/
checker.py
225 lines (202 loc) · 26.2 KB
/
checker.py
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#%%
#This code was used to check the accuracy of the parameters after they had been fitted
# loading functions
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import quad_vec
from scipy.constants import pi, c, h, e, m_e
from scipy.interpolate import RegularGridInterpolator
# Accelerating voltage, volts
V = 100000.0
# lorentz factor
gamma = 1 + (e*V)/(m_e*c**2)
# electron velocity
v = c*np.sqrt(1 - 1/gamma**2)
# wavelength
wav = 1e10* h/(gamma*m_e*v) # Angstroms
preFactor = 1e10*2*h/(m_e*c) # Angstroms
Z = 28
lobato_array = np.array([[6.473848488352918e-03,-4.901925767802290e-01,5.732841603908765e-01,-3.794033014839905e-01,5.544264747740791e-01,2.785198853791489e+00,2.776204283306448e+00,2.775385910506251e+00,2.767593028672588e+00,2.765118976429275e+00],
[3.057451160998355e+00,-6.200447791273253e+01,6.400555370846145e+01,-5.001325785427806e+00,1.517988287005264e-01,1.089672487260788e+00,9.398387981431211e-01,9.252890343862655e-01,8.229474987086506e-01,5.773931106754022e-01],
[3.926222728861479e+00,-4.548619626399980e+00,2.193353128786585e+00,6.994512650339657e-02,2.098642248519376e-03,8.142760135172804e+00,4.989410770078558e+00,4.144289992394109e+00,4.019223150656802e-01,1.564790347198236e-01],
[3.398249705570541e+00,-1.908668860956967e+00,3.907021175392274e-02,-1.116310102107145e-02,9.462044653575231e-03,4.442701786224095e+00,3.324515425264230e+00,1.897728803482149e-01,8.719186146446036e-02,8.278090600413406e-02],
[1.472792486393293e+00,-4.019330421993871e-01,3.059989569826894e-01,1.961442171731680e-02,9.771771060882025e-04,3.749740482818191e+00,5.880665361396738e-01,5.156396131030110e-01,1.213775700806037e-01,6.809824121603139e-02],
[1.244660886213433e+02,-2.203528570789638e+02,1.952353522804791e+02,-9.810793612697997e+01,1.420230412136232e-02,2.421208492560056e+00,2.305379437524258e+00,2.048519321065642e+00,1.933525529175474e+00,7.689768184783397e-02],
[5.813271507025561e+01,-1.475424090878127e+02,1.301430656496395e+02,-3.961956740841543e+01,1.059577633314809e-02,1.700448564134711e+00,1.559038526017404e+00,1.415768274731469e+00,1.278418182054558e+00,5.655877984748055e-02],
[2.994740452423624e+01,-7.761012662552783e+01,9.988177646231442e+01,-5.121270055056731e+01,8.196189544460320e-03,1.302839878800107e+00,1.157941052583095e+00,1.009885493380251e+00,9.433279714332660e-01,4.331976113218256e-02],
[9.489848945035248e-01,-3.013339230435549e+01,5.279650781273386e+01,-2.270627037952724e+01,6.569976645314410e-03,1.458829331986459e+00,6.887799931876800e-01,6.542398693466957e-01,6.148361308119943e-01,3.428374194950112e-02],
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[2.367006039467926e+01,-2.185317861597425e+01,5.924994481089464e-01,-2.446522903102440e-02,4.839502217065358e-03,8.451487735146031e+00,8.040966004742982e+00,6.249960005263150e-01,1.324503949472964e-01,2.339943620498786e-02],
[4.855010476871495e+00,-2.662209064768437e+00,4.780012360851080e-01,-7.023070646920648e-02,3.989058281040198e-03,5.946392738424565e+00,4.171303125206979e+00,3.982698081503743e-01,1.618861858374742e-01,1.953450563631035e-02],
