LINPACK Introduction

CSTL HPC IT Mu Wei

Agenda

• LINPACK

• LINPACK & MATRIX

• HPL TEST

What’s LINPACK

• A collection of Fortran subroutines that analyze and sovlve linear equations and linea least-squares problems

• LINPACK100,LINPACK1000,HPL

LINPACK AND MATRIX

• Based on decompositional approach to numerical linear algebra

• Divide computational problem into two parts

• Ax=b

Organized around matrix decompositions

LINPACK AND MATRIX

LU Cholesky

QR singular value

NAME OF LINPACK

• T - Type of arithmetic

• XX - Reflect a fundamental division

• YY - Specifies task the subroutine is to perform

Name of LINPACK subroutine is divided into a prefix, an infix, a suffix as follow

EFFICIENCY

• Column orientation of the algorithms

• Use of Basic Liear Algebra Subprograms

Effects of two aspects of LINPACK on efficiency

How to Setup HPL

• Download Open source HPL

• Prequisites: 1) BLAS; 2)MPI

• Edit Data File

• Compile: $ make arch=Linux_PII_CBLAS

• Execute

DATA FILE$ cat HPL.dat HPLinpack benchmark input file Innovative Computing Laboratory, University of Tennessee HPL.out output file name (if any) 6 device out (6=stdout,7=stderr,file) 4 # of problems sizes (N) 29 30 34 35 Ns 4 # of NBs 1 2 3 4 NBs 0 PMAP process mapping (0=Row-,1=Column-major) 3 # of process grids (P x Q) 2 1 4 Ps 2 4 1 Qs

Key Parameters

• Estimate the LARGEST PROBLEM SIZE

• Expected Execution Time

• Expected Gflops

• Sample - Choose N=14k, then Time=52s

RESULT

Q & A