Exemplo n.º 1
0
def run_example(with_plots=True):
    """
    This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)

    This simple example problem for CVode, due to Robertson, 
    is from chemical kinetics, and consists of the following three 
    equations::
    
       dy1/dt = -p1*y1 + p2*y2*y3
       dy2/dt = p1*y1 - p2*y2*y3 - p3*y2**2
       dy3/dt = p3*(y2)^2
    
    """
    
    def f(t, y, p):
        
        yd_0 = -p[0]*y[0]+p[1]*y[1]*y[2]
        yd_1 = p[0]*y[0]-p[1]*y[1]*y[2]-p[2]*y[1]**2
        yd_2 = p[2]*y[1]**2
        
        return N.array([yd_0,yd_1,yd_2])
    
    #The initial conditions
    y0 = [1.0,0.0,0.0]          #Initial conditions for y
    
    #Create an Assimulo explicit problem
    exp_mod = Explicit_Problem(f,y0)
    
    #Sets the options to the problem
    exp_mod.p0 = [0.040, 1.0e4, 3.0e7]  #Initial conditions for parameters
    exp_mod.pbar = [0.040, 1.0e4, 3.0e7]

    #Create an Assimulo explicit solver (CVode)
    exp_sim = CVode(exp_mod)
    
    #Sets the paramters
    exp_sim.iter = 'Newton'
    exp_sim.discr = 'BDF'
    exp_sim.rtol = 1.e-4
    exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
    exp_sim.suppress_sens = False       #Dont suppress the sensitivity variables in the error test.
    exp_sim.continuous_output = True

    #Simulate
    t, y = exp_sim.simulate(4,400) #Simulate 4 seconds with 400 communication points
    
    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
    nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
    nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
    nose.tools.assert_almost_equal(exp_sim.p_sol[0][-1][0], -1.8761, 2) #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
    nose.tools.assert_almost_equal(exp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
    
    #Plot
    if with_plots:
        P.plot(t, y)
        P.show()  
Exemplo n.º 2
0
    def _assimulo_problem(self):
        rhs = self._problem.right_hand_side_as_function
        parameters = self._parameters
        initial_conditions = self._initial_conditions
        initial_timepoint = self._starting_time

        # Solvers with sensitivity support should be able to accept parameters
        # into rhs function directly
        model = Explicit_Problem(lambda t, x, p: rhs(x, p),
                                 initial_conditions, initial_timepoint)

        model.p0 = np.array(parameters)
        return model
Exemplo n.º 3
0
    def _assimulo_problem(self):
        rhs = self._problem.right_hand_side_as_function
        parameters = self._parameters
        initial_conditions = self._initial_conditions
        initial_timepoint = self._starting_time

        # Solvers with sensitivity support should be able to accept parameters
        # into rhs function directly
        model = Explicit_Problem(lambda t, x, p: rhs(x, p), initial_conditions,
                                 initial_timepoint)

        model.p0 = np.array(parameters)
        return model
Exemplo n.º 4
0
def run_example(with_plots=True):
    """
    This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)

    This simple example problem for CVode, due to Robertson, 
    is from chemical kinetics, and consists of the following three 
    equations:

    .. math:: 
    
       \dot y_1 &= -p_1 y_1 + p_2 y_2 y_3 \\
       \dot y_2 &= p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2 \\
       \dot y_3 &= p_3  y_2^2
    
    on return:
    
       - :dfn:`exp_mod`    problem instance
    
       - :dfn:`exp_sim`    solver instance
    """
    def f(t, y, p):
        p3 = 3.0e7

        yd_0 = -p[0] * y[0] + p[1] * y[1] * y[2]
        yd_1 = p[0] * y[0] - p[1] * y[1] * y[2] - p3 * y[1]**2
        yd_2 = p3 * y[1]**2

        return N.array([yd_0, yd_1, yd_2])

    #The initial conditions
    y0 = [1.0, 0.0, 0.0]  #Initial conditions for y

    #Create an Assimulo explicit problem
    exp_mod = Explicit_Problem(f,
                               y0,
                               name='Sundials test example: Chemical kinetics')

    #Sets the options to the problem
    exp_mod.p0 = [0.040, 1.0e4]  #Initial conditions for parameters
    exp_mod.pbar = [0.040, 1.0e4]

    #Create an Assimulo explicit solver (CVode)
    exp_sim = CVode(exp_mod)

    #Sets the paramters
    exp_sim.iter = 'Newton'
    exp_sim.discr = 'BDF'
    exp_sim.rtol = 1.e-4
    exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    exp_sim.sensmethod = 'SIMULTANEOUS'  #Defines the sensitvity method used
    exp_sim.suppress_sens = False  #Dont suppress the sensitivity variables in the error test.
    exp_sim.report_continuously = True

    #Simulate
    t, y = exp_sim.simulate(
        4, 400)  #Simulate 4 seconds with 400 communication points

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

    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
    nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
    nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
    nose.tools.assert_almost_equal(
        exp_sim.p_sol[0][-1][0], -1.8761,
        2)  #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)

    return exp_mod, exp_sim
Exemplo n.º 5
0
def run_example(with_plots=True):
    """
    This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)

    This simple example problem for CVode, due to Robertson, 
    is from chemical kinetics, and consists of the following three 
    equations::
    
       dy1/dt = -p1*y1 + p2*y2*y3
       dy2/dt = p1*y1 - p2*y2*y3 - p3*y2**2
       dy3/dt = p3*(y2)^2
    
