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Numerical package for Lua – Cours et formation gratuit

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Numlua: a n umer ical pac kage for Lua Luis Car v alho

BrownUniversity carvalho@dam.brown.edu LuaWorkshop July,2008

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Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines

•Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(3)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel)

•Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(4)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua!

•Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(5)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint

•Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(6)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods

•Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(7)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC

•Easy:semanticallyrichbutsimple •Free:MITlicense

(8)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple

•Free:MITlicense

(9)

Introduction NumericLuaLuaWor

•Alotofproblemsinscientificcomputingneedhighperformance numericalroutines •Generalapproach:heavycomputationsinlowlevelroutines (FORTRANorC)wrappedinascriptingorOOlanguage(highlevel) •Promisingcandidate:Lua! •Performance:fastexecutionandsmallfootprint •Powerful:GC,functionalfacilities,coroutines,metamethods •Extensible:simpleandwelldefinedAPIinANSIC •Easy:semanticallyrichbutsimple •Free:MITlicense

(10)

NumericLua NumericLuaLuaWor

•Basedon“classical”numericalpackages

•Motivation:keepminimalistapproachfromLuainordertoprovidea basisformoreelaboratedscientificpackages •Components •Complexnumbers •Specialfunctions(Exps+CDFs+PDFs) •Randomnumbergeneration(MT+Ranlib) •Numericallinearalgebra(BLAS+LAPACK)

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NumericLua NumericLuaLuaWor

•Basedon“classical”numericalpackages •Motivation:keepminimalistapproachfromLuainordertoprovidea basisformoreelaboratedscientificpackages

•Components •Complexnumbers •Specialfunctions(Exps+CDFs+PDFs) •Randomnumbergeneration(MT+Ranlib) •Numericallinearalgebra(BLAS+LAPACK)

(12)

NumericLua NumericLuaLuaWor

•Basedon“classical”numericalpackages •Motivation:keepminimalistapproachfromLuainordertoprovidea basisformoreelaboratedscientificpackages •Components •Complexnumbers •Specialfunctions(Exps+CDFs+PDFs) •Randomnumbergeneration(MT+Ranlib) •Numericallinearalgebra(BLAS+LAPACK)

(13)

Numlua–Features NumericLuaLuaWor

•SomeOOandfunctionalflavor,butnoparadigmcompromise

•Matrixtypesystem:general,triangular,symmetric,andposdef •Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink) •ImplementedinANSICandthusasportableasLua •StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs •MITlicense

(14)

Numlua–Features NumericLuaLuaWor

•SomeOOandfunctionalflavor,butnoparadigmcompromise •Matrixtypesystem:general,triangular,symmetric,andposdef

•Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink) •ImplementedinANSICandthusasportableasLua •StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs •MITlicense

(15)

Numlua–Features NumericLuaLuaWor

•SomeOOandfunctionalflavor,butnoparadigmcompromise •Matrixtypesystem:general,triangular,symmetric,andposdef •Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink)

•ImplementedinANSICandthusasportableasLua •StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs •MITlicense

(16)

Numlua–Features NumericLuaLuaWor

•SomeOOandfunctionalflavor,butnoparadigmcompromise •Matrixtypesystem:general,triangular,symmetric,andposdef •Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink) •ImplementedinANSICandthusasportableasLua

•StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs •MITlicense

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Numlua–Features NumericLuaLuaWorkshop’08

•SomeOOandfunctionalflavor,butnoparadigmcompromise •Matrixtypesystem:general,triangular,symmetric,andposdef •Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink) •ImplementedinANSICandthusasportableasLua •StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs

•MITlicense

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Numlua–Features NumericLuaLuaWorkshop’08

•SomeOOandfunctionalflavor,butnoparadigmcompromise •Matrixtypesystem:general,triangular,symmetric,andposdef •Small:interpreter+libs≈1.25Mb(staticlink)or200Kb(dynamiclink) •ImplementedinANSICandthusasportableasLua •StandardinterfacetoBLAS/LAPACK:canbelinkedtomanyoptimized libs •MITlicense

(19)

Numlua–Examples NumericLuaLuaWor

functioncirc1(v) localn=table.getn(v) localm=matrix.zeros(n) fori=1,ndo forj=1,ndo m[i][j]=v[(j-i)%n+1] end end returnm end

functioncirc2(v) localn=table.getn(v) returnmatrix.zeros(n):apply( function(i,j)returnv[(j-i)%n+1]end) end

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Numlua–Examples NumericLuaLuaWor

functioncirc1(v) localn=table.getn(v) localm=matrix.zeros(n) fori=1,ndo forj=1,ndo m[i][j]=v[(j-i)%n+1] end end returnm end functioncirc2(v) localn=table.getn(v) returnmatrix.zeros(n):apply( function(i,j)returnv[(j-i)%n+1]end) end

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Numlua–Examples NumericLuaLuaWor

localr=rng(os.clock()) functionmvnorm(mean,var,n) localu,info=matrix.chol(var)--u’ *u=var assert(info==0,"matrixisnotpositivedefinite") --y:col(i)∼N(0_m,I_m) localm=mean:size() localy=matrix(m,n):map( function(e)returnr:norm(0,1)end) --u’*y+mean∼N(mean,var) y=#u*y fori,j,einy:entries()do y[i][j]=e+mean[i] end returny end

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Futurework NumericLuaLuaWor

•Documentation!

•MovetoLuarocks •Newinternalrepresentationformatrices •Usetokenfilterstomakematrixdeclarationeasier(lesspainfull) •Extensions:HDF5,sparsematrices,statlibrary,plottinglibrary,...

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Futurework NumericLuaLuaWor

•Documentation! •MovetoLuarocks

•Newinternalrepresentationformatrices •Usetokenfilterstomakematrixdeclarationeasier(lesspainfull) •Extensions:HDF5,sparsematrices,statlibrary,plottinglibrary,...

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Futurework NumericLuaLuaWor

•Documentation! •MovetoLuarocks •Newinternalrepresentationformatrices

•Usetokenfilterstomakematrixdeclarationeasier(lesspainfull) •Extensions:HDF5,sparsematrices,statlibrary,plottinglibrary,...

(25)

Futurework NumericLuaLuaWor

•Documentation! •MovetoLuarocks •Newinternalrepresentationformatrices •Usetokenfilterstomakematrixdeclarationeasier(lesspainfull)

•Extensions:HDF5,sparsematrices,statlibrary,plottinglibrary,...

(26)

Futurework NumericLuaLuaWor

•Documentation! •MovetoLuarocks •Newinternalrepresentationformatrices •Usetokenfilterstomakematrixdeclarationeasier(lesspainfull) •Extensions:HDF5,sparsematrices,statlibrary,plottinglibrary,...

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Thankyou! NumericLuaLuaWor

Lua Nu

er m

ic

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