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sev_filters_opt.py
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sev_filters_opt.py
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import cvxpy as cp
import numpy as np
from opt import filter_id
from scipy.linalg import khatri_rao
VERB = False
def filter_id_sevH(Y, X, S, gamma, delta, Cy, verb=VERB):
"""
Performs the filter identification step of the robust filter identification algorithm.
It estimates H using cvx, not the analytical solution.
"""
T, N, M = X.shape
Hs = [cp.Variable((N, N), symmetric=True) for _ in range(T)]
ls_loss = cp.sum([cp.sum_squares(Y[i,:,:] - Hs[i]@X[i,:,:]) for i in range(T)])
commut_loss = cp.sum([cp.sum_squares(Hs[i]@S - S@Hs[i]) for i in range(T)])
commut_cy_loss = cp.sum([cp.sum_squares(Hs[i]@Cy[i,:,:] - Cy[i,:,:]@Hs[i]) for i in range(T)])
obj = ls_loss + gamma*commut_loss + delta*commut_cy_loss
prob = cp.Problem(cp.Minimize(obj))
try:
prob.solve()
except cp.SolverError:
if verb:
print("WARNING: Could not find optimal H -- Solver Error")
try:
prob.solve(verbose=False)
if verb:
print("Solver error fixed")
except:
if verb:
print("A second solver error")
return None
if prob.status in ["optimal", "optimal_inaccurate"]:
return np.array([Hs[i].value for i in range(T)])
if verb:
print(f"WARNING: problem status: {prob.status}")
return None
def graph_id(Sn, Hs, Cy, lambd, gamma, delta, verb=VERB):
"""
Performs the filter identification step of the robust filter identification algorithm
"""
T, N, _ = Hs.shape
S = cp.Variable((N,N), symmetric=True)
s_loss = cp.sum(cp.abs(S - Sn))
commut_loss = cp.sum([cp.sum_squares(Hs[i,:,:]@S - S@Hs[i,:,:]) for i in range(T)])
#commut_loss = cp.sum_squares(Havg@S - S@Havg)
#commut_cy_loss = cp.sum_squares(S@Cy - Cy@S)
commut_cy_loss = cp.sum([cp.sum_squares(Cy[i,:,:]@S - S@Cy[i,:,:]) for i in range(T)])
obj = lambd*s_loss + gamma*commut_loss + delta*commut_cy_loss
constraints = [
S >= 0,
cp.diag(S) == 0
]
prob = cp.Problem(cp.Minimize(obj), constraints)
try:
prob.solve()
except cp.SolverError:
if verb:
print("WARNING: Could not find optimal S -- Solver Error")
try:
prob.solve(solver=cp.ECOS, verbose=False)
if verb:
print("Solver error fixed")
except cp.SolverError as e:
if verb:
print("A second solver error")
print(e)
return None
if prob.status in ["optimal", "optimal_inaccurate"]:
return S.value
else:
if verb:
print(f"WARNING: problem status: {prob.status}")
return None
def graph_id_rew(Sn, Hs, Cy, W1, W2, lambd, gamma, delta, beta, verb=VERB):
"""
Performs the filter identification step of the robust filter identification algorithm
with the reweighted alternative
"""
T, N, _ = Hs.shape
S = cp.Variable((N,N), symmetric=True)
sn_loss = cp.sum(cp.multiply(W1, cp.abs(S - Sn)))
s_loss = cp.sum(cp.multiply(W2, cp.abs(S)))
commut_loss = cp.sum([cp.sum_squares(Hs[i,:,:]@S - S@Hs[i,:,:]) for i in range(T)])
#commut_loss = cp.sum_squares(Havg@S - S@Havg)
#commut_cy_loss = cp.sum_squares(S@Cy - Cy@S)
commut_cy_loss = cp.sum([cp.sum_squares(Cy[i,:,:]@S - S@Cy[i,:,:]) for i in range(T)])
obj = lambd*sn_loss + beta*s_loss + gamma*commut_loss + delta*commut_cy_loss
