def case3():
y0 = [[5, -3], [2, 0], [-2, 3]]
t_tuple = 10
stepsize = 0.01
order = 3
start = time.time()
t_points, y_list = simulation_ode(fvdp2, 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()
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)
draw2D(y_list)
def case1():
y0 = [[a, b] for a in np.arange(-0.5, 0.5 + 0.25, 0.25)
for b in np.arange(-2.5, -1.5 + 0.25, 0.25)]
t_tuple = 1
stepsize = 0.001
order = 2
start = time.time()
t_points, y_list = simulation_ode(fvdp2_1, 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()
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)
draw2D(y_list)
def case2():
y0 = [[a, b] for a in np.arange(-0.5, 0.5 + 0.25, 0.25)
for b in np.arange(-2.5, -1.5 + 0.25, 0.25)]
t_tuple = 1
stepsize = 0.001
order = 2
start = time.time()
y_list_20 = []
y_list_ave = []
t_points = []
for i in range(0, 20):
t_points, y_list = simulation_ode(fvdp2_1,
y0,
t_tuple,
stepsize,
eps=0.01)
y_list_20.append(y_list)
for j in range(0, len(y_list_20[0])):
y_ppoints = np.zeros(
(y_list_20[0][0].shape[0], y_list_20[0][0].shape[1]))
for i in range(0, 20):
y_ppoints = y_ppoints + y_list_20[i][j]
y_ppoints = y_ppoints / 20.0
y_list_ave.append(y_ppoints)
end_simulation = time.time()
result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(
t_points, y_list_ave, stepsize, order)
end_inference = time.time()
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)
draw2D(y_list_ave)
def case10():
y0 = [[-1,1],[1,4],[2,-3]]
t_tuple = [(0,5),(0,5),(0,5)]
stepsize = 0.01
maxorder = 2
# start = time.time()
def labeltest(y):
if eventtr_1(0,y)<0 and eventtr_2(0,y)>0:
return 0
elif eventtr_1(0,y)>=0 and eventtr_2(0,y)>0:
return 1
else:
return 2
t_list, y_list = simulation_ode_3([modetr_1, modetr_2, modetr_3], [eventtr_1,eventtr_2,eventtr_2], labeltest, y0, t_tuple, stepsize)
draw2D(y_list)
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)
print(P)
print(G)
print(D)
# for p in P:
# print(len(p))
# tpar_list,ypar_list = parti(t_list,y_list,0.2,1/3)
# for temp in tpar_list:
# print(temp[-1])
# labels = infer_dynamic_modes_ex_dbs(tpar_list, ypar_list, stepsize, maxorder, 0.02)
# print(labels)
# draw2D(ypar_list)
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()
P,G = reclass(A,b,P,0.01)
for p in P:
print(len(p))
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()
P,D = dropclass(P,G,D,A,b,Y,0.01,0.01)
print(D)
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')
m = svm_train(prob, param)
svm_save_model('model_file', m)
print("pred")
p_label, p_acc, p_val = svm_predict(y, x, m)
# print(p_label)
nsv = m.get_nr_sv()
svc = m.get_sv_coef()
sv = m.get_SV()
# print(nsv)
# print(svc)
# print(sv)
# def clafun(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]))**3)
# return g
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)
print(a2)
print(g)
def f(x,y):
g = -m.rho[0]
for i in range(0,nsv):
g = g + svc[i][0] * (0.5*(x*sv[i][1]+y*sv[i][2])+1)
return g
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')
m = svm_train(prob, param)
svm_save_model('model_file', m)
print("pred")
p_label, p_acc, p_val = svm_predict(y, x, m)
# print(p_label)
nsv = m.get_nr_sv()
svc = m.get_sv_coef()
sv = m.get_SV()
# print(nsv)
# print(svc)
# print(sv)
# def clafun(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]))**3)
# return g
g1 = -m.rho[0]
b1 = 0
b2 = 0
for i in range(0,nsv):
b1 = b1 + svc[i][0] * 0.5 * sv[i][1]
b2 = b2 + svc[i][0] * 0.5 * sv[i][2]
g1 = g1 + svc[i][0]*1
# print(a1)
# print(a2)
# print(g)
def h(x,y):
g = -m.rho[0]
for i in range(0,nsv):
g = g + svc[i][0] * (0.5*(x*sv[i][1]+y*sv[i][2])+1)
return g
x = np.linspace(-10,10,100)
y = np.linspace(-10,10,100)
X,Y = np.meshgrid(x,y)#将x，y指传入网格中
# plt.contourf(X,Y,f(X,Y),8,alpha=0.75,cmap=plt.cm.hot)#8指图中的8+1根线，绘制等温线，其中cmap指颜色
C = plt.contour(X,Y,f(X,Y),[0])#colors指等高线颜色
plt.clabel(C,inline=True,fontsize=10)#inline=True指字体在等高线中
D = plt.contour(X,Y,h(X,Y),[0])#colors指等高线颜色
plt.clabel(D,inline=True,fontsize=10)#inline=True指字体在等高线中
plt.xticks(())
plt.yticks(())
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