High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

Algorithm 4

Advanced shifted histogram (1D algorithm).

(1)   procedure   ASH𝑎,𝑏,𝑛,𝑥,𝑛bin,𝑚,𝑓_𝑚

(2)    𝛿=(𝑏−𝑎)/𝑛bin; ℎ=𝑚𝛿;

(3)    for   𝑘=1…𝑛bin   do

(4)      𝑣_𝑘=0; 𝑦_𝑘=0;

(5)    end for

(6)    for   𝑖=1…𝑛   do

(7)      𝑘=𝑥_𝑖−𝑎/𝛿+1;

(8)      if   𝑘∈[1,𝑛bin]   then

(9)       𝑣_𝑘=𝑣_𝑘+1;

(10)     end if

(11)   end for

(12)   for   𝑘=1…𝑛bin   do

(13)     if   𝑣_𝑘=0   then

(14)      𝑘=𝑘+1;

(15)     end if

(16)     for   𝑖=max{1,𝑘−𝑚+1}…min{𝑛bin,𝑘+𝑚−1}   do

(17)      𝑦_𝑖=𝑦_𝑖+𝑣_𝑘𝑓_𝑚(𝑖−𝑘);

(18)     end for

(19)   end for

(20)   for   𝑘=1…𝑛bin   do

(21)     𝑦_𝑘=𝑦_𝑘/(𝑛ℎ);

(22)     𝑡_𝑘=𝑎+(𝑘−0.5)𝛿;

(23)   end for

(24)   return   {𝑡_𝑘}_{1≤𝑘≤𝑛bin}, {𝑦_𝑘}_{1≤𝑘≤𝑛bin}.

(25)  end procedure