Note
Go to the end to download the full example code
Fitting 1D dataset¶
In this example, we find the least square solution of a simple linear equation.
# sphinx_gallery_thumbnail_number = 2
import os
import spectrochempy as scp
Let’s take an IR spectrum
nd = scp.NDDataset.read_omnic(os.path.join("irdata", "nh4y-activation.spg"))
where we select only region (OH region)
<_Axes: xlabel='wavenumbers $\\mathrm{/\\ \\mathrm{cm}^{-1}}$', ylabel='absorbance $\\mathrm{/\\ \\mathrm{a.u.}}$'>
Perform a Fit Fit parameters are defined in a script (a single text as below)
script = """
#-----------------------------------------------------------
# syntax for parameters definition:
# name: value, low_bound, high_bound
# * for fixed parameters
# $ for variable parameters
# > for reference to a parameter in the COMMON block
# (> is forbidden in the COMMON block)
# common block parameters should not have a _ in their names
#-----------------------------------------------------------
#
COMMON:
# common parameters ex.
# $ gwidth: 1.0, 0.0, none
$ gratio: 0.1, 0.0, 1.0
MODEL: LINE_1
shape: asymmetricvoigtmodel
* ampl: 1.0, 0.0, none
$ pos: 3620, 3400.0, 3700.0
$ ratio: 0.0147, 0.0, 1.0
$ asym: 0.1, 0, 1
$ width: 200, 0, 1000
MODEL: LINE_2
shape: asymmetricvoigtmodel
$ ampl: 0.2, 0.0, none
$ pos: 3520, 3400.0, 3700.0
> ratio: gratio
$ asym: 0.1, 0, 1
$ width: 200, 0, 1000
"""
create a fit object
[1.0, 3620, 200, 0.0147, 0.1]
[200, 3620, 0.1]
[0.2, 3520, 200, 0.1, 0.1]
[200, 3520, 0.1]
Show plot and the starting model before the fit (of course it is advisable to be as close as possible of a good expectation
f1.dry_run()
ndOH.plot(plot_model=True)
f1.run(maxiter=1000)
[1.0, 3620.0, 200.0, 0.0147, 0.1]
[200.0, 3620.0, 0.1]
[0.2, 3520.0, 200.0, 0.1, 0.1]
[200.0, 3520.0, 0.1]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.21864679050166136, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.08652541588659518]
[200.0, 3620.0, 0.08652541588659518]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.08652541588659518]
[200.0, 3520.0, 0.08652541588659518]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.08652541588659518, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3623.1996213932966, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3623.1996213932966, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3518.521872937403, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3518.521872937403, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.007785399876451715, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 187.28747002333645, 0.01469999999999999, 0.09999999999999998]
[187.28747002333645, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 200.0, 0.09999999999999998, 0.09999999999999998]
[200.0, 3520.0, 0.09999999999999998]
[1.0, 3620.0, 200.0, 0.01469999999999999, 0.09999999999999998]
[200.0, 3620.0, 0.09999999999999998]
[0.19999999999999996, 3520.0, 187.28747002333645, 0.09999999999999998, 0.09999999999999998]
[187.28747002333645, 3520.0, 0.09999999999999998]
[1.0, 3620.7146585942987, 213.0230734426059, 0.012977439938251789, 0.09693030195702318]
[213.0230734426059, 3620.7146585942987, 0.09693030195702318]
[0.20408973866794144, 3519.6712592499066, 197.14768780924246, 0.09693030195702318, 0.09693030195702318]
[197.14768780924246, 3519.6712592499066, 0.09693030195702318]
[1.0, 3621.071217458728, 226.34320958327382, 0.012155883490435726, 0.0954114784431434]
[226.34320958327382, 3621.071217458728, 0.0954114784431434]
[0.20614629663606254, 3519.506945701611, 195.72732858914128, 0.0954114784431434, 0.0954114784431434]
[195.72732858914128, 3519.506945701611, 0.0954114784431434]