    """
    def f(t, y, p):

        yd_0 = -p[0] * y[0] + p[1] * y[1] * y[2]
        yd_1 = p[0] * y[0] - p[1] * y[1] * y[2] - p[2] * y[1]**2
        yd_2 = p[2] * y[1]**2

        return N.array([yd_0, yd_1, yd_2])

    #The initial conditions
    y0 = [1.0, 0.0, 0.0]  #Initial conditions for y

    #Create an Assimulo explicit problem
    exp_mod = Explicit_Problem(f, y0)

    #Sets the options to the problem
    exp_mod.p0 = [0.040, 1.0e4, 3.0e7]  #Initial conditions for parameters
    exp_mod.pbar = [0.040, 1.0e4, 3.0e7]

    #Create an Assimulo explicit solver (CVode)
    exp_sim = CVode(exp_mod)

    #Sets the paramters
    exp_sim.iter = 'Newton'
    exp_sim.discr = 'BDF'
    exp_sim.rtol = 1.e-4
    exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    exp_sim.sensmethod = 'SIMULTANEOUS'  #Defines the sensitvity method used
    exp_sim.suppress_sens = False  #Dont suppress the sensitivity variables in the error test.
    exp_sim.continuous_output = True

    #Simulate
    t, y = exp_sim.simulate(
        4, 400)  #Simulate 4 seconds with 400 communication points

    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
    nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
    nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
    nose.tools.assert_almost_equal(
        exp_sim.p_sol[0][-1][0], -1.8761,
        2)  #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
    nose.tools.assert_almost_equal(exp_sim.p_sol[2][-1][0], -4.9334e-10, 12)

    #Plot
    if with_plots:
        P.plot(t, y)
        P.show()
def run_example(with_plots=True):
    r"""
    This is the same example from the Sundials package (cvsRoberts_FSA_dns.c)
    Its purpose is to demonstrate the use of parameters in the differential equation.

    This simple example problem for CVode, due to Robertson
    see http://www.dm.uniba.it/~testset/problems/rober.php, 
    is from chemical kinetics, and consists of the system:
    
    .. math:: 
    
       \dot y_1 &= -p_1 y_1 + p_2 y_2 y_3 \\
       \dot y_2 &= p_1 y_1 - p_2 y_2 y_3 - p_3 y_2^2 \\
       \dot y_3 &= p_3  y_ 2^2
       
    
    on return:
    
       - :dfn:`exp_mod`    problem instance
    
       - :dfn:`exp_sim`    solver instance
    
    """
    
    def f(t, y, p):
        
        yd_0 = -p[0]*y[0]+p[1]*y[1]*y[2] 
        yd_1 = p[0]*y[0]-p[1]*y[1]*y[2]-p[2]*y[1]**2 
        yd_2 = p[2]*y[1]**2
        
        return N.array([yd_0,yd_1,yd_2])
        
    def jac(t,y, p):
        J = N.array([[-p[0], p[1]*y[2], p[1]*y[1]],
                     [p[0], -p[1]*y[2]-2*p[2]*y[1], -p[1]*y[1]],
                     [0.0, 2*p[2]*y[1],0.0]])
        return J
        
    def fsens(t, y, s, p):
        J = N.array([[-p[0], p[1]*y[2], p[1]*y[1]],
                     [p[0], -p[1]*y[2]-2*p[2]*y[1], -p[1]*y[1]],
                     [0.0, 2*p[2]*y[1],0.0]])
        P = N.array([[-y[0],y[1]*y[2],0],
                     [y[0], -y[1]*y[2], -y[1]**2],
                     [0,0,y[1]**2]])
        return J.dot(s)+P
    
    #The initial conditions
    y0 = [1.0,0.0,0.0]          #Initial conditions for y
    
    #Create an Assimulo explicit problem
    exp_mod = Explicit_Problem(f,y0, name='Robertson Chemical Kinetics Example')
    exp_mod.rhs_sens = fsens
    exp_mod.jac = jac
    
    #Sets the options to the problem
    exp_mod.p0 = [0.040, 1.0e4, 3.0e7]  #Initial conditions for parameters
    exp_mod.pbar = [0.040, 1.0e4, 3.0e7]

    #Create an Assimulo explicit solver (CVode)
    exp_sim = CVode(exp_mod)
    
    #Sets the solver paramters
    exp_sim.iter = 'Newton'
    exp_sim.discr = 'BDF'
    exp_sim.rtol = 1.e-4
    exp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
    exp_sim.suppress_sens = False       #Dont suppress the sensitivity variables in the error test.
    exp_sim.report_continuously = True

    #Simulate
    t, y = exp_sim.simulate(4,400) #Simulate 4 seconds with 400 communication points
    
    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 9.05518032e-01, 4)
    nose.tools.assert_almost_equal(y[-1][1], 2.24046805e-05, 4)
    nose.tools.assert_almost_equal(y[-1][2], 9.44595637e-02, 4)
    nose.tools.assert_almost_equal(exp_sim.p_sol[0][-1][0], -1.8761, 2) #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(exp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
    nose.tools.assert_almost_equal(exp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
    
    #Plot
    if with_plots:
        P.plot(t, y)
        P.title(exp_mod.name)
        P.xlabel('Time')
        P.ylabel('State')
        P.show()  
        
    return exp_mod, exp_sim