#!/usr/bin/env python 
# -*- coding: utf-8 -*-
"""
Tutorial example showing how to use the implicit solver IDA. To run the example
simply type,

    run tutorialIDA.py (in IPython)
    
or,

    python tutorialIDA.py (in a command prompt)
"""
import numpy as np
from assimulo.problem import Implicit_Problem #Imports the problem formulation from Assimulo
from assimulo.solvers import IDA              #Imports the solver IDA from Assimulo


def run_example():

    def residual(t,y,yd):

        res_0 = yd[0]-y[2]
        res_1 = yd[1]-y[3]
        res_2 = yd[2]+y[4]*y[0]
        res_3 = yd[3]+y[4]*y[1]+9.82
        res_4 = y[2]**2+y[3]**2-y[4]*(y[0]**2+y[1]**2)-y[1]*9.82

        return np.array([res_0,res_1,res_2,res_3,res_4])
    
    #The initial conditons
    t0  = 0.0 #Initial time
    y0  = [1.0, 0.0, 0.0, 0.0, 0.0] #Initial conditions
    yd0 = [0.0, 0.0, 0.0, -9.82, 0.0] #Initial conditions

    model = Implicit_Problem(residual, y0, yd0, t0)             #Create an Assimulo problem
    model.name = 'Pendulum'        #Specifies the name of problem (optional)

    sim = IDA(model) #Create the IDA solver
        
    tfinal = 10.0        #Specify the final time
    ncp = 500            #Number of communcation points (number of return points)

    t,y,yd = sim.simulate(tfinal, ncp) #Use the .simulate method to simulate and provide the final time and ncp (optional)
    
    sim.plot()

if __name__=='__main__':
    run_example()