class_docstr: Kowalik objective function.
  
  This class defines the Kowalik [1]_ global optimization problem. This
  is a multimodal minimization problem defined as follows:
  
  .. math::
  
      f_{\text{Kowalik}}(x) = \sum_{i=0}^{10} \left [ a_i
      - \frac{x_1 (b_i^2 + b_i x_2)} {b_i^2 + b_i x_3 + x_4} \right ]^2
  
  Where:
  
  .. math::
  
      \begin{matrix}
      a = [4, 2, 1, 1/2, 1/4 1/8, 1/10, 1/12, 1/14, 1/16] \\
      b = [0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
           0.0456, 0.0342, 0.0323, 0.0235, 0.0246]\\
      \end{matrix}
  
  
  Here, :math:`n` represents the number of dimensions and :math:`x_i \in 
  [-5, 5]` for :math:`i = 1, ..., 4`.
  
  *Global optimum*: :math:`f(x) = 0.00030748610` for :math:`x = 
  [0.192833, 0.190836, 0.123117, 0.135766]`.
  
  ..[1] https://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
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code: def __init__(self, dimensions=4):
      Benchmark.__init__(self, dimensions)
  
      self._bounds = list(zip([-5.0] * self.N, [5.0] * self.N))
      self.global_optimum = [[0.192833, 0.190836, 0.123117, 0.135766]]
      self.fglob = 0.00030748610
  
      self.a = asarray(
          [
              4.0,
              2.0,
              1.0,
              1 / 2.0,
              1 / 4.0,
              1 / 6.0,
              1 / 8.0,
              1 / 10.0,
              1 / 12.0,
              1 / 14.0,
              1 / 16.0,
          ]
      )
      self.b = asarray(
          [
              0.1957,
              0.1947,
              0.1735,
              0.1600,
              0.0844,
              0.0627,
              0.0456,
              0.0342,
              0.0323,
              0.0235,
              0.0246,
          ]
      )
  
file_path: scipy/benchmarks/benchmarks/go_benchmark_functions/go_funcs_K.py
imports: from numpy import asarray, atleast_2d, arange, sin, sqrt, prod, sum, round
  from .go_benchmark import Benchmark
label_desc: Use image node_id 1 to create a new Kowalik object from inherited base classes: Benchmark with example: obj = Kowalik(dimensions)