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feat: OVF formula 70

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mayge
2025-09-17 05:43:45 -04:00
parent e1bc69c6fb
commit 92f3cdf016
2 changed files with 475 additions and 79 deletions
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main.py
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@@ -17,101 +17,497 @@ poles = vf.poles
residues = vf.residues
y = vf.network.y
fig, ax = plt.subplots(2, 2)
fig.set_size_inches(12, 8)
vf.plot("mag",0,0,freqs,ax=ax[0][0],parameter="y")
rms_error11 = vf.get_rms_error(0,0,"y")
print("rms_error11",rms_error11)
vf.plot("mag",1,0,freqs,ax=ax[1][0],parameter="y")
rms_error21 = vf.get_rms_error(1,0,"y")
print("rms_error21",rms_error21)
vf.plot("mag",0,1,freqs,ax=ax[0][1],parameter="y")
rms_error12 = vf.get_rms_error(0,1,"y")
print("rms_error12",rms_error12)
vf.plot("mag",1,1,freqs,ax=ax[1][1],parameter="y")
rms_error22 = vf.get_rms_error(1,1,"y")
print("rms_error22",rms_error22)
fig.tight_layout()
plt.show()
plt.savefig(f"img.png")
# fig, ax = plt.subplots(2, 2)
# fig.set_size_inches(12, 8)
# vf.plot("mag",0,0,freqs,ax=ax[0][0],parameter="y")
# rms_error11 = vf.get_rms_error(0,0,"y")
# print("rms_error11",rms_error11)
# vf.plot("mag",1,0,freqs,ax=ax[1][0],parameter="y")
# rms_error21 = vf.get_rms_error(1,0,"y")
# print("rms_error21",rms_error21)
# vf.plot("mag",0,1,freqs,ax=ax[0][1],parameter="y")
# rms_error12 = vf.get_rms_error(0,1,"y")
# print("rms_error12",rms_error12)
# vf.plot("mag",1,1,freqs,ax=ax[1][1],parameter="y")
# rms_error22 = vf.get_rms_error(1,1,"y")
# print("rms_error22",rms_error22)
# fig.tight_layout()
# plt.show()
# plt.savefig(f"img.png")
diag_values = [y[i][0][0] for i in range(len(y))]
H = np.diag(diag_values)
P = 4
start_poles = generate_starting_poles(P,beta_min=1e8,beta_max=freqs[-1])
basis = generate_laguerre_basis(start_poles,s).T
print("start_poles",start_poles)
print("basis",basis)
def formula_67(s,y):
diag_values = [y[i][0][0] for i in range(len(y))]
H = np.diag(diag_values)
P = 2
start_poles = generate_starting_poles(P,beta_min=1e8,beta_max=freqs[-1])
basis = generate_laguerre_basis(start_poles,s).T
print("start_poles",start_poles)
print("basis",basis)
# first step iteration
# A*x = b
# first step iteration
# A*x = b
A11 = np.real(basis)
print("A11 shape:",A11.shape)
A12 = np.real(- H @ basis[:,1:])
print("A12 shape:",A12.shape)
# print("A11",A11)
A21 = np.imag(basis)
print("A21 shape:",A21.shape)
A22 = np.imag(- H @ basis[:,1:])
print("A22 shape:",A22.shape)
A1 = np.hstack([A11,A12])
A2 = np.hstack([A21,A22])
A = np.vstack([A1,A2])
print ("A shape:",A.shape)
b1 = np.real(H @ basis[:,0])
b2 = np.imag(H @ basis[:,0])
b = np.hstack([b1,b2])
Q, R = np.linalg.qr(A, mode='reduced')
print("Q :",Q)
print("R :",R)
print("b shape:",b.shape)
# x = np.linalg.solve(R, Q.T @ b)
x_star, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
# print("x_qr",x_star)
print("residuals",residuals)
