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@yangyushi
Last active October 23, 2020 12:15
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calculate the [r]adial [d]istribution [f]unction (g or r) in orthogonal PBC box with arbitrarily large cutoff distance in all the normal dimensions
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H 8.85685988796112 11.475363680892993 18.093864370219322
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H 11.533725234960965 6.029565784850126 6.905954377528626
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H 15.35087822170737 3.7134692457545686 4.237418066065057
125
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H 14.76743668065663 1.2613462374979916 13.390843039508631
H 17.622598229909343 12.200440106565635 11.265945326294716
H 14.812843422742061 13.331122539335457 5.9608418235030625
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H 8.066394408851291 11.731481984674268 16.326331985968416
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H 0.545772119678424 15.28878400512372 0.1098114622445645
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H 9.480940152809767 0.21583537078994364 13.237592659469994
H 17.814157071284246 7.305673644338866 13.502149206758938
H 7.1098351405840985 1.9538540756429086 18.45381110856244
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H 5.506839535275881 11.756885110857866 4.04812220775238
H 10.37168900031674 8.70461389635697 10.148540856147314
H 17.357761471466116 4.408890338137646 0.07181562324431212
H 9.638097826154612 3.0728046406749083 14.509344233156686
H 6.876083431446627 5.089528622561058 15.922089125201149
H 12.435292691838033 7.436718878327277 18.4752704674973
H 8.602700520774135 16.080687423630792 17.88557029882746
H 13.561007292290718 16.642718154732503 17.316521520426626
H 18.376474717309588 4.900505945990262 3.1437180638653874
H 10.453190945421799 3.5929405330839255 8.545761253798956
H 0.9740363082480359 6.503029979152291 15.220428269762294
H 17.824689727869448 4.36614573079545 13.43684359265855
H 15.832845144276122 12.15986286074208 5.899735862788261
H 7.641967556333924 1.2785308316678405 6.549283642689234
H 2.642716797351079 8.465760677189127 6.774159735674402
H 18.53670954724651 0.7542981528829562 12.541259841952524
H 9.052004233942174 13.405903755466161 7.219864100144899
H 14.251714047548733 8.131995345752463 13.39427716145746
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H 6.035230933220182 0.5340937791501332 7.121695971807118
H 8.618612247924986 8.703959693143505 12.80549785253556
H 0.1598640003113232 3.4480978543633367 0.707029865936962
H 1.377083830161844 0.1671399463943165 15.61020047419035
H 9.484522734830584 18.668086354448054 5.8473045569633575
H 13.274365253364603 18.37689311750024 2.353650465701764
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H 17.66381128964537 9.911235613791261 6.964093293884339
H 9.51269615034385 16.314223870374338 7.839098233662338
H 10.515491482699153 0.16832323697527807 4.528134804543805
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H 12.33457680925009 2.9471205729230405 17.94777027759144
H 15.216802361360187 3.160342530944496 5.580853428094482
125
H 17.41812775941719 5.436887576533634 13.31986788339071
H 10.900639858773804 7.521737569738298 12.42010585473735
H 9.504342912789344 6.774818090809076 3.240348555926727
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H 9.803824582516992 11.355585454636735 0.8836751480084146
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H 3.60786522936605 14.985007333840157 8.855823425992298
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H 9.321935770184629 14.710280131463403 15.015224714123745
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H 15.275567238786985 9.883108406504029 0.13996447987184268
H 15.063355787258152 7.828294119879166 3.6009343379911205
H 11.051841623366087 7.324167756533067 8.028748636603893
