Using the SATLAS interface#
As a stepping stone between SATLAS and SATLAS2, an interface has been provided which can mostly be used as a drop-in replacement for code that uses the SATLAS syntax. Note that not all functionalities have been implemented in this fashion. For users that require these functionalities, we recommend migrating to SATLAS2.
import sys
import time
import matplotlib.gridspec as gridspec
import matplotlib.pyplot as plt
import numpy as np
sys.path.insert(0, '..\src')
import satlas2
import satlas as sat
def modifiedSqrt(input):
output = np.sqrt(input)
output[input <= 0] = 1e-3
return output
Fitting a single hyperfine spectrum#
The most common task, and the one this interface is meant for, is fitting a single hyperfine spectrum. A special class in SATLAS2 called HFSModel has been created as a replacement for the equivalent SATLAS HFSModel. Note that the normal hyperfine spectrum model in SATLAS2 is called HFS.
spin = 3.5
J = [0.5, 1.5]
A = [9600, 175]
B = [0, 315]
C = [0, 0]
FWHMG = 135
FWHML = 101
centroid = 480
bkg = [100]
scale = 90
x = np.arange(-17500, -14500, 40)
x = np.hstack([x, np.arange(20000, 23000, 40)])
rng = np.random.default_rng(0)
hfs = satlas2.HFSModel(I=spin,
J=J,
ABC=[A[0], A[1], B[0], B[1], C[0], C[1]],
centroid=centroid,
fwhm=[FWHMG, FWHML],
scale=scale,
background_params=bkg,
use_racah=True)
hfs.set_variation({'Cu': False})
The object called hfs can be used with the syntax of SATLAS. Generating Poisson-distributed data is done by simply calling the function with frequency values as an argument, and using the result for the NumPy Poisson random number generator.
y = satlas2.generateSpectrum(hfs, x, rng.poisson)
In order to demonstrate the difference in performance, the centroid is offset by 100 from the actual value and the fitting is done by both the interface and SATLAS.
hfs.params['centroid'].value = centroid - 100
# Normal SATLAS implementation
hfs1 = sat.HFSModel(spin,
J, [A[0], A[1], B[0], B[1], C[0], C[1]],
centroid - 100, [FWHMG, FWHML],
scale=scale,
background_params=bkg,
use_racah=True)
hfs1.set_variation({'Cu': False})
# Interface fitting
print('Fitting 1 dataset with chisquare (Pearson, satlas2)...')
start = time.time()
satlas2.chisquare_fit(hfs, x, y, modifiedSqrt(y))
stop = time.time()
print(hfs.display_chisquare_fit(show_correl=False))
dt1 = stop - start
# SATLAS fitting
print('Fitting 1 dataset with chisquare (Pearson, satlas)...')
start = time.time()
sat.chisquare_fit(hfs1, x, y, modifiedSqrt(y))
stop = time.time()
hfs1.display_chisquare_fit(show_correl=False, scaled=True)
dt2 = stop - start
print('SATLAS2: {:.3} s'.format(dt1))
print('SATLAS1: {:.3} s'.format(dt2))
Fitting 1 dataset with chisquare (Pearson, satlas2)...
define whether you want to see the correlations in display_chisquare_fit(...)
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 137
# data points = 150
# variables = 8
chi-square = 151.188938
reduced chi-square = 1.06471083
Akaike info crit = 17.1842512
Bayesian info crit = 41.2693335
[[Variables]]
Fit___HFModel__3_5___centroid: 482.548151 +/- 7.56664202 (1.57%) (init = 380)
Fit___HFModel__3_5___Al: 9604.53249 +/- 6.41301505 (0.07%) (init = 9600)
Fit___HFModel__3_5___Au: 176.460909 +/- 2.73509340 (1.55%) (init = 175)
Fit___HFModel__3_5___Bl: 0 (fixed)
Fit___HFModel__3_5___Bu: 348.564588 +/- 19.6945285 (5.65%) (init = 315)
Fit___HFModel__3_5___Cl: 0 (fixed)
Fit___HFModel__3_5___Cu: 0 (fixed)
Fit___HFModel__3_5___FWHMG: 142.382607 +/- 57.6647366 (40.50%) (init = 135)
Fit___HFModel__3_5___FWHML: 100.522879 +/- 63.5247619 (63.19%) (init = 101)
Fit___HFModel__3_5___scale: 89.2398271 +/- 7.15348105 (8.02%) (init = 90)
Fit___HFModel__3_5___Amp3to2: 0.4545455 (fixed)
Fit___HFModel__3_5___Amp3to3: 0.4772727 (fixed)
Fit___HFModel__3_5___Amp3to4: 0.3409091 (fixed)
Fit___HFModel__3_5___Amp4to3: 0.1590909 (fixed)
Fit___HFModel__3_5___Amp4to4: 0.4772727 (fixed)
Fit___HFModel__3_5___Amp4to5: 1 (fixed)
Fit___bkg___p0: 100.670729 +/- 1.59295191 (1.58%) (init = 100)
Fitting 1 dataset with chisquare (Pearson, satlas)...
