# rotation basis (Skew Symmetric)
# E = np.array([[0, -1.], [1., 0]])
# warping basis (Fourier)
p = 20
f_basis = np.zeros((TT, p))
for i in range(0, int(p/2)):
f_basis[:, 2*i] = 1/np.sqrt(np.pi) * np.sin(2*np.pi*(i+1)*time)
f_basis[:, 2*i + 1] = 1/np.sqrt(np.pi) * np.cos(2*np.pi*(i+1)*time)
itr = 0
max_val = np.zeros(max_itr+1)
while itr <= max_itr:
# inner product value
A = np.zeros(m)
for i in range(0, m):
A[i] = fs.innerprod_q2(qtilde, nu[:, :, i])
# form gradient for rotation
# B = np.zeros((n, n, m))
# for i in range(0, m):
# B[:, :, i] = cf.innerprod_q2(E.dot(qtilde), nu[:, :, i]) * E
# tmp1 = np.sum(np.exp(alpha + A))
# tmp2 = np.sum(np.exp(alpha + A) * B, axis=2)
# hO = np.sum(y * B, axis=2) - (tmp2 / tmp1)
# O_new = O_old.dot(expm(deltaO * hO))
theta = np.arccos(O_old[0, 0])
Ograd = np.array([(-1*np.sin(theta), -1*np.cos(theta)),
(np.cos(theta), -1*np.sin(theta))])
B = np.zeros(m)
O = np.eye(n)
O_old = O.copy()
gam_old = gam.copy()
qtilde = q.copy()
# warping basis (Fourier)
p = 20
f_basis = np.zeros((TT, p))
for i in range(0, int(p/2)):
f_basis[:, 2*i] = 1/np.sqrt(np.pi) * np.sin(2*np.pi*(i+1)*time)
f_basis[:, 2*i + 1] = 1/np.sqrt(np.pi) * np.cos(2*np.pi*(i+1)*time)
itr = 0
max_val = np.zeros(max_itr+1)
while itr <= max_itr:
# inner product value
A = fs.innerprod_q2(qtilde, nu)
# form gradient for rotation
# B = np.zeros((n, n, m))
# for i in range(0, m):
# B[:, :, i] = cf.innerprod_q2(E.dot(qtilde), nu[:, :, i]) * E
# tmp1 = np.sum(np.exp(alpha + A))
# tmp2 = np.sum(np.exp(alpha + A) * B, axis=2)
# hO = np.sum(y * B, axis=2) - (tmp2 / tmp1)
# O_new = O_old.dot(expm(deltaO * hO))
theta = np.arccos(O_old[0, 0])
Ograd = np.array([(-1*np.sin(theta), -1*np.cos(theta)),
(np.cos(theta), -1*np.sin(theta))])
B = fs.innerprod_q2(Ograd.dot(qtilde), nu)
