code: def evaluate_lake(values: np.ndarray, seed=101) -> np.ndarray:
      """Evaluate the Lake Problem with an array of parameter values.
  
      References
      ----------
      .. [1] Hadka, D., Herman, J., Reed, P., Keller, K., (2015).
             "An open source framework for many-objective robust decision
             making."
             Environmental Modelling & Software 74, 114–129.
             doi:10.1016/j.envsoft.2015.07.014
  
      .. [2] Singh, R., Reed, P., Keller, K., (2015). "Many-objective robust
             decision making for managing an ecosystem with a deeply uncertain
             threshold response."
             Ecology and Society 20.
             doi:10.5751/ES-07687-200312
  
      Parameters
      ----------
      values : np.ndarray,
          model inputs in the (column) order of
          a, q, b, mean, stdev
  
          where
          * `a` is rate of anthropogenic pollution
          * `q` is exponent controlling recycling rate
          * `b` is decay rate for phosphorus
          * `mean` and
          * `stdev` set the log normal distribution of `eps`, see [2]
  
      Returns
      -------
      np.ndarray, of Phosphorus pollution over time `t`
      """
      rng = np.random.default_rng(seed)
  
      nvars = values.shape[0]
  
      a, q, b, mean, stdev = values.T
  
      sq_mean = mean**2
      sq_std = stdev**2
      eps = rng.lognormal(
          log(sq_mean / sqrt(sq_std + sq_mean)),
          sqrt(log(1.0 + sq_std / sq_mean)),
          size=nvars,
      )
  
      Y = np.zeros((nvars, nvars))
      for t in range(nvars):
          # First X value will be last Y value (should be 0 as we are filling
          # an array of zeros)
          Y[t] = lake_problem(Y[t - 1], a, q, b, eps)
  
      return Y
  
imports: from typing import Union
  import numpy
  from numpy import log, sqrt
  from scipy.optimize import brentq
label_desc: Use image node_id 2 for calling a global function with example usage: evaluate_lake(values, seed) and returns: Y