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Performance Evaluation of Parallel

Numerical Libraries

Outline

 Introduction

 To Whom it may concern

 Parallel Libraries

 Underlying Architecture

 Cluster  SGI

 Performance Metrics

 Project Schedule

Limits to Serial Computing

 Both physical and practical limits impose on development of serial computing  The speed of light  How fast data can move through hardware  The size of an atom  Limit will be reached on how small components can be  The time it takes for an electron to change state  Heating issues in processors  Economic limitations  It is increasingly expensive to make a single processor faster

To Whom it may Concern

 Top500.org provides statistics on parallel computing

Netlib.org

 Source of FREE mathematical libraries

 Collection of mathematical software, papers, and databases

 Primary Institutions:

• University of Tennessee, Knoxville
• Oak Ridge National Laboratory
• University of California: Berkeley

BLAS

 Basic Linear Algebra Subprograms

 Performs basic vector and matrix operations

 Originally the BLAS library is a Fortran library

 Possible to call the functions from this library from a C program

 A standardized C language interface, named

CBLAS is also available

PBLAS

 Parallel Basic Linear Algebra Subprograms

 Parallel version of BLAS

 Performs linear algebra operations on distributed-memory concurrent computers

 A major component of the ScaLAPACK library

PBLAS

 Three Levels  Level 1  Vector-Vector Operations (swap, copy, addition, dot product)  Level 2  Matrix-Vector Operations (multiply, rank-updates, outer-product)  Level 3  Matrix-Matrix Operations (multiply, transpose, rank-updates)

LAPACK

 Linear Algebra PACKage

 Interfaces

 FORTRAN, C , C++, Java…

 Languages

 FORTRAN-

 Tackle three types of advanced problems

 Solution to a set of simultaneous linear equations  Eigen-value/Eigen-vector problems  Linear least squares fitting

SCALAPACK

 Scalable Linear Algebra PACKage

 Most of LAPACK

 High level of portability

 ScaLAPACK contains and is built on PBLAS

PETSc

 Portable Extensible Toolkit for Scientific Computation

 Very popular parallel library

Who Uses PETSc??

 PETSc has been successfully employed in applications in:  Nano-simulations  Biology/Medical  Imaging and Surgery  Fusion  Environmental/Subsurface Flow  Computational Fluid Dynamics  Wave propagation and the Helmholz equation  Many and many more

Earlier Projects in PIEAS regarding parallel processing

 Some parallel algorithms developed at PIEAS

 Faster Matrix Multiplication Algorithm Student: Asif Raza batch-  Search Algorithms for Discrete Optimization Problems Student: Asim Anwar batch-

Cluster

 Cluster computing distributes the computational load to collections of similar machines

 Each Computer (Node) is a complete Computer

 Connected to each other via a high speed bus

 Job broken up into blocks of data and executed independently

 Cheap and easy to produce