1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
|
from lmfit import Parameters, minimize
from lmfit.printfuncs import report_fit
from numpy import linspace, zeros, sin, exp, random, pi, sign
try:
import pylab
HASPYLAB = True
except ImportError:
HASPYLAB = False
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.4321)
p_true.add('shift', value=0.12345)
p_true.add('decay', value=0.01000)
def residual(pars, x, data=None):
amp = pars['amp'].value
per = pars['period'].value
shift = pars['shift'].value
decay = pars['decay'].value
if abs(shift) > pi/2:
shift = shift - sign(shift)*pi
model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
if data is None:
return model
return (model - data)
n = 1500
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
fit = residual(fit_params, x)
print '# N_func_evals, N_free = ', out.nfev, out.nfree
print '# chi-square, reduced chi-square = % .7g, % .7g' % (out.chisqr, out.redchi)
report_fit(fit_params, show_correl=True, modelpars=p_true)
print 'Raw (unordered, unscaled) Covariance Matrix:'
print out.covar
if HASPYLAB:
pylab.plot(x, data, 'ro')
pylab.plot(x, fit, 'b')
pylab.show()
|