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[6.097881795995097e+00,2.194951647366750e+00,5.481727919600226e-01,6.166695732226626e-02,2.268073558647142e-04,1.242885443158548e+01,1.505359923520235e+00,3.337380397171243e-01,3.877445534999988e-02,8.240498840648670e-04],
[5.795268796472405e+00,2.370226641078433e+00,4.713987569011149e-01,5.743682605878668e-02,2.189794892596593e-04,1.428010550582560e+01,1.359690157191345e+00,3.020173496635141e-01,3.664367981470077e-02,7.954345265183711e-04],
[5.604062553775258e+00,2.357962595618129e+00,4.760010985728824e-01,5.441233743152471e-02,2.114146022051498e-04,1.395174902305747e+01,1.312397549174392e+00,2.949337011929565e-01,3.486015424623241e-02,7.682616826618097e-04],
[5.429083919697703e+00,2.336873253608803e+00,4.833735541048819e-01,5.146549645574790e-02,2.037761328637611e-04,1.365036494276600e+01,1.267598413903199e+00,2.886106815769299e-01,3.312918074466093e-02,7.423484838012663e-04],
[5.267744450894446e+00,2.308558133263050e+00,4.932654790260128e-01,4.863562797416966e-02,1.963088423206752e-04,1.336020968273946e+01,1.225858565869417e+00,2.829196321278669e-01,3.147353971271379e-02,7.176580250696152e-04],
[5.126804285170776e+00,2.269255340083806e+00,5.042093004533025e-01,4.569239924162220e-02,1.886750504938862e-04,1.315815010261290e+01,1.181295082433371e+00,2.771070382190629e-01,2.979576045495446e-02,6.940110991990983e-04],
[4.979623597498092e+00,2.241830874556695e+00,5.129339614028937e-01,4.298018484983344e-02,1.813816924857876e-04,1.283926630780338e+01,1.147054464204860e+00,2.703871609352437e-01,2.824187149526020e-02,6.714866031739924e-04],
[5.078358300456114e+00,1.957440271816590e+00,5.928259832213751e-01,4.195020341439256e-02,1.752410915283168e-04,1.051327254690473e+01,1.117649412815246e+00,2.843867418336752e-01,2.726633276413471e-02,6.503108607073037e-04],
[4.711616366573001e+00,2.172619507865789e+00,5.397176013428657e-01,3.797960045478111e-02,1.669237635648417e-04,1.231094159485391e+01,1.087437967674925e+00,2.598049655092755e-01,2.532899238951897e-02,6.292785669619112e-04],
[4.590755044851466e+00,2.135723730365674e+00,5.513555600941525e-01,3.560584067185138e-02,1.598240168567898e-04,1.206567406233699e+01,1.058117371158644e+00,2.539944389186618e-01,2.395087396496492e-02,6.094827484332881e-04],
[4.484001106267108e+00,2.089043470785398e+00,5.659326183161046e-01,3.327035902110630e-02,1.524456102828921e-04,1.187492506915706e+01,1.028284937087896e+00,2.489078079080760e-01,2.258440655321478e-02,5.903744451594245e-04],
[4.376651407869632e+00,2.046451503836341e+00,5.806628605915877e-01,3.123885283277667e-02,1.453748696625357e-04,1.166530807171395e+01,1.003147696754953e+00,2.441532926863124e-01,2.136185800007310e-02,5.721103384547666e-04],
[4.283083182474195e+00,1.995380014537307e+00,5.970535713325043e-01,2.909516688695599e-02,1.380647690375216e-04,1.149619059566834e+01,9.770391020188206e-01,2.394291329758291e-01,2.009122333272558e-02,5.543771384922663e-04],
[4.195638407371233e+00,1.943332859786456e+00,6.124466172854658e-01,2.715152076949324e-02,1.305947873519297e-04,1.141077504566523e+01,9.490119244548774e-01,2.349503265353047e-01,1.890515762809755e-02,5.372336492097111e-04],
[4.356925932963843e+00,1.695892047773159e+00,6.639045200684705e-01,2.630200187602814e-02,1.254973184998238e-04,9.294345147185689e+00,9.105000459574200e-01,2.387465959113764e-01,1.820985425464623e-02,5.215593719635622e-04],