constraints = [
S >= 0,
cp.diag(S) == 0
]
prob = cp.Problem(cp.Minimize(obj), constraints)
try:
prob.solve()
except cp.SolverError:
if verb:
print("WARNING: Could not find optimal S -- Solver Error")
try:
prob.solve(verbose=False)
if verb:
print("Solver error fixed")
except:
if verb:
print("A second solver error")
return None
except cp.DCPError:
raise RuntimeError("Could not find optimal S -- DCP Error")
if prob.status in ["optimal", "optimal_inaccurate"]:
S = S.value
else:
if verb:
print(f"WARNING: problem status: {prob.status}")
return None
return S
def estHs_iter(X, Y, Sn, Cy, params, max_iters=20, th=1e-3, patience=4, Hs_true=None, S_true=None):
import warnings
warnings.filterwarnings("ignore")
lambd, gamma, delta, inc_gamma = params
T, N, M = X.shape
S_prev = Sn
Hs_prev = np.array([Sn for _ in range(T)])
S = Sn
err = []
count_es = 0
min_err = np.inf
norm_Hs = (Hs_true**2).sum((1,2)) if Hs_true is not None else 0
norm_S = (N*(N-1)) if S_true is not None else 0
Hs = np.zeros((T,N,N))
for i in range(max_iters):
# Filter identification problem
for t in range(T):
H_id = filter_id(Y[t,:,:], X[t,:,:], S, gamma, delta, Cy[t,:,:])
Hs[t,:,:] = Hs_prev[t,:,:] if H_id is None else H_id
# Havg = np.mean(Hs, 0)
# Graph identification
S = graph_id(Sn, Hs, Cy, lambd, gamma, delta)
S = S_prev if S is None else S
if Hs_true is not None and S_true is not None:
# Early stopping is performed with variables error
err_Hs = np.median(((Hs - Hs_true)**2).sum((1,2)) / norm_Hs)
err_S = ((S - S_true)**2).sum() / norm_S
err.append(err_Hs + err_S)
#print(f"Sev: {i=}, {err_Hs=}, {err_S=}, {err[i]=}")
else:
ls_loss = ((Y - Hs@X)**2).sum()
s_loss = np.abs(S-Sn).sum()
commut_loss = ((S@Hs - Hs@S)**2).sum()
commut_cy_loss = ((Cy@Hs - Hs@Cy)**2).sum()
err.append(ls_loss + lambd*s_loss + gamma*commut_loss + delta*commut_cy_loss)
# print(f"Iter: {i} - err: {err[i]}")
if i > 0 and np.abs(err[i] - err[i-1]) < th and err[i] > err[i-1]:
Hs_min = Hs
S_min = S
i_min = i
break
if err[i] > min_err:
count_es += 1
else:
min_err = err[i]
Hs_min = Hs.copy()
S_min = S.copy()
i_min = i
count_es = 0
if count_es == patience:
break
gamma = inc_gamma*gamma if inc_gamma else gamma
Hs_prev = Hs
S_prev = S
return i_min, Hs_min, S_min
def estHs_iter_rew(X, Y, Sn, Cy, params, max_iters=20, th=1e-3, patience=4, Hs_true=None, S_true=None):
import warnings
warnings.filterwarnings("ignore")
lambd, gamma, delta, beta, inc_gamma = params
T, N, M = X.shape
S_prev = Sn
Hs_prev = np.array([Sn for _ in range(T)])
S = Sn
err = []
W1 = np.ones((N,N))
W2 = np.ones((N,N))
delta1 = 1e-3
delta2 = 1e-3
count_es = 0
min_err = np.inf
norm_Hs = (Hs_true**2).sum((1,2)) if Hs_true is not None else 0
norm_S = (N*(N-1)) if S_true is not None else 0
Hs = np.zeros((T,N,N))
for i in range(max_iters):
# Filter identification problem
for t in range(T):
H_id = filter_id(Y[t,:,:], X[t,:,:], S, gamma, delta, Cy[t,:,:])
Hs[t,:,:] = Hs_prev[t,:,:] if H_id is None else H_id
# Graph identification
S = graph_id_rew(Sn, Hs, Cy, W1, W2, lambd, gamma, delta, beta)
S = S_prev if S is None else S
W1 = lambd / (np.abs(S - Sn) + delta1)
