commit dbf0b1ddb4c95cdf9452e70cd3f982c6cf30b42b
Author: mayge <mayge@paramer.top>
Date:   Mon Sep 15 11:41:55 2025 -0400

    init: 验证robust算法

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..3117b89
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,7 @@
+__pycache__/
+*.pyc
+*.pyo
+*.pyd
+__pypackages__/
+env/
+.venv/
\ No newline at end of file
diff --git a/capa_results.json b/capa_results.json
new file mode 100644
index 0000000..7c73e82
--- /dev/null
+++ b/capa_results.json
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+]
\ No newline at end of file
diff --git a/core/__init__.py b/core/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/core/robust.py b/core/robust.py
new file mode 100644
index 0000000..ec80240
--- /dev/null
+++ b/core/robust.py
@@ -0,0 +1,191 @@
+from models.basic import ModelBasic
+from typing import List,Literal,Dict
+import numpy as np
+import random
+from pydantic import BaseModel
+from skrf import Network
+from models.basic import ModelBasicDatasetUnit
+
+class RobustParametricConfig(BaseModel):
+    n_poles: int
+    max_iter: int = 10
+    parameter_type: Literal["s","y","z"]
+
+class RobustParametricModel:
+    def __init__(self,model:ModelBasic,config:RobustParametricConfig):
+        self.model = model
+        self.config = config
+
+    # 区分训练集和测试集
+    def _train_test_split(self,train_ratio:float=0.8,random_state:int=42):
+        random.seed(random_state)
+        dataset = self.model.results
+        random.shuffle(dataset)
+        train_size = int(len(dataset)*train_ratio)
+        self.train_set = dataset[:train_size]
+        self.test_set = dataset[train_size:]
+        return self.train_set, self.test_set
+    
+    def first_iteration_step(self, datasets: List[ModelBasicDatasetUnit],
+                             param_degree: int = 1):
+        '''
+        SK 迭代的第一步 (t=0) – 对应论文公式 (3).
+
+        目标:
+            最小化  sum_{样本 n, 频点 f} | N^{(0)}(s_f, g_n) - H(s_f, g_n) |^2
+        在 t=0 阶段我们令 D^{(0)}(s,g)=1, 仅拟合分子:
+            N^{(0)}(s,g) = Σ_{p∈P} Σ_{v∈V} c_{p,v} * φ_freq_p(s) * φ_param_v(g)
+
+        因此是一个纯线性最小二乘:
+            H ≈  Σ_{p,v} c_{p,v}  F[:,p] ⊗ G[n,v]
+
+        记:
+            F: (Nf, P)  频率正交(或原始)基列
+            G: (Ns, V)  参数多项式（含常数）基列
+            设计矩阵 A 大小 (Ns*Nf, P*V), A[(n*Nf + f), (p*V + v)] = F[f,p] * G[n,v]
+
+        输出:
+            self.first_iter_coeffs[(i,j)] = C_{p,v}  (P × V)  每个端口对一套系数
+            self.freq_basis_F = F
+            self.param_basis_G = G
+            self.poles 初始极点 (供后续构造有理正交基 / SK 加权使用)
+
+        参数:
+            datasets: 训练用样本列表
+            param_degree: 参数多项式最大总次数 (默认 1 → 常数 + 线性)
+
+        注意:
+            这里使用简单频率基 [1, 1/(s-a_k)]，未做 QR 正交化;
+            后续 SK 迭代 / 正交化可在第二步再进行。
+        '''
+        assert len(datasets) > 0, "空数据集"
+        # ---------------- 收集频率与端口信息 ----------------
+        Ns = len(datasets)
+        freqs = datasets[0].freqs  # 频率需要对齐
+        Nf = freqs.shape[0]
+        nports = self.model.info.nports
+
+        # ---------------- 构造初始极点 (对数分布 + 阻尼) ----------------
+        def _init_poles(n_poles: int):
+            fmin, fmax = freqs[0], freqs[-1]
+            if n_poles <= 0:
+                return np.array([], dtype=complex)
+            # 避免 0 Hz，用第二个点或微小偏移
+            start_f = max(fmin if fmin > 0 else freqs[1] if Nf > 1 else 1.0e-3, 1e-12)
+            f_samples = np.logspace(np.log10(start_f), np.log10(fmax), n_poles)
+            sigma = 0.02 * 2 * np.pi * fmax  # 固定阻尼，可放入 config
+            return -sigma + 1j * 2 * np.pi * f_samples
+
+        self.poles = _init_poles(self.config.n_poles)
+        s_vec = 1j * 2 * np.pi * freqs  # (Nf,)
+
+        # ---------------- 频率基 F ----------------
+        # 列0: 常数 1, 后续列: 1/(s - a_k)
+        P = 1 + len(self.poles)
+        F = np.zeros((Nf, P), dtype=complex)
+        F[:, 0] = 1.0
+        for k, a in enumerate(self.poles, start=1):
+            F[:, k] = 1.0 / (s_vec - a)
+        self.freq_basis_F = F  # (Nf, P)
+
+        # ---------------- 参数基 G ----------------
+        # 取出参数向量 g = [param1, param2, ...]
+        # 假设 datasets[i].parameters 为 dict
+        param_keys = list(datasets[0].parameters.keys())
+        d = len(param_keys)
+        # 构造参数矩阵 (Ns,d)
+        Pmat = np.zeros((Ns, d), dtype=float)
+        for i, unit in enumerate(datasets):
+            for j, k in enumerate(param_keys):
+                Pmat[i, j] = float(unit.parameters[k])
+        # 标准化
+        mean = Pmat.mean(axis=0)
+        std = Pmat.std(axis=0) + 1e-15
+        Xn = (Pmat - mean) / std
+
+        # 生成多项式指数 (总次数 <= param_degree)
+        def _gen_param_exps(dim, D):
+            exps = []
+            def rec(cur, idx, rem):
+                if idx == dim:
+                    exps.append(tuple(cur)); return
+                for t in range(rem + 1):
+                    cur.append(t); rec(cur, idx + 1, rem - t); cur.pop()
+            rec([], 0, D)
+            return exps
+
+        exps = _gen_param_exps(d, param_degree)  # V_exps
+        V = len(exps)
+        G = np.zeros((Ns, V), dtype=float)
+        for vidx, e in enumerate(exps):
+            val = np.ones(Ns)
+            for j, p in enumerate(e):
+                if p:
+                    val *= Xn[:, j] ** p
+            G[:, vidx] = val
+        self.param_basis_G = G  # (Ns, V)
+        self.param_basis_meta = {
+            "keys": param_keys,
+            "mean": mean.tolist(),
+            "std": std.tolist(),
+            "exponents": exps,
+            "degree": param_degree
+        }
+
+        # ---------------- 构造设计矩阵 A (Kronecker) ----------------
+        # A shape: (Ns*Nf, P*V)
+        # 利用广播：A_block[n,f,p,v] = F[f,p] * G[n,v]
+        A4 = np.einsum('fp,nv->nfpv', F, G)   # (Ns, Nf, P, V)
+        A = A4.reshape(Ns * Nf, P * V)
+
+        # ---------------- 采集目标 H 数据 ----------------
+        # 对每个端口对 (i,j) 分别解一个向量 c_{p,v}
+        # 选择参数类型
+        param_type = self.config.parameter_type.lower()
+        valid_types = {"s", "y", "z"}
+        if param_type not in valid_types:
+            raise ValueError(f"parameter_type 必须在 {valid_types}")
+
+        # 预先载入全部 Network (避免重复 IO)
+        # H_data[(i,j)] -> (Ns,Nf) 复数
+        H_data = {}
+        for i_port in range(nports):
+            for j_port in range(nports):
+                H_mat = np.zeros((Ns, Nf), dtype=complex)
+                for n, unit in enumerate(datasets):
+                    net: Network = unit.network
+                    if param_type == "s":
+                        sij = net.s[:, i_port, j_port]
+                    elif param_type == "y":
+                        sij = net.y[:, i_port, j_port]
+                    else:
+                        sij = net.z[:, i_port, j_port]
+                    # 插值或对齐假设已完成
+                    H_mat[n, :] = sij
+                H_data[(i_port, j_port)] = H_mat
+
+        # ---------------- 最小二乘求系数 ----------------
+        self.first_iter_coeffs = {}
+        # 可选: 预计算 A^+ (伪逆) 如果数据不巨大
+        # pinv = np.linalg.pinv(A)
+        for key, Hmat in H_data.items():
+            b = Hmat.reshape(Ns * Nf)  # (Ns*Nf,)
+            # 解 x  (长度 P*V)
+            x, *_ = np.linalg.lstsq(A, b, rcond=None)
+            C = x.reshape(P, V)
+            self.first_iter_coeffs[key] = C
+
+        # ---------------- 存储便于后续 SK 迭代使用 ----------------
