def case1():
mode2 = experiment1.get_mode2(0)
event1 = experiment1.get_event1(0)
y0 = [[99.5,80],[97.5,100]]
stepsize = 0.1
maxorder = 1
boundary_order = 1
num_mode = 2
T = 50
ep = 0.01
mergeep = 0.01
method='piecelinear'
t_list, y_list = simulation_ode_2(mode2, event1, y0, T, stepsize)
with open('f1tr.txt','ab') as f:
for ypoints in y_list:
np.savetxt(f, ypoints, delimiter=" ")
P,G,C = infer_model(
t_list, y_list, stepsize=stepsize, maxorder=maxorder, boundary_order=boundary_order,
num_mode=num_mode, modelist=mode2, event=event1, ep=ep, mergeep = mergeep, method=method, verbose=False)
# A, b1, b2, Y, ytuple = diff_method_backandfor(t_list, y_list, maxorder, stepsize)
d_avg = test_model(
P, G, C, num_mode, y_list , mode2, event1, maxorder, boundary_order)
# d_avg = test_model2(
# P, G, C, num_mode, A, Y , mode2, event1, maxorder, boundary_order)
print(G)
print(C[0]/C[0],C[1]/C[0],C[2]/C[0])
print(d_avg)
@eventAttr()
def eventtest(t,y):
y0, y1 = y
return C[0] * y0 + C[1] * y1 + C[2]
ttest_list, ytest_list = simulation_ode_2([ode_test(G[0],maxorder),ode_test(G[1],maxorder)], eventtest, y0, T, stepsize)
for i, temp_y in enumerate(y_list):
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
if i == 0:
plt.plot(y0_list,y1_list,c='b',label='Original')
else:
plt.plot(y0_list,y1_list,c='b')
for i, temp_y in enumerate(ytest_list):
y0_list = temp_y.T[0][::5]
y1_list = temp_y.T[1][::5]
if i == 0:
plt.plot(y0_list,y1_list,mfc='None', mec='r',label='Inferred',marker='.',linestyle='None')
else:
# plt.plot(y0_list,y1_list,c='r',linestyle='--',marker=',')
plt.plot(y0_list,y1_list,mfc='None', mec='r',marker='.',linestyle='None')
plt.xlabel('x1')
plt.ylabel('x2')
plt.legend()
plt.show()
def case2():
fvdp3 = experiment2.get_fvdp3(0)
event1 = experiment2.get_event1(0)
y0 = [[5,5,5], [2,2,2]]
stepsize = 0.004
maxorder = 2
boundary_order = 1
num_mode = 2
T = 5
ep = 0.01
mergeep = 0.2
method='tolmerge'
t_list, y_list = simulation_ode_2(fvdp3, event1, y0, T, stepsize)
# A, b1, b2, Y, ytuple = diff_method_backandfor(t_list, y_list, maxorder, stepsize)
P,G,C = infer_model(
t_list, y_list, stepsize=stepsize, maxorder=maxorder, boundary_order=boundary_order,
num_mode=num_mode, modelist=fvdp3, event=event1, ep=ep, mergeep= mergeep,method=method, verbose=False)
d_avg = test_model(
P, G, C, num_mode, y_list , fvdp3, event1, maxorder, boundary_order)
# d_avg = test_model2(
# P, G, C, num_mode, A, Y , fvdp3, event1, maxorder, boundary_order)
print(G)
print(C[0]/C[0],C[1]/C[0],C[2]/C[0],C[3]/C[0])
print(d_avg)
with open('f2tr.txt','ab') as f:
for ypoints in y_list:
np.savetxt(f, ypoints, delimiter=" ")
@eventAttr()
def eventtest(t,y):
y0, y1, y2 = y
return C[0] * y0 + C[1] * y1 + C[2]* y2 + C[3]
ttest_list, ytest_list = simulation_ode_2([ode_test(G[0],maxorder),ode_test(G[1],maxorder)], eventtest, y0, T, stepsize)
ax = plt.axes(projection='3d')
for temp_y in y_list[0:1]:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
y2_list = temp_y.T[2]
ax.plot3D(y0_list, y1_list, y2_list,c='b',label='Original')
for temp_y in ytest_list[0:1]:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
y2_list = temp_y.T[2]
ax.plot3D(y0_list, y1_list, y2_list,c='r',label='Inferred', linestyle='--')
ax.set_xlabel('x1')
