init: 验证robust算法
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mayge
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core/robust.py
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191
core/robust.py
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from models.basic import ModelBasic
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from typing import List,Literal,Dict
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import numpy as np
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import random
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from pydantic import BaseModel
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from skrf import Network
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from models.basic import ModelBasicDatasetUnit
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class RobustParametricConfig(BaseModel):
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n_poles: int
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max_iter: int = 10
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parameter_type: Literal["s","y","z"]
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class RobustParametricModel:
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def __init__(self,model:ModelBasic,config:RobustParametricConfig):
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self.model = model
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self.config = config
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# 区分训练集和测试集
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def _train_test_split(self,train_ratio:float=0.8,random_state:int=42):
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random.seed(random_state)
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dataset = self.model.results
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random.shuffle(dataset)
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train_size = int(len(dataset)*train_ratio)
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self.train_set = dataset[:train_size]
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self.test_set = dataset[train_size:]
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return self.train_set, self.test_set
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def first_iteration_step(self, datasets: List[ModelBasicDatasetUnit],
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param_degree: int = 1):
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'''
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SK 迭代的第一步 (t=0) – 对应论文公式 (3).
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目标:
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最小化 sum_{样本 n, 频点 f} | N^{(0)}(s_f, g_n) - H(s_f, g_n) |^2
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在 t=0 阶段我们令 D^{(0)}(s,g)=1, 仅拟合分子:
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N^{(0)}(s,g) = Σ_{p∈P} Σ_{v∈V} c_{p,v} * φ_freq_p(s) * φ_param_v(g)
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因此是一个纯线性最小二乘:
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H ≈ Σ_{p,v} c_{p,v} F[:,p] ⊗ G[n,v]
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记:
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F: (Nf, P) 频率正交(或原始)基列
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G: (Ns, V) 参数多项式（含常数）基列
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设计矩阵 A 大小 (Ns*Nf, P*V), A[(n*Nf + f), (p*V + v)] = F[f,p] * G[n,v]
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输出:
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self.first_iter_coeffs[(i,j)] = C_{p,v} (P × V) 每个端口对一套系数
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self.freq_basis_F = F
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self.param_basis_G = G
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self.poles 初始极点 (供后续构造有理正交基 / SK 加权使用)
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参数:
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datasets: 训练用样本列表
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param_degree: 参数多项式最大总次数 (默认 1 → 常数 + 线性)
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注意:
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这里使用简单频率基 [1, 1/(s-a_k)]，未做 QR 正交化;
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后续 SK 迭代 / 正交化可在第二步再进行。
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'''
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assert len(datasets) > 0, "空数据集"
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# ---------------- 收集频率与端口信息 ----------------
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Ns = len(datasets)
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freqs = datasets[0].freqs # 频率需要对齐
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Nf = freqs.shape[0]
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nports = self.model.info.nports
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# ---------------- 构造初始极点 (对数分布 + 阻尼) ----------------
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def _init_poles(n_poles: int):
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fmin, fmax = freqs[0], freqs[-1]
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if n_poles <= 0:
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return np.array([], dtype=complex)
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# 避免 0 Hz，用第二个点或微小偏移
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start_f = max(fmin if fmin > 0 else freqs[1] if Nf > 1 else 1.0e-3, 1e-12)
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f_samples = np.logspace(np.log10(start_f), np.log10(fmax), n_poles)
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sigma = 0.02 * 2 * np.pi * fmax # 固定阻尼，可放入 config
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return -sigma + 1j * 2 * np.pi * f_samples
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self.poles = _init_poles(self.config.n_poles)
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s_vec = 1j * 2 * np.pi * freqs # (Nf,)
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# ---------------- 频率基 F ----------------
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# 列0: 常数 1, 后续列: 1/(s - a_k)
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P = 1 + len(self.poles)
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F = np.zeros((Nf, P), dtype=complex)
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F[:, 0] = 1.0
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for k, a in enumerate(self.poles, start=1):
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F[:, k] = 1.0 / (s_vec - a)
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self.freq_basis_F = F # (Nf, P)
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# ---------------- 参数基 G ----------------
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# 取出参数向量 g = [param1, param2, ...]
