def TrjRtrv(param, kedm_output):
N = param.N
d = param.d
P = param.P
N_trn = param.N_trn
mode = param.mode
omega = param.omega
K = param.K
anchor_idx = ktools.randomAnchor(N_trn, N, d+1)
tau_list = kedm_output.tau_list
trn_list = kedm_output.trn_list
tst_list = kedm_output.tst_list
A = kedm_output.A
G = kedm_output.G
N_tst = param.N_tst
output = TRJ_OUT()
M = np.shape(anchor_idx)[0]
if M != len(trn_list):
print('Fix this!')
return output
X_ = []
T = []
cnt_wrong = 0
cnt = 0
for m in range(M):
list_m = np.nonzero(anchor_idx[m,:])[0]
if len(list_m) < d:
cnt_wrong += 1
continue
t = trn_list[m]
Xt = ktools.X_t(A,t,param)
Xtm = Xt[:,list_m]
weights = ktools.W(t, tau_list, param)
Gt = ktools.G_t(G, weights, False)
Xt_ = ktools.gram2x(Gt, d)
Xt_m = Xt_[:,list_m]
R = ktools.rotationXY(Xtm, Xt_m)
Nt = Xtm.shape[1]
Xt_ = np.matmul(R,Xt_ - np.matmul(Xt_m,np.ones((Nt,N))/Nt) ) + np.matmul(Xtm,np.ones((Nt,N))/Nt)
Tt = ktools.T_t(t, param)
if cnt == 0:
X_ = Xt_
T = Tt
else:
X_ = np.concatenate((X_, Xt_), axis=0)
T = np.concatenate((T, Tt), axis=0)
cnt += 1
if cnt_wrong == M:
print('nonsense')
return output
T_inv = np.linalg.pinv(T)
A_ = np.matmul(T_inv,X_)
A_ = ktools.deconcat(A_, param)
def SketchX(param, A,colors, figName):
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
N = param.N
d = param.d
if d > 3 or d < 2:
print('There is something wrong, dude!')
return
M = 300
maxIter = param.maxIter
T_tst = param.T_tst
t = np.linspace(T_tst[0],T_tst[1],M)
fSize = 18
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
if d == 2:
plt.xlabel(r'\textit{x}_1',fontsize=18)
plt.ylabel(r'\textit{x}_2',fontsize=18)
else:
ax = plt.axes(projection='3d')
ax.set_xlabel(r'\textit{x}_1',fontsize=fSize)
ax.set_ylabel(r'\textit{x}_2',fontsize=fSize)
ax.set_zlabel(r'\textit{x}_3',fontsize=fSize);
i = 0
eX = 0
eDo = 0
eDi = 0
while i < maxIter:
kedm_output = KEDM(param, A)
cvx_status = kedm_output.status
if cvx_status == 'optimal':
i += 1
print(i,'out of', maxIter)
trj_output = TrjRtrv(param, kedm_output)
eX = eX + ktools.mean(trj_output.eX)/maxIter
eDo = eDo + ktools.mean(kedm_output.eo)/maxIter
eDi = eDi + ktools.mean(kedm_output.ei)/maxIter
A_ = trj_output.A_
X = np.zeros((M,d,N))
for m in range(M):
X[m,:,:] = ktools.X_t(A_,t[m],param)
for n in range(N):
if d == 2:
plt.plot(X[:,0,n], X[:,1,n],c = colors[:,n],linewidth=1/(maxIter**0.5))
else:
ax.plot3D(X[:,0,n], X[:,1,n],X[:,2,n],c = colors[:,n],linewidth=1/(maxIter**0.5))
plt.pause(0.01)
def PlotX(A, param, mode, xlim, ylim, name , color):
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
import math
N = param.N
d = param.d
print(d)
if d > 3 or d < 2:
print('There is something wrong, dude!')
