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

    This simple example problem for IDA, 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
       0   = y1 + y2 + y3 - 1
    
    """

    def f(t, y, yd, p):
        
        res1 = -p[0]*y[0]+p[1]*y[1]*y[2]-yd[0]
        res2 = p[0]*y[0]-p[1]*y[1]*y[2]-p[2]*y[1]**2-yd[1]
        res3 = y[0]+y[1]+y[2]-1
        
        return N.array([res1,res2,res3])

    #The initial conditons
    y0 = [1.0, 0.0, 0.0]        #Initial conditions for y
    yd0 = [0.1, 0.0, 0.0]       #Initial conditions for dy/dt
    p0 = [0.040, 1.0e4, 3.0e7]  #Initial conditions for parameters
    
    #Create an Assimulo implicit problem
    imp_mod = Implicit_Problem(f, y0, yd0,p0=p0)

    #Create an Assimulo implicit solver (IDA)
    imp_sim = IDA(imp_mod) #Create a IDA solver
    
    #Sets the paramters
    imp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    imp_sim.algvar = [1.0,1.0,0.0]
    imp_sim.suppress_alg = False #Suppres the algebraic variables on the error test
    imp_sim.continuous_output = True #Store data continuous during the simulation
    imp_sim.pbar = p0
    imp_sim.suppress_sens = False            #Dont suppress the sensitivity variables in the error test.

    #Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
    imp_sim.make_consistent('IDA_YA_YDP_INIT')
    
    #Simulate
    t, y, yd = imp_sim.simulate(4,400) #Simulate 4 seconds with 400 communication points
    print imp_sim.p_sol[0][-1] , imp_sim.p_sol[1][-1], imp_sim.p_sol[0][-1]
    #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(imp_sim.p_sol[0][-1][0], -1.8761, 2) #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(imp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
    nose.tools.assert_almost_equal(imp_sim.p_sol[2][-1][0], -4.9334e-10, 12)
    
    #Plot
    if with_plots:
        P.plot(t,y)
        P.show()    
Ejemplo n.º 2
0
def run_example(with_plots=True):
    """
    This is the same example from the Sundials package (idasRoberts_FSA_dns.c)

    This simple example problem for IDA, 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
       0   = y1 + y2 + y3 - 1
    
    """
    def f(t, y, yd, p):

        res1 = -p[0] * y[0] + p[1] * y[1] * y[2] - yd[0]
        res2 = p[0] * y[0] - p[1] * y[1] * y[2] - p[2] * y[1]**2 - yd[1]
        res3 = y[0] + y[1] + y[2] - 1

        return N.array([res1, res2, res3])

    #The initial conditons
    y0 = [1.0, 0.0, 0.0]  #Initial conditions for y
    yd0 = [0.1, 0.0, 0.0]  #Initial conditions for dy/dt
    p0 = [0.040, 1.0e4, 3.0e7]  #Initial conditions for parameters

    #Create an Assimulo implicit problem
    imp_mod = Implicit_Problem(f, y0, yd0, p0=p0)

    #Create an Assimulo implicit solver (IDA)
    imp_sim = IDA(imp_mod)  #Create a IDA solver

    #Sets the paramters
    imp_sim.atol = N.array([1.0e-8, 1.0e-14, 1.0e-6])
    imp_sim.algvar = [1.0, 1.0, 0.0]
    imp_sim.suppress_alg = False  #Suppres the algebraic variables on the error test
    imp_sim.continuous_output = True  #Store data continuous during the simulation
    imp_sim.pbar = p0
    imp_sim.suppress_sens = False  #Dont suppress the sensitivity variables in the error test.

