In [59]:
import ads
import numpy as np
import json
import matplotlib.pyplot as plt
from collections import Counter, defaultdict
from datetime import datetime
import scipy
from scipy import stats, optimize
import pandas as pd
import glob
import pickle
%matplotlib inline
In [89]:
def double_gaussian(x, height1, loc1, scale1, height2, loc2, scale2):
return stats.norm(loc=loc1, scale=scale1).cdf(x)*height1 +\
stats.norm(loc=loc2, scale=scale2).cdf(x)*height2
def double_gaussian_pdf(x, height1, loc1, scale1, height2, loc2, scale2):
return stats.norm(loc=loc1, scale=scale1).pdf(x)*height1 +\
stats.norm(loc=loc2, scale=scale2).pdf(x)*height2
In [90]:
def double_skewnorm(x, a1, height1, loc1, scale1, a2, height2, loc2, scale2):
return stats.skewnorm(a1, loc=loc1, scale=scale1).cdf(x)*height1 +\
stats.skewnorm(a2, loc=loc2, scale=scale2).cdf(x)*height2
def double_skewnorm_pdf(x, a1, height1, loc1, scale1, a2, height2, loc2, scale2):
return stats.skewnorm(a1, loc=loc1, scale=scale1).pdf(x)*height1 +\
stats.skewnorm(a2, loc=loc2, scale=scale2).pdf(x)*height2
In [100]:
def measure_rsquared(model, data):
SSres = sum((data - model)**2)
SStot = sum((data - np.mean(data))**2)
return 1 - (SSres / SStot)
In [3]:
journals = ['Astronomy and Astrophysics',
"Astronomical Journal",
"The Astrophysical Journal",
"Monthly Notices of the Royal Astronomical Society"]
In [4]:
with open('/Users/spardy/.config/OAUTHS/ADS.json') as f:
TOKEN = json.load(f)['TOKEN']
ads.config.token = TOKEN
In [10]:
paper_store = defaultdict(list)
for year in range(2000, 2005):
year = str(year)
for journal in journals:
papers = ads.SearchQuery(q="pub:\"{journal}\" year:{year}".format(journal=journal, year=year),
fl=['id', 'pubdate', 'property','title', 'citation',
'keyword'], max_pages=20, rows=1000)
try:
for paper in papers:
if 'REFEREED' not in paper.property:
continue
if paper.keyword is None:
continue
title = paper.title
pubdate = paper.pubdate
citations = paper.citation
paper_store[pubdate].append({'id': paper.id, 'title':title,
'citations': citations})
except IndexError as e:
print(e)
pass
In [9]:
In [32]:
cumulative_citations = []
citations_pdf = []
citations = []
years = []
for journal in ['AA', 'MNRAS', 'ApJ', 'AJ']:
for filename in glob.glob('/Users/spardy/Data/{:s}_papers/*.pl'.format(journal)):
with open(filename, 'rb') as pf:
papers = pickle.load(pf)
for paper in papers:
if paper['citations'] is None:
continue
if len(paper['citations']) < 5:
continue
cites = np.fromiter(map(lambda c: int(c[:4]), paper['citations']), dtype=int)
Bins = np.arange(min(cites), 2018)
ncites, bins = np.histogram(cites, bins=Bins)
citations_pdf.append(ncites)
citations.append(cites)
cumulative_citations.append(np.cumsum(ncites))
years.append(bins)
In [79]:
Npapers = len(cumulative_citations)
In [80]:
nplots = 50
random_inds = np.random.choice(range(Npapers), size=nplots)
In [101]:
params = []
for i, ind in enumerate(random_inds):
size = len(citations[ind])
param_dict = {}
for distname, dist in zip(['skewnorm', 'powerlaw', '2-gaussians'],
[stats.skewnorm, stats.powerlaw, double_gaussian]):