ax.set_ylabel('x2')
ax.set_zlabel('x3')
plt.legend()
plt.show()
def case2():
y0 = [[20]]
t_tuple = 4
stepsize = 0.001
order = 8
start = time.time()
t_points, y_list = simulation_ode(dydx2, y0, t_tuple, stepsize, eps=0)
end_simulation = time.time()
result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(
t_points, y_list, stepsize, order)
end_inference = time.time()
t_points, y_list_test = simulation_ode(ode_test(result_coef, order),
y0,
t_tuple,
stepsize,
eps=0)
print(result_coef)
print()
print("Total time: ", end_inference - start)
print("Simulation time: ", end_simulation - start)
print("Calc-diff time: ", calcdiff_time)
print("Pseudoinv time: ", pseudoinv_time)
for temp_y in y_list:
plt.scatter(t_points, temp_y, s=0.1, c='r')
for temp_y in y_list_test:
plt.scatter(t_points, temp_y, s=0.1, c='b')
plt.show()
def case5():
y0 = [[0,0],[1,0]]
t_tuple = 2
stepsize = 0.01
order = 2
maxorder = 3
t_list, y_list = simulation_ode(conti_test, y0, t_tuple, stepsize, eps=0)
tpar_list,ypar_list = parti(t_list,y_list,0.2,1/3)
print(len(tpar_list))
for i in range(0,len(tpar_list)):
print(tpar_list[i][0])
print(tpar_list[i][-1])
print(ypar_list[i][0])
print(ypar_list[i][-1])
for temp_y in y_list:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
plt.plot(y0_list,y1_list,'b')
plt.show()
# modes, coefs, mdors = infer_dynamic_modes_ex(tpar_list, ypar_list, stepsize, maxorder, 0.01)
# modes, coefs, mdors = infer_dynamic_modes_exx(tpar_list, ypar_list, stepsize, maxorder, 0.01)
# print(modes)
# print(coefs)
# print(mdors)
ttest_list=[]
ttest_list.append(tpar_list[0])
ttest_list.append(tpar_list[1])
ytest_list=[]
ytest_list.append(ypar_list[0])
ytest_list.append(ypar_list[1])
A, b = diff_method(ttest_list, ytest_list, 3, stepsize)
g = pinv2(A).dot(b)
print(g.T)
t_start = tpar_list[0][0]
t_end = tpar_list[0][-1]
t_start = 0
t_end = 0.01
t_points = np.arange(t_start, t_end + stepsize, stepsize)
tstart = time.time()
y_object = solve_ivp(ode_test(g.T,3), (t_start, t_end+stepsize), ypar_list[0][0], t_eval = t_points, rtol=1e-7, atol=1e-9)
y_points = y_object.y.T
tend = time.time()
print(y_points)
print(tend-tstart)
def case(y0, t_tuple, stepsize, maxorder, modelist, event, ep, method):
t_list, y_list = simulation_ode_2(modelist, event, y0, t_tuple, stepsize)
if method == "new":
A, b, Y = diff_method_new(t_list, y_list, maxorder, stepsize)
P, G, D = infer_dynamic_modes_new(t_list, y_list, stepsize, maxorder,
0.01)
P, D = dropclass(P, G, D, A, b, Y, 0.01, stepsize)
# print(len(P))
print(G)
y = []
x = []
for j in range(0, len(P[0])):
y.append(1)
x.append({1: Y[P[0][j], 0], 2: Y[P[0][j], 1], 3: Y[P[0][j], 2]})
for j in range(0, len(P[1])):
y.append(-1)
x.append({1: Y[P[1][j], 0], 2: Y[P[1][j], 1], 3: Y[P[1][j], 2]})
prob = svm_problem(y, x)
param = svm_parameter('-t 1 -d 1 -c 10 -r 1 -b 0 -q')
m = svm_train(prob, param)
svm_save_model('model_file', m)
nsv = m.get_nr_sv()
svc = m.get_sv_coef()
sv = m.get_SV()
g = -m.rho[0]
a1 = 0
a2 = 0
a3 = 0
for i in range(0, nsv):
a1 = a1 + svc[i][0] * 0.5 * sv[i][1]
a2 = a2 + svc[i][0] * 0.5 * sv[i][2]
a3 = a3 + svc[i][0] * 0.5 * sv[i][3]
g = g + svc[i][0]
print(a1 / a1, a2 / a1, a3 / a1, g / a1)
def f(x):
return a1 * x[0] + a2 * x[1] + a3 * x[2] + g > 0
