from core.orthonormal_basis import generate_laguerre_basis from core.sk_iter import generate_starting_poles import numpy as np 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 from core.freqency import auto_select from scipy.linalg import block_diag network = rf.Network("/tmp/paramer/simulation/3500/3500.s2p") freqs = network.f s = freqs * 2j * np.pi vf = rf.VectorFitting(network) vf.vector_fit(n_poles_real=2, n_poles_cmplx=1,parameter_type="y") 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") 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 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]) 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_psi: """ 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 """ # -------- internals -------- def __init__(self, s, P, H, beta_min, beta_max ,alpha_scale=0.01, n_iter=20, d0=1.0, include_const=True, include_linear=False, verbose=True): self.s = s self.P = P self.H = H self.beta_min = beta_min self.beta_max = beta_max self.alpha_scale = alpha_scale self.z0 = self._generate_starting_poles(P, beta_min=beta_min, beta_max=beta_max,alpha_scale=alpha_scale) self.z0 = np.array(self.z0, dtype=np.complex128) self.n_iter = n_iter self.d0 = d0 self.include_const = include_const self.include_linear = include_linear self.verbose = verbose self.rel_iteration = [] self.cond_iteration = [] self.conf_poles_recognize = [] self.rms_error_iteration = [] self.rms_error_poles_recongnize = [] @staticmethod def _generate_starting_poles(P, beta_min:float, beta_max:float, alpha_scale=0.01): """ 仅生成复共轭对: p = -alpha + j beta, p*。 n_pairs: 复对数量 (总极点数 = 2*n_pairs) beta_min,beta_max: 想要覆盖的虚部范围 (单位: rad/s) alpha_scale: alpha = alpha_scale * beta (文中 {α_p}=0.01{β_p}) 返回: list[complex] (正虚部先, 后跟共轭) """ betas = 2*np.pi*np.linspace(beta_min, beta_max, P) poles = [] for b in betas: alpha = alpha_scale * b p = -alpha + 1j * b poles += [p, np.conj(p)] return poles def _generate_laguerre_basis(self, s: np.ndarray, z: np.ndarray): poles = z poles = sorted(poles, key=lambda p: np.real(p)) basis = np.zeros((len(poles)+1,len(s)),dtype=complex) product = np.ones(len(s),dtype=complex) basis[0] = np.ones(len(s),dtype=complex) # φ_0 = 1 i = 0 while i < len(poles): if np.real(poles[i]) >= 0: raise ValueError(f"极点必须在左半平面: {poles[i]}") # 复对首 (正虚部) if np.iscomplex(poles[i]) and np.imag(poles[i]) > 0: if i + 1 >= len(poles): raise ValueError("复极点缺少共轭") pn = poles[i] pc = poles[i + 1] if not np.isclose(pc, np.conj(pn)): pc, pn = pn,pc if not np.isclose(pc, np.conj(pn)): raise ValueError("复极点未按 (p, p*) 顺序排列 (正虚部在前)") poles[i], poles[i+1] = pc, pn # swap sigma = -np.real(pn) # >0 scale = np.sqrt(2 * sigma) r = np.abs(pn) denom = (s - pn) * (s - pc) # 两个基函数 phi_p = scale * (s - r) / denom * product phi_pc = scale * (s + r) / denom * product # product 先乘 (s + p^*)/(s - p)，再乘 (s + p)/(s - p^*) product = product * (s + pc) / (s - pn) product = product * (s + pn) / (s - pc) basis[i + 1] = phi_p basis[i + 2] = phi_pc i += 2 continue # 复对次 (负虚部) —— 应该被首元素处理，出现表示顺序错误 if np.iscomplex(pn) and np.imag(pn) < 0: raise ValueError("检测到负虚部复极点但其共轭尚未处理，请将正虚部成员放在前面。") # 实极点 sigma = -np.real(pn) if sigma <= 0: raise ValueError("实极点实部应为负 (稳定)。") scale = np.sqrt(2 * sigma) phi = scale / (s - pn) * product # 更新乘积 product = product * (s + pn) / (s - pn) i += 1 basis[i + 1] = phi return basis def _orthonormal_psi(self,s,z): s = np.asarray(s, np.complex128).reshape(-1) z = np.asarray(z, np.complex128).reshape(-1) return self._generate_laguerre_basis(s,z).T @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 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) cond_poles_recognize = np.linalg.cond(A) rms_error_poles_recongnize = np.sqrt(np.mean(np.abs(A @ np.zeros(A.shape[1]) - b)**2)) return A, b, M, P, cond_poles_recognize, rms_error_poles_recongnize def _step_70(self, s, H_list, z_ref, d0=1.0, scale=True): A, b, M, P, cond_poles_recognize, rms_error_poles_recongnize = 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_iteration = np.linalg.cond(A) rms_error_iteration = np.sqrt(np.mean(np.abs(A @ x - b)**2)) else: x, *_ = np.linalg.lstsq(A, b, rcond=None) cond_iteration = np.linalg.cond(A) rms_error_iteration = np.sqrt(np.mean(np.abs(A @ x - b)**2)) c = x[:P] res_ratio = np.empty((P, M), np.complex128) off = P 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._lhp(z_new) # cond = np.linalg.cond(T) return z_new, c, cond_iteration, rms_error_iteration, cond_poles_recognize, rms_error_poles_recongnize, res_ratio # -------- public API -------- def fit(self): """ 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(self.H, (list, tuple)): H_list = [np.asarray(h, np.complex128).reshape(-1) for h in self.H] else: H_arr = np.asarray(self.H, np.complex128) if H_arr.ndim == 1: H_list = [H_arr] elif H_arr.ndim == 2 and H_arr.shape[0] == len(self.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) # z = self._lhp(np.asarray(self.z0, np.complex128)) z = self.z0 # SK/VF relocations for it in range(self.n_iter): z_next, c_last, cond_iteration, rms_error_iteration, cond_poles_recognize, rms_error_poles_recongnize, _ = self._step_70(self.s, H_list, z, d0=self.d0, scale=True) rel = np.linalg.norm(z_next) / max(1.0, np.linalg.norm(z)) if self.verbose: print(f"[VF-70] iter {it+1:02d}/{self.n_iter:02d} Δz_rel={rel}") self.cond_iteration.append(cond_iteration) self.rms_error_iteration.append(rms_error_iteration) self.conf_poles_recognize.append(cond_poles_recognize) self.rms_error_poles_recongnize.append(rms_error_poles_recongnize) self.rel_iteration.append(rel) z = z_next # ---- Finalize: refit residues with fixed poles z (pole–residue model) ---- Phi = self._psi(self.s, z) # K x P # Build design matrix for extras extras = [] if self.include_const: extras.append(np.ones(len(self.s), np.complex128)) if self.include_linear: extras.append(self.s.astype(np.complex128)) if extras: X_base = np.column_stack([Phi] + extras) # K x (P + E) else: X_base = Phi res = np.empty((len(z), M), np.complex128) h = np.zeros(M, np.complex128) g = np.zeros(M, np.complex128) 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] # store the rational function self.poles = z # (P,) self.res = res # (P, M) self.h = h # (M,) self.g = g # (M,) return self # 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 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=3, cols=2) fig.add_trace(plotly.graph_objs.Scatter(y=self.rel_iteration, mode='lines+markers', name='rel'), row=1, col=1) fig.add_trace(plotly.graph_objs.Scatter(y=self.cond_iteration, mode='lines+markers', name='cond_iteration'), row=2, col=1) fig.add_trace(plotly.graph_objs.Scatter(y=self.rms_error_iteration, mode='lines+markers', name='rms_error_iteration'), row=3, col=1) fig.add_trace(plotly.graph_objs.Scatter(y=self.conf_poles_recognize, mode='lines+markers', name='cond_poles_recognize'), row=2, col=2) fig.add_trace(plotly.graph_objs.Scatter(y=self.rms_error_poles_recongnize, mode='lines+markers', name='rms_error_poles_recognize'), row=3, col=2) 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 (Iteration)', row=2, col=1) fig.update_yaxes(title_text='RMS Error (Iteration)', row=3, col=1) fig.update_yaxes(title_text='Condition Number (Pole Recognition)', row=2, col=2) fig.update_yaxes(title_text='RMS Error (Pole Recognition)', row=3, col=2) 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() def evaluate_on_freq(self, freq_eval, m=None): return self.evaluate(1j * 2*np.pi * np.asarray(freq_eval, float), m=m) 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 K = 10 f70 = formula_70_psi(s_slice,P_pairs, H11_slice, beta_min=1e8, beta_max=freqs_slice[-1],alpha_scale=0.01, n_iter=K, d0=1.0, verbose=True) model = f70.fit() model.plot_rel_and_cond() Hfit_dense = model.evaluate_on_freq(freqs) 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")