def run_example(with_plots=True): """ This example show how to use Assimulo and CVode for simulating sensitivities for initial conditions.:: dy1/dt = -(k01+k21+k31)*y1 + k12*y2 + k13*y3 + b1 dy2/dt = k21*y1 - (k02+k12)*y2 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, p): y1, y2, y3 = y k01 = 0.0211 k02 = 0.0162 k21 = 0.0111 k12 = 0.0124 k31 = 0.0039 k13 = 0.000035 b1 = 49.3 yd_0 = -(k01 + k21 + k31) * y1 + k12 * y2 + k13 * y3 + b1 yd_1 = k21 * y1 - (k02 + k12) * y2 yd_2 = k31 * y1 - k13 * y3 return N.array([yd_0, yd_1, yd_2]) #The initial conditions y0 = [0.0, 0.0, 0.0] #Initial conditions for y 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 explicit problem exp_mod = Explicit_Problem(f, y0, p0=p0) #Sets the options to the problem exp_mod.yS0 = yS0 #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 = 1e-7 exp_sim.atol = 1e-6 exp_sim.pbar = [ 1, 1, 1 ] #pbar is used to estimate the tolerances for the parameters exp_sim.continuous_output = True #Need to be able to store the result using the interpolate methods exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test. #Simulate t, y = exp_sim.simulate(400) #Simulate 400 seconds #Basic test nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 5) nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 5) nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 5) nose.tools.assert_almost_equal(exp_sim.p_sol[0][1][0], 1.0) #Plot if with_plots: P.figure(1) P.subplot(221) P.plot(t, N.array(exp_sim.p_sol[0])[:, 0], t, N.array(exp_sim.p_sol[0])[:, 1], t, N.array(exp_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(exp_sim.p_sol[1])[:, 0], t, N.array(exp_sim.p_sol[1])[:, 1], t, N.array(exp_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(exp_sim.p_sol[2])[:, 0], t, N.array(exp_sim.p_sol[2])[:, 1], t, N.array(exp_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()
def run_example(with_plots=True): r""" This example shows how to use Assimulo and CVode for simulating sensitivities for initial conditions. .. math:: \dot y_1 &= -(k_{01}+k_{21}+k_{31}) y_1 + k_{12} y_2 + k_{13} y_3 + b_1\\ \dot y_2 &= k_{21} y_1 - (k_{02}+k_{12}) y_2 \\ \dot y_3 &= k_{31} y_1 - k_{13} y_3 with the parameter dependent inital conditions :math:`y_1(0) = 0, y_2(0) = 0, y_3(0) = 0` . The initial values are taken as parameters :math:`p_1,p_2,p_3` for the computation of the sensitivity matrix, see http://sundials.2283335.n4.nabble.com/Forward-sensitivities-for-initial-conditions-td3239724.html on return: - :dfn:`exp_mod` problem instance - :dfn:`exp_sim` solver instance """ def f(t, y, p): y1, y2, y3 = y k01 = 0.0211 k02 = 0.0162 k21 = 0.0111 k12 = 0.0124 k31 = 0.0039 k13 = 0.000035 b1 = 49.3 yd_0 = -(k01 + k21 + k31) * y1 + k12 * y2 + k13 * y3 + b1 yd_1 = k21 * y1 - (k02 + k12) * y2 yd_2 = k31 * y1 - k13 * y3 return N.array([yd_0, yd_1, yd_2]) #The initial conditions y0 = [0.0, 0.0, 0.0] #Initial conditions for y 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 explicit problem exp_mod = Explicit_Problem(f, y0, p0=p0, name='Example: Computing Sensitivities') #Sets the options to the problem exp_mod.yS0 = yS0 #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 = 1e-7 exp_sim.atol = 1e-6 exp_sim.pbar = [ 1, 1, 1 ] #pbar is used to estimate the tolerances for the parameters exp_sim.report_continuously = True #Need to be able to store the result using the