def case8():
# y0 = [[1,7]]
# t_tuple = [(0,30)]
# stepsize = 0.001
# order = 2
# maxorder = 4
# t_list, y_list = simulation_ode(mode2_1, y0, t_tuple, stepsize, eps=0.00001)
y0 = [[0,0],[1,0],[0.3,0]]
t_tuple = 2
stepsize = 0.01
order = 2
maxorder = 4
t_list, y_list = simulation_ode(conti_test, y0, t_tuple, stepsize, eps=0)
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')
for i in range(0,temp_y.shape[0]-4):
g = temp_y[i][:] - 4*temp_y[i+1][:] + 6*temp_y[i+2][:] - 4*temp_y[i+3][:] + temp_y[i+4][:]
gg = np.max(g)
if gg > 0.005:
plt.scatter(temp_y[i+4][0], temp_y[i+4][1], s= 10, c='r')
plt.show()
def case2():
y0 = [[0,0],[1,0],[0.3,0],[2.7,0]]
t_tuple = 2
stepsize = 0.001
order = 2
maxorder = 2
# start = time.time()
t_list, y_list = simulation_ode(conti_test, y0, t_tuple, stepsize, eps=0)
# end_simulation = time.time()
# result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(t_list, 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)
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()
P,G,D = infer_dynamic_modes_new(t_list, y_list, stepsize, maxorder, 0.01)
print(P)
print(G)
print(D)
def case11():
y0 = [[1,7],[2,6]]
t_tuple = 2
stepsize = 0.01
order = 2
maxorder = 2
# start = time.time()
t_list, y_list = simulation_ode(mode2_1, y0, t_tuple, stepsize, eps=0)
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()
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])
G,labels = infer_dynamic_modes_pie(tpar_list, ypar_list, stepsize, maxorder, 0.02)
# modes, coefs, mdors = infer_dynamic_modes_ex(tpar_list, ypar_list, stepsize, maxorder, 0.01)
# print(modes)
# print(coefs)
# print(mdors)
print(len(labels))
print(G)
def case3():
y0 = [[9]]
t_tuple = 3
stepsize = 0.01
order = 2
t_list, y_list = simulation_ode(dydx3, y0, t_tuple, stepsize, eps=0)
for i in range(0,len(y_list)):
plt.plot(t_list[i],y_list[i])
plt.show()
def case4():
y0 = [[5,5,5],[2,2,2]]
t_tuple = 5
stepsize = 0.01
maxorder = 2
t_list, y_list = simulation_ode(fvdp3_3, y0, t_tuple, stepsize, eps=0)
draw3D(y_list)
tpar_list,ypar_list = parti(t_list,y_list,0.2,1/3)
G,labels = infer_dynamic_modes_pie(tpar_list, ypar_list, stepsize, maxorder, 0.02)
print(labels)
print(G)
def case1():
y0 = [[1,7]]
t_tuple = 25
stepsize = 0.01
order = 2
maxorder = 4
# start = time.time()
t_list, y_list = simulation_ode(mode2_1, y0, t_tuple, stepsize, eps=0)
# end_simulation = time.time()
# result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(t_list, 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)
tpar_list,ypar_list = parti(t_list,y_list,0.05)
print(len(tpar_list))
for i in range(0,len(tpar_list)):
print(tpar_list[i][0],tpar_list[i][-1])
print(ypar_list[i][0],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()