param_dict[distname] = {}
if distname == '2-gaussians':
try:
popt, pcov = optimize.curve_fit(double_gaussian, years[ind][1:],
cumulative_citations[ind], p0=(1, 2000, 1, 1, 2000, 1))
if np.any(pcov == np.inf):
continue
cdf_fitted = double_gaussian(years[ind][1:], *popt)
param_dict[distname]['params'] = popt
except RuntimeError:
continue
else:
param = dist.fit(citations[ind])
cdf_fitted = dist.cdf(years[ind][1:], *param[:-2], loc=param[-2], scale=param[-1])*size
param_dict[distname]['params'] = param
rsqrd = measure_rsquared(cdf_fitted, cumulative_citations[ind])
param_dict[distname]['rsqrd'] = rsqrd
params.append(param_dict)
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1612: RuntimeWarning: divide by zero encountered in log
return log(self._pdf(x, *args))
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/optimize/minpack.py:779: OptimizeWarning: Covariance of the parameters could not be estimated
category=OptimizeWarning)
In [110]:
list(map(lambda x: max(x.items(), key=lambda kv: kv[1]['rsqrd'] if 'rsqrd' in kv[1] else 0), params))
Out[110]:
[('2-gaussians',
{'params': array([ 6.80954308e+00, 1.99734597e+03, 6.02815304e-01,
8.08895419e+00, 1.98793492e+03, 3.17786859e+00]),
'rsqrd': 0.99002994414494727}),
('2-gaussians',
{'params': array([ 2.96120722e+00, 2.00133321e+03, 3.09328260e+00,
2.06358479e+00, 2.00105836e+03, 1.19911920e-01]),
'rsqrd': 0.98169918182556593}),
('2-gaussians',
{'params': array([ 5.14617256e+00, 2.00655159e+03, 6.27978023e-01,
2.32791619e+01, 2.00236670e+03, 3.42460848e+00]),
'rsqrd': 0.99752919985357935}),
('2-gaussians',
{'params': array([ 1.89531892e+01, 2.00752655e+03, 7.05159071e+00,
1.45665091e+01, 2.00024932e+03, 1.58800612e+00]),
'rsqrd': 0.9912110580941943}),
('2-gaussians',
{'params': array([ 194.77288356, 2019.09822054, 6.82655019, 68.73584299,
2005.2685713 , 2.65616178]),
'rsqrd': 0.99511943449406948}),
('2-gaussians',
{'params': array([ 2.90203908e+01, 2.01549387e+03, 6.80904094e+00,
1.43476351e+01, 2.00351832e+03, 9.38746054e-01]),
'rsqrd': 0.99574713710284213}),
('2-gaussians',
{'params': array([ 3.12217105e+00, 1.97321156e+03, 4.51992931e-01,
4.88301967e+00, 1.98457916e+03, 3.35489474e+00]),
'rsqrd': 0.98804115405281079}),
('skewnorm',
{'params': (-1.5132612773171792, 2013.3936646356988, 4.51072755343354),
'rsqrd': 0.9418937099595176}),
('2-gaussians',
{'params': array([ 204.23970608, 2011.59793108, 19.90510767, 49.81313732,
1980.35167502, 2.85552894]),
'rsqrd': 0.99466968357804664}),
('2-gaussians',
{'params': array([ 71.35037065, 2013.31078354, 19.09069698, 33.58628231,
1977.64412055, 2.17724508]),
'rsqrd': 0.99494045567474365}),
('skewnorm',
{'params': (0.033137073180728352, 2009.2687839848545, 4.9656033202613425),
'rsqrd': 0.93906082799654067}),
('powerlaw',
{'params': (0.8454225220077668, 2009.9999999999995, 7.0079169869334947),
'rsqrd': 0.91651442253034088}),
('skewnorm',
{'params': (0.44471213103361196, 2011.4138520873428, 2.0878754706959173),
'rsqrd': 0.94064771728164132}),
('2-gaussians',