[1.0, 3617.000565547741, 205.75048799279554, 0.012426788654272547, 0.0959165618756711]
[205.75048799279554, 3617.000565547741, 0.0959165618756711]
[0.20545991541890563, 3519.5617126546763, 196.20035046858604, 0.0959165618756711, 0.0959165618756711]
[196.20035046858604, 3519.5617126546763, 0.0959165618756711]
[1.0, 3619.57553598697, 207.03658712747026, 0.011947218326675668, 0.09501946052825871]
[207.03658712747026, 3619.57553598697, 0.09501946052825871]
[0.2066807432915252, 3519.464352113427, 195.35972137725187, 0.112278083703794, 0.09501946052825871]
[195.35972137725187, 3519.464352113427, 0.09501946052825871]
[1.0, 3619.4811139367785, 208.6125023844247, 0.011373741066394327, 0.09392812976688869]
[208.6125023844247, 3619.4811139367785, 0.09392812976688869]
[0.20817655137953928, 3521.154474935219, 194.3341429819358, 0.10071345244745661, 0.09392812976688858]
[194.3341429819358, 3521.154474935219, 0.09392812976688858]
[1.0, 3619.3656615937475, 210.54458798345343, 0.010691765089312466, 0.09260195997558063]
[210.54458798345343, 3619.3656615937475, 0.09260195997558063]
[0.21001024551985092, 3519.930240842803, 193.08344201534533, 0.10087230328555263, 0.10967370866311155]
[193.08344201534533, 3519.930240842803, 0.10967370866311155]
[1.0, 3619.224482165677, 212.91487958890053, 0.009886572883812061, 0.09099259469604759]
[212.91487958890053, 3619.224482165677, 0.09099259469604759]
[0.21225958208602536, 3519.9147397274032, 191.5589831609839, 0.10106660521231492, 0.09768413099356016]
[191.5589831609839, 3519.9147397274032, 0.09768413099356016]
[1.0, 3619.0518236753187, 215.82501862472748, 0.008944845464245454, 0.10583326202586191]
[215.82501862472748, 3619.0518236753187, 0.10583326202586191]
[0.2150208845476087, 3519.895794374307, 189.70202476822496, 0.1013043106559317, 0.09717277837357369]
[189.70202476822496, 3519.895794374307, 0.09717277837357369]
[1.0, 3618.5764147059435, 223.90114135640437, 0.006596248694038909, 0.11612783215731126]
[223.90114135640437, 3618.5764147059435, 0.11612783215731126]
[0.2226824611150351, 3519.8436972342847, 184.63127198378348, 0.10195927740105781, 0.09577273950813414]
[184.63127198378348, 3519.8436972342847, 0.09577273950813414]
[1.0, 3618.734981603222, 221.1972819043118, 0.01587865910748021, 0.09536486716631781]
[221.1972819043118, 3618.734981603222, 0.09536486716631781]
[0.2201175931508097, 3519.8610625267697, 186.3156425814031, 0.10174074720298676, 0.0962384106792869]
[186.3156425814031, 3519.8610625267697, 0.0962384106792869]
[1.0, 3618.4530178638415, 226.01221466254208, 0.008851391171228906, 0.09434819412349216]
[226.01221466254208, 3618.4530178638415, 0.09434819412349216]
[0.20173934534875482, 3519.830191186859, 183.3252989453832, 0.1021293890012891, 0.09541124903355208]
[183.3252989453832, 3519.830191186859, 0.09541124903355208]
[1.0, 3618.107980313538, 231.94675657624663, 0.007750274277777303, 0.09311222691875681]
[231.94675657624663, 3618.107980313538, 0.09311222691875681]
[0.22084525778429454, 3519.792461357851, 195.03795433280385, 0.10260528707115929, 0.0944046131797524]
[195.03795433280385, 3519.792461357851, 0.0944046131797524]
[1.0, 3621.3371625790255, 231.85606359598177, 0.008577841405057351, 0.09651255623097482]
[231.85606359598177, 3621.3371625790255, 0.09651255623097482]
[0.2186766348352409, 3520.2822085900843, 185.8921741504893, 0.1083517209646912, 0.09811865979955825]
[185.8921741504893, 3520.2822085900843, 0.09811865979955825]
[1.0, 3623.4773457187666, 245.31663085854032, 0.006917963372155278, 0.09681117163477526]
[245.31663085854032, 3623.4773457187666, 0.09681117163477526]
[0.22539898637109435, 3520.642725527849, 180.81864361512484, 0.11481849194680133, 0.09922805868684498]
