lqcd, mg, and qlua - bu blogs

LQCD, MG, and Qlua

Andrew [email protected]

Monday, November 4, 13

mailto:[email protected]

mailto:[email protected]

OUTLINE

Iterative solvers and multigrid

Application domain: lattice QCD

Algorithm design with Qlua

References


ITERATIVE SOLVERS AND MULTIGRID



Ax=b



Hilbert spaces

Vector space operations

Homomorphisms

Linear operators


LATTICE QCD


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


QLUA


QLUA

Scripting language Lua with domain-specific extensions

$


QLUA


$ 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


$ 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$


QLUA

Extensions implement algebraic structuresLattices - Tori and Stencils


QLUA


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


QLUA


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


QLUA


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


QLUA


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


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


QLUA

Extensions implement algebraic structuresLQCD-specific data types


QLUA

Extensions implement algebraic structuresLQCD-specific data types - Vectors


QLUA


lx = qcd.lattice{24,48}


QLUA


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


QLUA


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


QLUA


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()


QLUA

Extensions implement algebraic structuresLQCD operations


QLUA

Extensions implement algebraic structuresLQCD operations - Vector spaces


QLUA

Extensions implement algebraic structuresLQCD operations - Vector spaces


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


QLUA

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


QLUA

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


rho = lx:DiracFermion()

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


QLUA

Extensions implement algebraic structuresCollectives - Linear maps


QLUA


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


QLUA



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


QLUA



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


QLUA

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


QLUA

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


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


http://www.usqcd.org

http://www.usqcd.org

http://www.lua.org

http://www.lua.org

https://usqcd.lns.mit.edu/qlua

https://usqcd.lns.mit.edu/qlua



lqcd, mg, and qlua - bu blogs

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