{'params': array([ 5.13511379e+00, 1.98539962e+03, 1.38774896e+00,
1.86875546e+00, 1.99164196e+03, 1.09988217e+00]),
'rsqrd': 0.98941877647744492}),
('skewnorm',
{'params': (4306379.8184352778, 2007.9999944983028, 4.5634520695645531),
'rsqrd': 0.93611586574130845}),
('2-gaussians',
{'params': array([ 5.40381724e+01, 2.00358822e+03, 3.12143616e+00,
6.22656079e+00, 2.01251271e+03, 5.58404079e-01]),
'rsqrd': 0.99486830364489331}),
('skewnorm',
{'params': (11.981616250594453, 2006.3267090973952, 5.2131192590821218),
'rsqrd': 0.95500639543842003}),
('2-gaussians',
{'params': array([ 29.91208178, 2000.90556518, 8.46556604, 27.52499431,
1990.80390359, 2.99318291]),
'rsqrd': 0.99289337358175356}),
('skewnorm',
{'params': (10.884373840649793, 2005.3807736864605, 5.2306170336156699),
'rsqrd': 0.97259295890522957}),
('2-gaussians',
{'params': array([ 13.18806033, 1984.4053614 , 4.28325318, 12.74932977,
1993.94656604, 18.44684988]),
'rsqrd': 0.9894727311365259}),
('2-gaussians',
{'params': array([ 22.64723786, 1994.21091117, 16.18021649, 20.47819747,
1980.27965979, 2.40724752]),
'rsqrd': 0.98186536861577189}),
('powerlaw',
{'params': (0.9592589819115338, 1978.9999999999998, 38.004588031634512),
'rsqrd': 0.98169098746235262}),
('2-gaussians',
{'params': array([ 3.19486497e+00, 2.00281845e+03, 3.41584568e+00,
5.78774082e+00, 1.99239327e+03, 1.28746977e+00]),
'rsqrd': 0.95205354730710046}),
('2-gaussians',
{'params': array([ 12.24911941, 1989.27969021, 2.06680684, 3.79978545,
1987.49577517, 9.13047446]),
'rsqrd': 0.98923212096563784}),
('skewnorm',
{'params': (8354776.6861654595, 2003.9999956879883, 6.5703425732245009),
'rsqrd': 0.33181170510658453}),
('skewnorm',
{'params': (21.493077850088838, 1995.3946254908133, 7.1309817810849427),
'rsqrd': 0.97862660758299735}),
('2-gaussians',
{'params': array([ 35.89327945, 1991.12549599, 5.209 , 13.14882748,
2009.73364803, 3.42521202]),
'rsqrd': 0.99443946506028136}),
('2-gaussians',
{'params': array([ 268.43532141, 2001.75051401, 9.13126514, 136.16441134,
1989.49418533, 4.35101564]),
'rsqrd': 0.9986415525285095}),
('2-gaussians',
{'params': array([ 175.7748337 , 2005.93674745, 8.55580373, 106.67426471,
2002.76487068, 2.74681026]),
'rsqrd': 0.99875513495173551}),
('2-gaussians', {}),
('2-gaussians',
{'params': array([ 2.47070802e+00, 2.01287267e+03, 1.52875949e-01,
3.80293085e+01, 1.99569080e+03, 3.89186034e+00]),
'rsqrd': 0.99439615941831372}),
('2-gaussians',
{'params': array([ 53.06040577, 1980.3038401 , 2.72240736, 41.93780355,
1990.78108616, 9.32107423]),
'rsqrd': 0.98910662443718111}),
('skewnorm',
{'params': (81194931.32888332, 2000.9999996030069, 5.8418494727221173),
'rsqrd': 0.97379618661612399}),
('2-gaussians',
{'params': array([ 7.07535250e+00, 2.01519920e+03, 3.57154184e-01,
1.89674706e+01, 2.00038806e+03, 3.33993517e+00]),
'rsqrd': 0.97572085334783198}),
('2-gaussians',
{'params': array([ 1.38495910e+01, 2.00072628e+03, 4.41105491e+00,
1.57935970e+01, 2.01132311e+03, 1.81935500e+00]),
'rsqrd': 0.99641083525552143}),
('skewnorm',
{'params': (7.9321391451662326e-05, 2012.8646944771472, 2.692955369402692),