[180.81864361512484, 3520.642725527849, 0.09922805868684498]
[1.0, 3619.6551285024107, 239.142176955556, 0.007918070253923548, 0.09781721151308737]
[239.142176955556, 3619.6551285024107, 0.09781721151308737]
[0.2216148681256367, 3520.6417062419137, 183.5049724931318, 0.09277317290450282, 0.09997409469179891]
[183.5049724931318, 3520.6417062419137, 0.09997409469179891]
[1.0, 3619.7881250756336, 244.45151207851455, 0.007693987549785952, 0.09980662467186951]
[244.45151207851455, 3619.7881250756336, 0.09980662467186951]
[0.2231044555423689, 3518.8391519373804, 182.12937886855502, 0.1021222228009151, 0.1024691970209492]
[182.12937886855502, 3518.8391519373804, 0.1024691970209492]
[1.0, 3619.997127468938, 250.16281953587915, 0.0076526355488465425, 0.10282124015149419]
[250.16281953587915, 3619.997127468938, 0.10282124015149419]
[0.22416930100713728, 3519.8188761193605, 180.94555939733104, 0.10224099471683112, 0.0857519530199341]
[180.94555939733104, 3519.8188761193605, 0.0857519530199341]
[1.0, 3620.3091591167454, 256.17868532511653, 0.007884880064608635, 0.10725545006054332]
[256.17868532511653, 3620.3091591167454, 0.10725545006054332]
[0.22454281695909994, 3519.8130734190568, 180.10291481410135, 0.10230726455512484, 0.0943820827182244]
[180.10291481410135, 3519.8130734190568, 0.0943820827182244]
[1.0, 3618.2859267945623, 248.8209299691939, 0.005354420770374124, 0.105259877268014]
[248.8209299691939, 3618.2859267945623, 0.105259877268014]
[0.23505940604023645, 3520.2891264989294, 172.69405871530597, 0.10973708090817968, 0.0964133107513015]
[172.69405871530597, 3520.2891264989294, 0.0964133107513015]
[1.0, 3620.5273091578692, 260.5095967574179, 0.0020751590739841452, 0.10756649923862766]
[260.5095967574179, 3620.5273091578692, 0.10756649923862766]
[0.22403095245060767, 3520.0299114758964, 178.80438152992463, 0.10495307926272057, 0.09562444198444447]
[178.80438152992463, 3520.0299114758964, 0.09562444198444447]
[1.0, 3621.68150033527, 255.7216386527544, 0.005510949624695893, 0.11333595866858798]
[255.7216386527544, 3621.68150033527, 0.11333595866858798]
[0.2240087924909444, 3520.151317673854, 166.91009276196772, 0.10460280898234087, 0.09774308857865416]
[166.91009276196772, 3520.151317673854, 0.09774308857865416]
[1.0, 3622.053602151134, 268.72705824336674, 0.004065771472017532, 0.11639848695488891]
[268.72705824336674, 3622.053602151134, 0.11639848695488891]
[0.2490665061315771, 3520.1849481252757, 174.55129288858046, 0.10563808170879974, 0.09724467134394832]
[174.55129288858046, 3520.1849481252757, 0.09724467134394832]
[1.0, 3621.1583390114624, 257.8189060787114, 0.005090770512758747, 0.1106953999865743]
[257.8189060787114, 3621.1583390114624, 0.1106953999865743]
[0.23689517785043446, 3520.0962425242383, 176.72898389424464, 0.10475600073380426, 0.09678485490748523]
[176.72898389424464, 3520.0962425242383, 0.09678485490748523]
[1.0, 3622.5002272325087, 278.84516997057847, 0.005543224735710062, 0.09348386471820364]
[278.84516997057847, 3622.5002272325087, 0.09348386471820364]
[0.23037123036752405, 3520.227574699243, 171.54960690809645, 0.10643967864637527, 0.09710636622375951]
[171.54960690809645, 3520.227574699243, 0.09710636622375951]
[1.0, 3619.563152126833, 237.2547276653728, 0.006324466919487737, 0.1102646628680427]
[237.2547276653728, 3619.563152126833, 0.1102646628680427]
[0.2245956795335453, 3519.9396474169807, 181.32567732349992, 0.1030713891191945, 0.09610537375303424]
[181.32567732349992, 3519.9396474169807, 0.09610537375303424]
[1.0, 3620.350923418188, 236.2597552969495, 0.013818279264308897, 0.1021238719127689]
[236.2597552969495, 3620.350923418188, 0.1021238719127689]