Chisquare fitting in progress (151.18893761580117): 172it [00:00, 182.60it/s]
NDoF: 142, Chisquare: 151.18894, Reduced Chisquare: 1.0647108
Akaike Information Criterium: 17.18425, Bayesian Information Criterium: 41.269333
Errors scaled with reduced chisquare.
[[Variables]]
FWHMG: 142.398642 +/- 57.6603105 (40.49%) (init = 142.3868)
FWHML: 100.507633 +/- 63.5294155 (63.21%) (init = 100.5189)
TotalFWHM: 203.616069 +/- 21.3016922 (10.46%) == '0.5346*FWHML+(0.2166*FWHML**2+FWHMG**2)**0.5'
Scale: 89.2388856 +/- 7.15309388 (8.02%) (init = 89.23958)
Saturation: 0 (fixed)
Amp3__2: 0.4546399 (fixed)
Amp3__3: 0.4773649 (fixed)
Amp3__4: 0.3410048 (fixed)
Amp4__3: 0.1591578 (fixed)
Amp4__4: 0.4773975 (fixed)
Amp4__5: 1 (fixed)
Al: 9604.53225 +/- 6.41310262 (0.07%) (init = 9604.532)
Au: 176.461706 +/- 2.73513443 (1.55%) (init = 176.4611)
Bl: 0 (fixed)
Bu: 348.556409 +/- 19.6948333 (5.65%) (init = 348.5625)
Cl: 0 (fixed)
Cu: 0 (fixed)
Centroid: 482.545220 +/- 7.56678464 (1.57%) (init = 482.5474)
Background0: 100.670920 +/- 1.59296489 (1.58%) (init = 100.6708)
N: 0 (fixed)
SATLAS2: 0.043 s
SATLAS1: 0.967 s
Note that the results are functionally identical: the slight difference is due to a more modern implementation of the least squares fitting routine that is used under the hood by SATLAS2. The speedup by using SATLAS 2 is about a factor 20 for a single spectrum.
left_x = x[x<0]
right_x = x[x>0]
left_y = y[x<0]
right_y = y[x>0]
fig = plt.figure(constrained_layout=True, figsize=(14, 9))
gs = gridspec.GridSpec(nrows=2, ncols=2, figure=fig)
ax11 = fig.add_subplot(gs[0, 0])
ax11.label_outer()
ax12 = fig.add_subplot(gs[0, 1], sharey=ax11)
ax12.label_outer()
ax21 = fig.add_subplot(gs[1, 0], sharex=ax11)
ax21.label_outer()
ax22 = fig.add_subplot(gs[1, 1], sharex=ax12, sharey=ax21)
ax22.label_outer()
ax11.errorbar(left_x, left_y, modifiedSqrt(left_y), fmt='.', label='Artificial data')
ax11.plot(left_x, hfs(left_x), '-', label='Fit')
ax12.errorbar(right_x, right_y, modifiedSqrt(right_y), fmt='.', label='Artificial data')
ax12.plot(right_x, hfs(right_x), '-', label='Fit')
ax21.errorbar(left_x, left_y, modifiedSqrt(left_y), fmt='.', label='Artificial data')
ax21.plot(left_x, hfs1(left_x), '-', label='SATLAS fit')
ax22.errorbar(right_x, right_y, modifiedSqrt(right_y), fmt='.', label='Artificial data')
ax22.plot(right_x, hfs1(right_x), '-', label='SATLAS fit')
ax11.legend()
ax21.legend()
ax11.set_ylabel('SATLAS2')
