TH4D test page

TH4D is a 3+1 dimension histogram to provide GetRandom4(x, y, z, u) function.
Essentially it's a 3-dim histogram derived from TH3D but equips extra-dimension in each bin, in this case, one-dimension TH1DEX derived from TH1D. You can use any function of TH3D like Fill(x,y,z) or GetRandom3(x,y,z) while equivalent functions of 4D are Fill(x,y,z,u) or GetRandom4(x,y,z,u), respectively.
To access the 4th dimension at (x, y, z), call

h4->GetExtraDimensionPtr(h4->TH3::FindBin(x, y, z)); // h4: TH4D object ptr

then you will get a pointer to TH1DEX object.

Technical notations

• Draw() function ignores last axis(extra-dimension) and return 3D view. Any TH3 function ignores extra-dimension except for Integral(Option_t *opt).
• extra-dimension at (x,y,z) is generated only when the bin (x,y,z) has entry. If bin (x, y, z) is empty, pointer to the extra-dimension of the bin is null.
• Currently the size of the TH4D is limited by the available size of fIntegral array. The size of fIntegral array is defined as (nx+2) * (ny+2) * (nz+2) * (nu+2) where nx, ny, nz, nu are the number of bins in each axis. If this size exceeds a limit, GetRandom4(x, y, z, u) function causes segmentation fault or serious problem. The limit might depend on machine environments, e.g., 113404926 * size(Double_t) at UW machine.

Source code

• TH4D.h
• TH4D.cxx
• TH1DEX.h
• TH1DEX.cxx

Test scripts

• TH4DTest.C (fill test, output file is test.root)
• GetRandomTest.C (call GetRamdom4, input file is test.root)
• FillRandom.C (call FillRandom, input file is test.root)

Test histograms of TH4D

Fill test

Plot of Fill(x, y, z, t),

  x = 0.9                     // costheta
  y = gRandom->Gaus(90,. 20)  // zenith
  z = gRandom->Gaus(180, 20)  // azimuth
  t = gRandom->Gaus(y/3, 5)   // time 

GetRandom4(x, y, z, t) test

Call GetRandom4(x, y, z, t) with referense TH4D (above plots), and fill them into new TH4D hist.