[0.22913532409728687, 3520.0212494259013, 177.84087292880434, 0.10301031944439248, 0.09736327537519496]
[177.84087292880434, 3520.0212494259013, 0.09736327537519496]
[1.0, 3621.3744901433693, 256.88530827641455, 0.006494285011332479, 0.11306386130341317]
[256.88530827641455, 3621.3744901433693, 0.11306386130341317]
[0.23327117152977195, 3519.272292176999, 171.9618121407883, 0.1182084285982678, 0.09250089781084919]
[171.9618121407883, 3519.272292176999, 0.09250089781084919]
[1.0, 3619.920889674147, 238.02970922203858, 0.010051206509137434, 0.10056226613104385]
[238.02970922203858, 3619.920889674147, 0.10056226613104385]
[0.2172956380225477, 3519.6340198685252, 177.59801322522011, 0.10848473411268272, 0.09467252793221115]
[177.59801322522011, 3519.6340198685252, 0.09467252793221115]
[1.0, 3620.6853255925225, 235.64964121230497, 0.007288822483496715, 0.1024238679105251]
[235.64964121230497, 3620.6853255925225, 0.1024238679105251]
[0.2278719982113968, 3519.877318860038, 173.69205205953082, 0.11240547191565414, 0.09714390627250669]
[173.69205205953082, 3519.877318860038, 0.09714390627250669]
[1.0, 3620.8731950585216, 225.60759059335876, 0.006999513877559926, 0.10004509198703432]
[225.60759059335876, 3620.8731950585216, 0.10004509198703432]
[0.22954330155232427, 3519.9094437407457, 170.5210498560718, 0.11760999586381693, 0.09853814132641242]
[170.5210498560718, 3519.9094437407457, 0.09853814132641242]
[1.0, 3619.5049325453097, 228.10754085563488, 0.008885646738316766, 0.09411034948678382]
[228.10754085563488, 3619.5049325453097, 0.09411034948678382]
[0.21840752104369288, 3520.560323355309, 181.53704823627842, 0.09674480086927706, 0.10043444507870802]
[181.53704823627842, 3520.560323355309, 0.10043444507870802]
[1.0, 3620.9084197953316, 249.58290943627205, 0.007057309964648262, 0.10818194383204877]
[249.58290943627205, 3620.9084197953316, 0.10818194383204877]
[0.22952173694929545, 3519.594082523425, 174.33647467298613, 0.11266610126407584, 0.09445690839894838]
[174.33647467298613, 3519.594082523425, 0.09445690839894838]
[1.0, 3621.3411791212884, 241.38746736721177, 0.0074504042913913215, 0.10893190092987842]
[241.38746736721177, 3621.3411791212884, 0.10893190092987842]
[0.2299291154081975, 3521.1626984078625, 169.6807706567627, 0.11487089922979471, 0.08884955684421514]
[169.6807706567627, 3521.1626984078625, 0.08884955684421514]
[1.0, 3622.1140364755183, 239.8603859844098, 0.007330070964505497, 0.11362574766838696]
[239.8603859844098, 3622.1140364755183, 0.11362574766838696]
[0.23336952608233474, 3522.3272109434706, 163.588094145059, 0.12148945910159531, 0.08236891940137475]
[163.588094145059, 3522.3272109434706, 0.08236891940137475]
[1.0, 3621.6031381715593, 233.48970865009377, 0.0074196968790293805, 0.10822878914417827]
[233.48970865009377, 3621.6031381715593, 0.10822878914417827]
[0.2309025009472776, 3520.7380984378797, 167.00676780063932, 0.11911016381585787, 0.10498911254893345]
[167.00676780063932, 3520.7380984378797, 0.10498911254893345]
[1.0, 3622.483777551769, 245.4796133859054, 0.009130464271417449, 0.10041118058304982]
[245.4796133859054, 3622.483777551769, 0.10041118058304982]
[0.23188097919779516, 3520.7947170666193, 163.52336869970762, 0.12191414938794476, 0.09613157904022657]
[163.52336869970762, 3520.7947170666193, 0.09613157904022657]
[1.0, 3624.657570781798, 233.2390913081318, 0.011418506660561434, 0.10422778353549916]
[233.2390913081318, 3624.657570781798, 0.10422778353549916]
[0.22077751146074598, 3520.5573430776944, 169.9215279966445, 0.1176409572759709, 0.09576157731333657]
[169.9215279966445, 3520.5573430776944, 0.09576157731333657]
[1.0, 3624.1012073824136, 242.88027847152787, 0.006603520382437222, 0.10983804858970392]
