ovf/main.py

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")