[4.331384056649235e+00,1.527648647286807e+00,7.357959228912380e-01,2.495263232014026e-02,1.187408525810578e-04,7.876844338102884e+00,9.425156426277488e-01,2.416994800398060e-01,1.728998944485090e-02,5.058346313135256e-04],
[4.197260013196420e+00,1.468548067747088e+00,7.839312482110882e-01,2.324940948643951e-02,1.112613586072860e-04,6.936740248944572e+00,1.017252766183483e+00,2.389489397150706e-01,1.623324330753810e-02,4.902390040211490e-04],
[3.976297158190774e+00,1.522926842573418e+00,7.977062463905613e-01,2.136667415586852e-02,1.030786893857173e-04,6.296857792287749e+00,1.112899511576911e+00,2.310570406784734e-01,1.510135455672045e-02,4.746824771050258e-04],
[3.751443814398119e+00,1.627688029776327e+00,7.817567554542718e-01,1.951708039122916e-02,9.431998042934275e-05,5.797546360829538e+00,1.182236310777107e+00,2.199135860247702e-01,1.398104554814566e-02,4.591271258298386e-04],
[3.484015173387116e+00,1.793779204169655e+00,7.448783566919203e-01,1.754277851624345e-02,8.448723515688600e-05,5.439988460809537e+00,1.227921341401281e+00,2.062088569929092e-01,1.278994017211460e-02,4.430322267874786e-04],
[1.599565781988442e+00,2.975344521941205e+00,6.950926783668822e-01,1.487796274586880e-02,6.905495791015833e-05,5.792444473855675e+00,1.553009829732260e+00,1.886263359366482e-01,1.117634706624533e-02,4.227723616555514e-04],
[2.040215639757283e+00,2.899226346248255e+00,6.363440838157977e-01,1.320719195954083e-02,5.673821925001312e-05,6.658194296096275e+00,1.413379237789324e+00,1.740001045021790e-01,1.006878045302105e-02,4.030771056922231e-04],
[1.675934670648708e+00,3.004866029697293e+00,5.953400131616355e-01,1.171631866230948e-02,4.296782976398171e-05,5.522310932114025e+00,1.380072230071963e+00,1.622292376559454e-01,9.018148904165756e-03,3.792776674776671e-04],
[2.235228504431053e+00,2.682766386519949e+00,5.551949262124333e-01,1.072733543662587e-02,3.284739920462629e-05,5.020309889602403e+00,1.230775905837777e+00,1.522481229928636e-01,8.283991169062104e-03,3.562419389317589e-04],
[2.803427374125100e+00,2.718827879660200e+00,5.224759153919996e-01,9.845378369710420e-03,2.345245265083162e-05,6.558768728045342e+00,1.169724225166679e+00,1.435566918001781e-01,7.619765262300398e-03,3.296276739029854e-04],
[3.608610209977714e+00,2.450567747371983e+00,4.786395001072570e-01,8.872142351692152e-03,1.040019329094673e-05,6.581625946219628e+00,1.027728526605885e+00,1.335336806347209e-01,6.848612389484298e-03,2.763888754566660e-04],
[4.242099010573159e+00,2.099943420558279e+00,4.328366313799229e-01,8.020215703810592e-03,7.217850308513403e-07,5.752801155360800e+00,8.739014891954615e-01,1.235999561805247e-01,6.176003330585702e-03,1.414951776172309e-04],
[4.636200956689623e+00,1.780633114269871e+00,4.037304439527385e-01,7.685395546686740e-03,8.954159028076436e-08,4.888252997809829e+00,7.563105268800747e-01,1.173023644522492e-01,5.930343942428942e-03,7.666686638730287e-05],
[4.965922505950705e+00,1.438155615070337e+00,3.712992005792981e-01,7.472564284502011e-03,1.141152841525851e-07,4.091293787874963e+00,6.292289966025513e-01,1.110966786955352e-01,5.772350103477618e-03,8.085118938793825e-05],
[5.306156144750332e+00,1.117331602360721e+00,3.158587231108543e-01,7.203422423102100e-03,1.073553305458635e-07,3.488007354816557e+00,4.811907411497712e-01,1.018744679457531e-01,5.592453744170787e-03,7.795066735407367e-05],