ax21.set_ylabel('SATLAS')
plt.show()
Overlapping hyperfine spectra#
The other most common usecase for SATLAS was analysis of spectra with an isomer present, resulting in overlapping spectra. In the SATLAS terminology, this would result in a SumModel being used. In SATLAS2, a second HFS is simply added to the Source. However, the interface does provide the folllowing functionality:
J = [0.5, 1.5]
FWHMG = 135
FWHML = 101
spin1 = 4
A1 = [5300, 100]
B1 = [0, 230]
C1 = [0, 0]
centroid1 = 400
bkg1 = 60
scale1 = 90
spin2 = 7
A2 = [3300, 60]
B2 = [0, 270]
C2 = [0, 0]
centroid2 = -100
bkg2 = 60
scale2 = 160
x = np.arange(-13000, -9000, 40)
x = np.hstack([x, np.arange(11000, 14000, 40)])
rng = np.random.default_rng(0)
# Interface models
hfs1 = satlas2.HFSModel(I=spin1,
J=J,
ABC=[A1[0], A1[1], B1[0], B1[1], C1[0], C1[1]],
centroid=centroid1,
fwhm=[FWHMG, FWHML],
scale=scale1,
background_params=[bkg1],
use_racah=True)
hfs1.set_variation({'Cu': False})
hfs2 = satlas2.HFSModel(I=spin2,
J=J,
ABC=[A2[0], A2[1], B2[0], B2[1], C2[0], C2[1]],
centroid=centroid2,
fwhm=[FWHMG, FWHML],
scale=scale2,
background_params=[bkg2],
use_racah=True)
hfs2.set_variation({'Cu': False})
y = satlas2.generateSpectrum([hfs1, hfs2, satlas2.Polynomial([bkg1])], x, rng.poisson)
hfs1.params['centroid'].value = centroid1 - 100
hfs2.params['centroid'].value = centroid2 - 100
summodel = satlas2.SumModel([hfs1, hfs2], {
'values': [bkg1, bkg2],
'bounds': [0]
})
# SATLAS implementation
hfs3 = sat.HFSModel(spin1,
J, [A1[0], A1[1], B1[0], B1[1], C1[0], C1[1]],
centroid1-100, [FWHMG, FWHML],
scale=scale1,
background_params=bkg,
use_racah=True)
hfs4 = sat.HFSModel(spin2,
J, [A2[0], A2[1], B2[0], B2[1], C2[0], C2[1]],
centroid2-100, [FWHMG, FWHML],
scale=scale2,
background_params=[0],
use_racah=True)
hfs3.set_variation({'Cu': False})
hfs4.set_variation({'Background0': False, 'Cu': False})
summodel2 = hfs3 + hfs4
print('Fitting 1 dataset with chisquare (Pearson, satlas2)...')
start = time.time()
f = satlas2.chisquare_fit(summodel, x, y, modifiedSqrt(y))
stop = time.time()
print(summodel.display_chisquare_fit(show_correl=False))
dt1 = stop - start
start = time.time()
sat.chisquare_fit(summodel2, x, y, modifiedSqrt(y))
stop = time.time()
summodel2.display_chisquare_fit(show_correl=False, scaled=True)
dt2 = stop - start
print('SATLAS2: {:.3} s'.format(dt1))
print('SATLAS1: {:.3} s'.format(dt2))
Fitting 1 dataset with chisquare (Pearson, satlas2)...
