-
Notifications
You must be signed in to change notification settings - Fork 0
/
ExactDMD.py
198 lines (157 loc) · 5.69 KB
/
ExactDMD.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
import numpy as np
from numpy import linalg as LA
import pandas as pd
from numpy import pi
import matplotlib.pyplot as plt
from matplotlib import style
import hdbscan
import seaborn as sns
# read data from excel
data = pd.read_csv("#P_car_data.csv", sep=",")
data = data[["field.q0", "field.q1", "field.dq0", "field.dq1", "field.u0"]]
def Exact_DMD(X, Y):
# find SVD
U, s, Vh = LA.svd(X, full_matrices=False) # Vh is the complex conjugate; full_matrices is disabled
V = np.conjugate(Vh)
V = V.T
Uh = np.conjugate(U)
Uh = Uh.T # Uh is the complex conjugate of U
s = np.diag(s) # resize the s
s_inv = LA.inv(s) # s_inv is the inverse of s
# define Nex matrix
A_Tilde = Uh @ Y @ V @ s_inv
# eig of A_Tilde
lamda, omega = LA.eig(A_Tilde)
# define phi
phi = Y @ V @ s_inv @ omega @ LA.inv(np.diag(lamda))
A = phi @ np.diag(lamda) @ LA.inv(phi)
return A
def Koopman(X, Y):
for i in range(0, len(X[0,:])):
if i == 0:
phi = X[:, i].reshape(10, 1)
phi1 = Y[:, i].reshape(10,1)
G = phi @ phi.T
A = phi @ phi1.T
else:
phi = X[:, i].reshape(10, 1)
phi1 = Y[:, i].reshape(10,1)
G += phi @ phi.T
A += phi @ phi1.T
print((G.shape))
G = 1/len(X[0, :])*G
A = 1/len(X[0, :])*A
K = LA.pinv(G)*A
return K
windowsize = 30
overlap = 5
# arrange the data
for i in range(0, 30):
X = data.iloc[(1 + i * 1802):(1801 + i * 1802), 0:5] # Take 1(z_0) to 1801(z_m-1) rows and 2 to 5 columns as X matrix
Y = data.iloc[(2 + i * 1802):(1802 + i * 1802), 0:5] # Take 2(z_0) to 1802(z_m) rows and 2 to 5 columns as Y matrix
uX_cos = np.multiply(np.cos(X.iloc[:, 0]), X.iloc[:, 4])
uY_cos = np.multiply(np.cos(Y.iloc[:, 0]), Y.iloc[:, 4])
uXdot_cos = np.multiply(np.cos(X.iloc[:, 2]), X.iloc[:, 4])
uYdot_cos = np.multiply(np.cos(Y.iloc[:, 2]), Y.iloc[:, 4])
uXcos2 = np.multiply(np.cos(X.iloc[:, 4] * pi / 20), np.cos(X.iloc[:, 4] * pi / 20))
uYcos2 = np.multiply(np.cos(Y.iloc[:, 4] * pi / 20), np.cos(Y.iloc[:, 4] * pi / 20))
uXdot2 = np.multiply(X.iloc[:, 3], X.iloc[:, 3])
uYdot2 = np.multiply(Y.iloc[:, 3], Y.iloc[:, 3])
Xones = np.ones(1800)
Yones = np.ones(1800)
X = np.column_stack((X, uX_cos))
Y = np.column_stack((Y, uY_cos))
X = np.column_stack((X, uXdot_cos))
Y = np.column_stack((Y, uYdot_cos))
X = np.column_stack((X, uXcos2))
Y = np.column_stack((Y, uYcos2))
X = np.column_stack((X, uXdot2))
Y = np.column_stack((Y, uYdot2))
X = np.column_stack((X, Xones.T))
Y = np.column_stack((Y, Yones.T))
X = X.T # X.T means transpose of X
Y = Y.T
K = np.zeros((int(1800/windowsize), 100))
for j in range(0, int(1800/windowsize)):
if j == 0:
A = Exact_DMD(X[:, 0:windowsize*(j+1)+overlap], Y[:, 0:windowsize*(j+1)+overlap])