return
M = 1000
J = np.eye(N) - np.ones((N,N))/N
if mode == 'test':
T_tst = param.T_tst
T_trn = param.T_trn
T1 = T_trn[0]- T_tst[0]
T2 = T_trn[1] - T_trn[0]
T3 = T_tst[1] - T_trn[1]
T = T1 + T2 + T3
int(np.floor(N/2))
M1 = int(np.floor(T1/T * M))
M3 = int(np.floor(T3/T * M))
M2 = M - M1 - M3
t = np.linspace(T_tst[0],T_tst[1],M)
dash=[8,3]
else:
T_tst = param.T_tst
t = np.linspace(T_tst[0],T_tst[1],M)
X = np.zeros((M,d,N))
ax = plt.gca()
ax.rc('text', usetex=True)
ax.rc('font', family='serif')
print(d)
if d == 2:
ax.xlabel(r'\textit{x}_1',fontsize=18)
ax.ylabel(r'\textit{x}_2',fontsize=18)
else:
ax = ax.axes(projection='3d')
ax.set_xlabel(r'\textit{x}_1',fontsize=fSize)
ax.set_ylabel(r'\textit{x}_2',fontsize=fSize)
ax.set_zlabel(r'\textit{x}_3',fontsize=fSize);
for m in range(M):
X[m,:,:] = ktools.X_t(A,t[m],param)
for n in range(N):
if mode == 'test':
idx1 = list(range(0,M1,1))
idx2 = list(range(M1,M1+M2,1))
idx3 = list(range(M1+M2,M,1))
if d==2:
ax.plot(X[idx2,0,n], X[idx2,1,n],c = color[:,n],linewidth=2)
ax.plot(X[idx1,0,n], X[idx1,1,n],c = np.zeros((3)),dashes=dash,linewidth=0.5)
ax.plot(X[idx3,0,n], X[idx3,1,n],c = np.zeros((3)),dashes=dash,linewidth=0.5)
elif d==3:
ax.plot3D(X[idx2,0,n], X[idx2,1,n],c = color[:,n],linewidth=2)
ax.plot3D(X[idx1,0,n], X[idx1,1,n],c = np.zeros((3)),dashes=dash,linewidth=1)
ax.plot3D(X[idx3,0,n], X[idx3,1,n],c = np.zeros((3)),dashes=dash,linewidth=1)
else:
if d==2:
plt.plot(X[:,0,n], X[:,1,n],c = color[:,n],linewidth=2)
elif d==3:
ax.plot3D(X[:,0,n], X[:,1,n],c = colors[:,n],linewidth=2)
if d==2:
plt.ylim(ylim)
plt.xlim(xlim)
plt.savefig(name+'.eps')
plt.show()
T = np.concatenate((T, Tt), axis=0)
cnt += 1
if cnt_wrong == M:
print('nonsense')
return output
T_inv = np.linalg.pinv(T)
A_ = np.matmul(T_inv,X_)
A_ = ktools.deconcat(A_, param)
if mode == 2:
A_ = ktools.sine2fourier(A_)
eX = np.zeros(N_tst)
for i_t, t in enumerate(tst_list):
X_ = ktools.X_t(A_,t,param)
X = ktools.X_t(A,t,param)
eX[i_t] = np.linalg.norm(X-X_,'fro')/np.linalg.norm(X,'fro')
output.A_ = A_
output.eX = eX
return output
###########################################################################
def PlotX(A, param, mode, xlim, ylim, name , color):
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
import math
N = param.N
t = np.linspace(param.T_tst[0], param.T_tst[1], M)
colors = np.random.rand(3, N)
fig_name = 'kedm_ambiguity.pdf'
fSize = 18
A = ktools.randomAs(param)
B0 = np.random.randn(d, d)
B1 = np.random.randn(d, d)
B2 = np.random.randn(d, d)
B3 = np.random.randn(d, d)
J = np.eye(N) - np.ones((N, N)) / N
X = np.zeros((M, d, N))
Y = np.zeros((M, d, N))
for m in range(M):
X[m, :, :] = ktools.X_t(A, t[m], param)
Y[m, :, :] = np.matmul(X[m, :, :], J)
f = B0 + t[m] / 10 * B1 + math.cos(t[m]) / 20 * B2 + math.sin(
t[m]) * B3 / 20
ff = np.matmul(f, f.T)
u, s, vh = np.linalg.svd(ff, full_matrices=True)
Y[m, :, :] = np.matmul(u, Y[m, :, :])
if d == 2:
fig, axes = plt.subplots(1, 2)
for n in range(N):
axes[0].plot(X[:, 0, n], X[:, 1, n], c=colors[:, n], linewidth=2)
for n in range(N):
axes[1].plot(Y[:, 0, n], Y[:, 1, n], c=colors[:, n], linewidth=2)
elif d == 3:
fig = plt.figure(figsize=plt.figaspect(0.5))