interpolate methods exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test. #Simulate t, y = exp_sim.simulate(400) #Simulate 400 seconds #Basic test nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 5) nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 5) nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 5) nose.tools.assert_almost_equal(exp_sim.p_sol[0][1][0], 1.0) #Plot if with_plots: title_text = r"Sensitivity w.r.t. ${}$" legend_text = r"$\mathrm{{d}}{}/\mathrm{{d}}{}$" P.figure(1) P.subplot(221) P.plot(t, N.array(exp_sim.p_sol[0])[:, 0], t, N.array(exp_sim.p_sol[0])[:, 1], t, N.array(exp_sim.p_sol[0])[:, 2]) P.title(title_text.format('p_1')) P.legend((legend_text.format('y_1', 'p_1'), legend_text.format('y_1', 'p_2'), legend_text.format('y_1', 'p_3'))) P.subplot(222) P.plot(t, N.array(exp_sim.p_sol[1])[:, 0], t, N.array(exp_sim.p_sol[1])[:, 1], t, N.array(exp_sim.p_sol[1])[:, 2]) P.title(title_text.format('p_2')) P.legend((legend_text.format('y_2', 'p_1'), legend_text.format('y_2', 'p_2'), legend_text.format('y_2', 'p_3'))) P.subplot(223) P.plot(t, N.array(exp_sim.p_sol[2])[:, 0], t, N.array(exp_sim.p_sol[2])[:, 1], t, N.array(exp_sim.p_sol[2])[:, 2]) P.title(title_text.format('p_3')) P.legend((legend_text.format('y_3', 'p_1'), legend_text.format('y_3', 'p_2'), legend_text.format('y_3', 'p_3'))) P.subplot(224) P.title('ODE Solution') P.plot(t, y) P.suptitle(exp_mod.name) P.show() return exp_mod, exp_sim
def run_example(with_plots=True): """ This example show how to use Assimulo and CVode for simulating sensitivities for initial conditions.:: dy1/dt = -(k01+k21+k31)*y1 + k12*y2 + k13*y3 + b1 dy2/dt = k21*y1 - (k02+k12)*y2 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, p): y1,y2,y3 = y k01 = 0.0211 k02 = 0.0162 k21 = 0.0111 k12 = 0.0124 k31 = 0.0039 k13 = 0.000035 b1 = 49.3 yd_0 = -(k01+k21+k31)*y1+k12*y2+k13*y3+b1 yd_1 = k21*y1-(k02+k12)*y2 yd_2 = k31*y1-k13*y3 return N.array([yd_0,yd_1,yd_2]) #The initial conditions y0 = [0.0,0.0,0.0] #Initial conditions for y 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 explicit problem exp_mod = Explicit_Problem(f, y0, p0=p0) #Sets the options to the problem exp_mod.yS0 = yS0 #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 = 1e-7 exp_sim.atol = 1e-6 exp_sim.pbar = [1,1,1] #pbar is used to estimate the tolerances for the parameters exp_sim.continuous_output = True #Need to be able to store the result using the interpolate methods exp_sim.sensmethod = 'SIMULTANEOUS' #Defines the sensitvity method used exp_sim.suppress_sens = False #Dont suppress the sensitivity variables in the error test. #Simulate t, y = exp_sim.simulate(400) #Simulate 400 seconds #Basic test nose.tools.assert_almost_equal(y[-1][0], 1577.6552477, 5) nose.tools.assert_almost_equal(y[-1][1], 611.9574565, 5) nose.tools.assert_almost_equal(y[-1][2], 2215.88563217, 5) nose.tools.assert_almost_equal(exp_sim.p_sol[0][1][0], 1.0) #Plot if with_plots: P.figure(1) P.subplot(221) P.plot(t, N.array(exp_sim.p_sol[0])[:,0], t, N.array(exp_sim.p_sol[0])[:,1], t, N.array(exp_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(exp_sim.p_sol[1])[:,0], t, N.array(exp_sim.p_sol[1])[:,1], t, N.array(exp_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(exp_sim.p_sol[2])[:,0], t, N.array(exp_sim.p_sol[2])[:,1], t, N.array(exp_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()