+        self.meta_first_iter = {
+            "A_shape": A.shape,
+            "num_samples": Ns,
+            "num_freqs": Nf,
+            "freq_basis_dim": P,
+            "param_basis_dim": V
+        }
+        if getattr(self.config, "verbose", True):
+            print(f"[t=0] 线性最小二乘完成: A={A.shape}, 频率基P={P}, 参数基V={V}, 端口对={nports*nports}")
+
+        return self.first_iter_coeffs
+
+        
\ No newline at end of file
diff --git a/core/sk_iter.py b/core/sk_iter.py
new file mode 100644
index 0000000..0cda0f1
--- /dev/null
+++ b/core/sk_iter.py
@@ -0,0 +1,250 @@
+import numpy as np
+from dataclasses import dataclass
+from typing import List, Sequence, Tuple, Optional
+
+@dataclass
+class OPVFConfig:
+    n_poles: int
+    max_iter: int = 5
+    tol: float = 1e-3
+    add_constraint: bool = True
+    real_split: bool = True
+    lambda_reg: float = 0.0
+    verbose: bool = True
+
+# ---------- 参数正交基 ----------
+class ParamOrthoBasis:
+    def __init__(self, params: np.ndarray, total_degree: int):
+        # params: (Ns, d)
+        self.mean = params.mean(0)
+        self.std = params.std(0) + 1e-15
+        self.exps = self._gen_exps(params.shape[1], total_degree)
+        M = self._build_monomial_matrix(params)  # (Ns,M)
+        Q,R = np.linalg.qr(M)
+        self.Q = Q
+        self.R = R
+    def _gen_exps(self, dim, D):
+        exps=[]
+        def rec(cur, i, rem):
+            if i==dim:
+                exps.append(tuple(cur)); return
+            for k in range(rem+1):
+                cur.append(k); rec(cur, i+1, rem-k); cur.pop()
+        rec([],0,D)
+        return exps
+    def _build_monomial_matrix(self, params):
+        X = (params - self.mean)/self.std
+        Ns = X.shape[0]
+        M = np.zeros((Ns, len(self.exps)))
+        for idx,e in enumerate(self.exps):
+            v = np.ones(Ns)
+            for j,p in enumerate(e):
+                if p: v *= X[:,j]**p
+            M[:,idx]=v
+        return M
+    def eval(self, g: np.ndarray) -> np.ndarray:
+        x = (g - self.mean)/self.std
+        mono=[]
+        for e in self.exps:
+            val=1.0
+            for j,p in enumerate(e):
+                if p: val*= x[j]**p
+            mono.append(val)
+        mono=np.array(mono)
+        # φ = mono @ R^{-1}
+        return mono @ np.linalg.inv(self.R)
+
+# ---------- 频率正交(有理)基 ----------
+class RationalFreqBasis:
+    def __init__(self, freqs: np.ndarray, poles: np.ndarray):
+        # 构造原始矩阵 G: 列0 常数 1, 后面 1/(s-a_k)
+        s = 1j*2*np.pi*freqs
+        cols=[np.ones_like(s)]
+        for a in poles:
+            cols.append(1.0/(s - a))
+        G = np.vstack(cols).T  # (Nf, K+1)
+        # 加权可加 w_f，这里统一 1
+        Q, R = np.linalg.qr(G)
+        self.Q = Q            # Φ(f)  (Nf, K+1) 频率正交基取样
+        self.R = R            # 变换: G = Q R
+        self.freqs = freqs
+    def eval(self) -> np.ndarray:
+        return self.Q   # 直接返回已正交基取样 (Nf, K+1)
+
+# ---------- 主模型 ----------
+class OrthonormalParametricVF:
+    """
+    H(s, μ) = N(s,μ)/D(s,μ)
+    N(s,μ)= Σ_k c_k(μ) φ_k(s);  D(s,μ)= Σ_k ĉ_k(μ) φ_k(s)
+    其中 φ_k(s) 是频率正交有理基; c_k(μ), ĉ_k(μ) 在参数正交基上展开:
+    c_k(μ)= Σ_q C[k,q] ψ_q(μ);  ĉ_k(μ)= Σ_q Ctilde[k,q] ψ_q(μ)
+    """
+    def __init__(self, cfg: OPVFConfig, freq_basis: RationalFreqBasis, param_basis: ParamOrthoBasis):
+        self.cfg = cfg
+        self.fb = freq_basis
+        self.pb = param_basis
+        Kp1 = self.fb.Q.shape[1]
+        Qp = self.pb.Q.shape[1]
+        self.C = np.zeros((Kp1, Qp), dtype=complex)        # 分子
+        self.Ct = np.zeros((Kp1, Qp), dtype=complex)       # 分母
+        # 初始化分母：ĉ_0 ≈ 1，其余 0
+        self.Ct[0,0] = 1.0
+
+    def _assemble_phi_param(self, params: np.ndarray) -> np.ndarray:
+        # 返回 (Ns, Qp)
+        return self.pb.Q
+
+    def fit(self, H_samples: List[np.ndarray], params: np.ndarray):
+        """
+        H_samples: list 长度 Ns, 每个 (Nf,) 复
+        params: (Ns,d)
+        """
+        Φf = self.fb.eval()           # (Nf, K+1)
+        Ns = len(H_samples)
+        Nf, Kp1 = Φf.shape
+        Φμ = self._assemble_phi_param(params)  # (Ns, Qp)
+        Qp = Φμ.shape[1]
+
+        # t=0: 只解 C (式3, D=1)
+        self._solve_t0(H_samples, Φf, Φμ)
+
+        D_prev = self._eval_D(Φf, Φμ)  # (Nf, Ns)
+
+        for it in range(1, self.cfg.max_iter+1):
+            A, b = self._build_iter_system(H_samples, Φf, Φμ, D_prev)
+            if self.cfg.lambda_reg>0:
+                lam = self.cfg.lambda_reg
+                A = np.vstack([A, lam*np.eye(A.shape[1])])
+                b = np.concatenate([b, np.zeros(A.shape[1])])
+            x, *_ = np.linalg.lstsq(A, b, rcond=None)
+            self._unpack_iter_solution(x, Kp1, Qp)
+            D_new = self._eval_D(Φf, Φμ)
+            rel = np.max(np.abs(D_new-D_prev)/(np.abs(D_prev)+1e-12))
+            if self.cfg.verbose:
+                print(f"[OPVF-Iter {it}] rel_change={rel:.3e}")
+            D_prev = D_new
+            if rel < self.cfg.tol:
+                if self.cfg.verbose:
+                    print(f"[OPVF] converged at {it}")
+                break
+        return self
+
+    def _solve_t0(self, H_samples, Φf, Φμ):
+        Ns = len(H_samples); Nf,Kp1 = Φf.shape; Qp = Φμ.shape[1]
+        # 设计矩阵行数 Ns*Nf；未知数 Kp1*Qp
+        cols = Kp1*Qp
+        A = np.zeros((Ns*Nf, cols), dtype=complex)
+        b = np.zeros(Ns*Nf, dtype=complex)
+        r = 0
+        for n,Hn in enumerate(H_samples):
+            phiμ = Φμ[n]  # (Qp,)
+            # Φf (Nf,Kp1) 外积 phiμ -> (Nf, Kp1*Qp)
+            blk = np.einsum('fk,q->fkq', Φf, phiμ).reshape(Nf, cols)
+            A[r:r+Nf,:] = blk
+            b[r:r+Nf] = Hn
+            r += Nf
+        x, *_ = np.linalg.lstsq(A, b, rcond=None)
+        self.C = x.reshape(Kp1, Qp)
+        # 分母保持初始 (ĉ_0=1)
+
+    def _build_iter_system(self, H_samples, Φf, Φμ, D_prev):
+        Ns = len(H_samples); Nf,Kp1 = Φf.shape; Qp=Φμ.shape[1]
+        # 未知：C (Kp1*Qp) + Ct (Kp1*Qp) 但固定 Ct[0,0]=1，可去掉该变量
+        mask_fix = np.zeros((Kp1,Qp), dtype=bool)
+        mask_fix[0,0]=True
+        idx_map={}
+        col=0
+        for i in range(Kp1):
+            for j in range(Qp):
+                idx_map[('C',i,j)] = col; col+=1
+        for i in range(Kp1):
+            for j in range(Qp):
+                if mask_fix[i,j]: continue
+                idx_map[('Ct',i,j)] = col; col+=1
+        cols = col
+        rows = Ns*Nf
+        A = np.zeros((rows, cols), dtype=complex)
+        b = np.zeros(rows, dtype=complex)
+        r=0
+        for n,Hn in enumerate(H_samples):
+            phiμ = Φμ[n]
+            Dp = D_prev[:,n]  # (Nf,)
+            invDp = 1.0/(Dp + 1e-12)
+            # 分子块: (Φf φμ^T) / D_prev
+            Num_blk = np.einsum('fk,q->fkq', Φf, phiμ).reshape(Nf, Kp1*Qp)
+            Num_blk = (Num_blk.T * invDp).T
+            # 填 C 部分
+            for i in range(Kp1):
+                for j in range(Qp):
+                    A[r:r+Nf, idx_map[('C',i,j)]] = Num_blk[:, i*Qp + j]
+            # 分母块: -(H * Φf φμ^T)/D_prev
+            Den_blk = (Num_blk.T * Hn).T * (-1.0)
+            for i in range(Kp1):
+                for j in range(Qp):
+                    if mask_fix[i,j]: continue
+                    A[r:r+Nf, idx_map[('Ct',i,j)]] = Den_blk[:, i*Qp + j]
+            # 右端 0
+            r += Nf
+