# print("rank",rank)
# print("s",s)
x_ne = np.linalg.inv(A.T @ A) @ A.T @ b
print("x_ne",x_ne)
# sk iteration
target_vec = np.array([1+0j] + list(x_ne[len(x_ne)//2+1:]))
D_t = basis @ target_vec
print("D_t",D_t)
K = 25
for i in range(K):
print(f"Iteration {i+1}/{K}")
A11 = np.real(basis / D_t[:, np.newaxis])
A12 = np.real(- H @ basis[:,1:] / D_t[:, np.newaxis])
A21 = np.imag(basis / D_t[:, np.newaxis])
A22 = np.imag(- H @ basis[:,1:] / D_t[:, np.newaxis])
A11 = np.real(basis)
print("A11 shape:",A11.shape)
A12 = np.real(- H @ basis[:,1:])
print("A12 shape:",A12.shape)
# print("A11",A11)
A21 = np.imag(basis)
print("A21 shape:",A21.shape)
A22 = np.imag(- H @ basis[:,1:])
print("A22 shape:",A22.shape)
A1 = np.hstack([A11,A12])
A2 = np.hstack([A21,A22])
A = np.vstack([A1,A2])
print ("A shape:",A.shape)
b1 = np.real(H @ basis[:,0])
b2 = np.imag(H @ basis[:,0])
b = np.hstack([b1,b2])
Q, R = np.linalg.qr(A, mode='reduced')
print("Q :",Q)
print("R :",R)
print("b shape:",b.shape)
# x = np.linalg.solve(R, Q.T @ b)
x_star, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
# print("x_lstsq",x_star)
# print("residuals",residuals)
# print("x_qr",x_star)
print("residuals",residuals)
# print("rank",rank)
# print("s",s)
x_ne = np.linalg.inv(A.T @ A) @ A.T @ b
# print("x_ne",x_ne)
print("x_ne",x_ne)
# sk iteration
target_vec = np.array([1+0j] + list(x_ne[len(x_ne)//2+1:]))
D_t_pre = D_t
D_t = basis @ target_vec
print("D_t/D_t_pre",np.linalg.norm(D_t)/np.linalg.norm(D_t_pre))
# print("D_t",D_t)
n_target_vec = np.array(list(x_ne[:len(x_ne)//2+1]))
N_t = basis @ n_target_vec
# print("H = N_t / D_t",np.linalg.norm(H - N_t / D_t)/np.linalg.norm(H))
print("D_t",D_t)
K = 25
for i in range(K):
print(f"Iteration {i+1}/{K}")
A11 = np.real(basis / D_t[:, np.newaxis])
A12 = np.real(- H @ basis[:,1:] / D_t[:, np.newaxis])
A21 = np.imag(basis / D_t[:, np.newaxis])
A22 = np.imag(- H @ basis[:,1:] / D_t[:, np.newaxis])
A1 = np.hstack([A11,A12])
A2 = np.hstack([A21,A22])
A = np.vstack([A1,A2])
b1 = np.real(H @ basis[:,0])
b2 = np.imag(H @ basis[:,0])
b = np.hstack([b1,b2])
x_star, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
# print("x_lstsq",x_star)
# print("residuals",residuals)
# print("rank",rank)
# print("s",s)
x_ne = np.linalg.inv(A.T @ A) @ A.T @ b
# print("x_ne",x_ne)
target_vec = np.array([1+0j] + list(x_ne[len(x_ne)//2+1:]))
D_t_pre = D_t
D_t = basis @ target_vec
print("Dt", D_t)
# print("D_t/D_t_pre",D_t/D_t_pre)
# print("D_t",D_t)
n_target_vec = np.array(list(x_ne[:len(x_ne)//2+1]))
N_t = basis @ n_target_vec
# print("H = N_t / D_t",np.abs(N_t / D_t))
class formula_70:
# ---------- helpers ----------
def _psi(self,s, z_prev):
"""Psi[k,p] = 1/(s_k + z_prev[p]) (shape: Kf x P)"""
s = np.asarray(s, dtype=np.complex128).reshape(-1)
z_prev = np.asarray(z_prev, dtype=np.complex128).reshape(-1)
return 1.0 / (s[:, None] + z_prev[None, :])
def _enforce_lhp_conjugate(self, poles):
"""Reflect any RHP poles across the imag axis and pair conjugates loosely."""