elif j == 1800/windowsize - 1:
A = Exact_DMD(X[:, windowsize*j-overlap:windowsize*(j+1)], Y[:, windowsize*j-overlap:windowsize*(j+1)])
else:
A = Exact_DMD(X[:, windowsize*j-overlap:windowsize*(j+1)+overlap], Y[:, windowsize*j-overlap:windowsize*(j+1)+overlap])
K[j, :] = A.flatten()
if i == 0:
K1 = K
else:
K1 = np.append(K1, K, axis=0)
print(K1.shape)
#clustering
print("Start clustering")
clusterer = hdbscan.HDBSCAN()
clusterer.fit(K1)
#printout the label
print(max(clusterer.labels_))
clusterer.condensed_tree_.plot(select_clusters=True, selection_palette=sns.color_palette("deep", 8))
plt.show()
"""
i = 29
X = data.iloc[(1 + i * 1802):(1801 + i * 1802), 0:5] # Take 1(z_0) to 1801(z_m-1) rows and 2 to 5 columns as X matrix
Y = data.iloc[(2 + i * 1802):(1802 + i * 1802), 0:5] # Take 2(z_0) to 1802(z_m) rows and 2 to 5 columns as Y matrix
uX_cos = np.multiply(np.cos(X.iloc[:, 0]), X.iloc[:, 4])
uY_cos = np.multiply(np.cos(Y.iloc[:, 0]), Y.iloc[:, 4])
uXdot_cos = np.multiply(np.cos(X.iloc[:, 2]), X.iloc[:, 4])
uYdot_cos = np.multiply(np.cos(Y.iloc[:, 2]), Y.iloc[:, 4])
uXcos2 = np.multiply(np.cos(X.iloc[:, 4] * pi / 20), np.cos(X.iloc[:, 4] * pi / 20))
uYcos2 = np.multiply(np.cos(Y.iloc[:, 4] * pi / 20), np.cos(Y.iloc[:, 4] * pi / 20))
uXdot2 = np.multiply(X.iloc[:, 3], X.iloc[:, 3])
uYdot2 = np.multiply(Y.iloc[:, 3], Y.iloc[:, 3])
Xones = np.ones(1800)
Yones = np.ones(1800)
X = np.column_stack((X, uX_cos))
Y = np.column_stack((Y, uY_cos))
X = np.column_stack((X, uXdot_cos))
Y = np.column_stack((Y, uYdot_cos))
X = np.column_stack((X, uXcos2))
Y = np.column_stack((Y, uYcos2))
X = np.column_stack((X, uXdot2))
Y = np.column_stack((Y, uYdot2))
X = np.column_stack((X, Xones.T))
Y = np.column_stack((Y, Yones.T))
X1 = X.T # X.T means transpose of X
Y1 = Y.T
A = Exact_DMD(X1, Y1)
K = Koopman(X1, Y1)
print("X1 ", X1.shape)
print("Y1 ", Y1.shape)
#simulation
errorq = np.zeros(1800)
errorx = np.zeros(1800)
errorqdot = np.zeros(1800)
errorxdot = np.zeros(1800)
X_test = X1[:, 0]
err_max = 0
time = 0
for k in range(0, 1800):
Y_test = Y1[:, k]
Y_est = LA.matrix_power(np.eye(10)+K*1/60, k) @ X_test
Y_est = A*X1[:, k]
errorq[k] = LA.norm(Y_test[1] - Y_est[1]) / LA.norm(Y_test[1])
errorx[k] = LA.norm(Y_test[2] - Y_est[2]) / LA.norm(Y_test[2])
if LA.norm(Y_est[3]) == 0:
errorqdot[k] = 0
else:
errorqdot[k] = LA.norm(Y_test[3] - Y_est[3]) / LA.norm(Y_test[3])
errorxdot[k] = LA.norm(Y_test[4] - Y_est[4]) / LA.norm(Y_test[4])
t = np.arange(0, 1800)
style.use("ggplot")
fig, axs = plt.subplots(2,2)
axs[0, 0].plot(t, errorq)
axs[0, 0].set_title('q')
axs[0, 1].plot(t, errorx)
axs[0, 1].set_title('x')
axs[1, 0].plot(t, errorqdot)
axs[1, 0].set_title('qdot')
axs[1, 1].plot(t, errorxdot)
axs[1, 1].set_title('xdot')
plt.show()
"""