+        # 约束行 (式5)(8) 可选：Re( Σ_k D^{(t)}/D^{(t-1)} ) = K+1
+        if self.cfg.add_constraint:
+            row_c = np.zeros(cols, dtype=complex)
+            # D^{(t)} ≈ Σ Ct_k φ_k(s) ; 用代表样本 n=0, 对所有频率平均
+            n0=0
+            phiμ0=Φμ[n0]
+            mean_phiμ = phiμ0  # 可换平均
+            # φ_k(s) 平均
+            mean_phif = Φf.mean(0)  # (Kp1,)
+            for i in range(Kp1):
+                for j in range(Qp):
+                    if mask_fix[i,j]: continue
+                    row_c[idx_map[('Ct',i,j)]] = mean_phif[i]*mean_phiμ[j]
+            rhs = (Kp1)  # K+1
+            A = np.vstack([A, np.real(row_c) if self.cfg.real_split else row_c])
+            b = np.concatenate([b, [rhs]])
+
+        # 拆实虚
+        if self.cfg.real_split:
+            A_real = np.vstack([np.real(A), np.imag(A)])
+            b_real = np.concatenate([np.real(b), np.imag(b)])
+        else:
+            A_real, b_real = A, b
+        return A_real, b_real
+
+    def _unpack_iter_solution(self, x, Kp1, Qp):
+        # 重新填回 C, Ct (保持 Ct[0,0]=1)
+        # 构建与 _build_iter_system 相同的 idx_map
+        mask_fix = np.zeros((Kp1,Qp), dtype=bool); mask_fix[0,0]=True
+        idx_C = Kp1*Qp
+        # 注意：我们当时 C 索引从 0..(Kp1*Qp-1)
+        self.C = x[:idx_C].reshape(Kp1, Qp)
+        Ct_new = self.Ct.copy()
+        pos = idx_C
+        for i in range(Kp1):
+            for j in range(Qp):
+                if mask_fix[i,j]: continue
+                Ct_new[i,j]=x[pos]; pos+=1
+        self.Ct = Ct_new
+
+    def _eval_C_mu(self, phiμ):
+        # 返回 c_k(μ) (Kp1,)
+        return self.C @ phiμ
+    def _eval_Ct_mu(self, phiμ):
+        return self.Ct @ phiμ
+    def _eval_D(self, Φf, Φμ):
+        # D(f, sample)= Σ_k ĉ_k(μ_n) φ_k(f)
+        Kp1 = Φf.shape[1]
+        Ns = Φμ.shape[0]
+        D = np.zeros((Φf.shape[0], Ns), dtype=complex)
+        for n in range(Ns):
+            ct_mu = self._eval_Ct_mu(Φμ[n])
+            D[:,n] = Φf @ ct_mu
+        return D
+
+    def evaluate(self, freqs: np.ndarray, g: np.ndarray):
+        assert np.allclose(freqs, self.fb.freqs), "频率需在训练网格上 (示例简化)"
+        Φf = self.fb.Q            # (Nf,K+1)
+        phiμ = self.pb.eval(g)    # (Qp,)
+        num = Φf @ (self.C @ phiμ)
+        den = Φf @ (self.Ct @ phiμ)
+        return num / (den + 1e-15)
\ No newline at end of file
diff --git a/main.py b/main.py
new file mode 100644
index 0000000..609d240
--- /dev/null
+++ b/main.py
@@ -0,0 +1,15 @@
+from models.capa import Capa
+W = []
+L = []
+i = 15.52
+
+while i <= 100:
+    W.append(i)
+    L.append(i)
+    i = int(i*1.05*100 +0.5) / 100.0
+
+capa = Capa()
+capa.sweep(W,L)
+print(capa.network(result_dir=capa.results[0].result_dir,id=capa.results[0].id))
+
+
diff --git a/models/basic.py b/models/basic.py
new file mode 100644
index 0000000..10f81ad
--- /dev/null
+++ b/models/basic.py
@@ -0,0 +1,149 @@
+from abc import abstractmethod
+from skrf import Network
+from schemas.paramer import SimulationRequestUnit, UuidResponseUnit, SimulationResponseUnit
+from typing import List, Literal, Union, Dict
+import requests
+import time
+from utils import send_get_request
+from pydantic import BaseModel, Field
+import itertools
+import json
+import numpy as np
+
+class ModelBasicParametersUnit(BaseModel):
+    name: str
+    type: Literal["number","integer","string","boolean"]
+    range: List[Union[float,int,str,bool]]
+
+class ModelBasicInfo(BaseModel):
+    base_url = "http://localhost:8105/api/v1"
+    nports: int = Field(default=2)
+    cell_name: str
+    template_name: str
+    user_id: int = Field(default=0)
+    template_version: str = Field(default="")
+
+class ModelBasicDatasetUnit(BaseModel):
+    nports: int = Field(default=2)
+    parameters: Dict[str, Union[float, int, str, bool]]
+    id: int = Field(default=0)
+    result_dir: str = Field(default="")
+
+    @property
+    def network(self) -> Network:
+        try:
+            network = Network(f"{self.result_dir}/{self.id}.s{self.nports}p")
+            return network
+        except Exception as e:
+            raise RuntimeError(f"Error loading network from {self.result_dir}: {e}")
+        
+    @property
+    def s_params(self) -> np.ndarray:
+        return self.network.s
+    
+    @property
+    def y_params(self) -> np.ndarray:
+        return self.network.y
+    
+    @property
+    def z_params(self) -> np.ndarray:
+        return self.network.z
+    
+    @property
+    def freqs(self) -> np.ndarray:
+        return self.network.f
+
+
+class ModelBasic:
+    def __init__(self):
+        self._dataset:List[ModelBasicDatasetUnit] = []
+
+    @property
+    @abstractmethod
+    def info(self)->ModelBasicInfo:
+        pass
+
+    @property
+    @abstractmethod
+    def parameters(self)->List[ModelBasicParametersUnit]:
+        pass
+
+    @property
+    @abstractmethod
+    def settings(self)->dict:
+        pass
+
+    def sweep(self):
+        parameters_list = []
+        lst = [res.range for res in self.parameters]
+        parameters_name = [res.name for res in self.parameters]
+        result = [list(item) for item in itertools.product(*lst)]
+        for res in result:
+            parameters_list.append({parameters_name[i]:res[i] for i in range(len(res))})
+
+        for res in parameters_list:
+            request_unit = SimulationRequestUnit(
+                user_id=self.info.user_id,
+                template_name=self.info.template_name,
+                template_version=self.info.template_version,
+                cell_name=self.info.cell_name,
+                parameters=res,
+                settings=self.settings
+            )
+            response = self.simulate(request_unit)
+
+            self._dataset.append(ModelBasicDatasetUnit(nports=self.info.nports,parameters=res, id=response.id, result_dir=response.result_path))
+
+    @property
+    def results(self)->List[ModelBasicDatasetUnit]:
+        return self._dataset
+
+    def export(self, path:str|None):
+        if path is None:
+            path = f"{self.info.cell_name}_dataset.json"
+        with open(path,"w") as f:
+            json.dump([dict(item) for item in self.results],f,indent=4)
+
+    def load(self, path:str|None):
+        if path is None:
+            path = f"{self.info.cell_name}_dataset.json"
+        with open(path,"r") as f:
+            data = json.load(f)
+            self._dataset += [ModelBasicDatasetUnit(**item) for item in data]
+    
+    def clear(self):
+        self._dataset = []
+
+    def simulate(self,simulation_request:SimulationRequestUnit)->UuidResponseUnit:
+        def send_simulate_request(url, data:list)->list[dict]:
+            response = requests.post(url, json = data)
+            if response.status_code not in [200,201,202]:
+                raise RuntimeError(f"send_simulate_request: {response.status_code}, {response.text}")
+            return response.json()
+            
+        response = send_simulate_request(f"{self.info.base_url}/simulations/create", [dict(simulation_request)])
+
+        simulation_response_model:SimulationResponseUnit = SimulationResponseUnit(**(response[0]))
+
+        time.sleep(0.01)
+
+        response = send_get_request(f"{self.info.base_url}/simulations/input_hash/{simulation_response_model.input_hash}")
+        assert isinstance(response, dict), "Response is not a dictionary."