z = np.array(poles, dtype=np.complex128)
for i in range(len(z)):
if z[i].real > 0:
z[i] = -np.conj(z[i])
return z
# ---------- build Ax=b for (70) ----------1
def build_vf70_system(self,s, H_list, z_prev, d0=1.0):
"""
s: (Kf,) complex sample points (e.g. j*2πf)
H_list: list of (Kf,) complex responses, one per MIMO element you want to fit
z_prev: (P,) complex poles from previous iteration
d0: fixed scalar, usually 1.0
Returns: A (2*Kf*M, (M+1)*P), b (2*Kf*M,), plus Psi for convenience
Unknown vector x = [c (P), r^(1) (P), ..., r^(M) (P)]
"""
H_list = [np.asarray(h, dtype=np.complex128).reshape(-1) for h in H_list]
Kf = len(s)
P = len(z_prev)
M = len(H_list)
Psi = self._psi(s, z_prev) # Kf x P
zerosP = np.zeros((Kf, P)) # convenience
rows = []
rhs = []
for m, H in enumerate(H_list):
Hp = H[:, None] # Kf x 1
# Left block (shared c): H * Psi
L_re = np.real(Hp * Psi) # Kf x P
L_im = np.imag(Hp * Psi) # Kf x P
# Right block for this response: -Psi
R_re = -np.real(Psi) # Kf x P
R_im = -np.imag(Psi) # Kf x P
# Assemble columns: [c | r^(1) | r^(2) | ... | r^(M)]
# Real rows
cols_re = [L_re]
for j in range(M):
cols_re.append(R_re if j == m else zerosP)
rows.append(np.hstack(cols_re))
# Imag rows
cols_im = [L_im]
for j in range(M):
cols_im.append(R_im if j == m else zerosP)
rows.append(np.hstack(cols_im))
# RHS (move d0*H to the right)
rhs.append(-np.real(d0 * H))
rhs.append(-np.imag(d0 * H))
A = np.vstack(rows) # (2*Kf*M) x ((M+1)*P)
b = np.concatenate(rhs) # (2*Kf*M,)
return A, b, Psi
# ---------- one relocation step ----------
def vf70_step_once(self,s, H_list, z_prev, d0=1.0, column_scale=True):
"""
Returns: z_new (P,), c (P,), residues (list of M arrays length P)
"""
P = len(z_prev)
M = len(H_list)
A, b, Psi = self.build_vf70_system(s, H_list, z_prev, d0=d0)
# optional simple column scaling for conditioning
if column_scale:
col_norm = np.maximum(np.linalg.norm(A, axis=0), 1e-12)
x, *_ = np.linalg.lstsq(A / col_norm, b, rcond=None)
x = x / col_norm
else:
x, *_ = np.linalg.lstsq(A, b, rcond=None)
# unpack unknowns
c = x[:P]
residues = []
off = P
for _ in range(M):
residues.append(x[off:off+P])
off += P
# pole relocation (zeros of d0 + Psi @ c)
Sigma = np.diag(-np.asarray(z_prev, dtype=np.complex128))
T = Sigma - (np.ones((P, 1), dtype=np.complex128) @ (c.reshape(1, -1) / d0))
z_new = -np.linalg.eigvals(T)
z_new = self._enforce_lhp_conjugate(z_new)
return z_new, c, residues
# ---------- iterate K times (K == n_iter) ----------
def vf70_iterate(self,s, H_list, z0, n_iter=15, d0=1.0, verbose=True):
z = np.array(z0, dtype=np.complex128)
c = None
residues = None
for it in range(n_iter):
z_next, c, residues = self.vf70_step_once(s, H_list, z, d0=d0)
if verbose:
rel = np.linalg.norm(z_next) / max(1.0, np.linalg.norm(z))
print(f"[VF-70] iter {it+1:02d}/{n_iter:02d} Δz_rel = {rel}")
z = z_next
return z, c, residues
def eval_Hfit_from_70(self,s, z_prev, c, residues_m, d0=1.0):
"""
Evaluate H_fit for one response m using (70):
H_fit = (Psi @ residues_m) / (d0 + Psi @ c)
"""
Psi = 1.0 / (s[:, None] + np.asarray(z_prev)[None, :])
D_ratio = d0 + Psi @ c
N_part = Psi @ residues_m
return N_part / D_ratio
def rms_abs(self,y):
return np.sqrt(np.mean(np.abs(y)**2))
def rms_error(self,H, Hfit):
"""
Returns (abs_rms, relative_rms). Relative RMS is normalized by RMS of H.
"""
err = Hfit - H
abs_rms = self.rms_abs(err)
ref = max(self.rms_abs(H), 1e-16)
rel_rms = abs_rms / ref
return abs_rms, rel_rms
# --- run K (== n_iter) VF-(70) steps and record history ---
def run_vf70_with_history(self,s, H, z0, K=25, d0=1.0, verbose=True):
"""
H: 1D complex array (single response). If you want multi-response,
pass a list [H11, H21, ...] and adapt the evaluation below.