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 423
# data points = 175
# variables = 16
chi-square = 177.052463
reduced chi-square = 1.11353750
Akaike info crit = 34.0405200
Bayesian info crit = 84.6770956
[[Variables]]
Fit___HFModel__4___centroid: 392.980617 +/- 13.2182180 (3.36%) (init = 300)
Fit___HFModel__4___Al: 5306.16636 +/- 9.74519323 (0.18%) (init = 5300)
Fit___HFModel__4___Au: 103.560669 +/- 4.03858459 (3.90%) (init = 100)
Fit___HFModel__4___Bl: 0 (fixed)
Fit___HFModel__4___Bu: 195.784015 +/- 32.9150928 (16.81%) (init = 230)
Fit___HFModel__4___Cl: 0 (fixed)
Fit___HFModel__4___Cu: 0 (fixed)
Fit___HFModel__4___FWHMG: 251.277769 +/- 25.0965330 (9.99%) (init = 135)
Fit___HFModel__4___FWHML: 0.01000055 +/- 4.50439705 (45041.49%) (init = 101)
Fit___HFModel__4___scale: 79.7727405 +/- 7.53870955 (9.45%) (init = 90)
Fit___HFModel__4___Amp7_2to5_2: 0.5 (fixed)
Fit___HFModel__4___Amp7_2to7_2: 0.4938272 (fixed)
Fit___HFModel__4___Amp7_2to9_2: 0.3395062 (fixed)
Fit___HFModel__4___Amp9_2to7_2: 0.1728395 (fixed)
Fit___HFModel__4___Amp9_2to9_2: 0.4938272 (fixed)
Fit___HFModel__4___Amp9_2to11_2: 1 (fixed)
Fit___HFModel__7___centroid: -104.843040 +/- 5.61216015 (5.35%) (init = -200)
Fit___HFModel__7___Al: 3299.38314 +/- 2.54164939 (0.08%) (init = 3300)
Fit___HFModel__7___Au: 60.0125639 +/- 0.99398820 (1.66%) (init = 60)
Fit___HFModel__7___Bl: 0 (fixed)
Fit___HFModel__7___Bu: 273.049192 +/- 15.5843734 (5.71%) (init = 270)
Fit___HFModel__7___Cl: 0 (fixed)
Fit___HFModel__7___Cu: 0 (fixed)
Fit___HFModel__7___FWHMG: 121.107402 +/- 39.0810172 (32.27%) (init = 135)
Fit___HFModel__7___FWHML: 112.746219 +/- 36.9166340 (32.74%) (init = 101)
Fit___HFModel__7___scale: 163.484079 +/- 9.34512379 (5.72%) (init = 160)
Fit___HFModel__7___Amp13_2to11_2: 0.6666667 (fixed)
Fit___HFModel__7___Amp13_2to13_2: 0.5530864 (fixed)
Fit___HFModel__7___Amp13_2to15_2: 0.3358025 (fixed)
Fit___HFModel__7___Amp15_2to13_2: 0.2246914 (fixed)
Fit___HFModel__7___Amp15_2to15_2: 0.5530864 (fixed)
Fit___HFModel__7___Amp15_2to17_2: 1 (fixed)
Fit___bkg___value1: 60.4476367 +/- 2.36128234 (3.91%) (init = 60)
Fit___bkg___value0: 61.4896354 +/- 2.12969392 (3.46%) (init = 60)
Chisquare fitting done: 421it [00:12, 32.65it/s]
NDoF: 160, Chisquare: 177.29488, Reduced Chisquare: 1.108093
Akaike Information Criterium: 32.27996, Bayesian Information Criterium: 79.751749
Errors scaled with reduced chisquare.
[[Variables]]
s0_FWHMG: 250.753540 +/- 26.0746636 (10.40%) (init = 250.7535)
s0_FWHML: 1.00000275 +/- 11.8677590 (1186.77%) (init = 1.000003)
s0_TotalFWHM: 251.288574 +/- 24.9165138 (9.92%) == '0.5346*s0_FWHML+(0.2166*s0_FWHML**2+s0_FWHMG**2)**0.5'
s0_Scale: 79.7123062 +/- 7.13677345 (8.95%) (init = 79.71231)
s0_Saturation: 0 (fixed)
s0_Amp7_2__5_2: 0.5000937 (fixed)
s0_Amp7_2__7_2: 0.4939217 (fixed)
s0_Amp7_2__9_2: 0.3396039 (fixed)
s0_Amp9_2__7_2: 0.172911 (fixed)
s0_Amp9_2__9_2: 0.4939521 (fixed)
s0_Amp9_2__11_2: 1 (fixed)
s0_Al: 5306.11719 +/- 9.76080435 (0.18%) (init = 5306.117)
s0_Au: 103.549437 +/- 4.12089719 (3.98%) (init = 103.5494)
s0_Bl: 0 (fixed)
s0_Bu: 196.011593 +/- 32.8509112 (16.76%) (init = 196.0116)
s0_Cl: 0 (fixed)
s0_Cu: 0 (fixed)
s0_Centroid: 392.909905 +/- 13.1577474 (3.35%) (init = 392.9099)