+        uuid_model = UuidResponseUnit(**response)
+        
+
+        time.sleep(0.01)  # Wait for 2 seconds before checking the status again
+
+        status = uuid_model.status
+        while status != "completed" and status != "failed":
+            time.sleep(0.01)  # Wait for 2 seconds before checking again
+            response = send_get_request(f"{self.info.base_url}/simulations/input_hash/{simulation_response_model.input_hash}")
+            assert isinstance(response, dict), "Response is not a dictionary."
+            uuid_model = UuidResponseUnit(**response)
+            assert response is not None, "No response received from the server."
+            status = uuid_model.status
+
+        if status == "failed":
+            raise RuntimeError(f"Simulation failed: {uuid_model.error_message}")
+        else:
+            return uuid_model
\ No newline at end of file
diff --git a/models/capa.py b/models/capa.py
new file mode 100644
index 0000000..885253b
--- /dev/null
+++ b/models/capa.py
@@ -0,0 +1,45 @@
+from typing import List,Optional
+from pydantic import BaseModel, Field
+from schemas.paramer import SimulationRequestUnit
+from skrf import Network
+import re
+from models.basic import ModelBasic, ModelBasicParametersUnit, ModelBasicInfo, ModelBasicDatasetUnit
+
+W = []
+L = []
+i = 15.52
+while i <= 100:
+    W.append(i)
+    L.append(i)
+    i = int(i*1.05*100 + 0.5) / 100.0
+
+class Capa(ModelBasic):
+    def __init__(self):
+        super().__init__()
+
+    @property
+    def info(self) -> ModelBasicInfo:
+        return ModelBasicInfo(
+            nports=2,
+            cell_name="capa",
+            template_name="em_interface_compound",
+            user_id=0,
+            template_version=""
+        )
+
+    @property
+    def settings(self) -> dict:
+        return {}
+
+    @property
+    def parameters(self) -> List[ModelBasicParametersUnit]:
+        return [
+            ModelBasicParametersUnit(name="W",type="number",range=W),
+            ModelBasicParametersUnit(name="L",type="number",range=L)
+        ]
+        
+
+
+
+    
+    
\ No newline at end of file
diff --git a/outputs/capa_parametric.s2p b/outputs/capa_parametric.s2p
new file mode 100644
index 0000000..dccfb21
--- /dev/null
+++ b/outputs/capa_parametric.s2p
@@ -0,0 +1,309 @@
+! Created with skrf 1.8.0 (http://scikit-rf.org).
+# Hz S RI R 50.0 
+!freq ReS11 ImS11 ReS21 ImS21 ReS12 ImS12 ReS22 ImS22
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diff --git a/outputs/pvf_test_sample.s2p b/outputs/pvf_test_sample.s2p
new file mode 100644
index 0000000..0855f1c
--- /dev/null
+++ b/outputs/pvf_test_sample.s2p
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diff --git a/param_vf.py b/param_vf.py
new file mode 100644
index 0000000..d1f97f7
--- /dev/null
+++ b/param_vf.py
@@ -0,0 +1,583 @@
+"""
+Parametric (multivariate) orthonormal vector fitting for geometry + frequency.
+
+根据论文: Robust Parametric Macromodeling Using Multivariate Orthonormal Vector Fitting
+
+核心思想 (简化实现版本):
+1. 在频域上使用一组全局极点 a_k, 通过所有参数样本共享。
+2. 对每个几何样本 s (由 (W,L) 给出) 与端口对 (i,j) 构建线性最小二乘问题, 固定极点估计该样本的残值 r_{k,s}, 以及常数/斜率项 d_s, e_s。
+3. 将随几何参数变化的残值/常数/斜率在一个离散正交 (QR) 的多元多项式基 Φ_q(W,L) 上展开: r_k(W,L) ≈ Σ_q c_{k,q} Φ_q(W,L)。
+4. 评价阶段: 先用 (W,L) 计算 Φ(W,L), 再恢复 r_k,d,e, 组合成有理函数 Σ_k r_k/(p-a_k)+d+p e。
+
+该文件实现一个最小可用版本, 方便后续扩展(极点迭代 / 被动性约束 / 模型压缩等)。
+"""
+
+from __future__ import annotations
+
+from dataclasses import dataclass
+from typing import List, Tuple, Dict, Any, Optional
+import numpy as np
+from skrf import Network
+import skrf as rf
+from models.capa import Capa
+from models.basic import ModelBasicDatasetUnit
+import warnings
+
+
+@dataclass
+class ParametricVFConfig:
+    # 有理函数项数量 (K 个极点)
+    n_poles: int = 8
+    # 参数多项式最大总次数 (a+b <= degree)
+    param_total_degree: int = 3
+    # 频率单位: Hz (Network 中 f 默认 Hz)
+    damping: float = 0.02  # 极点实部相对于 2π f_max 的比例, 保证稳定
+    # 最大保留频率点 (特征频率抽样); None 表示不裁剪
+    max_freq_points: Optional[int] = None
+    # 频率选择方法: 'curvature' 或 'uniform'
+    freq_selection_method: str = 'curvature'
+    # 曲率阈值(可选), 仅 method='curvature' 时生效
+    curvature_threshold: Optional[float] = None
+    # VF 极点迭代次数 (0 表示不迭代)
+    vf_iterations: int = 0
+    # 极点迭代时是否打印警告
+    verbose: bool = True
+    # 未来可添加: 加权, 正则, 被动性投影等
+
+
+def generate_monomial_exponents(dim: int, total_degree: int) -> List[Tuple[int, ...]]:
+    """生成所有满足指数和 <= total_degree 的多元单项式指数。
+    对于 2 维 (W,L) 返回 (a,b) 列表。
+    """
+    exps: List[Tuple[int, ...]] = []
+    def rec(prefix: Tuple[int, ...], remaining_dim: int, max_sum: int):
+        if remaining_dim == 1:
+            for i in range(max_sum + 1):
+                exps.append(prefix + (i,))
+            return
+        for i in range(max_sum + 1):
+            rec(prefix + (i,), remaining_dim - 1, max_sum - i)
+    rec(tuple(), dim, total_degree)
+    return exps
+
+
+class OrthonormalParamBasis:
+    """离散点集上 (W,L) 的多项式基 QR 正交化封装。"""
+    def __init__(self, W: np.ndarray, L: np.ndarray, total_degree: int):
+        assert W.shape == L.shape
+        self.W_mean = W.mean()
+        self.W_std = W.std() or 1.0
+        self.L_mean = L.mean()
+        self.L_std = L.std() or 1.0
+        self.exps = generate_monomial_exponents(2, total_degree)
+        # 构建单项式矩阵 M (Ns x M)
+        M = []
+        Wn = (W - self.W_mean) / self.W_std
+        Ln = (L - self.L_mean) / self.L_std
+        for a, b in self.exps:
+            M.append((Wn ** a) * (Ln ** b))
+        M = np.stack(M, axis=1)  # (Ns, M)
+        # QR 分解获得离散正交基 Q, R 上三角
+        Q, R = np.linalg.qr(M)
+        self.Q = Q  # (Ns, Q)
+        self.R = R  # (Q, Q)
+        self.R_inv = np.linalg.inv(R)
+
+    @property
+    def n_basis(self) -> int:
+        return self.Q.shape[1]
+
+    def phi_matrix(self) -> np.ndarray:
+        return self.Q  # 对应样本点的基函数值
+
+    def eval(self, W: float, L: float) -> np.ndarray:
+        Wn = (W - self.W_mean) / self.W_std
+        Ln = (L - self.L_mean) / self.L_std
+        monomials = []
+        for a, b in self.exps:
+            monomials.append((Wn ** a) * (Ln ** b))
+        m = np.asarray(monomials)  # (M,)
+        # M = Q R => 对新点 m = phi R => phi = m R^{-1}
+        phi = m @ self.R_inv
+        return phi  # (Q,)
+
+
+class ParametricVectorFitting:
+    """多参数 (W,L) 二端口/多端口 S 参数的简化 Parametric VF。
+
+    模型形式 (单个端口对):
+        H(p; μ) ≈ Σ_{k=1..K} r_k(μ)/(p - a_k) + d(μ) + p e(μ)
+    其中 μ = (W,L)。r_k, d, e 在参数域被正交基展开。
+    """
+    def __init__(self, config: ParametricVFConfig):
+        self.cfg = config
+        self.frequencies: np.ndarray | None = None  # (Nf,)
+        self.poles: np.ndarray | None = None  # (K,)
