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CPS615-Linear Programming and Whirlwind Full Matrix Discussion

Given by Geoffrey C. Fox at Delivered Lectures of CPS615 Basic Simulation Track for Computational Science on 5 Decemr 96. Foils prepared 29 December 1996

Secs 66.2

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


This mixed presentation uses parts of the following base foilsets which can also be looked at on their own!
Master Set of Foils for 1996 Session of CPS615
CPS713 Lectures on Practical Optimization Methods 1994-1996
Parallel Full Matrix Algorithms

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

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CPS 615 Lectures 1996 Fall Semester -- December 5 1996
1 Delivered Lectures for CPS615 -- Base Course for the Simulation Track of Computational Science
Fall Semester 1996 --
Lecture of December 5 - 1996
2 Abstract of Dec 5 1996 CPS615 Lecture

Linear Programming
3 5:Examples IV -- Linear Programming
4 46:Linear Programming
5 47:Convex Regions and Linear Programming
6 48:Matrix Formulation of Linear Programming

Full Matrix Problems
7 Review of Matrices seen in PDE's
8 Examples of Full Matrices in Chemistry
9 Operations used with Hamiltonian operator
10 Examples of Full Matrices in Electromagnetics
11 Computational Electromagnetics Formalism I
12 Computational Electromagnetics Formalism II
13 Comments on Computational Electromagnetics
14 Summary of Use of Full Matrices in Chemistry
15 Notes on the use of full matrices
16 Full Matrix Multiplication
17 Sub-block definition of Matrix Multiply
18 Some References
19 The First Algorithm
(Broadcast, Multiply, and Roll)
20 The first stage -- index n=0 in sub-block sum -- of the algorithm on N=16 example
21 The second stage -- n=1 in sum over subblock indices -- of the algorithm on N=16 example
22 Second stage, continued
23 Look at the whole algorithm on one element
24 Cartesian Topology in MPI -- General
25 Matrix Multiplication MPI Style Pseudocode
26 Matrix Multiplication Pseudocode, continued
27 Performance Analysis of Matrix Multiplication
28 Cannon's Algorithm for Matrix Multiplication
29 Parallel Decomposition

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