H 6.750727772430191 13.4408068992779 18.33978363834091
H 15.613423338729177 16.43070804856341 12.321707529348485
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H 17.088221858717365 8.6493940741267 15.219088571545146
H 14.837936937696826 8.57798935449494 12.65574168958918
H 4.245067121984768 11.73638842350163 6.360547203928534
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H 13.847079987214931 18.412378954524364 0.928867539083617
H 12.352497274377466 4.6214611134547114 7.139377724712727
H 9.30842364652706 5.432457580604612 2.7546470639961083
H 15.122216349090335 2.8901986440761656 4.602834490056972
H 11.119706435153933 2.56830929223681 11.448234005643476
H 14.7579572860039 17.2190678560154 14.116694715462426
H 16.103201343018373 14.410138034948632 11.618051509772787
H 14.587072056614865 13.114295788620769 14.823543322326827
H 11.30784462239878 12.43777927772255 18.292577647638723
H 14.327076376576066 1.7138792417274857 10.116624847677473
H 18.651074547414776 12.831573445150742 6.38768139535004
H 5.56207281998711 17.973861037550382 2.2664765855969806
H 9.76969999195874 13.60836305337839 6.1453588828197185
H 0.6317073134795308 2.7913285867344886 6.0981449013918265
H 17.775002772434746 13.610093883973477 0.11026030521404062
H 15.866464610057061 13.87436500037777 9.652400148284729
H 15.477766177939179 8.49309918485448 6.44353983881046
H 18.602397962951432 16.067708976795515 4.730173591987141
H 11.971723182771546 13.322420278005332 6.929202783069561
H 1.1915344862854753 1.5932369436858618 3.885025301303367
H 15.910973781245607 13.257171444652954 11.29408118533151
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H 17.142064060612714 14.952547847639707 2.2509113464715265
H 12.914702249895 11.946903213785081 13.98899216698733
H 12.458454854514608 13.081488656863543 13.41949747041435
H 13.8365361775814 18.54153338303793 12.364442483752955
H 14.08610954115306 11.079464662619689 9.13522183108783
H 9.435343239595037 13.411500667888573 16.908344842754044
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H 10.544003639460984 5.099840665298024 4.282441661811617
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H 16.595166063059775 9.873292081910776 11.6267310490043
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H 0.23178635508473633 7.809057497360066 7.144463372399265
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H 14.044286105508835 1.0977325427858005 14.010594761707086
H 4.206234728228982 13.173290079171279 4.6893117100090596
H 11.373728663352752 9.122533446714682 10.511895767079107
H 18.40235157448609 0.15823568568246316 16.45845212491345
H 7.902197575177482 14.757629596131984 4.690842666264177
H 9.240951785080238 6.707370581393266 14.138512708482839
H 16.137352490302966 10.479653244807627 4.779659885148764
H 4.433109951963385 0.7177382960617267 18.598658776196512
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H 14.287479570224978 0.5336838640892649 7.221127355263923
H 10.096132427740375 3.632614595964159 5.0879470381804675
H 14.924115893902801 10.55101705633545 10.950858585126234
H 12.395346547264701 16.91149206699945 7.946820711032409
H 17.455368120815947 12.595576920085955 8.093491492393396
H 16.43908659023517 15.808277045992117 9.85684394097283
H 10.583089386413905 2.746844644402495 9.245837470278415
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H 15.740315782027574 7.5878298610356225 12.950731529076345
H 0.17273295136326539 3.2820528665202677 11.485138137138104
125
H 6.820791021264398 4.048217881915716 10.1847574618887
H 15.884897314226313 6.338259707822174 12.430340244549722
H 7.760736319725101 3.585843193864675 1.4225352597109293
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H 7.3184066676505095 1.6047909219917527 6.986847262774014
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H 4.835355461286977 10.974153643587226 9.654444341833523
H 15.213796616589248 2.0829357388573193 2.409345643816072