@eventAttr()
def eventtest(t, y):
y0, y1, y2 = y
return a1 * y0 + a2 * y1 + a3 * y2 + g
ttest_list, ytest_list = simulation_ode_2(
[ode_test(G[0], maxorder),
ode_test(G[1], maxorder)], eventtest, y0, t_tuple, stepsize)
ax = plt.axes(projection='3d')
for temp_y in y_list[0:1]:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
y2_list = temp_y.T[2]
ax.plot3D(y0_list, y1_list, y2_list, c='b')
for temp_y in ytest_list[0:1]:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
y2_list = temp_y.T[2]
ax.plot3D(y0_list, y1_list, y2_list, c='r')
plt.show()
sum = 0
num = 0
def get_poly_pt(x):
gene = generate_complete_polynomial(len(x), maxorder)
val = []
for i in range(gene.shape[0]):
val.append(1.0)
for j in range(gene.shape[1]):
val[i] = val[i] * (x[j]**gene[i, j])
poly_pt = np.mat(val)
return poly_pt
for ypoints in y_list:
num = num + ypoints.shape[0]
for i in range(ypoints.shape[0]):
if event(0, ypoints[i]) > 0:
exact = modelist[0](0, ypoints[i])
else:
exact = modelist[1](0, ypoints[i])
if f(ypoints[i]) == 1:
predict = np.matmul(get_poly_pt(ypoints[i]), G[0].T)
else:
predict = np.matmul(get_poly_pt(ypoints[i]), G[1].T)
exact = np.mat(exact)
diff = exact - predict
c = 0
a = 0
b = 0
for j in range(diff.shape[1]):
c = c + diff[0, j]**2
a = a + exact[0, j]**2
b = b + predict[0, j]**2
f1 = np.sqrt(c)
f2 = np.sqrt(a) + np.sqrt(b)
sum = sum + f1 / f2
return sum / num
def case(y0, t_tuple, stepsize, maxorder, modelist, eventlist, labeltest, ep,
method):
t_list, y_list = simulation_ode_3(modelist, eventlist, labeltest, y0,
t_tuple, stepsize)
if method == "new":
A, b, Y = diff_method_new(t_list, y_list, maxorder, stepsize)
P, G, D = infer_dynamic_modes_new(t_list, y_list, stepsize, maxorder,
ep)
P, G = reclass(A, b, P, ep)
P, D = dropclass(P, G, D, A, b, Y, ep, stepsize)
print(G)
for i in range(0, len(P)):
y0_list = []
y1_list = []
for j in range(0, len(P[i])):
y0_list.append(Y[P[i][j], 0])
y1_list.append(Y[P[i][j], 1])
plt.scatter(y0_list, y1_list, s=1)
plt.show()
y = []
x = []
for j in range(0, len(P[2])):
y.append(1)
x.append({1: Y[P[2][j], 0], 2: Y[P[2][j], 1]})
for j in range(0, len(P[1])):
y.append(-1)
x.append({1: Y[P[1][j], 0], 2: Y[P[1][j], 1]})
for j in range(0, len(P[0])):
y.append(-1)
x.append({1: Y[P[0][j], 0], 2: Y[P[0][j], 1]})
prob = svm_problem(y, x)
param = svm_parameter('-t 1 -d 1 -c 100 -r 1 -b 0 -q')
m = svm_train(prob, param)
svm_save_model('model_file1', m)
nsv = m.get_nr_sv()
svc = m.get_sv_coef()
sv = m.get_SV()
g = -m.rho[0]
a1 = 0
a2 = 0
for i in range(0, nsv):
a1 = a1 + svc[i][0] * 0.5 * sv[i][1]
a2 = a2 + svc[i][0] * 0.5 * sv[i][2]
g = g + svc[i][0] * 1
print(a1 / a2, a2 / a2, g / a2)
def f(x):
g = -m.rho[0]
for i in range(0, nsv):
g = g + svc[i][0] * (0.5 *
(x[0] * sv[i][1] + x[1] * sv[i][2]) + 1)
return g > 0
x = []
y = []
for j in range(0, len(P[1])):
y.append(1)
x.append({1: Y[P[1][j], 0], 2: Y[P[1][j], 1]})
for j in range(0, len(P[0])):
y.append(-1)
x.append({1: Y[P[0][j], 0], 2: Y[P[0][j], 1]})
prob = svm_problem(y, x)
param = svm_parameter('-t 1 -d 1 -c 100 -r 1 -b 0 -q')
n = svm_train(prob, param)
svm_save_model('model_file2', n)
# p_label, p_acc, p_val = svm_predict(y, x, n)
nsv1 = n.get_nr_sv()
svc1 = n.get_sv_coef()