[242.88027847152787, 3624.1012073824136, 0.10983804858970392]
[0.2394410945534584, 3521.4188004119164, 163.43526486924958, 0.12102642393066765, 0.09775597119229668]
[163.43526486924958, 3521.4188004119164, 0.09775597119229668]
[1.0, 3624.504678249081, 246.15033568869114, 0.0031157257019644446, 0.10996170955332613]
[246.15033568869114, 3624.504678249081, 0.10996170955332613]
[0.22967598935801803, 3521.34159533441, 160.06731720437395, 0.13115139741261406, 0.09514662036168509]
[160.06731720437395, 3521.34159533441, 0.09514662036168509]
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[1.0, 3623.054022876188, 38.30325413488678, 0.12290410183922562, 0.9140559272583177]
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[1.2600246882690893, 3536.647331075932, 78.44132888501527, 0.4422401727699491, 0.927634832297458]
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[1.0, 3622.9190329192083, 39.763947267867636, 0.1495973329518056, 0.912762456188236]
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[1.0, 3622.9563091185532, 39.63181587156522, 0.15101470089992952, 0.9268824086866234]
[39.63181587156522, 3622.9563091185532, 0.9268824086866234]
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[1.0, 3623.025803648659, 40.24453497684149, 0.1749181409641412, 0.9305869922179781]
[40.24453497684149, 3623.025803648659, 0.9305869922179781]
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[39.31774576649699, 3622.953603615015, 0.9208744262211894]
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[77.43387927491186, 3536.482014255213, 0.9338981640037461]
[1.0, 3622.87789426777, 40.1177849968643, 0.15414592176318132, 0.9233605556941223]
[40.1177849968643, 3622.87789426777, 0.9233605556941223]
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[1.0, 3622.7725030276315, 41.09373343240874, 0.17354199855551966, 0.9304853008119449]
[41.09373343240874, 3622.7725030276315, 0.9304853008119449]
[1.2092866659248744, 3536.6132712235717, 77.53943361549092, 0.4533157372744936, 0.9388837654699786]
[77.53943361549092, 3536.6132712235717, 0.9388837654699786]
[1.0, 3623.0236777411887, 40.18244855576697, 0.171323717086863, 0.9352189776832192]
[40.18244855576697, 3623.0236777411887, 0.9352189776832192]
[1.2312586694016803, 3536.4941404032224, 78.15742301737033, 0.45837617286933374, 0.9311161924479607]
[78.15742301737033, 3536.4941404032224, 0.9311161924479607]
[1.0, 3622.910610106765, 40.69808395417823, 0.18569498009390978, 0.9390718512786342]
[40.69808395417823, 3622.910610106765, 0.9390718512786342]
[1.227451752221687, 3536.539065274206, 78.42978777851556, 0.4700086382441434, 0.9323286742401666]
[78.42978777851556, 3536.539065274206, 0.9323286742401666]
[1.0, 3622.8650431772135, 41.32461485190575, 0.18795054930652166, 0.9349963799239585]
[41.32461485190575, 3622.8650431772135, 0.9349963799239585]
[1.209836120820213, 3536.4474397018203, 77.84739319807044, 0.4676740184693075, 0.9380253151811131]
[77.84739319807044, 3536.4474397018203, 0.9380253151811131]
/home/runner/micromamba-root/envs/scpy/lib/python3.9/site-packages/spectrochempy/application.py:1258: UserWarning: Maximum number of iterations reached.
warnings.warn(msg, *args, **kwargs)
[1.0, 3622.8779, 40.1178, 0.1541, 0.9234]
[40.1178, 3622.8779, 0.9234]
[1.2257, 3536.5874, 77.6198, 0.4444, 0.9382]
[77.6198, 3536.5874, 0.9382]
Show the result after 1000 iterations
ndOH.plot(plot_model=True)
# scp.show() # uncomment to show plot if needed (not necessary in jupyter notebook)
<_Axes: xlabel='wavenumbers $\\mathrm{/\\ \\mathrm{cm}^{-1}}$', ylabel='absorbance $\\mathrm{/\\ \\mathrm{a.u.}}$'>
Total running time of the script: ( 0 minutes 14.298 seconds)