55 lines
1.3 KiB
Python
55 lines
1.3 KiB
Python
import numpy as np
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def Jfunc1(k, l, t):
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"""
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Computes J1(k, l, t) = (exp(-lt) - exp(-kt)) / (k - l)
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Uses Taylor expansion when k ≈ l.
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k: scalar or array
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l: array
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t: scalar or array
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"""
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# 广播所有变量到相同 shape（自动支持 k 是标量、l 是向量）
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k, l, t_array = np.broadcast_arrays(k, l, t)
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delta = (k - l) * t_array
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Jout = np.zeros_like(delta)
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mask_far = np.abs(delta) > 1e-3
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mask_near = ~mask_far
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# 正常计算
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Jout[mask_far] = (
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np.exp(-l[mask_far] * t_array[mask_far]) -
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np.exp(-k[mask_far] * t_array[mask_far])
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) / (k[mask_far] - l[mask_far])
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# k ≈ l 的情况，使用二阶展开
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d = delta[mask_near]
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Jout[mask_near] = 0.5 * t_array[mask_near] * (
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np.exp(-k[mask_near] * t_array[mask_near]) +
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np.exp(-l[mask_near] * t_array[mask_near])
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) * (1 - d * d / 12)
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return Jout
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def Jfunc2(k, l, t):
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k, l, t_array = np.broadcast_arrays(k, l, t)
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delta = (k + l) * t_array
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Jout = np.zeros_like(k)
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mask_far = np.abs(delta) > 1e-3
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mask_near = ~mask_far
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Jout[mask_far] = (1 - np.exp(-delta[mask_far])) / (k[mask_far] + l[mask_far])
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d = delta[mask_near]
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Jout[mask_near] = t_array[mask_near] * (1 - 0.5 * d + d ** 2 / 6)
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return Jout
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def Jfunc3(k, l, t):
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return Jfunc2(k, l, t)
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