Hydra A library for data analysis in massively parallel platforms - - PowerPoint PPT Presentation
Hydra A library for data analysis in massively parallel platforms A. Augusto Alves Jr and Michael D. Sokoloff University of Cincinnati aalvesju@cern.ch Presented at NVIDIAs GPU Technology Conference, May 8-11, 2017 - Silicon Valley, US A.
University of Cincinnati aalvesju@cern.ch
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s t r u c t MyFunctor : p u b l i c hydra : : BaseFunctor<MyFunctor , double ,N > { // MyFunctor c o n s t r u c t o r and
implementation d e t a i l s . . . // User always need to implement the Evaluate () method template<typename T > __host__ __device__ i n l i n e double Evaluate (T∗ x ) { // a c t u a l c a l c u l a t i o n } } ;
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. . . // b a s i c a r i t h m e t i c
auto A_plus_B = A + B; auto A_minus_B = A − B; auto A_times_B = A ∗ B; auto A_per_B = A/B; // any composition
b a s i c
auto any_functor = (A − B)∗(A + B)∗(A/C ) ; // C(A,B) i s r e p r e s e n t e d by : auto compose_functor = hydra : : compose (C, A, B) . . .
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. . . double two = 2 . 0 ; // d e f i n e a si mpl e lambda and capture "two" auto my_lambda = [ ] __host__ __device__( double ∗ x ) { return two∗ s i n ( x [ 0 ] ) ; }; // c o n v e r t i s i n t o a Hydra f u n c t o r auto my_lamba_wrapped = hydra : : wrap_lambda (my_lambda ) ; . . .
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//two d i m e n s i o n a l p o i n t typedef hydra : : Point<GReal_t , 2> point_t ; //two d i m e n s i o n a l data s e t
the d e v i c e hydra : : PointVector <point_t , device > data_d (1 e6 ) ; . . . // get data from d e v i c e hydra : : PointVector <point_t , host> data_h ( data_d ) ; // f i l l a ROOT 2D histogram TH2D h i s t ( " h i s t " , "my histogram " , 100 , min , max ) ; f o r ( auto row : data_h ){ auto p o i n t ( row ) ; h i s t . F i l l ( p o i n t . GetCoordinate (0 ) , p o i n t . GetCoordinate ( 1 ) ) ; }
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// VegasState hold r e s o u r c e s and c o n f i g u r a t i o n s VegasState<N, device > State_d (_min , _max ) ; State_d . S e t I t e r a t i o n s ( i t e r a t i o n s ) ; State_d . SetMaxError ( max_error ) ; State_d . S e t C a l l s ( c a l l s ) ; State_d . S e t T r a i n i n g C a l l s ( t c a l l s ) ; State_d . S e t T r a i n i n g I t e r a t i o n s ( 1 ) ; // Vegas i n t e g r a t o r
Vegas<N, device > Vegas_d ( State_d ) ; // i n t e g r a t e a Gaussian Vegas_d . I n t e g r a t e ( Gaussian ) ;
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Iteration 1 2 3 4 5 6 7 8 9 Integral result 0.5 0.6 0.7 0.8 0.9 1
GPU Iteration result Cumulative result Number of samples 500 1000 1500 2000 2500 3000 3500 4000 4500
3
10 × Duration [ms] 5000 10000 15000 20000 25000 30000 Number of samples 500 1000 1500 2000 2500 3000 3500 4000 4500
3
10 × Speed-up GPU vs CPU 2 4 6 8 10 12 14
GPU CPU speed-up
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// Masses
the p a r t i c l e s hydra : : Vector4R Mother ( mother_mass ,
0 .0 , 0 . 0 ) ; double Daughter_Masses [ 3 ] { daughter1_mass , daughter2_mass , daughter3_mass }; // Create PhaseSpace
hydra : : PhaseSpace<3> phsp ( Mother_mass , Daughter_Masses ) ; // A l l o c a t e the c o n t a i n e r f o r the eve n ts hydra : : Events <3, device > even t s ( ndecays ) ; // Generate phsp . Generate ( Mother , even t s . begin ( ) , e ven ts . end ( ) ) ;
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) π M(K 0.5 1 1.5 2 2.5 3 3.5 4 4.5 ) π Ψ M(J/ 12 14 16 18 20 22 dalitz
Entries 1e+07 Mean x 2.312 Mean y 16.5 Std Dev x 1.105 Std Dev y 3.038
50 100 150 200 250 300 350 400 dalitz
Entries 1e+07 Mean x 2.312 Mean y 16.5 Std Dev x 1.105 Std Dev y 3.038
Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Duration [ms] 1 10
2
10
3
10 Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Speed-up GPU vs CPU 50 100 150 200 250 300
GPU CPU speed-up
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G a u s s A n a l y t i c I n t e g r a l G a u s s I n t e g r a l ( min , max ) ; E x p A n a l y t i c I n t e g r a l E x p I n t e g r a l ( min , max ) ; auto Gaussian_PDF = hydra : : make_pdf ( Gaussian , G a u s s I n t e g r a l ) ; auto Exponentia_PDF = hydra : : make_pdf ( Exponentia , E x p I n t e g r a l ) ; //add the pds to make a extended pdf model std : : array <hydra : : Parameter ∗ , 3> y i e l d s { NGaussian , NExponential } ; auto Model = hydra : : add_pdfs ( y i e l d s , Gaussian_PDF , Exponentia_PDF ) ; model . SetExtended ( 1 ) ; // get the FCN auto Model_FCN = hydra : : make_loglikehood_fcn ( Model , data_d ) ; // pass the FCN to Minuit2 . . .
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data
Entries 2e+07 Mean 5.499 Std Dev 3.694
X 2 4 6 8 10 12 14 Yield 100 200 300 400 500 600 700 800 900
3
10 × data
Entries 2e+07 Mean 5.499 Std Dev 3.694
data
Entries 2e+07 Mean 5.499 Std Dev 3.694
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The project is hosted on GitHub: https://github.com/MultithreadCorner/Hydra The package includes a suite of examples. It is being used at CERN on analyses aiming to measure the Kaon mass using large datasets.
To Karen Tomko and Bradley Hittle from the Ohio Supercomputer Center. To the University of Cincinnati LHCb group.
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Number of OpenMP threads 5 10 15 20 25 30 35 40 Duration [ms] 50 100 150 200 250 300 350
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Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Duration [ms] 1 10
2
10 Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Speed-up GPU vs CPU 2 4 6 8 10 12 14
GPU CPU speed-up
Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Duration [ms] 1 10
2
10 Number of events 1 2 3 4 5 6 7 8 9 10
6
10 × Speed-up GPU vs CPU 2 4 6 8 10 12 14
GPU CPU speed-up
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Number of OpenMP threads 5 10 15 20 25 30 35 40 Duration [ms] 1000 1500 2000 2500 3000 3500 4000 4500 5000
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