LQCD, MG, and Qlua

Andrew Pochinskyavp@mit.edu

Monday, November 4, 13

OUTLINE

Iterative solvers and multigrid

Application domain: lattice QCD

Algorithm design with Qlua

References

ITERATIVE SOLVERS AND MULTIGRID

Hilbert spaces

Vector space operations

Homomorphisms

Linear operators

LATTICE QCD

Tori in n-dim

LATTICE QCD

Tori in n-dim

Simple (constant) stencil structures

LATTICE QCD

Tori in n-dim

Physics encoded in parallel transport coefficients

LATTICE QCD

Tori in n-dim

Non-hermitian operators

LATTICE QCD

Tori in n-dim

Non-hermitian operators

Large condition numbers

Scripting language Lua with domain-specific extensions

$ cat sines.qluarequire "stdlib"for i = 1, 5 do printf("sin(%d deg) = %7.5f\n", i, math.sin(i*math.pi/180));end$

$ cat sines.qluarequire "stdlib"for i = 1, 5 do printf("sin(%d deg) = %7.5f\n", i, math.sin(i*math.pi/180));end$ qlua sines.qluasin(1 deg) = 0.01745sin(2 deg) = 0.03490sin(3 deg) = 0.05234sin(4 deg) = 0.06976sin(5 deg) = 0.08716$

Extensions implement algebraic structuresLattices - Tori and Stencils

require "stdlib"lx = qcd.lattice {4, 2}

require "stdlib"lx = qcd.lattice {4, 2}A = lx:Real(lx:pcoord(1) + 10 * lx:pcoord(0))

require "stdlib"lx = qcd.lattice {4, 2}A = lx:Real(lx:pcoord(1) + 10 * lx:pcoord(0))B = A:shift(0, "from_backward")

require "stdlib"lx = qcd.lattice {4, 2}A = lx:Real(lx:pcoord(1) + 10 * lx:pcoord(0))B = A:shift(0, "from_backward")for i = 0, lx[0] -‐ 1 do for j = 0, lx[1] -‐ 1 do printf("[%d %d]: %3d %3d\n", i, j, A[{i,j}], B[{i,j}]) endend

require "stdlib"lx = qcd.lattice {4, 2}A = lx:Real(lx:pcoord(1) + 10 * lx:pcoord(0))B = A:shift(0, "from_backward")for i = 0, lx[0] -‐ 1 do for j = 0, lx[1] -‐ 1 do printf("[%d %d]: %3d %3d\n", i, j, A[{i,j}], B[{i,j}]) endend$ qlua ts.qlua[0 0]: 0 30[0 1]: 1 31[1 0]: 10 0[1 1]: 11 1[2 0]: 20 10[2 1]: 21 11[3 0]: 30 20[3 1]: 31 21

Extensions implement algebraic structuresLQCD-specific data types

Extensions implement algebraic structuresLQCD-specific data types - Vectors

lx = qcd.lattice{24,48}

lx = qcd.lattice{24,48}rnd = lx:RandomState(35, lx:pcoord(0) + 24 * lx:pcoord(1))

lx = qcd.lattice{24,48}rnd = lx:RandomState(35, lx:pcoord(0) + 24 * lx:pcoord(1))phi = rnd:gaussian_DiracFermion()

lx = qcd.lattice{24,48}rnd = lx:RandomState(35, lx:pcoord(0) + 24 * lx:pcoord(1))phi = rnd:gaussian_DiracFermion()g = rnd:gaussian_ColorMatrix()r = lx:Real(lx:pcoord(0)) + 0.5 * rnd:gaussian_Real()

Extensions implement algebraic structuresLQCD operations

Extensions implement algebraic structuresLQCD operations - Vector spaces

rho = lx:DiracFermion()psi = g * phi + 6.5 * rho

Extensions implement algebraic structuresFull set of arithmetic operations on lattice data objects

rho = lx:DiracFermion()

function LinOp(x) return g * x + r * xend

Extensions implement algebraic structuresCollectives - Linear maps

srcL = qcd.lattice{7,6}dstL = qcd.lattice{4,2}I0 = srcL:Int(...)I1 = srcL:Int(...)V = srcL:Int(...)

gx = qcd.gather(dstL, srcL, {I0, I1})

gx = qcd.gather(dstL, srcL, {I0, I1})Wadd = gx:add(V)Wmax = gx:max(V)Wxor = gx:xor(V)

Scripting language Lua with domain-specific extensionsExtensions implement algebraic structures

Lattices - Tori and StencilsLQCD-specific data types - VectorsLQCD operations - Vector spaces, OperatorsCollectives - Linear mapsAccess to QIO files - real data

More tutorials at https://usqcd.lns.mit.edu/w/index.php/QLUA_tutorials

REFERENCES

http://www.usqcd.org/http://www.lua.org/https://usqcd.lns.mit.edu/qluahttps://usqcd.lns.mit.edu/w/index.php/QLUA_tutorials

LQCD, MG, and Qlua - BU Blogs

Documents

May 25-26, 2006 LQCD Computing Review1 Jefferson Lab 2006 LQCD Analysis Cluster Chip Watson Jefferson Lab, High Performance Computing

Meson spectrum in the SU(Nc) phase of finite T & mu in SC-LQCD

Blogs @ Butlerblogs.butler.edu/marykatebueltmanneportfolio/files/2012/...Blogs @ Butler

LQCD Workflow Discussion

Culture meets Blogs: Fallbeispiele kultureller Blogs & Blogaktionen

Automatic LQCD Code Generation

Estudios de caso de blogs corporativos y blogs periodísticos

Introducción a los blogs Curso Blogs Tutoriales Academia Usero

BLOGS EDUCATIVOS ¿Qué es un blog? Estructura de un blog La blogosferaEdublogs Blogs personales Blogs Colaborativos Blogs de Centros Blogs de Alumnos Blogs

LQCD Project Execution Plan · 2015-04-22 · LQCD-ext II Project Execution Plan Change Log Revision No. Description / Pages Affected Effective Date Preliminary Project Execution

level Accelerating LQCD with GPUs - Fermilabconferences.fnal.gov/supercomputing/SC2011/images/LQCD-2.pdfof Domain Decomposition Algorithm Fermilab has just deployed a GPU cluster with

LQCD Workflow Discussion Fermilab, 18 Dec 2006 Mike Wilde

Planning Library Blogs. Creating Usable Blogs

Blogs de la UAB · Blogs de la UAB

SWOT Analysis Music Blogs Kyle Krahenbuhl. The Blogs

LQCD Clusters at JLab

Causal Mechanisms: Yes, But - BU Blogs - Boston University

Lattice QCD, Programming Models and Porting LQCD codes to ... · Lattice QCD, Programming Models and Porting LQCD codes to Exascale Bálint Joó - Jefferson Lab Feb 19, 2020 HPC Roundtable

Bu bu bu !!!

7 Immunology and the enigma of selfhood - BU Blogs - Boston