from d3s.tools import printVector, printMatrix
#%% load variables from mat file into main scope
data = sp.io.loadmat('data/lorenz.mat', squeeze_me=True)
for s in data.keys():
if s[:2] == '__' and s[-2:] == '__': continue
exec('%s = data["%s"]' % (s, s))
#%% apply SINDy
d = X.shape[0]
p = 2 # maximum order of monomials
psi = observables.monomials(p)
Xi1 = algorithms.sindy(X, Y, psi, iterations=1)
c = observables.allMonomialPowers(d, p)
n = c.shape[1] # number of functions
#%% output results
printMatrix(c)
printMatrix(Xi1)
#%% apply gEDMD
K, _, _ = algorithms.gedmd(X, Y, None, psi)
# construct projection onto full-state observable
B = np.zeros((10, d))
for i in range(3):
B[i+1, i] = 1
Xi2 = (K@B).T
printMatrix(Xi2)
# apply generator EDMD
evs = 3 # number of eigenvalues/eigenfunctions to be computed
K, d, V = algorithms.gedmd(X, Y, Z, psi, evs=evs, operator='K')
printVector(np.real(d), 'd')
# plot eigenfunctions
c = Omega.midpointGrid()
Psi_c = psi(c)
for i in range(evs):
plt.figure(i + 1)
plt.clf()
Omega.plot(np.real(V[:, i].T @ Psi_c), mode='3D')
#%% system identification
order = 4 # reduce order of monomials
p = observables.allMonomialPowers(2, order)
n = p.shape[1] # number of monomials up to order 4
printMatrix(p, 'p')
printMatrix(K[:n, :n], 'K')
# compute entries of a evaluated in c
b_c = K[:, 1:3].T @ Psi_c
a_11 = K[:, 3].T @ Psi_c - 2 * b_c[0, :] * c[0, :]
a_12 = K[:, 4].T @ Psi_c - b_c[0, :] * c[1, :] - b_c[1, :] * c[0, :]
a_22 = K[:, 5].T @ Psi_c - 2 * b_c[1, :] * c[1, :]
plt.figure(evs + 1)
Omega.plot(a_11, mode='3D')
plt.figure(evs + 2)