+        self.basis: OrthonormalParamBasis | None = None
+        # 残值系数: (nports, nports, K, Q)
+        self.residue_coeffs: np.ndarray | None = None
+        # d,e 系数: (nports, nports, Q)
+        self.d_coeffs: np.ndarray | None = None
+        self.e_coeffs: np.ndarray | None = None
+        self.meta: Dict[str, Any] = {}
+
+    def _init_global_poles(self, freqs: np.ndarray) -> np.ndarray:
+        f_min, f_max = freqs.min(), freqs.max()
+        # 使用对数均匀分布 (排除 0) + 负实部保证稳定
+        f_samples = np.logspace(np.log10(max(f_min, freqs[1] if len(freqs) > 1 else f_min*1.1)), np.log10(f_max), self.cfg.n_poles)
+        # 极点: -σ + j 2π f_k
+        sigma = self.cfg.damping * 2 * np.pi * f_max
+        poles = -sigma + 1j * 2 * np.pi * f_samples
+        return poles
+
+    # ----------------- 内部工具函数 (前置以便类型检查) -----------------
+    def _build_frequency_matrix(self, p_vec: np.ndarray, poles: np.ndarray) -> np.ndarray:
+        K = len(poles)
+        F_base = np.zeros((len(p_vec), K + 2), dtype=complex)
+        for k, a_k in enumerate(poles):
+            F_base[:, k] = 1.0 / (p_vec - a_k)
+        F_base[:, K] = 1.0
+        F_base[:, K + 1] = p_vec
+        return F_base
+
+    def _solve_residues_given_poles(self, aligned_S: List[np.ndarray], p_vec: np.ndarray):
+        assert self.poles is not None, "Poles not initialized"
+        nports = aligned_S[0].shape[1]
+        Ns = len(aligned_S)
+        K = len(self.poles)
+        residues_samples = np.zeros((nports, nports, K, Ns), dtype=complex)
+        d_samples = np.zeros((nports, nports, Ns), dtype=complex)
+        e_samples = np.zeros((nports, nports, Ns), dtype=complex)
+        F_base = self._build_frequency_matrix(p_vec, self.poles)
+        for s_idx, Sdata in enumerate(aligned_S):
+            for i in range(nports):
+                for j in range(nports):
+                    y = Sdata[:, i, j]
+                    x, *_ = np.linalg.lstsq(F_base, y, rcond=None)
+                    residues_samples[i, j, :, s_idx] = x[:K]
+                    d_samples[i, j, s_idx] = x[K]
+                    e_samples[i, j, s_idx] = x[K+1]
+        return residues_samples, d_samples, e_samples
+
+    def _select_characteristic_freqs(self, freqs: np.ndarray, S_list: List[np.ndarray], max_points: int,
+                                     method: str = 'curvature', threshold: Optional[float] = None) -> np.ndarray:
+        Nf = len(freqs)
+        if max_points >= Nf:
+            return np.arange(Nf)
+        if method == 'uniform':
+            idx = np.linspace(0, Nf-1, max_points, dtype=int)
+            return np.unique(idx)
+        mags = []
+        for S in S_list:
+            mags.append(np.mean(np.abs(S), axis=(1,2)))  # (Nf,)
+        agg = np.mean(np.stack(mags, axis=1), axis=1)  # (Nf,)
+        curv = np.zeros_like(agg)
+        curv[1:-1] = np.abs(agg[2:] - 2*agg[1:-1] + agg[:-2])
+        base = {0, Nf-1}
+        if threshold is not None:
+            cand = np.where(curv >= threshold)[0]
+        else:
+            order = np.argsort(-curv)
+            cand = order
+        selected = list(base)
+        for idx in cand:
+            if idx in base:
+                continue
+            selected.append(idx)
+            if len(selected) >= max_points:
+                break
+        return np.array(sorted(selected))
+
+    def _vf_iterate_poles(self, aligned_S: List[np.ndarray], p_vec: np.ndarray,
+                           residues_samples: np.ndarray, d_samples: np.ndarray, e_samples: np.ndarray) -> np.ndarray:
+        assert self.poles is not None, "Poles not initialized"
+        nports = residues_samples.shape[0]
+        K = len(self.poles)
+        Ns = len(aligned_S)
+        Nf = len(p_vec)
+        n_pairs = nports * nports
+        n_r = n_pairs * K
+        n_c = K
+        n_d = n_pairs
+        n_e = n_pairs
+        total_unknowns = n_r + n_c + n_d + n_e
+        rows = Ns * Nf * n_pairs
+        A = np.zeros((rows, total_unknowns), dtype=complex)
+        b = np.zeros(rows, dtype=complex)
+        def pair_index(i,j):
+            return i*nports + j
+        row = 0
+        for s_idx, Sdata in enumerate(aligned_S):
+            for f_idx, p in enumerate(p_vec):
+                denom = p - self.poles
+                basis_freq = 1.0/denom
+                for i in range(nports):
+                    for j in range(nports):
+                        H = Sdata[f_idx, i, j]
+                        b[row] = H
+                        pair = pair_index(i,j)
+                        r_offset = pair*K
+                        A[row, r_offset:r_offset+K] = basis_freq
+                        A[row, n_r:n_r+K] = -H * basis_freq
+                        A[row, n_r + n_c + pair] = 1.0
+                        A[row, n_r + n_c + n_d + pair] = p
+                        row += 1
+        x, *_ = np.linalg.lstsq(A, b, rcond=None)
+        c_k = x[n_r:n_r+n_c]
+        poly_total = np.poly(self.poles)
+        acc = poly_total.copy()
+        for k in range(K):
+            others = [self.poles[m] for m in range(K) if m != k]
+            term = c_k[k] * np.poly(others)
+            acc = np.polyadd(acc, term)
+        new_poles = np.roots(acc)
+        return new_poles
+
+    def fit(self, dataset: List[ModelBasicDatasetUnit], network_loader=Capa.network):
+        # 载入所有 Network
+        networks: List[Network] = []
+        W_list, L_list = [], []
+        for unit in dataset:
+            net = network_loader(unit.result_dir, unit.id)
+            networks.append(net)
+            W_list.append(unit.parameters["W"])
+            L_list.append(unit.parameters["L"])
+        assert len(networks) > 0, "Empty dataset"
+        # 处理不同频率点数量: 取公共重叠频段并插值到统一网格
+        freqs_list = [n.f for n in networks]
+        f_start = max(f[0] for f in freqs_list)
+        f_stop = min(f[-1] for f in freqs_list)
+        if f_stop <= f_start:
+            raise ValueError("No overlapping frequency range among networks")
+        # 选择基准网格: 使用第一个网络在重叠区间内的频点, 若其它网络缺该点则插值
+        base_freqs = networks[0].f
+        mask = (base_freqs >= f_start) & (base_freqs <= f_stop)
+        freqs = base_freqs[mask]
+        # 如果其它网络点数差异较大, 可选: 统一稠密度 (这里只在差异>5%时使用最小长度网格)
+        for f in freqs_list[1:]:
+            # 判断差异比例
+            if abs(len(f) - len(freqs)) / max(len(freqs),1) > 0.2:
+                # 使用所有网络在重叠区间内最少点数, 构造等间距网格
+                n_common = min(len(ff[(ff>=f_start)&(ff<=f_stop)]) for ff in freqs_list)
+                freqs = np.linspace(f_start, f_stop, n_common)
+                warnings.warn("Frequency grids differ significantly; using uniform linspace for interpolation.")