s0_Background0: 181.069305 +/- 1.91537125 (1.06%) (init = 181.0693)
s0_N: 0 (fixed)
s1_FWHMG: 121.817424 +/- 39.1318124 (32.12%) (init = 121.8174)
s1_FWHML: 112.056361 +/- 37.1055724 (33.11%) (init = 112.0564)
s1_TotalFWHM: 192.416653 +/- 15.7236790 (8.17%) == '0.5346*s1_FWHML+(0.2166*s1_FWHML**2+s1_FWHMG**2)**0.5'
s1_Scale: 163.317972 +/- 9.22593437 (5.65%) (init = 163.318)
s1_Saturation: 0 (fixed)
s1_Amp13_2__11_2: 0.666746 (fixed)
s1_Amp13_2__13_2: 0.5531882 (fixed)
s1_Amp13_2__15_2: 0.3359059 (fixed)
s1_Amp15_2__13_2: 0.2247785 (fixed)
s1_Amp15_2__15_2: 0.55321 (fixed)
s1_Amp15_2__17_2: 1 (fixed)
s1_Al: 3299.37436 +/- 2.48138492 (0.08%) (init = 3299.374)
s1_Au: 60.0050608 +/- 0.98060493 (1.63%) (init = 60.00506)
s1_Bl: 0 (fixed)
s1_Bu: 273.161795 +/- 15.4999419 (5.67%) (init = 273.1618)
s1_Cl: 0 (fixed)
s1_Cu: 0 (fixed)
s1_Centroid: -104.833860 +/- 5.57438226 (5.32%) (init = -104.8339)
s1_Background0: 0 (fixed)
s1_N: 0 (fixed)
SATLAS2: 0.226 s
SATLAS1: 12.9 s
The difference in coding implementation is a result of the interface automatically implementing a PiecewiseConstant background, where the background is a constant for different regions in x-space. Notice here that the speedup due using the SATLAS2 implementation has risen from a factor 20 for a single spectrum to almost a factor 60.
left_x = x[x<0]
right_x = x[x>0]
left_y = y[x<0]
right_y = y[x>0]
fig = plt.figure(constrained_layout=True, figsize=(14, 9))
gs = gridspec.GridSpec(nrows=2, ncols=2, figure=fig)
ax11 = fig.add_subplot(gs[0, 0])
ax11.label_outer()
ax12 = fig.add_subplot(gs[0, 1], sharey=ax11)
ax12.label_outer()
ax21 = fig.add_subplot(gs[1, 0], sharex=ax11)
ax21.label_outer()
ax22 = fig.add_subplot(gs[1, 1], sharex=ax12, sharey=ax21)
ax22.label_outer()
ax11.errorbar(left_x, left_y, modifiedSqrt(left_y), fmt='.', label='Artificial data')
ax11.plot(left_x, hfs1(left_x), '-', label='SATLAS2 fit model 1')
ax11.plot(left_x, hfs2(left_x), '-', label='SATLAS2 fit model 2')
ax11.plot(left_x, summodel(left_x), '-', label='Sum of models')
ax12.errorbar(right_x, right_y, modifiedSqrt(right_y), fmt='.', label='Artificial data')
ax12.plot(right_x, hfs1(right_x), '-', label='SATLAS2 fit model 1')
ax12.plot(right_x, hfs2(right_x), '-', label='SATLAS2 fit model 2')
ax12.plot(right_x, summodel(right_x), '-', label='Sum of models')
ax11.legend()
ax21.errorbar(left_x, left_y, modifiedSqrt(left_y), fmt='.', label='Artificial data')
ax21.plot(left_x, hfs3(left_x), '-', label='SATLAS fit model 1')
ax21.plot(left_x, hfs4(left_x), '-', label='SATLAS fit model 2')
ax21.plot(left_x, summodel2(left_x), '-', label='Sum of models')
ax22.errorbar(right_x, right_y, modifiedSqrt(right_y), fmt='.', label='Artificial data')
ax22.plot(right_x, hfs3(right_x), '-', label='SATLAS fit model 1')
ax22.plot(right_x, hfs4(right_x), '-', label='SATLAS fit model 2')
ax22.plot(right_x, summodel2(right_x), '-', label='Sum of models')
ax21.legend()
ax11.set_ylabel('SATLAS2')
ax21.set_ylabel('SATLAS')
plt.show()
Different background for multiplets#
To demonstrate the convenience of the PiecewiseConstant background, the same results are coded with SATLAS, where the use of LinkedModel is required. Note that here, the interface is not used.