    #Let Sundials find consistent initial conditions by use of 'IDA_YA_YDP_INIT'
    imp_sim.make_consistent('IDA_YA_YDP_INIT')

    #Simulate
    t, y, yd = imp_sim.simulate(
        4, 400)  #Simulate 4 seconds with 400 communication points
    print imp_sim.p_sol[0][-1], imp_sim.p_sol[1][-1], imp_sim.p_sol[0][-1]
    #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(
        imp_sim.p_sol[0][-1][0], -1.8761,
        2)  #Values taken from the example in Sundials
    nose.tools.assert_almost_equal(imp_sim.p_sol[1][-1][0], 2.9614e-06, 8)
    nose.tools.assert_almost_equal(imp_sim.p_sol[2][-1][0], -4.9334e-10, 12)

    #Plot
    if with_plots:
        P.plot(t, y)
        P.show()
Ejemplo n.º 3
0
def run_example(with_plots=True):
    """
    This example show how to use Assimulo and IDA for simulating sensitivities
    for initial conditions.::
    
        0 = dy1/dt - -(k01+k21+k31)*y1 - k12*y2 - k13*y3 - b1
        0 = dy2/dt - k21*y1 + (k02+k12)*y2
        0 = dy3/dt - k31*y1 + k13*y3
     
        y1(0) = p1, y2(0) = p2, y3(0) = p3
        p1=p2=p3 = 0 
    
    See http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html
    """
    
    def f(t, y, yd,p):
        y1,y2,y3 = y
        yd1,yd2,yd3 = yd
        k01 = 0.0211
        k02 = 0.0162
        k21 = 0.0111
        k12 = 0.0124
        k31 = 0.0039
        k13 = 0.000035
        b1 = 49.3
        
        res_0 = -yd1 -(k01+k21+k31)*y1+k12*y2+k13*y3+b1
        res_1 = -yd2 + k21*y1-(k02+k12)*y2
        res_2 = -yd3 + k31*y1-k13*y3
        
        return N.array([res_0,res_1,res_2])
    
    #The initial conditions
    y0 = [0.0,0.0,0.0]          #Initial conditions for y
    yd0 = [49.3,0.,0.]
    p0 = [0.0, 0.0, 0.0]  #Initial conditions for parameters
    yS0 = N.array([[1,0,0],[0,1,0],[0,0,1.]])
    
    #Create an Assimulo implicit problem
    imp_mod = Implicit_Problem(f,y0,yd0,p0=p0)
    
    #Sets the options to the problem
    imp_mod.yS0=yS0

    #Create an Assimulo explicit solver (IDA)
    imp_sim = IDA(imp_mod)
    
    #Sets the paramters
    imp_sim.rtol = 1e-7
    imp_sim.atol = 1e-6
    imp_sim.pbar = [1,1,1] #pbar is used to estimate the tolerances for the parameters
    imp_sim.continuous_output = True #Need to be able to store the result using the interpolate methods
    imp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used
    imp_sim.suppress_sens = False            #Dont suppress the sensitivity variables in the error test.

    #Simulate
    t, y, yd = imp_sim.simulate(400) #Simulate 400 seconds
    
    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 1577.6552477,3)
    nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 3)
    nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 3)
    nose.tools.assert_almost_equal(imp_sim.p_sol[0][1][0], 1.0)
    
    #Plot
    if with_plots:
        P.figure(1)
        P.subplot(221)
        P.plot(t, N.array(imp_sim.p_sol[0])[:,0],
               t, N.array(imp_sim.p_sol[0])[:,1],
               t, N.array(imp_sim.p_sol[0])[:,2])
        P.title("Parameter p1")
        P.legend(("p1/dy1","p1/dy2","p1/dy3"))
        P.subplot(222)
        P.plot(t, N.array(imp_sim.p_sol[1])[:,0],
               t, N.array(imp_sim.p_sol[1])[:,1],
               t, N.array(imp_sim.p_sol[1])[:,2])
        P.title("Parameter p2")
        P.legend(("p2/dy1","p2/dy2","p2/dy3"))
        P.subplot(223)
        P.plot(t, N.array(imp_sim.p_sol[2])[:,0],
               t, N.array(imp_sim.p_sol[2])[:,1],
               t, N.array(imp_sim.p_sol[2])[:,2])
        P.title("Parameter p3")
        P.legend(("p3/dy1","p3/dy2","p3/dy3"))
        P.subplot(224)
        P.plot(t,y)
        P.show()
Ejemplo n.º 4
0
def run_example(with_plots=True):
    """
    This example show how to use Assimulo and IDA for simulating sensitivities
    for initial conditions.::
    
