33 lines
1.4 KiB
Python
33 lines
1.4 KiB
Python
import numpy as np
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from dataclasses import dataclass
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from typing import List, Dict, Tuple
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def cond_row_inf(A, use_pinv=True):
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"""行条件数 κ∞(A) = ||A||∞ * ||A^{-1}||∞；矩形阵用广义逆。"""
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A = np.asarray(A)
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Ainv = np.linalg.pinv(A) if (use_pinv or A.shape[0] != A.shape[1]) else np.linalg.inv(A)
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return np.linalg.norm(A, ord=np.inf) * np.linalg.norm(Ainv, ord=np.inf)
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def cond_col_one(A, use_pinv=True):
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"""列条件数 κ1(A) = ||A||1 * ||A^{-1}||1；矩形阵用广义逆。"""
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A = np.asarray(A)
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Ainv = np.linalg.pinv(A) if (use_pinv or A.shape[0] != A.shape[1]) else np.linalg.inv(A)
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return np.linalg.norm(A, ord=1) * np.linalg.norm(Ainv, ord=1)
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def generate_starting_poles(n_pairs: int, beta_min: float, beta_max: float, alpha_scale: float = 0.01):
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"""
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仅生成复共轭对: p = -alpha + j beta, p*。
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n_pairs: 复对数量 (总极点数 = 2*n_pairs)
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beta_min,beta_max: 想要覆盖的虚部范围 (单位: rad/s)
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alpha_scale: alpha = alpha_scale * beta (文中 {α_p}=0.01{β_p})
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返回: list[complex] (正虚部先, 后跟共轭)
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"""
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betas = 2*np.pi*np.linspace(beta_min, beta_max, n_pairs)
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poles = []
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for b in betas:
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alpha = alpha_scale * b
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p = -alpha + 1j * b
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poles += [p, np.conj(p)]
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print(f"生成 {len(poles)} 个初始极点 (复对) {poles}]")
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return poles
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