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

Algorithm 3

1-Dimensional Monte Carlo Markovian Algorithm.

(1)   Generate 𝑡₁ according with 𝑝𝑡₁=𝑝𝑡₁∣𝑡₀=0

(2)   if   𝑡₁<𝑡_max   then             ▹  Generate the initial state.

(3)    𝑃_𝑁≥1=∫^𝑡max₀𝑝𝑡₁∣𝑡₀𝑑𝑡₁;        ▹  Compute the initial probability.

(4)    Retain   𝑡₁;

(5)   end if

(6)   if   𝑡₁>𝑡_max   then          ▹  Discard all generated and computed data.

(7)    𝑁=0; 𝑃₀=∫^∞_𝑡max𝑝𝑡₁∣𝑡₀𝑑𝑡₁=𝑒^−𝑡max;

(8)    Delete   𝑡₁;

(9)    EXIT.               ▹  The algorithm ends here.

(10)  end if

(11)   𝑖=2;

(12)  while (1) do            ▹  Infinite loop until a successful EXIT.

(13)   Generate 𝑡_𝑖 according with 𝑝𝑡_𝑖∣𝑡_𝑖−1

(14)   if   𝑡_𝑖<𝑡_max   then          ▹  Generate a new state and new probability.

(15)    𝑃_𝑁≥𝑖=∫^𝑡max_𝑡𝑖𝑝𝑡_𝑖∣𝑡_𝑖−1𝑑𝑡_𝑖;

(16)    Retain   𝑡_𝑖;

(17)   end if

(18)   if   𝑡_𝑖>𝑡_max   then           ▹  Discard all generated and computed data.

(19)    𝑁=𝑖−1; 𝑃_𝑖=∫^∞_𝑡max𝑝𝑡_𝑖∣𝑡_𝑖−1𝑑𝑡_𝑖;

(20)    Retain   𝑡₁,𝑡₂,…,𝑡_𝑖−1;  Delete   𝑡_𝑖;

(21)    EXIT.                  ▹  The algorithm ends here.

(22)   end if

(23)   𝑖=𝑖+1;

(24)  end while