'rsqrd': 0.85856359025878271}),
('skewnorm',
{'params': (-7689.8355968700853, 2014.0028095590278, 6.1669987648521509),
'rsqrd': 0.8369471538111376}),
('skewnorm',
{'params': (-0.25425301423539626, 2012.0543317018564, 2.8624825395372144),
'rsqrd': 0.95603370560723056}),
('2-gaussians',
{'params': array([ 1.43762199e+01, 1.98726134e+03, 4.59317580e-01,
1.55529935e+01, 1.99461530e+03, 4.88686234e+00]),
'rsqrd': 0.99475548627116905}),
('2-gaussians',
{'params': array([ 45.36669809, 1997.65700802, 3.33459076, 14.3086384 ,
2004.68202823, 5.51807102]),
'rsqrd': 0.99451180590230948}),
('skewnorm',
{'params': (-0.36600476072543298, 2011.0479977287778, 4.428805469144752),
'rsqrd': 0.92973895371064463}),
('skewnorm',
{'params': (0.35593893574209601, 2012.0321695565922, 2.5771185425242376),
'rsqrd': 0.95512979992020564}),
('skewnorm',
{'params': (8486857.7085234374, 2002.9999961477715, 5.9749503612422004),
'rsqrd': 0.98218379807469058}),
('skewnorm',
{'params': (1358219.977682176, 2009.9999863713174, 3.8738428644446721),
'rsqrd': 0.79347033130794298}),
('skewnorm',
{'params': (11094442.740932308, 2005.9999976081072, 5.1644614473787911),
'rsqrd': 0.95947587662810496}),
('2-gaussians',
{'params': array([ 9.74793032e+01, 1.99132191e+03, 7.53024346e+00,
2.89180842e+01, 1.97995819e+03, 1.46207055e+00]),
'rsqrd': 0.99638211843852942}),
('2-gaussians',
{'params': array([ 8.60264877, 2012.52581719, 2.68777557, 17.38115869,
1999.59145319, 3.26008135]),
'rsqrd': 0.99140140675310595}),
('skewnorm',
{'params': (2.4487762062790868, 1994.8338839448322, 10.160270802548466),
'rsqrd': 0.96267875940754699}),
('2-gaussians',
{'params': array([ 5.74116964e+00, 1.98156554e+03, 1.24756091e+01,
1.34246322e+00, 1.98898936e+03, 3.29714754e-02]),
'rsqrd': 0.95482511759052513}),
('2-gaussians',
{'params': array([ 2.54361114e+01, 2.00519397e+03, 4.59612183e+00,
6.93541166e+00, 1.99440381e+03, 3.39188776e-01]),
'rsqrd': 0.99646776417874328})]
In [116]:
cumulative_citations[ind]
Out[116]:
array([3, 3, 3, 3, 3, 4, 4, 5])
In [117]:
param = params_['skewnorm']['params']
cdf_fitted = stats.powerlaw.cdf(years[ind][1:], *param[:-2], loc=param[-2], scale=param[-1])*size
In [119]:
measure_rsquared(cdf_fitted, cumulative_citations[ind])
Out[119]:
-8.25
In [115]:
params_
Out[115]:
{'2-gaussians': {},
'powerlaw': {'params': (1.2102806958182812,
2007.8775209581715,
8.1224790424038567),
'rsqrd': -1.0326488933964972},
'skewnorm': {'params': (9292214.6605320293,
2008.9999978741771,
3.8471536164923581),
'rsqrd': -0.72880246812840577}}
In [124]:
colors = {'2-gaussians': '#66c2a5', 'powerlaw': '#fc8d62', 'skewnorm': '#8da0cb'}
In [125]:
ncols = 5
nrows = int(np.ceil(nplots / ncols))
fig, axes = plt.subplots(nrows, ncols, figsize=(ncols*2, nrows*2))
axes = axes.flatten()
for i, ind in enumerate(random_inds):
axis = axes[i]
axis.plot(years[ind][1:], citations_pdf[ind], color='black', linewidth=2)
maxy = max(citations_pdf[ind])
size = len(citations[ind])
axis.set_ylim(0, maxy+2)
axis.set_title(str(ind))
try:
params_ = params[i]
