set of Foils for 1996 Session 
                                  of CPS615
CPS713OPT                        CPS713 Lectures on Practical 
                                  Optimization Methods 1994-1996
CPS615Matrix95                   Parallel Full Matrix Algorithms

Table of Contents for CPS615-Linear Programming and Whirlwind Full Matrix Discussion

                   CPS615Master96 083 001 Delivered Lectures for 
                                          CPS615 -- Base Course for 
                                          the Simulation Track of 
                                          Computational Science
                                          Fall Semester 1996 --
                                          Lecture of December 5 - 1996
                   CPS615Master96 086 002 Abstract of Dec 5 1996 
                                          CPS615 Lecture

                        CPS713OPT 005 003 5:Examples IV -- Linear 
                                          Programming
                        CPS713OPT 046 004 46:Linear Programming
                        CPS713OPT 047 005 47:Convex Regions and Linear
                                           Programming
                        CPS713OPT 048 006 48:Matrix Formulation of 
                                          Linear Programming

                   CPS615Matrix95 003 007 Review of Matrices seen in 
                                          PDE's
                   CPS615Matrix95 004 008 Examples of Full Matrices in
                                           Chemistry
                   CPS615Matrix95 005 009 Operations used with 
                                          Hamiltonian operator
                   CPS615Matrix95 006 010 Examples of Full Matrices in
                                           Electromagnetics
                   CPS615Matrix95 007 011 Computational 
                                          Electromagnetics Formalism I
                   CPS615Matrix95 008 012 Computational 
                                          Electromagnetics Formalism 
                                          II
                   CPS615Matrix95 009 013 Comments on Computational 
                                          Electromagnetics
                   CPS615Matrix95 010 014 Summary of Use of Full 
                                          Matrices in Chemistry
                   CPS615Matrix95 011 015 Notes on the use of full 
                                          matrices
                   CPS615Matrix95 012 016 Full Matrix Multiplication
                   CPS615Matrix95 013 017 Sub-block definition of 
                                          Matrix Multiply
                   CPS615Matrix95 014 018 Some References
                   CPS615Matrix95 015 019 The First Algorithm
                                          (Broadcast, Multiply, and 
                                          Roll)
                   CPS615Matrix95 016 020 The first stage -- index n=0
                                           in sub-block sum -- of the 
                                          algorithm on N=16 example
                   CPS615Matrix95 017 021 The second stage -- n=1 in 
                                          sum over subblock indices --
                                           of the algorithm on N=16 
                                          example
                   CPS615Matrix95 018 022 Second stage, continued
                   CPS615Matrix95 019 023 Look at the whole algorithm 
                                          on one element
                   CPS615Matrix95 020 024 Cartesian Topology in MPI --
                                           General
                   CPS615Matrix95 026 025 Matrix Multiplication MPI 
                                          Style Pseudocode
                   CPS615Matrix95 027 026 Matrix Multiplication 
                                          Pseudocode, continued
                   CPS615Matrix95 032 027 Performance Analysis of 
                                          Matrix Multiplication
                   CPS615Matrix95 033 028 Cannon's Algorithm for 
                                          Matrix Multiplication
                   CPS615Matrix95 043 029 Parallel Decomposition

List of Foils Used as they occur

CPS615Master96                   Master Set of Foils for 1996 Session 
                                  of CPS615

CPS713OPT                        CPS713 Lectures on Practical 
                                  Optimization Methods 1994-1996

CPS615Matrix95                   Parallel Full Matrix Algorithms

CPS615Master96                   Master Set of Foils for 1996 Session 
                                  of CPS615

CPS713OPT                        CPS713 Lectures on Practical 
                                  Optimization Methods 1994-1996

CPS615Matrix95                   Parallel Full Matrix Algorithms