"""
# Wrap single response as a list for the step function
H_list = [np.asarray(H, dtype=np.complex128)]
z = np.array(z0, dtype=np.complex128)
hist = {
"z": [z.copy()],
"c": [],
"r": [],
"Hfit": [],
"rms_abs": [],
"rms_rel": [],
}
for it in range(K):
z_new, c, residues = self.vf70_step_once(s, H_list, z, d0=d0, column_scale=True)
# Evaluate fitted response after this iteration
Hfit = self.eval_Hfit_from_70(s, z, c, residues[0], d0=d0)
abs_r, rel_r = self.rms_error(H, Hfit)
if verbose:
drel = np.linalg.norm(z_new - z) / max(1.0, np.linalg.norm(z))
print(f"[VF-70] iter {it+1:02d}/{K:02d} Δz_rel={drel:.3e} RMS={abs_r:.3e} RMSrel={rel_r:.3e}")
# save
hist["c"].append(c.copy())
hist["r"].append(residues[0].copy())
hist["Hfit"].append(Hfit.copy())
hist["rms_abs"].append(abs_r)
hist["rms_rel"].append(rel_r)
z = z_new
hist["z"].append(z.copy())
return hist
def evaluate(self, s_eval, z_ref, c, residues, d0=1.0):
"""
Evaluate the (70) model on any frequency grid.
Parameters
----------
s_eval : (K_eval,) complex
Points where to evaluate (e.g., 1j*2π*freq_eval).
z_ref : (P,) complex
The *reference* poles used in the LS system that produced (c, residues).
For the last iteration in run_vf70_with_history, this is hist['z'][-2].
c : (P,) complex
Denominator-update coefficients from (70).
residues : (P,) complex OR list of (P,) for multi-response
Residues for the response(s) from (70).
d0 : scalar, default 1.0
Returns
-------
H_eval : (K_eval,) complex OR (K_eval, M) for M responses
"""
s_eval = np.asarray(s_eval, dtype=np.complex128).reshape(-1)
z_ref = np.asarray(z_ref, dtype=np.complex128).reshape(-1)
Psi_eval = 1.0 / (s_eval[:, None] + z_ref[None, :]) # K_eval x P
Den = d0 + Psi_eval @ np.asarray(c, dtype=np.complex128)
# Single response
if not isinstance(residues, (list, tuple)):
r = np.asarray(residues, dtype=np.complex128).reshape(-1)
Num = Psi_eval @ r
return Num / Den
# Multi-response
M = len(residues)
H_eval = np.empty((s_eval.size, M), dtype=np.complex128)
for m, r_m in enumerate(residues):
r_m = np.asarray(r_m, dtype=np.complex128).reshape(-1)
H_eval[:, m] = (Psi_eval @ r_m) / Den
return H_eval
def auto_select(H, freq,
n_baseline=64, # log-spaced backbone points
peak_prominence=0.05, # fraction of |H| dB dynamic range for peak detection
peak_window=5, # take ±peak_window samples around each peak
topgrad_q=0.98, # keep top 2% largest slope/phase-change points
max_points=25, # final cap on selected samples (None = no cap)
ensure_ends=True):
"""
Select several significant sample points for vector fitting.
Strategy:
1) Always keep endpoints (optional).
2) Add a log-spaced baseline over the band.
3) Detect resonance peaks in |H| (on a log scale) and keep small windows around them.
4) Add points with the largest magnitude slope and phase-change (w.r.t log-f).
5) De-duplicate, sort, and optionally thin to 'max_points' with priority
to endpoints and detected peaks.
Parameters
----------
H : (N,) complex array
Frequency response samples.
freq : (N,) float array
Frequency axis [Hz], strictly increasing.
n_baseline : int
Count of log-spaced baseline samples across the band.
peak_prominence : float
Peak prominence threshold as a fraction of the dynamic range in log|H|.
0.05 ≈ keep peaks ≥ 5% of the range.
peak_window : int
Number of neighbor indices to include on each side of every detected peak.
topgrad_q : float in (0,1)
Quantile for selecting strong slope/phase points.
0.98 ⇒ keep the top 2% largest derivatives.
max_points : int or None
If not None, cap the total number of selected indices to this value.
ensure_ends : bool
Always include the first and last samples.
Returns
-------
H_sel : (K,) complex array
freq_sel : (K,) float array
"""
H = np.asarray(H).reshape(-1)
f = np.asarray(freq).reshape(-1)
if H.size != f.size:
raise ValueError("H and freq must have the same length.")