[4.520533990423360e+00,4.106953979091246e+00,7.139468785037285e-01,1.692940276874539e-02,8.574921291917244e-05,1.944822342329488e+01,1.898246731559969e+00,1.695535635953418e-01,1.148195675489342e-02,3.461220382579827e-04],
[6.524010720018733e+00,3.207870807456613e+00,5.404787743496377e-01,8.782788068988532e-03,6.910106029491315e-06,1.400925542989749e+01,1.326350359616653e+00,1.314085683860361e-01,6.286474345204096e-03,2.278399814589510e-04],
[6.896028535596191e+00,2.835141545365232e+00,5.035068818888151e-01,8.022945109667069e-03,9.204009547587397e-08,1.107638256703987e+01,1.171326162905030e+00,1.234946513917999e-01,5.735155957904971e-03,7.197075418025232e-05],
[7.093749001626302e+00,2.529123739031940e+00,4.821078198888890e-01,7.719366741451110e-03,7.271141994250414e-08,9.094737951659447e+00,1.063916670331612e+00,1.186194466218779e-01,5.539457088950347e-03,6.584947305284627e-05],
[6.434013247972842e+00,2.970999705357888e+00,4.607966517878480e-01,7.240331257754553e-03,6.362366643091279e-08,1.025968513072979e+01,1.131774523061633e+00,1.127759353623823e-01,5.274595833531321e-03,6.192638240887597e-05],
[6.210708267840199e+00,3.039344538256235e+00,4.373399844391628e-01,6.807147641473166e-03,6.182293277428513e-08,1.002141058591628e+01,1.103998801558834e+00,1.072189731624539e-01,5.024321308506824e-03,6.005069941971958e-05],
[6.004315983089865e+00,3.094316545314180e+00,4.128084877164170e-01,6.408916578800669e-03,6.730073762160754e-08,9.817930467191061e+00,1.069787050680294e+00,1.016352914486458e-01,4.795248468887250e-03,6.028065987264629e-05],
[5.200617168103042e+00,3.498494403671440e+00,4.054149311313203e-01,6.223437008265299e-03,6.008593295434409e-08,1.120383101944067e+01,1.128463695469282e+00,9.893334726861316e-02,4.659174319779507e-03,5.725906389623341e-05],
[5.025338600360291e+00,3.518439882851541e+00,3.819503494462722e-01,5.821102080962110e-03,6.526093388297119e-08,1.097721906976287e+01,1.084772148326308e+00,9.367468748538359e-02,4.426823468734856e-03,5.738568370505115e-05],
[5.346561002606197e+00,3.224684665609108e+00,3.494617526254452e-01,5.292517567488151e-03,6.159176302362374e-08,9.231183797524494e+00,9.728362291938352e-01,8.705962209665623e-02,4.130119644650323e-03,5.494638944496757e-05],
[5.225823503340047e+00,3.228188739952953e+00,3.270988788238514e-01,4.888825755922390e-03,5.212722694193633e-08,9.071357066187183e+00,9.311242774566348e-01,8.207206020598455e-02,3.890296559934166e-03,5.103679766366416e-05],
[4.586412477535479e+00,3.518695956651012e+00,3.192617142012054e-01,4.729796479856258e-03,5.513244808062041e-08,1.031861020923352e+01,9.572788378292328e-01,7.968074314438807e-02,3.771931999968489e-03,5.097508603760111e-05],
[4.457994806754126e+00,3.508672126376623e+00,3.013753805283154e-01,4.407637462144819e-03,4.887879032285916e-08,1.008906933834013e+01,9.194464473616226e-01,7.564191777863293e-02,3.570264651248093e-03,4.804951743958113e-05],
[4.338975764011709e+00,3.491850988964034e+00,2.814710990162868e-01,4.002092714990461e-03,5.529298081955140e-08,9.963309372238362e+00,8.780839569829744e-01,7.116371157687776e-02,3.321524042150777e-03,4.851031794603728e-05],
[4.227294704031012e+00,3.472492275106616e+00,2.648222294968986e-01,3.690728778331929e-03,6.258714262002473e-08,9.724006020400314e+00,8.428737759602104e-01,6.735347439748511e-02,3.123646062633208e-03,4.912170970176192e-05],