+                break
+        # 对每个网络插值到 freqs (实部/虚部分开线性插值)
+        aligned_S = []  # List[(Nf, nports, nports)]
+        for net in networks:
+            f_src = net.f
+            # 获取在目标范围内原始数据 (若后面改用插值网格不同于原点, 仍需完整插值)
+            S_src = net.s  # (Nf_src, nports, nports)
+            nports = net.nports
+            if not np.array_equal(f_src, freqs):
+                # 线性插值 (对每个端口对实部与虚部)
+                S_interp = np.zeros((len(freqs), nports, nports), dtype=complex)
+                for i in range(nports):
+                    for j in range(nports):
+                        y = S_src[:, i, j]
+                        # numpy.interp 需要单调递增; 为类型检查器显式转为 np.ndarray
+                        y_arr = np.asarray(y)
+                        y_real = np.real(y_arr)
+                        y_imag = np.imag(y_arr)
+                        real_part = np.interp(freqs, f_src, y_real)
+                        imag_part = np.interp(freqs, f_src, y_imag)
+                        S_interp[:, i, j] = real_part + 1j * imag_part
+                aligned_S.append(S_interp)
+            else:
+                aligned_S.append(S_src[mask] if len(S_src)==len(base_freqs) and mask.sum()!=len(base_freqs) else S_src)
+        self.frequencies = freqs
+        nports = networks[0].nports
+        Ns = len(networks)
+        # 参数正交基
+        self.basis = OrthonormalParamBasis(np.array(W_list), np.array(L_list), self.cfg.param_total_degree)
+        Phi = self.basis.phi_matrix()  # (Ns, Q)
+        Qn = Phi.shape[1]
+        # (可选) 特征频率子采样
+        if self.cfg.max_freq_points is not None and len(freqs) > self.cfg.max_freq_points:
+            sel_idx = self._select_characteristic_freqs(freqs, aligned_S, self.cfg.max_freq_points,
+                                                        method=self.cfg.freq_selection_method,
+                                                        threshold=self.cfg.curvature_threshold)
+            freqs = freqs[sel_idx]
+            aligned_S = [S[sel_idx, :, :] for S in aligned_S]
+            if self.cfg.verbose:
+                warnings.warn(f"Frequency reduced to {len(freqs)} points (method={self.cfg.freq_selection_method}).")
+        # 初始化极点
+        self.poles = self._init_global_poles(freqs)
+        p_vec = 1j * 2 * np.pi * freqs
+        # 首次求解残值
+        residues_samples, d_samples, e_samples = self._solve_residues_given_poles(aligned_S, p_vec)
+        # 极点迭代 (简化共享极点 VF)
+        if self.cfg.vf_iterations > 0:
+            for it in range(self.cfg.vf_iterations):
+                new_poles = self._vf_iterate_poles(aligned_S, p_vec, residues_samples, d_samples, e_samples)
+                # 反射不稳定极点
+                new_poles = np.array([p if p.real < 0 else complex(-p.real, p.imag) for p in new_poles])
+                # 去重: 近似重复 (距离 < 1e-3 * |p|) 过滤
+                filtered = []
+                for p in new_poles:
+                    if all(abs(p - q) > 1e-3*max(1.0, abs(p)) for q in filtered):
+                        filtered.append(p)
+                if self.cfg.verbose:
+                    print(f"[VF-Iter {it+1}] poles -> {len(filtered)} kept")
+                self.poles = np.array(filtered, dtype=complex)
+                p_vec = 1j * 2 * np.pi * freqs
+                residues_samples, d_samples, e_samples = self._solve_residues_given_poles(aligned_S, p_vec)
+        # 在参数基上再拟合: 由于 Phi 正交, 系数 = Phi^H * values
+        PhiH = Phi.conj().T  # (Q, Ns)
+        K = self.poles.shape[0]
+        self.residue_coeffs = np.zeros((nports, nports, K, Qn), dtype=complex)
+        self.d_coeffs = np.zeros((nports, nports, Qn), dtype=complex)
+        self.e_coeffs = np.zeros((nports, nports, Qn), dtype=complex)
+        for i in range(nports):
+            for j in range(nports):
+                for k in range(K):
+                    vk = residues_samples[i, j, k, :]  # (Ns,)
+                    self.residue_coeffs[i, j, k, :] = PhiH @ vk
+                self.d_coeffs[i, j, :] = PhiH @ d_samples[i, j, :]
+                self.e_coeffs[i, j, :] = PhiH @ e_samples[i, j, :]
+        # 简单误差评估 (训练点重建 RMS)
+        F_base = self._build_frequency_matrix(p_vec, self.poles)
+        train_rms = self._compute_training_rms(residues_samples, d_samples, e_samples, F_base, aligned_S)
+        self.meta['train_rms'] = train_rms
+        self.meta['nports'] = nports
+        self.meta['Ns'] = Ns
+        self.meta['Q'] = Qn
+        return self
+
+    def _compute_training_rms(self, residues_samples, d_samples, e_samples, F_base, original_S_list):
+        """计算每个样本的平均端口对 RMS 误差。"""
+        nports = residues_samples.shape[0]
+        K = residues_samples.shape[2]
+        Ns = residues_samples.shape[3]
+        Nf = F_base.shape[0]
+        rms = []
+        for s in range(Ns):
+            err_sq_sum = 0.0
+            count = 0
+            S_ref = original_S_list[s]
+            for i in range(nports):
+                for j in range(nports):
+                    x = np.concatenate([
+                        residues_samples[i, j, :, s],
+                        [d_samples[i, j, s], e_samples[i, j, s]]
+                    ])  # (K+2,)
+                    y_hat = F_base @ x  # (Nf,)
+                    y_ref = S_ref[:, i, j]
+                    err = y_ref - y_hat
+                    err_sq_sum += np.mean(np.abs(err)**2)
+                    count += 1
+            rms.append(np.sqrt(err_sq_sum / max(count,1)))
+        return rms
+
+    def evaluate(self, W: float, L: float, freqs: np.ndarray | None = None) -> np.ndarray:
+        """返回插值后的 S 参数 (Nf, nports, nports)。"""
+        assert self.frequencies is not None and self.poles is not None
+        assert self.basis is not None
+        assert self.residue_coeffs is not None and self.d_coeffs is not None and self.e_coeffs is not None, "Model not fitted"
+        if freqs is None:
+            freqs = self.frequencies
+        # 若请求频率网格不同, 需要重建频率矩阵
+        p_vec = 1j * 2 * np.pi * freqs
+        K = len(self.poles)
+        nports = self.residue_coeffs.shape[0]
+        phi = self.basis.eval(W, L)  # (Q,)
+        # 预分配
+        S_eval = np.zeros((len(freqs), nports, nports), dtype=complex)
+        denom_cache = np.zeros((len(freqs), K), dtype=complex)
+        for k, a_k in enumerate(self.poles):
+            denom_cache[:, k] = 1.0 / (p_vec - a_k)
+        for i in range(nports):
+            for j in range(nports):
+                # 恢复参数依赖的残值/常数/斜率
+                r_k = (self.residue_coeffs[i, j, :, :] @ phi)  # (K,)
+                d = self.d_coeffs[i, j, :] @ phi
+                e = self.e_coeffs[i, j, :] @ phi
+                Hf = denom_cache @ r_k + d + p_vec * e  # (Nf,)
+                S_eval[:, i, j] = Hf
+        return S_eval
+
+    def export_s2p(self, W: float, L: float, filepath: str, freqs: np.ndarray | None = None, z0: float | complex = 50) -> str:
+        """在给定几何参数 (W,L) 下计算 S 并写入 Touchstone (.sNp) 文件。
+
+        参数:
+            W, L: 几何参数
+            filepath: 目标文件完整路径, 可包含或不包含 .s2p/.sNp 后缀
+            freqs: 可选自定义频率数组 (需在训练频率范围内); 默认使用训练频率
+            z0: 端口参考阻抗 (标量或与端口数相同长度可扩展)
+
+        返回:
+            实际写入的文件路径
+        """
+        assert self.frequencies is not None, "Model not fitted"
+        S_eval = self.evaluate(W, L, freqs)
+        if freqs is None:
+            freqs = self.frequencies
+        nports = S_eval.shape[1]
+        freqs_arr = np.asarray(freqs)
+        # 构建 Network 对象
+        ntw = rf.Network(f=freqs_arr, s=S_eval, z0=z0)
+        # 解析输出路径
+        import os
+        base_dir = os.path.dirname(filepath) or '.'
