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#!/usr/bin/env python
"""
Bevington & Robinson's model of dual exponential decay
References::
[5] Bevington & Robinson (1992).
Data Reduction and Error Analysis for the Physical Sciences,
Second Edition, McGraw-Hill, Inc., New York.
"""
import numpy as np
from numpy import exp, inf, sqrt
def dual_exponential(t,a):
"""
Computes dual exponential decay.
y = a1 + a2 exp(-t/a3) + a4 exp(-t/a5)
"""
a1,a2,a3,a4,a5 = a
t = np.asarray(t)
return a1 + a2*exp(-t/a4) + a3*exp(-t/a5)
# data from Chapter 8 of [5].
data = np.array([[15, 775], [30, 479], [45, 380], [60, 302],
[75, 185], [90, 157], [105,137], [120, 119], [135, 110],
[150, 89], [165, 74], [180, 61], [195, 66], [210, 68],
[225, 48], [240, 54], [255, 51], [270, 46], [285, 55],
[300, 29], [315, 28], [330, 37], [345, 49], [360, 26],
[375, 35], [390, 29], [405, 31], [420, 24], [435, 25],
[450, 35], [465, 24], [480, 30], [495, 26], [510, 28],
[525, 21], [540, 18], [555, 20], [570, 27], [585, 17],
[600, 17], [615, 14], [630, 17], [645, 24], [660, 11],
[675, 22], [690, 17], [705, 12], [720, 10], [735, 13],
[750, 16], [765, 9], [780, 9], [795, 14], [810, 21],
[825, 17], [840, 13], [855, 12], [870, 18], [885, 10]])
x = data[:,0]
y = data[:,1]
dy = sqrt(data[:,1])
Po = [1,1,1,1,1]
Plo = [-inf,0,0,0,0]
Phi = [inf,inf,inf,inf,inf]
from .model import Fitness
decay = Fitness(f=dual_exponential, data=(x,y,dy),
limits=(Plo,Phi), start=Po)
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