N = f.size
if N < 4:
return H.copy(), f.copy()
eps = 1e-16
mag = np.abs(H)
logmag = np.log10(mag + eps)
phase = np.unwrap(np.angle(H))
# log-frequency axis (scale-invariant derivatives)
# keep it linear if any non-positive freq sneaks in
if np.all(f > 0):
lf = np.log(f)
else:
lf = f.copy()
dlf = np.gradient(lf)
d_logmag = np.gradient(logmag) / (dlf + 1e-16)
d_phase = np.gradient(phase) / (dlf + 1e-16)
idx = set()
if ensure_ends:
idx.update([0, N-1])
# 1) log-spaced baseline
if n_baseline > 0:
# map a log grid to nearest indices
grid = np.linspace(lf.min(), lf.max(), n_baseline)
base_idx = np.clip(np.searchsorted(lf, grid), 0, N-1)
idx.update(np.unique(base_idx).tolist())
# 2) peaks in |H|
try:
from scipy.signal import find_peaks
dyn = logmag.max() - logmag.min()
prom = peak_prominence * (dyn + 1e-12)
peaks, _ = find_peaks(logmag, prominence=prom)
except Exception:
# simple fallback: strict local maxima
peaks = np.where((mag[1:-1] > mag[:-2]) & (mag[1:-1] > mag[2:]))[0] + 1
for p in peaks:
lo = max(0, p - peak_window)
hi = min(N, p + peak_window + 1)
idx.update(range(lo, hi))
# 3) strongest slope / phase-change points
thr_slope = np.quantile(np.abs(d_logmag), topgrad_q)
thr_phase = np.quantile(np.abs(d_phase), topgrad_q)
idx.update(np.where(np.abs(d_logmag) >= thr_slope)[0].tolist())
idx.update(np.where(np.abs(d_phase) >= thr_phase)[0].tolist())
# 4) finalize set
sel = np.array(sorted(idx), dtype=int)
# 5) optional thinning with priority to endpoints and peaks
if max_points is not None and sel.size > max_points:
priority = np.zeros(sel.size, dtype=int)
if ensure_ends:
priority[(sel == 0) | (sel == N-1)] = 3
if peaks.size:
priority[np.isin(sel, peaks)] = np.maximum(priority[np.isin(sel, peaks)], 2)
keep = []
budget = max_points
# keep highest-priority first
for lev in (3, 2, 1, 0):
cand = sel[priority == lev]
if cand.size == 0:
continue
if cand.size <= budget:
keep.extend(cand.tolist())
budget -= cand.size
else:
step = max(1, int(np.ceil(cand.size / budget)))
keep.extend(cand[::step][:budget].tolist())
budget = 0
if budget == 0:
break
sel = np.array(sorted(set(keep)), dtype=int)
return H[sel], f[sel]
if __name__ == "__main__":
# formula_67(s,y)
H11 = np.array([y[i,0,0] for i in range(len(y))])
H11_slice,freqs_slice = auto_select(H11,freqs,max_points=20)
s_slice = freqs_slice * 2j * np.pi
P_pairs = 2
z0 = generate_starting_poles(P_pairs, beta_min=1e8, beta_max=freqs_slice[-1])
z0 = np.array(z0, dtype=np.complex128)
f70 = formula_70()
K = 25
hist = f70.run_vf70_with_history(s_slice, H11_slice, z0, K=K, d0=1.0, verbose=True)
it_show = K-1
Hfit_final = hist["Hfit"][it_show]
s_dense = 1j * 2*np.pi * freqs
c_final = hist["c"][it_show]
r_final = hist["r"][it_show] # single response
z_ref = hist["z"][it_show]
Hfit_dense = f70.evaluate(s_dense, z_ref, c_final, r_final, d0=1.0)
fig, axes = plt.subplots(2, 1, figsize=(10, 8), sharex=False)
# (1) Magnitude plot like your screenshot
ax0 = axes[0]
ax0.plot(freqs, np.abs(H11), 'o', ms=4, color='red', label='Samples')
ax0.plot(freqs, np.abs(Hfit_dense), '-', lw=2, color='k', label='Fit')
ax0.plot(freqs_slice, np.abs(H11_slice), 'x', ms=4, color='blue', label='Input Samples')
ax0.set_title("Response i=0, j=0")
ax0.set_ylabel("Magnitude")
ax0.legend(loc="best")
# (2) RMS error vs iteration
ax1 = axes[1]
its = np.arange(1, K+1)
ax1.plot(its, hist["rms_rel"], '-o', lw=2)
ax1.set_xlabel("Iteration")
ax1.set_ylabel("RMS error (relative)")
ax1.grid(True, alpha=0.3)
ax1.set_title(f"RMS(final) = {hist['rms_rel'][-1]:.3e}")
fig.tight_layout()
plt.savefig(f"img_formula_70.png")