text: __copyright__ = """
  Copyright (C) 2020 George N Wong
  Copyright (C) 2020 Zachary J Weiner
  """
  
  __license__ = """
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
  
  The above copyright notice and this permission notice shall be included in
  all copies or substantial portions of the Software.
  
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  THE SOFTWARE.
  """
  
  import numpy as np
  import pytest
  from pydemic import GammaProcess, Simulation
  
  
  @pytest.mark.parametrize("shape", [1, 2, 8])
  @pytest.mark.parametrize("scale", [1, 1.4])
  def test_gamma(shape, scale):
      reactions = (
          GammaProcess('a', 'b', shape=shape, scale=lambda t, y: scale),
      )
  
      simulation = Simulation(reactions)
  
      y0 = {'a': np.array(1), 'b': np.array(0)}
      tspan = (0, 10)
      dt = 1e-3
  
      result = simulation(tspan, y0, dt=dt)
      t = result.t
  
      def f(t, y):
          dy = np.zeros_like(y)
          for i in range(1, len(y)-1):
              dy[i] = - y[i] / scale + y[i-1] / scale
          dy[0] = - y[0] / scale
          dy[-1] = y[-2] / scale
          return dy
  
      compartments = ('a', 'b')
  
      y0 = np.zeros(2 + shape-1)
      y0[0] = 1
      from scipy.integrate import solve_ivp
      res = solve_ivp(f, tspan, y0, rtol=1.e-13,
                      dense_output=True)
  
      scipy_sol = {'a': np.sum(res.sol(t)[:-1], axis=0), 'b': res.sol(t)[-1]}
      for i, name in enumerate(compartments):
          non_zero = np.logical_and(scipy_sol[name] > 0, result.y[name] > 0)
          test = np.logical_and(non_zero, t > 1)
          relerr = np.abs(1 - scipy_sol[name][test] / result.y[name][test])
          print('max err for', name, 'is', np.max(relerr))
          assert np.max(relerr) < .05
  
      all_keys = simulation.compartments
      total_people = sum(result.y[key] for key in all_keys)
      total_pop = total_people[0]
      total_err = np.max(np.abs(1 - total_people / total_pop))
      print('total error is', np.max(total_err))
      assert np.max(total_err) < 1.e-13
  
  
  if __name__ == "__main__":
      test_gamma(3, 2.3)
  