W2 = beta / (S + delta2)
if Hs_true is not None and S_true is not None:
# Early stopping is performed with variables error
err_Hs = (((Hs - Hs_true)**2).sum((1,2)) / norm_Hs).mean()
err_S = ((S - S_true)**2).sum() / norm_S
err.append(err_Hs + err_S)
#print(i, err_H, err_S, err[i])
else:
ls_loss = ((Y - Hs@X)**2).sum()
s_loss = np.abs(S-Sn).sum()
commut_loss = ((S@Hs - Hs@S)**2).sum()
commut_cy_loss = ((Cy@Hs - Hs@Cy)**2).sum()
err.append(ls_loss + lambd*s_loss + gamma*commut_loss + delta*commut_cy_loss)
# print(f"Iter: {i} - err: {err[i]}")
if i > 0 and np.abs(err[i] - err[i-1]) < th and err[i] > err[i-1]:
Hs_min = Hs
S_min = S
i_min = i
break
if err[i] > min_err:
count_es += 1
else:
min_err = err[i]
Hs_min = Hs.copy()
S_min = S.copy()
i_min = i
count_es = 0
if count_es == patience:
break
if inc_gamma:
gamma = inc_gamma*gamma
Hs_prev = Hs
S_prev = S
return i_min, Hs_min, S_min
def estHs_denS(X, Y, Sn, Cy, params, verb=VERB):
import warnings
warnings.filterwarnings("ignore")
T, N, M = X.shape
gamma, delta = params
# Denoise S
S = cp.Variable((N,N), symmetric=True)
s_loss = cp.sum(cp.abs(S - Sn))
#commut_cy_loss = cp.sum_squares(S@Cy - Cy@S)
commut_cy_loss = cp.sum([cp.sum_squares(Cy[i,:,:]@S - S@Cy[i,:,:]) for i in range(T)])
obj = s_loss + delta*commut_cy_loss
constraints = [
S >= 0,
cp.diag(S) == 0,
#commut_cy_loss <= delta
]
prob = cp.Problem(cp.Minimize(obj), constraints)
try:
prob.solve()
except cp.SolverError:
#print("estHs_denS -- Could not find denoised version of S - SolverError")
S = Sn
if prob.status in ["optimal", "optimal_inaccurate"]:
S = S.value
else:
#print("estHs_denS -- Could not find denoised version of S - Not optimal")
S = Sn
# Compute H from S
Hs = [cp.Variable((N,N), symmetric=True) for _ in range(T)]
ls_loss = cp.sum([cp.sum_squares(Y[i,:,:] - Hs[i]@X[i,:,:]) for i in range(T)])
try:
commut_loss = cp.sum([cp.sum_squares(Hs[i]@S - S@Hs[i]) for i in range(T)])
commut_cy_loss = cp.sum([cp.sum_squares(Hs[i]@Cy[i,:,:] - Cy[i,:,:]@Hs[i]) for i in range(T)])
except ValueError:
raise RuntimeError("Value Error when defining Commut Loss")
obj = ls_loss + gamma*commut_loss + delta*commut_cy_loss
#const = [commut_loss <= 0]
prob = cp.Problem(cp.Minimize(obj))#, const)
try:
prob.solve()
except cp.SolverError:
print("estHs_denS -- Could not find optimal H -- Solver Error")
Hs = np.zeros((T, N, N))
if prob.status in ["optimal", "optimal_inaccurate"]:
Hs = np.array([Hs[i].value for i in range(T)])
else:
if verb:
print("estHs_denS -- Could not find optimal H")
Hs = np.zeros((T, N, N))
#ls_loss = ((Y - Hs@X)**2).sum()
#s_loss = np.abs(S-Sn).sum()
#commut_loss = ((S@Hs - Hs@S)**2).sum()
#commut_cy_loss = ((Cy@Hs - Hs@Cy)**2).sum()
#err = ls_loss + s_loss + gamma*commut_loss + delta*commut_cy_loss
return -1, Hs, S
def estHs_unpertS(X, Y, S, Cy, params):
import warnings
warnings.filterwarnings("ignore")
_, eigvecs = np.linalg.eigh(S)
Hs = []
for i in range(X.shape[0]):
Z = khatri_rao(X[i,:,:].T @ eigvecs, eigvecs)
h_freq, _, _, _ = np.linalg.lstsq(Z, Y[i,:,:].flatten('F'))
Hs.append(eigvecs @ np.diag(h_freq) @ eigvecs.T)
return -1, np.array(Hs), S