code: def generate_asymgauss_problem(ndim):
      asym_sigma = 0.1 / (1 + 4 * np.arange(ndim))
      asym_sigma_max = asym_sigma.max()
  
      def loglike_asymgauss(x):
          """assymmetric gaussian problem"""
          return -0.5 * (((x - 0.5) / asym_sigma) ** 2).sum()
  
      def volume_asymgauss(loglike, ndim):
          """compute volume enclosed at loglike threshold"""
          sqr_radius = -2 * loglike
          radius = sqr_radius**0.5
          # assume that all of that is in the asym_sigma_max direction
          # how far would that be?
          if radius * asym_sigma_max >= 0.5:
              # the volume is still touching the unit cube
              return np.nan
  
          # compute volume of a n-sphere
          return nsphere_volume(radius, ndim) * np.product(
              asym_sigma / asym_sigma_max
          )
  
      gradient_asymgauss = gradient_to_center
  
      def warmup_asymgauss(ndim):
          return 0.5 + random_point_in_sphere(ndim, radius=asym_sigma)
  
      return (
          loglike_asymgauss,
          gradient_asymgauss,
          volume_asymgauss,
          warmup_asymgauss,
      )
  
imports: import numpy
  from math import gamma, pi, exp
label_desc: Use image node_id 9 for calling a global function with example usage: generate_asymgauss_problem(ndim) and returns: loglike_asymgauss,  gradient_asymgauss,  volume_asymgauss,  warmup_asymgauss, unknown, unknown, unknown, np