H 6.756003890409128 11.1709430289391 15.466454690587936
H 1.7162541966343805 16.547961973290533 6.566162871973474
H 1.9686336905551824 1.1792504853828938 8.126885129897422
H 10.622950894147188 3.6559564030737395 2.5168472199079046
H 16.293209271770316 2.548339800883271 7.440028787760353
H 18.559010608043724 11.81385556743065 6.385955170254395
H 4.4140555773491075 8.576641483482659 15.778638674288496
H 2.0127190126644092 17.778386867495392 11.21831433210488
H 8.184833791406415 1.0583563968994985 11.033495052797136
H 6.317183869664049 8.73032655077915 2.9850030684836986
H 7.91994985475459 16.176947115092272 17.529321229145665
H 13.19038354352145 11.394920941486324 7.41549418366518
H 15.392099865236151 3.7998148374535043 2.081434268225096
H 14.817678968122614 0.8677655825540215 3.759159451345354
H 15.363632527022402 1.7617447350503932 6.61095560834779
H 12.59728668654626 11.94471176436655 17.772505624471304
H 8.215937748427004 6.5913600938934875 5.776489213261147
H 12.487597555492146 9.154529404068205 15.406687009844795
H 3.817362423722545 3.6470013465796693 1.0522881639181638
H 14.016129673280524 16.2453360132558 14.844421972262591
H 8.731499303033107 16.18516157585087 9.846275113595201
H 16.739472353718675 4.087176892078464 9.365265222997387
H 18.134380738745417 12.864798399116221 15.596198687766604
H 3.078058558485591 10.79317672117708 1.2053555026764726
H 0.15633288767676135 17.6062578813516 2.1789268797032424
H 2.3200109829585025 2.8584778106290365 0.4734251800821667
H 9.623590768751601 10.365792456548483 6.42560780344396
H 0.6520287565104131 16.797177625393815 12.51441264029466
H 12.169092978141535 1.5221735320266832 0.8410153618644154
H 6.241894160098482 17.42156020972759 8.36975471296109
H 4.584868469117276 2.6997089335098394 11.29256612064307
H 14.287107748535881 8.549032429269396 8.73059233206088
H 5.673051693912817 13.395447376887189 0.7689710601277132
H 13.158586623050486 18.342063616280157 2.9775726190813563
H 12.454743386334592 3.715100724589702 7.8969838137435096
H 11.091679134694104 4.411930400623877 1.9152327607237383
H 14.464916068253835 3.809242277160694 4.077111232302279
H 11.78596710262234 3.321249840315984 12.359550467354357
H 14.640999539964445 17.1596668399594 14.421930525229698
H 15.399571790206792 13.787358004734225 10.541944300338306
H 14.908307441053372 13.215189954570217 17.258955815637062
H 11.30784462239878 12.43777927772255 18.292577647638723
H 13.558760827180436 3.986056161766278 10.246592048316487
H 16.966641025954385 12.352404551630867 6.123875497473172
H 6.4646013154106186 18.44036243917419 2.0607142210677876
H 9.685899365388147 14.06064917660365 7.239388328097285
H 0.6317073134795308 2.7913285867344886 6.0981449013918265
H 16.33689218277348 12.950975843740734 2.540556629538069
H 15.866464610057061 13.87436500037777 9.652400148284729
H 16.466447195971664 8.504345537623768 5.897069791008915
H 1.0706304715058437 17.380535709827676 3.7062203987906477
H 11.78138699687605 13.586829569841639 7.331691400021761
H 2.23798173487514 0.07952723165186781 4.290340750977406
H 18.320426267741883 14.422468245450755 11.506789842855577
H 9.50331595602356 11.610131550361897 0.04528846130002645
H 17.76611301179453 14.990887158337118 2.3008122979364516
H 11.980264875011724 14.42908194746537 14.341302363586149
H 11.91223512874211 13.39450724897945 13.371086006206724
H 12.65703488189005 18.508718338165234 11.691098301811266
H 14.959863510745393 10.087331848084917 8.430396709018599
H 9.664200970824547 14.704915941795516 17.652369140720122
H 2.5815373580231222 4.591740144853639 14.878519085263136
H 17.81085927295698 12.644977182396884 1.5285435118956834
H 4.217431293330807 6.437339027829182 16.5442063193805
H 6.758063951186341 2.931267678677922 17.97651199730571
H 8.602844868920608 8.26611155253698 14.57593505936244
H 2.219858595830835 8.022444314764645 2.4268639268436476