        0 = dy1/dt - -(k01+k21+k31)*y1 - k12*y2 - k13*y3 - b1
        0 = dy2/dt - k21*y1 + (k02+k12)*y2
        0 = dy3/dt - k31*y1 + k13*y3
     
        y1(0) = p1, y2(0) = p2, y3(0) = p3
        p1=p2=p3 = 0 
    
    See http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html
    """
    def f(t, y, yd, p):
        y1, y2, y3 = y
        yd1, yd2, yd3 = yd
        k01 = 0.0211
        k02 = 0.0162
        k21 = 0.0111
        k12 = 0.0124
        k31 = 0.0039
        k13 = 0.000035
        b1 = 49.3

        res_0 = -yd1 - (k01 + k21 + k31) * y1 + k12 * y2 + k13 * y3 + b1
        res_1 = -yd2 + k21 * y1 - (k02 + k12) * y2
        res_2 = -yd3 + k31 * y1 - k13 * y3

        return N.array([res_0, res_1, res_2])

    #The initial conditions
    y0 = [0.0, 0.0, 0.0]  #Initial conditions for y
    yd0 = [49.3, 0., 0.]
    p0 = [0.0, 0.0, 0.0]  #Initial conditions for parameters
    yS0 = N.array([[1, 0, 0], [0, 1, 0], [0, 0, 1.]])

    #Create an Assimulo implicit problem
    imp_mod = Implicit_Problem(f, y0, yd0, p0=p0)

    #Sets the options to the problem
    imp_mod.yS0 = yS0

    #Create an Assimulo explicit solver (IDA)
    imp_sim = IDA(imp_mod)

    #Sets the paramters
    imp_sim.rtol = 1e-7
    imp_sim.atol = 1e-6
    imp_sim.pbar = [
        1, 1, 1
    ]  #pbar is used to estimate the tolerances for the parameters
    imp_sim.continuous_output = True  #Need to be able to store the result using the interpolate methods
    imp_sim.sensmethod = 'SIMULTANEOUS'  #Defines the sensitvity method used
    imp_sim.suppress_sens = False  #Dont suppress the sensitivity variables in the error test.

    #Simulate
    t, y, yd = imp_sim.simulate(400)  #Simulate 400 seconds

    #Basic test
    nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 3)
    nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 3)
    nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 3)
    nose.tools.assert_almost_equal(imp_sim.p_sol[0][1][0], 1.0)

    #Plot
    if with_plots:
        P.figure(1)
        P.subplot(221)
        P.plot(t,
               N.array(imp_sim.p_sol[0])[:, 0], t,
               N.array(imp_sim.p_sol[0])[:, 1], t,
               N.array(imp_sim.p_sol[0])[:, 2])
        P.title("Parameter p1")
        P.legend(("p1/dy1", "p1/dy2", "p1/dy3"))
        P.subplot(222)
        P.plot(t,
               N.array(imp_sim.p_sol[1])[:, 0], t,
               N.array(imp_sim.p_sol[1])[:, 1], t,
               N.array(imp_sim.p_sol[1])[:, 2])
        P.title("Parameter p2")
        P.legend(("p2/dy1", "p2/dy2", "p2/dy3"))
        P.subplot(223)
        P.plot(t,
               N.array(imp_sim.p_sol[2])[:, 0], t,
               N.array(imp_sim.p_sol[2])[:, 1], t,
               N.array(imp_sim.p_sol[2])[:, 2])
        P.title("Parameter p3")
        P.legend(("p3/dy1", "p3/dy2", "p3/dy3"))
        P.subplot(224)
        P.plot(t, y)
        P.show()