J = [0.5, 1.5]
FWHMG = 135
FWHML = 101
spin1 = 4
A1 = [5300, 100]
B1 = [0, 230]
C1 = [0, 0]
centroid1 = 400
bkg1 = 90
scale1 = 90
x = np.arange(-13000, -9000, 40)
x = np.hstack([x, np.arange(11000, 14000, 40)])
hfs = satlas2.HFS(spin1,
J=J,
A=[A1[0], A1[1]],
B=[B1[0], B1[1]],
C=[C1[0], C1[1]],
df=centroid1,
fwhmg=FWHMG,
fwhml=FWHML,
scale=scale1,
racah=True
)
hfs.params['Cu'].vary = False
bkg = satlas2.PiecewiseConstant([bkg1, bkg2], [0])
y = satlas2.generateSpectrum([hfs1, bkg], x, rng.poisson)
s = satlas2.Source(x, y, yerr=modifiedSqrt, name='Artificial')
s.addModel(hfs)
s.addModel(bkg)
f = satlas2.Fitter()
f.addSource(s)
hfs2 = sat.HFSModel(spin1,
J, [A1[0], A1[1], B1[0], B1[1], C1[0], C1[1]],
centroid - 100, [FWHMG, FWHML],
scale=scale1,
background_params=[bkg1],
use_racah=True)
hfs3 = sat.HFSModel(spin1,
J, [A1[0], A1[1], B1[0], B1[1], C1[0], C1[1]],
centroid - 100, [FWHMG, FWHML],
scale=scale1,
background_params=[bkg1],
use_racah=True)
hfs2.set_variation({'Cu': False})
hfs3.set_variation({'Cu': False})
linkedmodel = sat.LinkedModel([hfs2, hfs3])
linkedmodel.shared = ['Al', 'Au', 'Bl', 'Bu', 'Centroid']
linked_x = [x[x<0], x[x>0]]
linked_y = [y[x<0], y[x>0]]
print('Fitting 1 dataset with chisquare (Pearson, satlas2)...')
start = time.time()
f.fit()
stop = time.time()
print(f.reportFit())
dt1 = stop - start
start = time.time()
sat.chisquare_spectroscopic_fit(linkedmodel, linked_x, linked_y, func=modifiedSqrt)
stop = time.time()
linkedmodel.display_chisquare_fit(show_correl=False, scaled=True)
dt2 = stop - start
print('SATLAS2: {:.3} s'.format(dt1))
print('SATLAS1: {:.3} s'.format(dt2))
Fitting 1 dataset with chisquare (Pearson, satlas2)...
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 202
# data points = 175
# variables = 9
chi-square = 162.334878
reduced chi-square = 0.97792095
Akaike info crit = 4.85319079
Bayesian info crit = 33.3362646
[[Variables]]
Artificial___HFS___centroid: 379.439738 +/- 11.8479412 (3.12%) (init = 400)
Artificial___HFS___Al: 5300.53685 +/- 8.60042067 (0.16%) (init = 5300)
Artificial___HFS___Au: 100.910641 +/- 3.43441833 (3.40%) (init = 100)
Artificial___HFS___Bl: 0 (fixed)
Artificial___HFS___Bu: 167.829114 +/- 27.5840684 (16.44%) (init = 230)
Artificial___HFS___Cl: 0 (fixed)
Artificial___HFS___Cu: 0 (fixed)
Artificial___HFS___FWHMG: 257.963959 +/- 23.7214758 (9.20%) (init = 135)
Artificial___HFS___FWHML: 0.01005831 +/- 46.0743167 (458072.02%) (init = 101)
Artificial___HFS___scale: 73.5969741 +/- 6.04333358 (8.21%) (init = 90)
Artificial___HFS___Amp7_2to5_2: 0.5 (fixed)
Artificial___HFS___Amp7_2to7_2: 0.4938272 (fixed)
Artificial___HFS___Amp7_2to9_2: 0.3395062 (fixed)
Artificial___HFS___Amp9_2to7_2: 0.1728395 (fixed)
Artificial___HFS___Amp9_2to9_2: 0.4938272 (fixed)
Artificial___HFS___Amp9_2to11_2: 1 (fixed)
Artificial___PiecewiseConstant___value1: 122.518511 +/- 1.44251185 (1.18%) (init = 60)
Artificial___PiecewiseConstant___value0: 151.305847 +/- 1.37967336 (0.91%) (init = 90)
Chisquare fitting done: 619it [00:19, 31.30it/s]
NDoF: 163, Chisquare: 158.72971, Reduced Chisquare: 0.97380192
Akaike Information Criterium: 6.9229505, Bayesian Information Criterium: 44.900382
Errors scaled with reduced chisquare.