best_fit = max(params_.items(), key=lambda kv: kv[1]['rsqrd'] if 'rsqrd' in kv[1] else 0)
distname = best_fit[0]
best_params = best_fit[1]['params']
except KeyError:
continue
if distname == '2-gaussians':
axis.plot(years[ind][1:], double_gaussian_pdf(years[ind][1:], *best_params),
color=colors[distname])
elif distname == 'powerlaw':
pdf_fitted = stats.powerlaw.pdf(years[ind][1:], *best_params[:-2],
loc=best_params[-2], scale=best_params[-1])*size
axis.plot(years[ind][1:], pdf_fitted,
color=colors[distname])
elif distname == 'skewnorm':
pdf_fitted = stats.skewnorm.pdf(years[ind][1:], *best_params[:-2],
loc=best_params[-2], scale=best_params[-1])*size
axis.plot(years[ind][1:], pdf_fitted,
color=colors[distname])
fig.suptitle('Citations per year', y=1.01)
fig.text(0.5, -0.01, 'Year', ha='center', fontsize=14)
fig.text(-0.01, 0.5, 'Citations', va='center', rotation='vertical', fontsize=14)
fig.tight_layout()
#fig.savefig('/Users/spardy/Desktop/citations_per_year.pdf', dpi=300, bbox_inches='tight')
In [126]:
fig, axes = plt.subplots(nrows, ncols, figsize=(ncols*2, nrows*2))
axes = axes.flatten()
for i, ind in enumerate(random_inds):
axis = axes[i]
axis.plot(years[ind][1:], cumulative_citations[ind], color='black', linewidth=2)
maxy = max(cumulative_citations[ind])
size = len(citations[ind])
axis.set_ylim(0, maxy*1.1)
axis.set_title(str(ind))
try:
params_ = params[i]
best_fit = max(params_.items(), key=lambda kv: kv[1]['rsqrd'] if 'rsqrd' in kv[1] else 0)
distname = best_fit[0]
best_params = best_fit[1]['params']
except KeyError:
continue
if distname == '2-gaussians':
axis.plot(years[ind][1:], double_gaussian(years[ind][1:], *best_params),
color=colors[distname])
elif distname == 'powerlaw':
cdf_fitted = stats.powerlaw.cdf(years[ind][1:], *best_params[:-2],
loc=best_params[-2], scale=best_params[-1])*size
axis.plot(years[ind][1:], cdf_fitted,
color=colors[distname])
elif distname == 'skewnorm':
cdf_fitted = stats.skewnorm.cdf(years[ind][1:], *best_params[:-2],
loc=best_params[-2], scale=best_params[-1])*size
axis.plot(years[ind][1:], cdf_fitted,
color=colors[distname])
fig.suptitle('Cumulative Citations', y=1.01)
fig.text(0.5, -0.01, 'Year', ha='center', fontsize=14)
fig.text(-0.01, 0.5, 'Cumulative Citations', va='center', rotation='vertical', fontsize=14)
fig.tight_layout()
#fig.savefig('/Users/spardy/Desktop/cumulative_citations.pdf', dpi=300, bbox_inches='tight')
In [155]:
param
Out[155]:
(14445359.301196963, 2008.9999983427651, 4.612964068572615)
In [159]:
import multiprocess
In [157]:
parameters = []
for paper_citations in citations:
size = len(paper_citations)
a, loc, scale = dist.fit(paper_citations)
parameters.append({'a': a, 'loc': loc, 'scale': scale})
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py:1612: RuntimeWarning: divide by zero encountered in log
return log(self._pdf(x, *args))
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
<ipython-input-157-e08a7a2f91ba> in <module>()
2 for paper_citations in citations:
3 size = len(paper_citations)
----> 4 a, loc, scale = dist.fit(paper_citations)
