Kernel: C++17
XEUS C++17 running GSL
Tipp: Use the doube-arrow ("fast forward") to restart and run all cells after any changes!
In [1]:
In [2]:
In [3]:
Computation of the integral,
The exact answer is
This example is taken from C.Itzykson, J.M.Drouffe, "Statistical Field Theory - Volume 1", Section 1.1, p21, which cites the original paper M.L.Glasser, I.J.Zucker, Proc.Natl.Acad.Sci.USA 74 1800 (1977)
For simplicity we compute the integral over the region (0,0,0) -> (pi,pi,pi) and multiply by 8
In [4]:
In [5]:
In [6]:
In [7]:
================== plain ==================
result = 1.41221
sigma = 0.0134359
exact = 1.3932
error = 0.0190048 = 1.41448 sigma
================== miser ==================
result = 1.39132
sigma = 0.00346056
exact = 1.3932
error = -0.00188235 = 0.543944 sigma
================== vegas warm-up ==================
result = 1.39267
sigma = 0.00341041
exact = 1.3932
error = -0.000531339 = 0.155799 sigma
================== vegas final ==================
result = 1.39328
sigma = 0.00036248
exact = 1.3932
error = 7.74556e-05 = 0.213682 sigma
In [0]:
In [0]: