feat: plot condition number
This commit is contained in:
mayge
380
main.py
380
main.py
@@ -5,6 +5,8 @@ import skrf as rf
|
||||
import matplotlib.pyplot as plt
|
||||
import sympy as sp
|
||||
from scipy.linalg import null_space
|
||||
from plotly.subplots import make_subplots
|
||||
import plotly.graph_objs
|
||||
|
||||
|
||||
network = rf.Network("/tmp/paramer/simulation/4000/4000.s2p")
|
||||
@@ -115,223 +117,190 @@ def formula_67(s,y):
|
||||
# print("H = N_t / D_t",np.abs(N_t / D_t))
|
||||
|
||||
class formula_70:
|
||||
"""
|
||||
VF-(70) with final pole-residue model.
|
||||
After fit():
|
||||
self.poles : (P,) complex
|
||||
self.res : (P, M) complex # residues per response (columns)
|
||||
self.h : (M,) complex # optional constants
|
||||
self.g : (M,) complex # optional proportional terms
|
||||
"""
|
||||
|
||||
# ---------- 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, :])
|
||||
# -------- internals --------
|
||||
|
||||
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])
|
||||
def __init__(self):
|
||||
self.cond = []
|
||||
self.rel = []
|
||||
@staticmethod
|
||||
def _psi(s, z):
|
||||
s = np.asarray(s, np.complex128).reshape(-1)
|
||||
z = np.asarray(z, np.complex128).reshape(-1)
|
||||
return 1.0 / (s[:, None] + z[None, :])
|
||||
|
||||
@staticmethod
|
||||
def _lhp(z):
|
||||
z = np.asarray(z, np.complex128).reshape(-1).copy()
|
||||
z[z.real > 0] = -np.conj(z[z.real > 0])
|
||||
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)
|
||||
def _build_70(self, s, H_list, z_ref, d0):
|
||||
Hs = [np.asarray(h, np.complex128).reshape(-1) for h in H_list]
|
||||
K, P, M = len(s), len(z_ref), len(Hs)
|
||||
Psi = self._psi(s, z_ref)
|
||||
Z = np.zeros((K, P))
|
||||
rows, rhs = [], []
|
||||
for m, H in enumerate(Hs):
|
||||
Hp = H[:, None]
|
||||
L_re = np.real(Hp * Psi); L_im = np.imag(Hp * Psi) # acts on c
|
||||
R_re = -np.real(Psi); R_im = -np.imag(Psi) # acts on r^(m)
|
||||
rows.append(np.hstack([L_re] + [R_re if j == m else Z for j in range(M)]))
|
||||
rhs.append(-np.real(d0 * H))
|
||||
rows.append(np.hstack([L_im] + [R_im if j == m else Z for j in range(M)]))
|
||||
rhs.append(-np.imag(d0 * H))
|
||||
A = np.vstack(rows)
|
||||
b = np.concatenate(rhs)
|
||||
return A, b, M, P
|
||||
|
||||
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
|
||||
def _step_70(self, s, H_list, z_ref, d0=1.0, scale=True):
|
||||
A, b, M, P = self._build_70(s, H_list, z_ref, d0)
|
||||
if scale:
|
||||
coln = np.maximum(np.linalg.norm(A, axis=0), 1e-12)
|
||||
x, *_ = np.linalg.lstsq(A / coln, b, rcond=None)
|
||||
x = x / coln
|
||||
cond = np.linalg.cond(A)
|
||||
else:
|
||||
x, *_ = np.linalg.lstsq(A, b, rcond=None)
|
||||
cond = np.linalg.cond(A)
|
||||
|
||||
# unpack unknowns
|
||||
c = x[:P]
|
||||
residues = []
|
||||
res_ratio = np.empty((P, M), np.complex128)
|
||||
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))
|
||||
for m in range(M):
|
||||
res_ratio[:, m] = x[off:off+P]; off += P
|
||||
# relocate poles with test matrix
|
||||
Sigma = np.diag(-np.asarray(z_ref, np.complex128))
|
||||
T = Sigma - (np.ones((P, 1), np.complex128) @ (c.reshape(1, -1) / d0))
|
||||
z_new = -np.linalg.eigvals(T)