H 17.070061152268337 2.3716307819973985 5.375565000694929
H 6.060366882252932 6.3945275747279915 4.067508016257363
H 6.420281904665208 12.28195032175605 15.136933614125777
H 17.189100501937773 13.648828637378596 7.694716651994433
H 16.07928338826822 7.301869177337895 4.274787999571641
H 18.11159815168549 12.856810185741624 13.041968131286119
H 0.23829419227822157 17.081572992463293 11.247304131909699
H 5.737461987667607 16.881291440811687 17.118333373680574
H 13.722716017613202 13.506420577987733 12.640784180892675
H 10.596872754951193 13.579327441244018 12.251322966410383
H 17.138469121355847 9.242186030922511 13.521254047519736
H 6.998005547468847 18.627293885909747 16.684698378564654
H 11.509543205104125 18.514590393307476 5.327616383896223
H 2.6171543976398226 13.48775638360419 16.703494047669285
H 6.97482978374208 16.42451413045871 11.688153242291756
H 15.536537585713624 5.9987521712058784 15.125215538471387
H 16.342575630486998 2.307958508842907 18.642704851998896
H 13.758527540576978 4.116389445099166 7.694435033245728
H 6.813517976960297 4.259942915577923 6.745367869974976
H 11.274776134197152 9.974138241458244 12.034985536932377
H 9.242933728551035 12.97592861969883 13.810605286218824
H 8.066769312715907 11.497844687686088 14.650974594783204
H 9.852507922518948 2.005960500784252 8.931490751467623
H 10.046533961427915 6.299155388065749 4.167318275398929
H 12.811820742812335 11.3895297472878 14.582872921800167
H 17.16888430287516 10.735357830760105 10.465606802523768
H 16.4738244490699 12.123617967505295 7.546207416466313
H 17.36898784579118 10.20650278733117 6.53090321187765
H 3.33930749654492 8.994283299718946 10.171334262866765
H 14.681678239231324 2.6893180129916994 13.128141370730422
H 5.155692327743454 13.274496070969564 5.958965836029858
H 10.049433630146641 7.844802077025108 11.324450544175027
H 1.2890664008611559 17.999350875427993 15.75956455879095
H 7.643413137460716 17.163150433629127 4.747687097614999
H 11.128860958802502 5.12506258398842 13.854611210927294
H 14.734713398690698 10.776785923042262 3.842314575270753
H 3.5801848538892855 1.1131940257845732 17.460721957476377
H 14.432392809697367 1.2482157467011064 8.719861011176244
H 14.287479570224978 0.5336838640892649 7.221127355263923
H 9.3866707353352 4.491171252618175 4.121345352241799
H 15.411003822036871 10.824977576208433 11.206872714200559
H 12.62625498757488 16.61622731158044 7.849653528231167
H 16.447451468188106 14.393759417227372 8.403236615246524
H 17.654358282166456 18.677233706112624 11.899052166901672
H 10.42216131867333 4.106441413594265 7.665220677580171
H 14.890131674398859 1.3117824780111804 14.886031712832084
H 3.316266556821728 8.556149697235197 16.78507048748696
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"""
This modules provides functions to load xyz files
and claculate the radial distribution function
"""
import re
import numpy as np
from itertools import product
from scipy.spatial.distance import cdist
def get_frames_from_xyz(filename, ncols=3):
"""
Load the configurations of particles inside an xyz file
Args:
filename (str): the name/path of xyz file
ncols (int): the number of columns to read, 3 = x, y, z
Return:
np.ndarray: the positions of particles in each frame,
shape (n_frame, n_particle, n_cols)
"""
f = open(filename, 'r')
frames = []
for line in f:
is_head = re.match(r'(\d+)\n', line)
if is_head:
frames.append([])
particle_num = int(is_head.group(1))
f.readline() # jump through comment line
for j in range(particle_num):
data = re.split(r'\s', f.readline())[1: 1 + ncols]
frames[-1].append(list(map(float, data)))
f.close()
return np.array(frames)
def get_rdf(positions, box, cutoff, bins):
"""
Calculate the radial distribution function (g or r) given particles
inside a box with periodic boundary
Args:
positiosn (np.ndarray): the positions of all particles, shape (n, dim)
box (iterable or float): the length of the box with periodic boundaries.