sv1 = n.get_SV()
g1 = -n.rho[0]
b1 = 0
b2 = 0
for i in range(0, nsv1):
b1 = b1 + svc1[i][0] * 0.5 * sv1[i][1]
b2 = b2 + svc1[i][0] * 0.5 * sv1[i][2]
g1 = g1 + svc1[i][0] * 1
print(b1 / b1, b2 / b1, g1 / b1)
def h(x):
g = -n.rho[0]
for i in range(0, nsv1):
g = g + svc1[i][0] * (0.5 *
(x[0] * sv1[i][1] + x[1] * sv1[i][2]) +
1)
return g > 0
@eventAttr()
def eventtest1(t, y):
y0, y1 = y
return a1 * y0 + a2 * y1 + g
@eventAttr()
def eventtest2(t, y):
y0, y1 = y
return b1 * y0 + b2 * y1 + g1
def labeltesttest(y):
if eventtest1(0, y) > 0:
return 2
elif eventtest2(0, y) > 0:
return 1
else:
return 0
ttest_list, ytest_list = simulation_ode_3([
ode_test(G[0], maxorder),
ode_test(G[1], maxorder),
ode_test(G[2], maxorder)
], [eventtest1, eventtest2], labeltesttest, y0, t_tuple, stepsize)
for temp_y in y_list:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
plt.plot(y0_list, y1_list, c='b')
for temp_y in ytest_list:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
plt.plot(y0_list, y1_list, c='r')
plt.show()
sum = 0
num = 0
def get_poly_pt(x):
gene = generate_complete_polynomial(len(x), maxorder)
val = []
for i in range(gene.shape[0]):
val.append(1.0)
for j in range(gene.shape[1]):
val[i] = val[i] * (x[j]**gene[i, j])
poly_pt = np.mat(val)
return poly_pt
for ypoints in y_list:
num = num + ypoints.shape[0]
for i in range(ypoints.shape[0]):
exact = modelist[labeltest(ypoints[i])](0, ypoints[i])
if f(ypoints[i]) == 1:
predict = np.matmul(get_poly_pt(ypoints[i]), G[2].T)
elif h(ypoints[i]) == 1:
predict = np.matmul(get_poly_pt(ypoints[i]), G[1].T)
else:
predict = np.matmul(get_poly_pt(ypoints[i]), G[0].T)
exact = np.mat(exact)
diff = exact - predict
c = 0
a = 0
b = 0
for j in range(diff.shape[1]):
c = c + diff[0, j]**2
a = a + exact[0, j]**2
b = b + predict[0, j]**2
f1 = np.sqrt(c)
f2 = np.sqrt(a) + np.sqrt(b)
sum = sum + f1 / f2
return sum / num
def case5():
modetr = experiment5.get_modetr(0)
event = experiment5.get_event(0)
labeltest = experiment5.get_labeltest(0)
y0 = [[-1,1],[1,4],[2,-3]]
T = 5
stepsize = 0.01
maxorder = 2
boundary_order = 1
num_mode = 3
ep = 0.01
mergeep=0.01
method = 'piecelinear'
t_list, y_list = simulation_ode_3(modetr, event, labeltest, y0, T, stepsize)
P, G, (coeff1, coeff2, [first,second,third]) = infer_model(
t_list, y_list, stepsize=stepsize, maxorder=maxorder, boundary_order=boundary_order,
num_mode=num_mode, modelist=modetr, event=event, ep=ep, mergeep= mergeep,method=method, verbose=False,
labeltest=labeltest)
boundary = (coeff1, coeff2, [first,second,third])
d_avg = test_model(
P, G, boundary, num_mode, y_list, modetr, event, maxorder, boundary_order,
labeltest=labeltest)
print(d_avg)
print(coeff1[0]/coeff1[0],coeff1[1]/coeff1[0],coeff1[2]/coeff1[0])
print(coeff1[0]/coeff1[1],coeff1[1]/coeff1[1],coeff1[2]/coeff1[1])
print(coeff2[0]/coeff2[0],coeff2[1]/coeff2[0],coeff2[2]/coeff2[0])
print(coeff2[0]/coeff2[1],coeff2[1]/coeff2[1],coeff2[2]/coeff2[1])
@eventAttr()
def eventtest1(t,y):
y0, y1 = y
return coeff1[0] * y0 + coeff1[1] * y1 + coeff1[2]
@eventAttr()
def eventtest2(t,y):
y0, y1 = y
return coeff2[0] * y0 + coeff2[1] * y1 + coeff2[2]
def labeltesttest(y):
if eventtest1(0,y)>0:
return first
elif eventtest2(0,y)>0:
return second
else:
return third