5 parameters.append({'a': a, 'loc': loc, 'scale': scale})
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/stats/_distn_infrastructure.py in fit(self, data, *args, **kwds)
2206 raise TypeError("Unknown arguments: %s." % kwds)
2207
-> 2208 vals = optimizer(func, x0, args=(ravel(data),), disp=0)
2209 if restore is not None:
2210 vals = restore(args, vals)
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/optimize/optimize.py in fmin(func, x0, args, xtol, ftol, maxiter, maxfun, full_output, disp, retall, callback, initial_simplex)
391 'initial_simplex': initial_simplex}
392
--> 393 res = _minimize_neldermead(func, x0, args, callback=callback, **opts)
394 if full_output:
395 retlist = res['x'], res['fun'], res['nit'], res['nfev'], res['status']
/Users/spardy/anaconda/lib/python3.6/site-packages/scipy/optimize/optimize.py in _minimize_neldermead(func, x0, args, callback, maxiter, maxfev, disp, return_all, initial_simplex, xatol, fatol, **unknown_options)
525
526 while (fcalls[0] < maxfun and iterations < maxiter):
--> 527 if (numpy.max(numpy.ravel(numpy.abs(sim[1:] - sim[0]))) <= xatol and
528 numpy.max(numpy.abs(fsim[0] - fsim[1:])) <= fatol):
529 break
/Users/spardy/anaconda/lib/python3.6/site-packages/numpy/core/fromnumeric.py in ravel(a, order)
1466 return asarray(a).ravel(order=order)
1467 else:
-> 1468 return asanyarray(a).ravel(order=order)
1469
1470
/Users/spardy/anaconda/lib/python3.6/site-packages/numpy/core/numeric.py in asanyarray(a, dtype, order)
581
582 """
--> 583 return array(a, dtype, copy=False, order=order, subok=True)
584
585
KeyboardInterrupt:
In [160]:
parameters
Out[160]:
[{'a': -105831.93078715907,
'loc': 2014.0002410584984,
'scale': 6.1401893670710255},
{'a': -554.56428039992898,
'loc': 2015.0280468613018,
'scale': 5.7025861994756539},
{'a': -551621.12788155023,
'loc': 2009.0000332565232,
'scale': 3.9823697698643343},
{'a': -3.7719269495250654,
'loc': 2011.2982376901869,
'scale': 4.8914792625754888},
{'a': 8203130.5841140319,
'loc': 2000.9999973338199,
'scale': 4.3589383118075169},
{'a': 0.000239735465342864,
'loc': 2009.3170490759044,
'scale': 4.9274370436964592},
{'a': -419.12460439411825,
'loc': 2017.054677142125,
'scale': 9.1469058223477546},
{'a': -3.5202786714769068,
'loc': 2016.2422862872627,
'scale': 7.4636553615064294},
{'a': -4471.4733269034405,
'loc': 2017.0066092522611,
'scale': 8.6245277160400562},
{'a': 9.7896514530872807,
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...]
In [163]:
params = pd.DataFrame(parameters)
In [169]:
fig, axes = plt.subplots(1, 3, figsize=(15, 5))
axis = axes[0]
axis.plot(params['a'], params['loc'], 'k.', alpha=0.2)
axis.set_xlabel('a')
axis.set_ylabel('loc')
axis = axes[1]
axis.plot(params['a'], params['scale'], 'k.', alpha=0.2)
axis.set_xlabel('a')
axis.set_ylabel('scale')
axis = axes[2]
axis.plot(params['loc'], params['scale'], 'k.', alpha=0.2)
axis.set_xlabel('loc')
axis.set_ylabel('scale')
Out[169]:
<matplotlib.text.Text at 0x1354b18d0>
In [ ]:
Content source: stephenpardy/PythonNotebooks
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