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# 假设 datasets[i].parameters 为 dict
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param_keys = list(datasets[0].parameters.keys())
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d = len(param_keys)
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# 构造参数矩阵 (Ns,d)
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Pmat = np.zeros((Ns, d), dtype=float)
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for i, unit in enumerate(datasets):
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for j, k in enumerate(param_keys):
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Pmat[i, j] = float(unit.parameters[k])
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# 标准化
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mean = Pmat.mean(axis=0)
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std = Pmat.std(axis=0) + 1e-15
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Xn = (Pmat - mean) / std
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# 生成多项式指数 (总次数 <= param_degree)
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def _gen_param_exps(dim, D):
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exps = []
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def rec(cur, idx, rem):
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if idx == dim:
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exps.append(tuple(cur)); return
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for t in range(rem + 1):
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cur.append(t); rec(cur, idx + 1, rem - t); cur.pop()
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rec([], 0, D)
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return exps
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exps = _gen_param_exps(d, param_degree) # V_exps
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V = len(exps)
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G = np.zeros((Ns, V), dtype=float)
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for vidx, e in enumerate(exps):
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val = np.ones(Ns)
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for j, p in enumerate(e):
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if p:
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val *= Xn[:, j] ** p
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G[:, vidx] = val
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self.param_basis_G = G # (Ns, V)
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self.param_basis_meta = {
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"keys": param_keys,
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"mean": mean.tolist(),
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"std": std.tolist(),
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"exponents": exps,
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"degree": param_degree
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}
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# ---------------- 构造设计矩阵 A (Kronecker) ----------------
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# A shape: (Ns*Nf, P*V)
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# 利用广播：A_block[n,f,p,v] = F[f,p] * G[n,v]
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A4 = np.einsum('fp,nv->nfpv', F, G) # (Ns, Nf, P, V)
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A = A4.reshape(Ns * Nf, P * V)
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# ---------------- 采集目标 H 数据 ----------------
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# 对每个端口对 (i,j) 分别解一个向量 c_{p,v}
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# 选择参数类型
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param_type = self.config.parameter_type.lower()
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valid_types = {"s", "y", "z"}
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if param_type not in valid_types:
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raise ValueError(f"parameter_type 必须在 {valid_types}")
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# 预先载入全部 Network (避免重复 IO)
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# H_data[(i,j)] -> (Ns,Nf) 复数
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H_data = {}
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for i_port in range(nports):
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for j_port in range(nports):
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H_mat = np.zeros((Ns, Nf), dtype=complex)
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for n, unit in enumerate(datasets):
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net: Network = unit.network
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if param_type == "s":
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sij = net.s[:, i_port, j_port]
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elif param_type == "y":
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sij = net.y[:, i_port, j_port]
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else:
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sij = net.z[:, i_port, j_port]
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# 插值或对齐假设已完成
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H_mat[n, :] = sij
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H_data[(i_port, j_port)] = H_mat
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# ---------------- 最小二乘求系数 ----------------
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self.first_iter_coeffs = {}
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# 可选: 预计算 A^+ (伪逆) 如果数据不巨大
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# pinv = np.linalg.pinv(A)
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for key, Hmat in H_data.items():
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b = Hmat.reshape(Ns * Nf) # (Ns*Nf,)
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# 解 x (长度 P*V)
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x, *_ = np.linalg.lstsq(A, b, rcond=None)
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C = x.reshape(P, V)
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self.first_iter_coeffs[key] = C
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# ---------------- 存储便于后续 SK 迭代使用 ----------------
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self.meta_first_iter = {
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"A_shape": A.shape,
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"num_samples": Ns,
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"num_freqs": Nf,
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"freq_basis_dim": P,
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"param_basis_dim": V
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}
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if getattr(self.config, "verbose", True):
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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}")
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return self.first_iter_coeffs
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