Multiple Integrands Simultaneously

[dsmic]

I get into problems, if I integrate functions simultaneously, which have very different function values:

import vegas

integrator = vegas.Integrator([[0, 1], [0, 1]])

def f(x):
    return [1,1e60]

result = integrator(f, nitn=10, neval=1000)

print(result.summary())

print(result)

gives the following output:

itn   integral         wgt average     chi2/dof        Q
--------------------------------------------------------
  1   1.0000000000(15) 0(0)                0.00     1.00
  2   1.0000000000(18) 0(0)                 nan      nan
  3   1.0000000000(22) 0(0)                 nan      nan
  4   1.0000000000(22) 0(0)                 nan      nan
  5   1.0000000000(21) 0(0)                 nan      nan
  6   1.0000000000(21) 0(0)                 nan      nan
  7   1.0000000000(20) 0(0)                 nan      nan
  8   1.0000000000(20) 0(0)                 nan      nan
  9   1.0000000000(22) 0(0)                 nan      nan
 10   1.0000000000(22) 0(0)                 nan      nan

[0(0) 1.00000000000(63)e+60]

Any idea, what is happening here?

[gplepage]

This is due to roundoff error in the weighted average of results. I can fix this but it will be several days before I can get to it.

If you need it to work right now, one possibility is to install the lsqfit module and use lsqfit.wavg(result.itn_results) for the weighted average:

import vegas
import lsqfit 

integrator = vegas.Integrator([[0, 1], [0, 1]])
def f(x):
   return [1, 1e60]

result = integrator(f, nitn=10, neval=1000)

print(result.summary())

print(result)

answer = lsqfit.wavg(result.itn_results)
print(answer, 'chi2/dof =', answer.chi2/answer.dof)

This prints out the following, with the correct answer in the final line:

itn   integral         wgt average     chi2/dof        Q
--------------------------------------------------------
  1   1.0000000000(15) 0(0)                0.00     1.00
  2   1.0000000000(19) 0(0)                 nan      nan
  3   1.0000000000(21) 0(0)                 nan      nan
  4   1.0000000000(21) 0(0)                 nan      nan
  5   1.0000000000(22) 0(0)                 nan      nan
  6   1.0000000000(21) 0(0)                 nan      nan
  7   1.0000000000(22) 0(0)                 nan      nan
  8   1.0000000000(20) 0(0)                 nan      nan
  9   1.0000000000(21) 0(0)                 nan      nan
 10   1.0000000000(22) 0(0)                 nan      nan

[0(0) 1.00000000000(64)e+60]
[1.00000000000(64) 1.00000000000(64)e+60] chi2/dof = 2.768095398562126e-12

Thanks for pointing out the problem.

[dsmic]

Thanks a lot for the very quick reply! I do not really understand, how the implemented averaging works to produce such kind of roundoff error, but ...

Not a problem at the moment, but in my real live problem I get

mean field itn   integral        wgt average     chi2/dof        Q
-------------------------------------------------------
  1   4.752(35)e+11   0(0)                0.00     1.00
  2   4.732(32)e+11   0(0)                1.32     0.26
  3   4.768(31)e+11   0(0)                0.71     0.69
  4   4.767(30)e+11   0(0)                0.48     0.93
  5   4.774(30)e+11   0(0)                0.37     0.99
  6   4.783(29)e+11   0(0)                0.33     1.00
  7   4.761(27)e+11   0(0)                0.28     1.00
  8   4.775(27)e+11   0(0)                0.25     1.00
  9   4.728(28)e+11   0(0)                0.22     1.00
 10   4.805(27)e+11   0(0)                0.20     1.00

Test: 11:07:38 mean field [0(0) 0(0) 0(0) 6.055(79)e+63]
lsqfit [4.7646(91)e+11 3.8674(72)e+13 3.91281225(13)e+13
 6.107230208142814475991144718136638402938842773437500000000000000000000000000000000000000000000000000000000(23)e+63]

There is no way I believe the error estimate of the 4. integrand :)

May I ask: is there an easy way to install vegas to use the pyx file (instead of the c file) for debugging (understanding) proposes?

[gplepage]

This is fixed in v5.4 of vegas (which I just uploaded). Thanks for pointing out the problem.

[gplepage]

I am closing this issue because v5.4 of vegas addresses it. Running the code you posted above now gives the following greatly improved result:

itn   integral         wgt average       chi2/dof        Q
----------------------------------------------------------
  1   1.0000000000(15) 1.0000000000(15)      0.00     1.00
  2   1.0000000000(18) 1.0000000000(12)      0.00     1.00
  3   1.0000000000(21) 1.0000000000(10)      0.00     1.00
  4   1.0000000000(20) 1.00000000000(90)     0.00     1.00
  5   1.0000000000(21) 1.00000000000(83)     0.00     1.00
  6   1.0000000000(21) 1.00000000000(77)     0.00     1.00
  7   1.0000000000(21) 1.00000000000(72)     0.00     1.00
  8   1.0000000000(21) 1.00000000000(68)     0.00     1.00
  9   1.0000000000(22) 1.00000000000(65)     0.00     1.00
 10   1.0000000000(22) 1.00000000000(63)     0.00     1.00

[1.00000000000(63) 1.00000000000(63)e+60]

Thanks again for pointing out the problem.