+        os.makedirs(base_dir, exist_ok=True)
+        base_name = os.path.basename(filepath)
+        # 去掉可能已有的扩展名, 由 skrf 自动加 .sNp
+        if '.' in base_name:
+            base_name = '.'.join(base_name.split('.')[:-1]) or base_name
+        # 写文件
+        ntw.write_touchstone(base_name, dir=base_dir)
+        # 构造最终文件名 (.sNp)
+        final_path = os.path.join(base_dir, f"{base_name}.s{nports}p")
+        return final_path
+
+    def to_dict(self) -> Dict[str, Any]:
+        return {
+            'config': self.cfg.__dict__,
+            'frequencies': self.frequencies.tolist() if self.frequencies is not None else None,
+            'poles': self.poles.tolist() if self.poles is not None else None,
+            'basis': {
+                'W_mean': getattr(self.basis, 'W_mean', None),
+                'W_std': getattr(self.basis, 'W_std', None),
+                'L_mean': getattr(self.basis, 'L_mean', None),
+                'L_std': getattr(self.basis, 'L_std', None),
+                'exps': getattr(self.basis, 'exps', None),
+                'R': (lambda _R: _R.tolist() if _R is not None else None)(getattr(self.basis, 'R', None)),
+            },
+            'residue_coeffs': self.residue_coeffs.tolist() if self.residue_coeffs is not None else None,
+            'd_coeffs': self.d_coeffs.tolist() if self.d_coeffs is not None else None,
+            'e_coeffs': self.e_coeffs.tolist() if self.e_coeffs is not None else None,
+            'meta': self.meta,
+        }
+
+    @staticmethod
+    def from_dict(data: Dict[str, Any]) -> 'ParametricVectorFitting':
+        cfg = ParametricVFConfig(**data['config'])
+        obj = ParametricVectorFitting(cfg)
+        obj.frequencies = np.array(data['frequencies']) if data['frequencies'] is not None else None
+        obj.poles = np.array(data['poles']) if data['poles'] is not None else None
+        # 重建 basis (仅用于 eval); 重新构造 R_inv
+        if data.get('basis') and data['basis']['R'] is not None:
+            basis_stub = OrthonormalParamBasis(np.array([0.0, 1.0]), np.array([0.0, 1.0]), 1)  # 占位
+            basis_stub.W_mean = data['basis']['W_mean']
+            basis_stub.W_std = data['basis']['W_std']
+            basis_stub.L_mean = data['basis']['L_mean']
+            basis_stub.L_std = data['basis']['L_std']
+            basis_stub.exps = [tuple(e) for e in data['basis']['exps']]
+            R = np.array(data['basis']['R'])
+            basis_stub.R = R
+            basis_stub.R_inv = np.linalg.inv(R)
+            # Q 不需要 (仅用于训练点), 设为 None
+            basis_stub.Q = None  # type: ignore
+            obj.basis = basis_stub
+        if data.get('residue_coeffs') is not None:
+            obj.residue_coeffs = np.array(data['residue_coeffs'])
+        if data.get('d_coeffs') is not None:
+            obj.d_coeffs = np.array(data['d_coeffs'])
+        if data.get('e_coeffs') is not None:
+            obj.e_coeffs = np.array(data['e_coeffs'])
+        obj.meta = data.get('meta', {})
+        return obj
+
+# 划分
+def split_dataset(dataset: List[ModelBasicDatasetUnit], train_ratio: float = 0.7, shuffle: bool = True, seed: int = 0) -> Tuple[List[ModelBasicDatasetUnit], List[ModelBasicDatasetUnit]]:
+    """划分数据集 70% 训练 / 30% 测试 (默认可改)。"""
+    ds = list(dataset)
+    if shuffle:
+        rng = np.random.default_rng(seed)
+        rng.shuffle(ds)
+    n_train = int(len(ds) * train_ratio)
+    return ds[:n_train], ds[n_train:]
+
+
+def _interp_s_to_freqs(S: np.ndarray, f_src: np.ndarray, f_tgt: np.ndarray) -> np.ndarray:
+    """将 S(f_src) 线性插值到 f_tgt (复数分离实虚部)。"""
+    if np.array_equal(f_src, f_tgt):
+        return S
+    nports = S.shape[1]
+    S_new = np.zeros((len(f_tgt), nports, nports), dtype=complex)
+    for i in range(nports):
+        for j in range(nports):
+            y = S[:, i, j]
+            real_part = np.interp(f_tgt, f_src, np.real(y))
+            imag_part = np.interp(f_tgt, f_src, np.imag(y))
+            S_new[:, i, j] = real_part + 1j * imag_part
+    return S_new
+
+
+def evaluate_dataset(model: ParametricVectorFitting,
+                     subset: List[ModelBasicDatasetUnit],
+                     network_loader=Capa.network) -> Dict[str, Any]:
+    """对一个子集评估拟合质量，输出每样本与整体统计."""
+    assert model.frequencies is not None
+    freqs = model.frequencies
+    results = []
+    mag_err_db_all = []
+    rms_all = []
+    for unit in subset:
+        net = network_loader(unit.result_dir, unit.id)
+        S_ref = _interp_s_to_freqs(net.s, net.f, freqs)  # (Nf, nports, nports)
+        S_pred = model.evaluate(unit.parameters["W"], unit.parameters["L"], freqs)
+        err = S_pred - S_ref
+        rms = float(np.sqrt(np.mean(np.abs(err)**2)))
+        # 幅度 dB 误差
+        mag_ref_db = 20*np.log10(np.clip(np.abs(S_ref), 1e-15, None))
+        mag_pred_db = 20*np.log10(np.clip(np.abs(S_pred), 1e-15, None))
+        mag_err_db = float(np.mean(np.abs(mag_pred_db - mag_ref_db)))
+        rms_all.append(rms)
+        mag_err_db_all.append(mag_err_db)
+        results.append({
+            'id': unit.id,
+            'W': unit.parameters['W'],
+            'L': unit.parameters['L'],
+            'rms': rms,
+            'mag_err_db': mag_err_db
+        })
+    summary = {
+        'count': len(subset),
+        'rms_mean': float(np.mean(rms_all)) if rms_all else None,
+        'rms_max': float(np.max(rms_all)) if rms_all else None,
+        'mag_err_db_mean': float(np.mean(mag_err_db_all)) if mag_err_db_all else None,
+        'mag_err_db_max': float(np.max(mag_err_db_all)) if mag_err_db_all else None,
+        'details': results
+    }
+    return summary
+
+
+# 简要使用示例 (非执行):
+if __name__ == "__main__":
+
+    capa = Capa()
+    capa.sweep()
+    print("sweep finished")
+    capa.export('capa_results.json')
+    capa.clear()
+    capa.load('capa_results.json')
+    dataset = capa.results
+
+    # 70% 训练 / 30% 测试
+    train_set, test_set = split_dataset(dataset, train_ratio=0.7, shuffle=True, seed=42)
+    print(f"Train: {len(train_set)}  Test: {len(test_set)}")
+
+    cfg = ParametricVFConfig(n_poles=10, param_total_degree=3, vf_iterations=2,
+                             max_freq_points=50)
+    pvf = ParametricVectorFitting(cfg).fit(train_set)
+
+    train_metrics = evaluate_dataset(pvf, train_set)
+    test_metrics = evaluate_dataset(pvf, test_set)
+
+    pvf.meta['train_eval'] = train_metrics
+    pvf.meta['test_eval'] = test_metrics
+
+    def _print_metrics(title: str, m: Dict[str, Any]):
+        print(f"[{title}] samples={m['count']}"
+              f"  RMS_mean={m['rms_mean']:.4e}  RMS_max={m['rms_max']:.4e}"
+              f"  |Δ|dB_mean={m['mag_err_db_mean']:.3f}dB  |Δ|dB_max={m['mag_err_db_max']:.3f}dB")
+
+    _print_metrics("TRAIN", train_metrics)
+    _print_metrics("TEST", test_metrics)
+
+    # 示例：导出一个测试点的拟合结果为 s2p
+    if test_set:
+        sample = test_set[0]
+        out_path = pvf.export_s2p(sample.parameters["W"], sample.parameters["L"], filepath='outputs/pvf_test_sample')
+        print("Exported:", out_path)
\ No newline at end of file
diff --git a/schemas/paramer.py b/schemas/paramer.py
new file mode 100644
index 0000000..be0fc37
--- /dev/null
+++ b/schemas/paramer.py
@@ -0,0 +1,50 @@
+from pydantic import BaseModel, Field
+from typing import List,Union,Literal,Optional
+
+class SimulationRequestUnit(BaseModel):
+    user_id:int = Field(default=0)
+    template_name:str = Field(default="em_interface_compound")
+    template_version:str = Field(default="")
+    cell_name:str = Field(default="capa")
+    parameters:dict = Field(default={"W":10,"L":10})
+    settings:dict = Field(default={})
+
+class UuidResponseUnit(BaseModel):
+    id:int
+    user_id:Optional[int]
+    template_name:str
+    template_version:str
+    cell_name:str
+    status:Literal["pending","running","completed","failed"]
+    parameters:dict
+    settings:dict
+    input_hash:str
+    storage_type: str
+    result_path:str
+    started_at:str
+    completed_at:str
+    result_json:Optional[dict]
+    error_message:Optional[str]
+    failure_count:Optional[int]
+    last_failed_at:Optional[str]
+    cpu_usage:Optional[float]
+    memory_usage:Optional[float]
+    disk_usage:Optional[float]
+    gpu_usage:Optional[float]
+    node_name:Optional[str]
+    jobs:Optional[List]
+    results:Optional[List]
+    created_at:str
+    updated_at:str
+
+class SimulationResponseUnit(BaseModel):
+    template_name:str
+    template_version:str
+    template_id:int
+    cell_name:str
+    cell_id:int
+    parameters:dict
+    settings:dict
+    input_hash:str
+    status:str
+    message:str
\ No newline at end of file
diff --git a/test/lazy_evaulation.py b/test/lazy_evaulation.py
new file mode 100644
index 0000000..446c5cc
--- /dev/null
+++ b/test/lazy_evaulation.py
@@ -0,0 +1,125 @@
+import numpy as np
+
+class PhiBasisIterator:
+    """
+    逐步生成有理正交 (类 Muntz-Laguerre) 基函数 φ_p(s) / (或复对产生两列) 的迭代器。
+
+    给定:
+        s: 标量或数组 (复频率采样点)  s = j*2*pi*f
+        poles: 极点序列 (允许包含复共轭对). 约定:
+            - 纯实极点按自身顺序出现: a = -alpha (alpha>0)
+            - 复极点以正虚部在前, 紧跟其共轭: a = -σ + jω,  a* = -σ - jω
+
+    迭代:
+        每次 __next__ 返回一个 list:
+            - 实极点 -> [φ_p(s)]
+            - 复成对 -> [φ_p^(1)(s), φ_p^(2)(s)]
+        使用时可把返回列表中函数 append 到总基函数数组中。
+
+    说明:
+        这里实现的公式与用户原始代码意图相同, 但修正了:
+            1) 原代码 sqrt(2*Re(a)) 在 Re(a)<0 (典型稳定极点) 下产生 NaN, 改为 alpha=-Re(a) >0.