|
||||
z_new = self._enforce_lhp_conjugate(z_new)
|
||||
z_new = self._lhp(z_new)
|
||||
# cond = np.linalg.cond(T)
|
||||
return z_new, c, cond, res_ratio
|
||||
|
||||
return z_new, c, residues
|
||||
# -------- public API --------
|
||||
def fit(self, s, H, z0, n_iter=20, d0=1.0, include_const=True, include_linear=False, verbose=True):
|
||||
"""
|
||||
s : (K,) complex samples (j*2π*f_sel)
|
||||
H : (K,) complex or (K,M) or list of M vectors
|
||||
z0: initial poles (P,) complex (LHP + conjugate pairs recommended)
|
||||
"""
|
||||
# normalize responses -> list
|
||||
if isinstance(H, (list, tuple)):
|
||||
H_list = [np.asarray(h, np.complex128).reshape(-1) for h in H]
|
||||
else:
|
||||
H_arr = np.asarray(H, np.complex128)
|
||||
if H_arr.ndim == 1:
|
||||
H_list = [H_arr]
|
||||
elif H_arr.ndim == 2 and H_arr.shape[0] == len(s):
|
||||
H_list = [H_arr[:, i].copy() for i in range(H_arr.shape[1])]
|
||||
else:
|
||||
raise ValueError("H must be (K,), list of (K,), or (K,M) with M responses.")
|
||||
M = len(H_list)
|
||||
|
||||
# ---------- 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
|
||||
z = self._lhp(np.asarray(z0, np.complex128))
|
||||
# SK/VF relocations
|
||||
for it in range(n_iter):
|
||||
z_next, c, residues = self.vf70_step_once(s, H_list, z, d0=d0)
|
||||
z_next, c_last, cond, _ = self._step_70(s, H_list, z, d0=d0, scale=True)
|
||||
rel = np.linalg.norm(z_next) / max(1.0, np.linalg.norm(z))
|
||||
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}")
|
||||
print(f"[VF-70] iter {it+1:02d}/{n_iter:02d} Δz_rel={rel} cond(z)={cond}")
|
||||
self.cond.append(cond)
|
||||
self.rel.append(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
|
||||
# ---- Finalize: refit residues with fixed poles z (pole–residue model) ----
|
||||
Phi = self._psi(s, z) # K x P
|
||||
# Build design matrix for extras
|
||||
extras = []
|
||||
if include_const: extras.append(np.ones(len(s), np.complex128))
|
||||
if include_linear: extras.append(s.astype(np.complex128))
|
||||
if extras:
|
||||
X_base = np.column_stack([Phi] + extras) # K x (P + E)
|
||||
else:
|
||||
X_base = Phi
|
||||
|
||||
def rms_abs(self,y):
|
||||
return np.sqrt(np.mean(np.abs(y)**2))
|
||||
res = np.empty((len(z), M), np.complex128)
|
||||
h = np.zeros(M, np.complex128)
|
||||
g = np.zeros(M, np.complex128)
|
||||
|
||||
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
|
||||
for m, Hm in enumerate(H_list):
|
||||
theta, *_ = np.linalg.lstsq(X_base, Hm, rcond=None) # complex LS
|
||||
res[:, m] = theta[:len(z)]
|
||||
e = len(theta) - len(z)
|
||||
if e >= 1: h[m] = theta[len(z)]
|
||||
if e >= 2: g[m] = theta[len(z)+1]
|
||||
|
||||
# --- 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)
|
||||
# store the rational function
|
||||
self.poles = z # (P,)
|
||||
self.res = res # (P, M)
|
||||
self.h = h # (M,)
|
||||
self.g = g # (M,)
|
||||
return self
|
||||
|
||||
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
|
||||
# Evaluate the stored **rational** model on any grid
|
||||
def evaluate(self, s_eval, m=None):
|
||||
if not hasattr(self, "poles"):
|
||||
raise RuntimeError("Model not fitted. Call fit(...) first.")
