54 lines
2.0 KiB
Python
54 lines
2.0 KiB
Python
import numpy as np
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def generate_laguerre_basis(poles:list|np.ndarray, s: np.ndarray):
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basis = np.zeros((len(poles)+1,len(s)),dtype=complex)
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product = np.ones(len(s),dtype=complex)
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basis[0] = np.ones(len(s),dtype=complex) # φ_0 = 1
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i = 0
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while i < len(poles):
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if np.real(poles[i]) >= 0:
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raise ValueError(f"极点必须在左半平面: {poles[i]}")
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# 复对首 (正虚部)
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if np.iscomplex(poles[i]) and np.imag(poles[i]) > 0:
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if i + 1 >= len(poles):
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raise ValueError("复极点缺少共轭")
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pc = poles[i + 1]
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if not np.isclose(pc, np.conj(poles[i])):
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raise ValueError("复极点未按 (p, p*) 顺序排列 (正虚部在前)")
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sigma = -np.real(poles[i]) # >0
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scale = np.sqrt(2 * sigma)
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r = np.abs(poles[i])
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denom = (s - poles[i]) * (s - pc)
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# 两个基函数
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phi_p = scale * (s - r) / denom * product
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phi_pc = scale * (s + r) / denom * product
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# product 先乘 (s + p^*)/(s - p)，再乘 (s + p)/(s - p^*)
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product = product * (s + pc) / (s - poles[i])
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product = product * (s + poles[i]) / (s - pc)
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basis[i + 1] = phi_p
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basis[i + 2] = phi_pc
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i += 2
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continue
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# 复对次 (负虚部) —— 应该被首元素处理，出现表示顺序错误
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if np.iscomplex(poles[i]) and np.imag(poles[i]) < 0:
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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。")
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# 实极点
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sigma = -np.real(poles[i])
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if sigma <= 0:
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raise ValueError("实极点实部应为负 (稳定)。")
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scale = np.sqrt(2 * sigma)
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phi = scale / (s - poles[i]) * product
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# 更新乘积
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product = product * (s + poles[i]) / (s - poles[i])
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i += 1
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basis[i + 1] = phi
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return basis
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