[[Variables]]
s0_FWHMG: 287.317538 (init = 287.3175)
s0_FWHML: 1.00000004 (init = 1)
s0_TotalFWHM: 287.852515 == '0.5346*s0_FWHML+(0.2166*s0_FWHML**2+s0_FWHMG**2)**0.5'
s0_Scale: 72.0818067 (init = 72.08181)
s0_Saturation: 0 (fixed)
s0_Amp7_2__5_2: 0.5000937 (fixed)
s0_Amp7_2__7_2: 0.4939217 (fixed)
s0_Amp7_2__9_2: 0.3396039 (fixed)
s0_Amp9_2__7_2: 0.172911 (fixed)
s0_Amp9_2__9_2: 0.4939521 (fixed)
s0_Amp9_2__11_2: 1 (fixed)
s0_Al: 5300.79815 (init = 5300.798)
s0_Au: 101.129022 (init = 101.129)
s0_Bl: 0 (fixed)
s0_Bu: 171.971287 (init = 171.9713)
s0_Cl: 0 (fixed)
s0_Cu: 0 (fixed)
s0_Centroid: 377.508491 (init = 377.5085)
s0_Background0: 150.539789 (init = 150.5398)
s0_N: 0 (fixed)
s1_FWHMG: 208.133894 (init = 208.1339)
s1_FWHML: 1.00001971 (init = 1.00002)
s1_TotalFWHM: 208.669025 == '0.5346*s1_FWHML+(0.2166*s1_FWHML**2+s1_FWHMG**2)**0.5'
s1_Scale: 82.8509918 (init = 82.85099)
s1_Saturation: 0 (fixed)
s1_Amp7_2__5_2: 0.5000937 (fixed)
s1_Amp7_2__7_2: 0.4939217 (fixed)
s1_Amp7_2__9_2: 0.3396039 (fixed)
s1_Amp9_2__7_2: 0.172911 (fixed)
s1_Amp9_2__9_2: 0.4939521 (fixed)
s1_Amp9_2__11_2: 1 (fixed)
s1_Al: 5300.79815 == 's0_Al'
s1_Au: 101.129022 == 's0_Au'
s1_Bl: 0.00000000 == 's0_Bl'
s1_Bu: 171.971287 == 's0_Bu'
s1_Cl: 0 (fixed)
s1_Cu: 0 (fixed)
s1_Centroid: 377.508491 == 's0_Centroid'
s1_Background0: 123.248661 (init = 123.2487)
s1_N: 0 (fixed)
SATLAS2: 0.107 s
SATLAS1: 19.8 s
fig = plt.figure(constrained_layout=True, figsize=(14, 9))
gs = gridspec.GridSpec(nrows=2, ncols=2, figure=fig)
ax11 = fig.add_subplot(gs[0, 0])
ax11.label_outer()
ax12 = fig.add_subplot(gs[0, 1], sharey=ax11)
ax12.label_outer()
ax21 = fig.add_subplot(gs[1, 0], sharex=ax11)
ax21.label_outer()
ax22 = fig.add_subplot(gs[1, 1], sharex=ax12, sharey=ax21)
ax22.label_outer()
ax11.errorbar(linked_x[0], linked_y[0], modifiedSqrt(linked_y[0]), fmt='.', label='Artificial data')
ax11.plot(linked_x[0], s.evaluate(linked_x[0]), '-', label='Fit')
ax12.errorbar(linked_x[1], linked_y[1], modifiedSqrt(linked_y[1]), fmt='.', label='Artificial data')
ax12.plot(linked_x[1], s.evaluate(linked_x[1]), '-', label='SATLAS2 fit model 1')
ax11.legend()
ax21.errorbar(linked_x[0], linked_y[0], modifiedSqrt(linked_y[0]), fmt='.', label='Artificial data')
ax21.plot(linked_x[0], linkedmodel.models[0](linked_x[0]), '-', label='Fit')
ax22.errorbar(linked_x[1], linked_y[1], modifiedSqrt(linked_y[1]), fmt='.', label='Artificial data')
ax22.plot(linked_x[1], linkedmodel.models[1](linked_x[1]), '-', label='Fit')
ax21.legend()
ax11.set_ylabel('SATLAS2')
ax21.set_ylabel('SATLAS')
plt.show()