if given a number, then assume the box is inside a cubic box
if given a iterable, its length must be the dimension
cutoff (float): the maximum r value in the rdf
bins (iterable or int): specifying the bins of the radius
if given a number, the bin edges are `np.linspace(0, cutoff, bins + 1)`
if given an iterable, then the bin edges equals `bins`
Return:
tuple: the rdial distribution function in the form of (r, g(r))
Example:
>>> np.random.seed(0)
>>> ideal_gas = np.random.random((250, 2))
>>> r, rdf = get_rdf(ideal_gas, box=1, cutoff=3, bins=20)
>>> np.isclose(rdf, 1, atol=0.1).all()
True
>>> len(r), len(rdf)
(20, 20)
"""
# processing parameters
n, dim = positions.shape
if type(box) in [int, float]:
box = np.array([box] * dim, dtype=float)
else:
box = np.fromiter(box, dtype=float)
if len(box) != dim:
raise ValueError(
"".join(["The size of the box (", str(len(box)),
") does not match the dimension (", str(dim), ")"])
)
if type(bins) == int:
bins = np.linspace(0, cutoff, bins + 1)
else:
bins = np.fromtier(bins, dtype=float)
# calculate the density
box_volumn = 1
for box_1d in box:
box_volumn *= box_1d
density = n / box_volumn
n_level = np.ceil(cutoff / box).astype(int).max() # n = neighbour
n_indices = np.arange(-n_level, n_level + 1) # e.g. (-2, -1, 0, 1, 2)
n_indices = list(product(n_indices, repeat=dim))
n_shift = np.array(n_indices) * box[None, :]
n_cells = n_shift[:, None, :] + positions[None, :, :] # shape (n_cell, n, dim)
distances = [cdist(positions, nc) for nc in n_cells]
for i in range(n_cells.shape[0]): # remove self overlapping
np.fill_diagonal(distances[i], np.nan)
hist, _ = np.histogram(np.concatenate(distances).ravel(), bins=bins)
r = (bins[1:] + bins[:-1]) / 2
dr = bins[1] - bins[0]
if dim == 1:
v_shell = 2 * dr
elif dim == 2:
v_shell = 2 * np.pi * r * dr
elif dim == 3:
v_shell = 4 * np.pi * r**2 * dr
else:
raise ValueError(r"RDF for dimensions higher than 3 not implemented")
rdf = hist / (n * v_shell * density)
return r, rdf
if __name__ == "__main__":
import matplotlib as mpl
mpl.rcParams['font.family'] = 'serif'
mpl.rcParams['font.size'] = 14
import matplotlib.pyplot as plt
frames = get_frames_from_xyz('positions_hard_sphere.xyz')
cutoff = 10
box = 18.70550963409122
rdfs = []
for xyz in frames:
r, rdf = get_rdf(xyz, box=box, cutoff=cutoff, bins=50)
rdfs.append(rdf)
plt.plot(r, np.mean(rdfs, axis=0), color='teal')
plt.plot((0, cutoff), (1, 1), lw=1, color='k')
plt.xlim(0, cutoff)
plt.xlabel('r')
plt.ylabel('g(r)')
plt.tight_layout()
plt.savefig('rdf_hard_sphere.pdf')
plt.show()
@yangyushi
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yangyushi commented Oct 21, 2020

This is what I got with the ideal gas.

200 ideal gas particles in different dimensions with non-cubic box

@yangyushi
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This is what I got with different systems in 3D

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