|
||||
s_eval = np.asarray(s_eval, np.complex128).reshape(-1)
|
||||
Phi = self._psi(s_eval, self.poles) # K_eval x P
|
||||
if m is None:
|
||||
H = Phi @ self.res
|
||||
if np.any(self.h): H += self.h
|
||||
if np.any(self.g): H += s_eval[:, None] * self.g
|
||||
return H # (K_eval, M) or (K_eval,1)
|
||||
m = int(m)
|
||||
H = Phi @ self.res[:, m]
|
||||
H += self.h[m]
|
||||
H += s_eval * self.g[m]
|
||||
return H # (K_eval,)
|
||||
|
||||
def evaluate(self, s_eval, z_ref, c, residues, d0=1.0):
|
||||
"""
|
||||
Evaluate the (70) model on any frequency grid.
|
||||
# def plot_rel_and_cond(self):
|
||||
# fig, (ax1, ax2) = plt.subplots(2,1,figsize=(15,20))
|
||||
# ax1.plot(np.log(self.rel), 'g-', label='rel')
|
||||
# ax2.plot(np.log(self.cond), 'b-', label='cond')
|
||||
# ax1.set_xlabel('Iteration')
|
||||
# ax1.set_ylabel('Relative Change', color='g')
|
||||
# ax2.set_ylabel('Condition Number', color='b')
|
||||
# ax1.tick_params(axis='y', labelcolor='g')
|
||||
# ax2.tick_params(axis='y', labelcolor='b')
|
||||
# fig.tight_layout()
|
||||
# plt.title('Relative Change and Condition Number per Iteration')
|
||||
# # plt.show()
|
||||
# plt.savefig(f"img_rel_cond.png")
|
||||
def plot_rel_and_cond(self):
|
||||
fig = make_subplots(rows=2, cols=1, subplot_titles=('Relative Change', 'Condition Number'))
|
||||
fig.add_trace(plotly.graph_objs.Scatter(y=self.rel, mode='lines+markers', name='rel'), row=1, col=1)
|
||||
fig.add_trace(plotly.graph_objs.Scatter(y=self.cond, mode='lines+markers', name='cond'), row=2, col=1)
|
||||
fig.update_xaxes(title_text='Iteration', row=1, col=1)
|
||||
fig.update_yaxes(title_text='Relative Change', row=1, col=1)
|
||||
fig.update_yaxes(title_text='Condition Number', row=2, col=1)
|
||||
fig.update_layout(height=800, width=800, title_text='Relative Change and Condition Number per Iteration')
|
||||
fig.write_image("img_rel_cond.png")
|
||||
# fig.show()
|
||||
|
||||
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
|
||||
def evaluate_on_freq(self, freq_eval, m=None):
|
||||
return self.evaluate(1j * 2*np.pi * np.asarray(freq_eval, float), m=m)
|
||||
|
||||
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)
|
||||
# Optional: save/load the final rational model
|
||||
def save(self, path):
|
||||
if not hasattr(self, "poles"):
|
||||
raise RuntimeError("Nothing to save; call fit(...) first.")
|
||||
np.savez(path, poles=self.poles, res=self.res, h=self.h, g=self.g)
|
||||
|
||||
# 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
|
||||
@classmethod
|
||||
def load(cls, path):
|
||||
d = np.load(path, allow_pickle=False)
|
||||
obj = cls()
|
||||
obj.poles = d["poles"]; obj.res = d["res"]; obj.h = d["h"]; obj.g = d["g"]
|
||||
return obj
|
||||
|
||||
def auto_select(H, freq,
|
||||
n_baseline=64, # log-spaced backbone points
|
||||
@@ -470,22 +439,17 @@ if __name__ == "__main__":
|
||||
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
|
||||
P_pairs = 1
|
||||
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)
|
||||
K = 10
|
||||
model = f70.fit(s_slice, H11_slice, z0, n_iter=K, d0=1.0, verbose=True)
|
||||
model.save("vf70_model.npz")
|
||||
model.plot_rel_and_cond()
|
||||
|
||||
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)
|
||||
Hfit_dense = model.evaluate_on_freq(freqs)
|
||||
|
||||
fig, axes = plt.subplots(2, 1, figsize=(10, 8), sharex=False)
|
||||
|
||||
@@ -499,13 +463,13 @@ if __name__ == "__main__":
|
||||
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}")
|
||||
# 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")
|
||||
|
||||
Reference in New Issue
Block a user