ttest_list, ytest_list = simulation_ode_3([ode_test(G[0],maxorder),ode_test(G[1],maxorder),ode_test(G[2],maxorder)], [eventtest1,eventtest2], labeltesttest, y0, T, stepsize)
for i, temp_y in enumerate(y_list):
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
if i == 0:
plt.plot(y0_list,y1_list,c='b',label='Original')
else:
plt.plot(y0_list,y1_list,c='b')
for i, temp_y in enumerate(ytest_list):
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
if i == 0:
plt.plot(y0_list,y1_list,c='r', label='Inferred',linestyle='--')
else:
plt.plot(y0_list,y1_list,c='r',linestyle='--')
plt.xlabel('x1')
plt.ylabel('x2')
plt.legend()
plt.show()
def case(y0, t_tuple, stepsize, maxorder, modelist, event, ep, method):
# print('Simulating')
t_list, y_list = simulation_ode_2(modelist, event, y0, t_tuple, stepsize)
draw2D(y_list)
if method == "new":
# print('Classifying')
A, b, Y = diff_method_new(t_list, y_list, maxorder, stepsize)
P, G, D = infer_dynamic_modes_new(t_list, y_list, stepsize, maxorder,
ep)
P, G = reclass(A, b, P, ep)
print(G)
P, D = dropclass(P, G, D, A, b, Y, ep, stepsize)
# print('Number of modes:', len(P))
y = []
x = []
for j in range(0, len(P[0])):
y.append(1)
x.append({1: Y[P[0][j], 0], 2: Y[P[0][j], 1]})
for j in range(0, len(P[1])):
y.append(-1)
x.append({1: Y[P[1][j], 0], 2: Y[P[1][j], 1]})
prob = svm_problem(y, x)
param = svm_parameter('-t 1 -d 1 -c 10 -r 1 -b 0 -q')
m = svm_train(prob, param)
svm_save_model('model_file', m)
nsv = m.get_nr_sv()
svc = m.get_sv_coef()
sv = m.get_SV()
g = -m.rho[0]
a1 = 0
a2 = 0
for i in range(0, nsv):
a1 = a1 + svc[i][0] * 0.5 * sv[i][1]
a2 = a2 + svc[i][0] * 0.5 * sv[i][2]
g = g + svc[i][0]
def f(x):
return a1 * x[0] + a2 * x[1] + g > 0
print(a1 / a1, a2 / a1, g / a1)
sum = 0
num = 0
@eventAttr()
def eventtest(t, y):
y0, y1 = y
return a1 * y0 + a2 * y1 + g
ttest_list, ytest_list = simulation_ode_2(
[ode_test(G[0], maxorder),
ode_test(G[1], maxorder)], eventtest, y0, t_tuple, stepsize)
for i, temp_y in enumerate(y_list):
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
if i == 0:
plt.plot(y0_list, y1_list, c='b', label='Original')
else:
plt.plot(y0_list, y1_list, c='b')
for i, temp_y in enumerate(ytest_list):
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
if i == 0:
plt.plot(y0_list, y1_list, c='r', label='Inferred')
else:
plt.plot(y0_list, y1_list, c='r')
plt.xlabel('x1')
plt.ylabel('x2')
plt.legend()
plt.show()
def get_poly_pt(x):
gene = generate_complete_polynomial(len(x), maxorder)
val = []
for i in range(gene.shape[0]):
val.append(1.0)
for j in range(gene.shape[1]):
val[i] = val[i] * (x[j]**gene[i, j])
poly_pt = np.mat(val)
return poly_pt
for ypoints in y_list:
num = num + ypoints.shape[0]
for i in range(ypoints.shape[0]):
if event(0, ypoints[i]) > 0:
exact = modelist[0](0, ypoints[i])
else:
exact = modelist[1](0, ypoints[i])
if f(ypoints[i]) == 1:
predict = np.matmul(get_poly_pt(ypoints[i]), G[0].T)
else:
predict = np.matmul(get_poly_pt(ypoints[i]), G[1].T)
exact = np.mat(exact)
diff = exact - predict
c = 0
a = 0
b = 0
for j in range(diff.shape[1]):
c = c + diff[0, j]**2
a = a + exact[0, j]**2
b = b + predict[0, j]**2
f1 = np.sqrt(c)
f2 = np.sqrt(a) + np.sqrt(b)
sum = sum + f1 / f2
return sum / num