#!/usr/bin/env python
# -*- coding: utf-8 -*-

# Copyright (C) 2010 Modelon AB
#
# This program is free software: you can redistribute it and/or modify
# the Free Software Foundation, version 3 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.

import numpy as N
import pylab as P
import nose
from assimulo.solvers import RungeKutta4
from assimulo.problem import Explicit_Problem

def run_example(with_plots=True):
r"""
Demonstration of the use of the use of Runge-Kutta 4 by solving the
linear test equation :math:\dot y = - y

on return:

- :dfn:exp_mod    problem instance

- :dfn:exp_sim    solver instance

"""

#Defines the rhs
def f(t,y):
ydot = -y[0]
return N.array([ydot])

#Define an Assimulo problem
exp_mod = Explicit_Problem(f, 4.0,
name = 'RK4 Example: $\dot y = - y$')

exp_sim = RungeKutta4(exp_mod) #Create a RungeKutta4 solver

#Simulate
t, y = exp_sim.simulate(5, 100) #Simulate 5 seconds

#Basic test
nose.tools.assert_almost_equal(y[-1],0.02695179)

#Plot
if with_plots:
P.plot(t, y)
P.title(exp_mod.name)
P.ylabel('y')
P.xlabel('Time')
P.show()

return exp_mod, exp_sim

if __name__=='__main__':
mod,sim = run_example()