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()
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()