[4.109517024430204e+00,3.457991325227507e+00,2.470873512223867e-01,3.304239209409952e-03,5.991049262319316e-08,9.677359945101202e+00,8.069400424708172e-01,6.328154369541671e-02,2.875446396412092e-03,4.706791536975981e-05]])
def lobato(s, Z):
ab = lobato_array[Z-1]
g = 2*s
f = ab[0]*(2 + ab[5]*g**2)/(1 + ab[5]*g**2)**2 + \
ab[1]*(2 + ab[6]*g**2)/(1 + ab[6]*g**2)**2 + \
ab[2]*(2 + ab[7]*g**2)/(1 + ab[7]*g**2)**2 + \
ab[3]*(2 + ab[8]*g**2)/(1 + ab[8]*g**2)**2 + \
ab[4]*(2 + ab[9]*g**2)/(1 + ab[9]*g**2)**2
return f
def integrand(sx, sy, s, M, Z):
s1 = np.sqrt((s/2 + sx)**2 + sy**2)
s2 = np.sqrt((s/2 - sx)**2 + sy**2)
s_square = sx**2 + sy**2 - (s**2/4)
result = lobato(s1, Z)*lobato(s2, Z)*(1 - np.exp(-2*M*s_square))
return result
def integral1(sy, s, M, Z):
return quad_vec(integrand, 0, np.inf, args=(sy, s, M, Z))[0]
def fprime(s, M, Z):
return preFactor*4*quad_vec(integral1, 0, np.inf, args=(s, M, Z))[0]
#%%
# loading fit functions
def gauss(x, a, b):
return a*np.exp(-b*x**2)
def curve(x, *args):
S = np.zeros(len(x))
for i in range(len(args)//2):
S += gauss(x, *args[i*2 : (i+1)*2])
return S + args[len(args)-1]
#%%
# 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.7, 1, 1.5, 2, 2.75, 4
Mvals = np.array([0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.7, 1, 1.5, 2, 2.75, 4])
svals = np.linspace(0, 4, 50)
finex = np.linspace(0, 6, 100)
filename = "element " + str(Z) + ".txt"
coefflist = np.loadtxt(filename, delimiter = ',')
#%%
#first the curves were plotted to check if there was any anomalous behaviour in the parameterisation
# plotting gaussians
colours = plt.cm.jet(np.linspace(0, 1, 6))
fig, ax = plt.subplots(figsize=(10,10))
ax.set_title("fit comparisons", fontsize=15)
ax.set_xlabel("s", fontsize=20)
ax.set_ylabel("f'", fontsize=20)
svals = np.linspace(0, 6, 50)
Smesh, Mmesh = np.meshgrid(svals, Mvals)
zvals = fprime(Smesh, Mmesh, Z)
zpos = np.where(zvals > 0, zvals, 0)
fitlist = []
for i in range(len(Mvals)):
fitdata0 = curve(finex, *coefflist[i])
fitdata0 = np.where(fitdata0 > 0, fitdata0, 0)
ax.plot(svals, zpos[i], label= 'actual function', color = colours[1])
ax.plot(finex, fitdata0, label= 'fit function', color = colours[4])
fitlist.append(fitdata0)
fit_array = np.asarray(fitlist)
#%%
# interpolation between curves
finex = np.linspace(0, 6, 100)
finey = np.linspace(0, 4, 100)
fitdata0 = np.vstack((np.zeros(100), fit_array))
Mvals0 = np.concatenate((np.array([0]), Mvals))
interp = RegularGridInterpolator((finex, Mvals0), np.transpose(fitdata0))
fineX, fineY = np.meshgrid(finex, finey)
interpZ = interp((fineX, fineY))
interpZ_pos = np.where(interpZ > 0 , interpZ, 0)
#%%
# comparison data
compareZ = fprime(fineX, fineY, element)
compareZpos = np.where(compareZ > 0, compareZ, np.nan)
#%%
# error plot
# a heat map was also created to check the accuracy of the linear interpolation between curves
error = abs(compareZpos - interpZ_pos)/compareZpos
fzeros = np.where(compareZ <= 0, 0, np.nan)
fig, ax = plt.subplots(figsize=(10,10))
ax.set_title("4 gaussians and a constant" + " parameterisation element " + str(Z), fontsize=15)
ax.set_xlabel("s (Å⁻¹)", fontsize=15)
ax.set_ylabel("B (Ų)", fontsize=15)
plot = ax.pcolormesh(fineX, fineY, error, cmap='plasma', vmin=0.01, vmax=0.05)
ax.pcolormesh(fineX, fineY, fzeros, cmap='inferno')
fig.colorbar(plot)
#%%