docstr: evaluates Paviani's function for a list of coeffs
  
  f(x) = f_0(x) - f_1(x)
  
  Where:
  f_0(x) = \sum_(i=0)^(N-1) (\ln(x_i - 2)^2 + \ln(10 - x_i)^2)
  and
  f_1(x) = \prod_(i=0)^(N-1) x_(i)^(.2)
  
  Inspect with mystic_model_plotter using::
      mystic.models.paviani -b "2:10:.1, 2:10:.1" -d
  
  For N=1, the minimum is f(x)=2.133838 at x_i=8.501586,
  for N=3, the minimum is f(x)=7.386004 at x_i=8.589578,
  for N=5, the minimum is f(x)=9.730525 at x_i=8.740743,
  for N=8, the minimum is f(x)=-3.411859 at x_i=9.086900,
  for N=10, the minimum is f(x)=-45.778470 at x_i=9.350241.
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code: def function(self, coeffs):
      r"""evaluates Paviani's function for a list of coeffs
  
      f(x) = f_0(x) - f_1(x)
  
      Where:
      f_0(x) = \sum_(i=0)^(N-1) (\ln(x_i - 2)^2 + \ln(10 - x_i)^2)
      and
      f_1(x) = \prod_(i=0)^(N-1) x_(i)^(.2)
  
      Inspect with mystic_model_plotter using::
          mystic.models.paviani -b "2:10:.1, 2:10:.1" -d
  
      For N=1, the minimum is f(x)=2.133838 at x_i=8.501586,
      for N=3, the minimum is f(x)=7.386004 at x_i=8.589578,
      for N=5, the minimum is f(x)=9.730525 at x_i=8.740743,
      for N=8, the minimum is f(x)=-3.411859 at x_i=9.086900,
      for N=10, the minimum is f(x)=-45.778470 at x_i=9.350241."""
      s = 0.0
      for x in coeffs:
          if x >= 10.0 or x <= 2.0:
              s = inf
              break
          s += log(x - 2.0) ** 2 + log(10.0 - x) ** 2
      p = reduce(lambda x, y: x * y, coeffs) ** (0.2)
      return s - p
  
imports: from .abstract_model import AbstractFunction
  from math import sin, cos, sqrt, pi, exp, log
  from numpy import inf
label_desc: Use image node_id 2 for calling the Paviani obj's underlying member method code with example usage: obj.function(coeffs) and returns: unknown