+            2) 原来在 __next__ 中使用 yield (非法); 改为标准迭代协议返回 list。
+            3) 复极点的乘积与后续迭代用的累计乘积 product 分开维护。
+        若需严格匹配论文中“多变量正交化”可再加数值正交 (QR) 步骤。
+
+    注意:
+        本实现假设 poles 已排序; 若不确定, 可预处理把正虚部极点放在其共轭之前。
+    """
+    def __init__(self, s, poles):
+        self.s = np.asarray(s, dtype=complex)  # (Nf,) 或标量
+        self.poles = list(poles)
+        self.k = 0                # 当前处理到第 k 个极点(或复对的首元素)
+        self.N = len(self.poles)
+        # 累计乘积 Π_{已完成的块} ( (s - a_i*)/(s + a_i) )  (复对时使用 (s - a)(s - a*) / (s + a)(s + a*))
+        self.product = np.ones_like(self.s, dtype=complex)
+
+    def __iter__(self):
+        return self
+
+    def __next__(self):
+        if self.k >= self.N:
+            raise StopIteration
+
+        a = self.poles[self.k]
+
+        # 复对: 需要检查正虚部并且下一个是共轭
+        if np.iscomplex(a) and np.imag(a) > 0:
+            if self.k + 1 >= self.N or not np.isclose(self.poles[self.k + 1], np.conj(a)):
+                raise ValueError(f"极点序列中复极点 {a} 未紧跟其共轭, 请排序.")
+            a_conj = self.poles[self.k + 1]
+            sigma = -np.real(a)          # >0
+            alpha = sigma
+            # (s + a)(s + a*) = (s + a)(s + conj(a))
+            denom = (self.s + a) * (self.s + a_conj)
+            # |a| 用于生成两组分子 (参考原代码的构造方式)
+            r = np.abs(a)
+            scale = np.sqrt(2 * alpha)
+
+            numerator1 = scale * (self.s - r)
+            numerator2 = scale * (self.s + r)
+
+            phi1 = numerator1 / denom * self.product
+            phi2 = numerator2 / denom * self.product
+
+            # 更新累计乘积用于后续阶次：
+            # 对复对的“整体”传统一致写成 ((s - a)(s - a*) / (s + a)(s + a*))
+            self.product = self.product * ((self.s - a) * (self.s - a_conj)) / denom
+
+            self.k += 2
+            return [phi1, phi2]
+
+        else:
+            # 实极点 (允许传入 float 或实部为负的 complex(实数))
+            a_real = np.real(a)
+            # 稳定极点: a_real < 0, 令 alpha = -a_real > 0
+            if a_real >= 0:
+                raise ValueError(f"实极点需要在左半平面 (负实部), 得到 {a_real}")
+            alpha = -a_real
+            scale = np.sqrt(2 * alpha)
+            # Laguerre 风格: (s - alpha)/(s + alpha)
+            numerator = scale * (self.s - alpha)
+            denom = (self.s + alpha)
+            phi = numerator / denom * self.product
+            # 更新累计乘积
+            self.product = self.product * (self.s - alpha) / (self.s + alpha)
+            self.k += 1
+            return [phi]
+
+# ------------------ 辅助函数: 批量生成全部基函数 ------------------
+def generate_phi_basis(s, poles):
+    """
+    返回一个 list, 其中包含依次生成的所有基函数 (按 real → 1 函数, complex pair → 2 函数).
+    """
+    basis = []
+    it = PhiBasisIterator(s, poles)
+    for block in it:
+        basis.extend(block)
+    return basis
+
+# ------------------ 示例与自测 ------------------
+if __name__ == "__main__":
+    # 示例极点: 1 个实极点 (-1), 一个复对 (-2+0.5j, -2-0.5j), 再一个复对 (-3+1.2j, -3-1.2j)
+    poles = [-0.005+500j, -0.005-500j, -0.012+1200j, -0.012-1200j]
+    f = np.linspace(1e9, 1e11, 200)            # 频率 (Hz)
+    s = 1j * 2 * np.pi * f
+
+    basis_funcs = generate_phi_basis(s, poles)
+    print(f"生成基函数数量 = {len(basis_funcs)}")  # 实极点 1 →1, 两个复对 →2+2 共 5 个
+    # 简单数值检查 (避免 NaN/Inf)
+    for i, bf in enumerate(basis_funcs):
+        if not np.all(np.isfinite(bf)):
+            print(f"第 {i} 个基函数存在非有限值")
+        else:
+            # print(f"phi[{i}] max|.|={np.max(np.abs(bf)):.3e}, min|.|={np.min(np.abs(bf)):.3e}")
+            print(f"phi[{i}] = {bf}")
+
+    # 验证是否为正交基
+    for i, bf in enumerate(basis_funcs):
+        print(f"phi[{i}]*phi[{i}] = {np.vdot(bf, bf)}")  # 自身内积
+        for j in range(i+1, len(basis_funcs)):
+            bf2 = basis_funcs[j]
+            ip = np.vdot(bf, bf2)
+            print(f"phi[{i}] 与 phi[{j}] 内积 = {ip}")
+            if np.abs(ip) > 1e-6:
+                print(f"phi[{i}] 与 phi[{j}] 非正交, 内积={ip}")
\ No newline at end of file
diff --git a/utils.py b/utils.py
new file mode 100644
index 0000000..36dd88a
--- /dev/null
+++ b/utils.py
@@ -0,0 +1,55 @@
+import requests
+import time
+from schemas.paramer import SimulationRequestUnit, SimulationResponseUnit, UuidResponseUnit
+import skrf as rf
+from typing import Literal
+import matplotlib.pyplot as plt
+
+
+def send_get_request(url):
+    try:
+        response = requests.get(url)
+        response.raise_for_status()  # Raise an error for bad responses
+        return response.json()
+    except requests.exceptions.RequestException as e:
+        print(f"An error occurred: {e}")
+        return None
+
+def get_network(file_path: str) -> rf.Network:
+    network = rf.Network(file_path)
+    return network
+
+def get_rms_error(vf: rf.VectorFitting,parameter_type:Literal['s','y','z']):
+    rms_error = []
+    for i in range(vf.network.nports):
+        rms_error_row = []
+        for j in range(vf.network.nports):
+            rms_error = vf.get_rms_error(i, j, parameter_type)
+            rms_error_row.append(rms_error)
+        rms_error.append(rms_error_row)
+    return rms_error
+
+def show_rms_error(vf: rf.VectorFitting,parameter_type:Literal['s','y','z'],show_plot:bool=True,save_path:str|None=None):
+    freqs = vf.network.f
+    nports = vf.network.nports
+    fig, ax = plt.subplots(nports, nports)
+    fig.set_size_inches(6*nports, 4*nports)
+    for i in range(nports):
+        for j in range(nports):
+            vf.plot("mag",0,1,freqs,ax=ax[i][j],parameter=parameter_type)
+    fig.tight_layout()
+    if show_plot:
+        plt.show()
+    if save_path:
+        plt.savefig(save_path)
+
+def remove_simulation_with_high_rms_error(simulations:list[rf.VectorFitting],limit:float=0.015,parameter_type:Literal['s','y','z']='s'):
+    nports = simulations[0].network.nports
+    index_of_filtered_simulations = []
+    for res in simulations:
+        for i in range(nports):
+            for j in range(nports):
+                rms_error = res.get_rms_error(i, j, parameter_type)
+                if rms_error > limit:
+                    index_of_filtered_simulations.append(i*nports+j)
+                    break