# result_coef, calcdiff_time, pseudoinv_time = infer_dynamic([tpar_list[0],tpar_list[1]], [ypar_list[0],ypar_list[1]], stepsize, 4)
# print(result_coef)
# tstart = time.time()
# comt,comy = simulation_ode_stiff(ode_test(result_coef,4), [ypar_list[0][0],ypar_list[1][0]], [(tpar_list[0][0], tpar_list[0][-1]),(tpar_list[1][0], tpar_list[1][-1])], stepsize,eps=0)
# tend = time.time()
# print(dist(comy,[ypar_list[0],ypar_list[1]]))
# print(tend-tstart)
# print(dist([ypar_list[0],ypar_list[2],ypar_list[4]],comy))
# result_coef = np.matrix([[ 0, 0, 0, -0.26, 0.26, 0], [0, 0, 0, 0, 0, -1]])
# comt,comy = simulation_ode(ode_test(result_coef,2), [ypar_list[0][0],ypar_list[2][0],ypar_list[4][0]], [(tpar_list[0][0], tpar_list[0][-1]),(tpar_list[2][0], tpar_list[2][-1]),(tpar_list[4][0], tpar_list[4][-1])], stepsize,eps=0)
# print(dist([ypar_list[0],ypar_list[2],ypar_list[4]],comy))
# result_coef = np.matrix([[ 0, 0, 0, -0.26, 0.26, 0], [0, 0, 0, 0, 0, 1]])
# comt,comy = simulation_ode(ode_test(result_coef,2), [ypar_list[1][0],ypar_list[3][0],ypar_list[5][0]], [(tpar_list[1][0], tpar_list[1][-1]),(tpar_list[3][0], tpar_list[3][-1]),(tpar_list[5][0], tpar_list[5][-1])], stepsize,eps=0)
# print(dist([ypar_list[1],ypar_list[3],ypar_list[5]],comy))
tstart = time.time()
modes, coefs, mdors = infer_dynamic_modes_ex(tpar_list, ypar_list, stepsize, maxorder, 0.001)
# modes, coefs, mdors = infer_dynamic_modes_exx(tpar_list, ypar_list, stepsize, maxorder, 0.01)
tend = time.time()
print(modes)
print(coefs)
print(mdors)
print(tend-tstart)
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 case3():
y0 = [[5,5,5],[2,2,2]]
t_tuple = 5
stepsize = 0.01
maxorder = 2
t_list, y_list = simulation_ode(fvdp3_3, y0, t_tuple, stepsize, eps=0)
draw3D(y_list)
A, b, Y = diff_method_new(t_list, y_list, maxorder, stepsize)
# A, b1, b2, Y = diff_method_backandfor(t_list, y_list, maxorder, stepsize)
# print(b1)
# print(b2)
P,G,D = infer_dynamic_modes_new(t_list, y_list, stepsize, maxorder, 0.02)
print(P)
print(G)
print(D)
def case():
y0 = [[5, 5, 5], [2, 2, 2]]
stepsize = 0.01
maxorder = 2
T = 5
t_list, y_list = simulation_ode(fvdp3_1, y0, T, stepsize, eps=0.02)
A, b, Y = diff_method_new(t_list, y_list, maxorder, stepsize)
clf = linear_model.LinearRegression(fit_intercept=False)
clf.fit(A, b)
g = clf.coef_
print(g)
A, b, Y = diff_method_new_6(t_list, y_list, maxorder, stepsize)
clf.fit(A, b)
g = clf.coef_
print(g)
def case5():
y0 = [[5,5,5], [2,2,2]]
t_tuple = 5
stepsize = 0.01
maxorder = 2
t_list, y_list = simulation_ode(fvdp3_3, y0, t_tuple, stepsize, eps=0)
clfs, boundary = infer_multi_ch.infer_multi_linear(t_list, y_list, stepsize, maxorder)
for clf in clfs:
print(clf.coef_)
print(boundary)
num_pt0 = y_list[0].shape[0]
num_pt1 = y_list[1].shape[0]
sum = 0
for i in range(100):
# index = random.choice(range(num_pt0))
x = y_list[0][i]
# sum += infer_multi_ch.test_classify(fvdp3_3, clfs, boundary, maxorder, x)
print(infer_multi_ch.test_classify(fvdp3_3, clfs, boundary, maxorder, x))
def case2():
# y0 = [[1,3],[-1,-2],[-3,-5],[2,4],[-2,3],[-4,5],[4,7],[-2,-10],[5,8]]
# t_tuple = [(0,2),(0,3),(0,4),(0,5),(0,1),(0,1),(0,5),(0,6),(0,6)]
y0 = [[1,3]]
t_tuple = 2
stepsize = 0.01
order = 2
maxorder = 4
t_list, y_list = simulation_ode(mode2_1, y0, t_tuple, stepsize, eps=0)
# modes, coefs = infer_dynamic_modes(t_list, y_list, stepsize, maxorder, 0.001)
modes, coefs, mdors = infer_dynamic_modes_ex(t_list, y_list, stepsize, maxorder, 0.01)
print(modes)
print(coefs)
print(mdors)
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()
def case9():
y0 = [[0,0]]
t_tuple = 7
stepsize = 0.001
order = 2
maxorder = 4
t_list, y_list = simulation_ode(mode2_11, y0, t_tuple, stepsize, eps=0)
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()
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])
labels = infer_dynamic_modes_ex_dbs(tpar_list, ypar_list, stepsize, maxorder, 0.0001)
print(labels)
def case4():
y0 = [[0,0],[1,0]]
t_tuple = [(0,2.5),(0,2)]
stepsize = 0.01
order = 2
maxorder = 4
# start = time.time()
t_list, y_list = simulation_ode(conti_test, y0, t_tuple, stepsize, eps=0)
# end_simulation = time.time()
# result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(t_list, 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)
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, 0.0001)
# modes, coefs, mdors = infer_dynamic_modes_exx(tpar_list, ypar_list, stepsize, maxorder, 0.0001)
print(modes)
print(coefs)
print(mdors)
def case10():
y0 = [[0,0],[1,0],[0.3,0],[2.7,0]]
t_tuple = 2
stepsize = 0.01
order = 2
maxorder = 3
# start = time.time()
t_list, y_list = simulation_ode(conti_test, y0, t_tuple, stepsize, eps=0)
# end_simulation = time.time()
# result_coef, calcdiff_time, pseudoinv_time = infer_dynamic(t_list, 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)
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()
G,labels = infer_dynamic_modes_pie(tpar_list, ypar_list, stepsize, maxorder, 0.15)
print(labels)
print(G)
def case1():
# y0 = [[1,3],[-1,-2],[-3,-5],[2,4]]
# t_tuple = [(0,20),(0,10),(0,15),(0,15)]
y0 = [[1,3],[-1,-2]]
t_tuple = 20
stepsize = 0.01
order = 2
maxorder = 2
# start = time.time()
t_list, y_list = simulation_ode(mode2_1, y0, t_tuple, stepsize, eps=0)
# 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()
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)
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 -b 0 ')
m = svm_train(prob, param)
svm_save_model('model_file', m)
yt = [-1,-1,1,1]
xt = [{1:1, 2:1},{1:-1, 2:1},{1:1, 2:-1},{1:-1, 2:-1}]
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]
print("a1",a1/a1)
print("a2",a2/a1)
print("g",g/a1)
# ax.plot_surface(X,Y,Z,rstride=1,cstride=1,cmap='rainbow')
# plt.show()
dim = G[0].shape[0]
A = generate_complete_polynomial(dim,maxorder)
def odepre(t,y):
# print("in")
basicf = []
for i in range(0,A.shape[0]):
ap = 1
for j in range(0,A.shape[1]):
ap = ap*(y[j]**A[i][j])
basicf.append(ap)
b = np.array(basicf)
dydt = np.zeros(dim)
if a1 * y[0] + a2 * y[1] + g > 0:
for l in range(0,dim):
dydt[l] = G[0][l].dot(b)
else:
for l in range(0,dim):
dydt[l] = G[1][l].dot(b)
# print("out")
return dydt
py0 = [[2,4],[-1,-3]]
pt_tuple = [(0,10),(0,10)]
start = time.time()
print("origin")
tp_list, yp_list = simulation_ode(mode2_1, py0, pt_tuple, stepsize, eps=0)
end1 = time.time()
print("predict")
tpre_list, ypre_list = simulation_ode(odepre, py0, pt_tuple, stepsize, eps=0)
end2 = time.time()
print("simutime",end1-start)
print("predtime",end2-end1)
for temp_y in yp_list:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
plt.plot(y0_list,y1_list,'b')
for temp_y in ypre_list:
y0_list = temp_y.T[0]
y1_list = temp_y.T[1]
plt.plot(y0_list,y1_list,'r')
plt.show()