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step4_SupplementaryFigures.py
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# -*- coding: utf-8 -*-
import os, sys
import numpy as np
import pandas as pd
import datetime
import csv, pickle, json, geojson
from gekko import GEKKO
import matplotlib.pyplot as plt
import seaborn as sns
import itertools, collections
from sklearn.metrics import r2_score
from scipy import stats
import scipy.optimize as optimization
# from scipy.stats import ks_2samp
# other distance metrics beyond KS test
# from scipy.stats import wasserstein_distance # accept the values of samples
# the following two distance only accept probility / histogram
# from scipy.stats import entropy # Kullback-Leibler divergence S = sum(pk * log(pk / qk), axis=axis).
from scipy.spatial import distance # Jensen-Shannon distance (JSD)
from scipy.integrate import odeint
from scipy.stats import lognorm, beta
# !pip install lmfit
import lmfit
from lmfit.lineshapes import gaussian, lorentzian
import statsmodels.api as sm
import step0_dataPreparation
import step3_socioeconomic
dataPath = "/Volumes/TOSHIBA EXT/Study/HuMNetLab/Data/Spain/"
cities_Luis = ["LA", "Atlanta", "Bogota", "Boston", "SFBay", "Lisbon",
"Porto", "Rio", "Shenzhen", "Wuhan"]
cities_Spain = ["Madrid", "Barcelona", "Valencia", "Alicante", "Coruna", \
"Zaragoza", "Sevilla", "Malaga", "Bilbao", "SantaCruz", "Granada"]
provinces_spain = ["Madrid", "Barcelona", "Valencia/València", "Alicante/Alacant", "Coruña, A", "Zaragoza",
"Sevilla", "Málaga", "Bizkaia", "Santa Cruz de Tenerife", "Granada"]
city_To_CCAA = {"Madrid": "Madrid", "Barcelona": 'Cataluña', "Valencia": 'CValenciana',
"Alicante": 'CValenciana', "Coruna": 'Galicia', \
"Zaragoza": 'Aragón', "Sevilla": 'Andalucía', "Malaga": 'Andalucía',\
"Bilbao": 'PaísVasco', "SantaCruz": 'Canarias', "Granada": 'Andalucía'}
cityColors = {"Madrid": "#990000", "Barcelona": "#C855F0", "Valencia": "#5a463f", \
"Alicante": "#000000", "Coruna": "#145450", "Zaragoza": "#080358", \
"Sevilla": "#2569b4", "Malaga": "#19a1db", "Bilbao": "#d51968",\
"SantaCruz": "#a56405", "Granada": "#f7a81b",
"LA": "#b41f24", "Atlanta": "#ef4b57",
"Bogota": "#95ad05", "Boston": "#009145", "SFBay": "#207492",
"Lisbon": "#5c2b7c", "Porto": "#ba2db3", "Rio": "#f7987f",
"Shenzhen": "#1fc1b1", "Wuhan": "#b7583e", "Shanghai": "#4f4e4e"}
cityMarkers = {"Madrid": "o", "Barcelona": "s", "Valencia": "^", \
"Alicante": "H", "Coruna": "D", "Zaragoza": "P", \
"Sevilla": "<", "Malaga": "X", "Bilbao": "v",\
"SantaCruz": "d", "Granada": "*",
"LA": "o", "Atlanta": "s",
"Bogota": "^", "Boston": "H", "SFBay": "D",
"Lisbon": "P", "Porto": "<", "Rio": "X",
"Shenzhen": "v", "Wuhan": "d", "Shanghai": "*"}
cityFaceColors = {"Madrid": "None", "Barcelona": "None", "Valencia": "None", \
"Alicante": "None", "Coruna": "None", "Zaragoza": "None", \
"Sevilla": "None", "Malaga": "None", "Bilbao": "None",\
"SantaCruz": "None", "Granada": "None",
"LA": "#b41f24", "Atlanta": "#ef4b57",
"Bogota": "#95ad05", "Boston": "#009145", "SFBay": "#207492",
"Lisbon": "#5c2b7c", "Porto": "#ba2db3", "Rio": "#f7987f",
"Shenzhen": "#1fc1b1", "Wuhan": "#b7583e", "Shanghai": "#4f4e4e"}
def scatterfit_linear(x, y, a=None, b=None):
"""
Compute the mean deviation of the data about the linear model given if A,B
(y=ax+b) provided as arguments. Otherwise, compute the mean deviation about
the best-fit line.
x,y assumed to be Numpy arrays. a,b scalars.
Returns the float sd with the mean deviation.
Author: Rodrigo Nemmen
"""
if a == None:
print("err, pls input fitted parameters.")
return -1
# Std. deviation of an individual measurement (Bevington, eq. 6.15)
N = np.size(x)
yHat = np.multiply(x, a) + b
sd = 1. / (N - 2.) * np.sum((y - yHat) ** 2)
sd = np.sqrt(sd)
return sd
def confband_linear(xd, yd, a, b, conf=0.95, x=None):
"""
Calculates the confidence band of the linear regression model at the desired confidence
level, using analytical methods. The 2sigma confidence interval is 95% sure to contain
the best-fit regression line. This is not the same as saying it will contain 95% of
the data points.
Arguments:
- conf: desired confidence level, by default 0.95 (2 sigma)
- xd,yd: data arrays
- a,b: linear fit parameters as in y=ax+b
- x: (optional) array with x values to calculate the confidence band. If none is provided, will
by default generate 100 points in the original x-range of the data.
Returns:
Sequence (lcb,ucb,x) with the arrays holding the lower and upper confidence bands
corresponding to the [input] x array.
Usage:
>>> lcb,ucb,x=nemmen.confband(all.kp,all.lg,a,b,conf=0.95)
calculates the confidence bands for the given input arrays
>>> pylab.fill_between(x, lcb, ucb, alpha=0.3, facecolor='gray')
plots a shaded area containing the confidence band
References:
1. http://en.wikipedia.org/wiki/Simple_linear_regression, see Section Confidence intervals
2. http://www.weibull.com/DOEWeb/confidence_intervals_in_simple_linear_regression.htm
Author: Rodrigo Nemmen
v1 Dec. 2011
v2 Jun. 2012: corrected bug in computing dy
"""
alpha = 1. - conf # significance
n = xd.size # data sample size
# if x == None:
# x = np.linspace(xd.min(), xd.max(), 100)
# Predicted values (best-fit model)
# y = a * x + b
y = np.multiply(x, a) + b
# Auxiliary definitions
sd = scatterfit_linear(xd, yd, a, b) # Scatter of data about the model
sxd = np.sum((xd - xd.mean()) ** 2)
sx = (x - xd.mean()) ** 2 # array
# Quantile of Student's t distribution for p=1-alpha/2
q = stats.t.ppf(1. - alpha / 2., n - 2)
# Confidence band
dy = q * sd * np.sqrt(1. / n + sx / sxd)
ucb = y + dy # Upper confidence band
lcb = y - dy # Lower confidence band
return lcb, ucb, x
def scatterfit_scaling(x, y, a=None, b=None):
"""
Compute the mean deviation of the data about the linear model given if A,B
(y=ax+b) provided as arguments. Otherwise, compute the mean deviation about
the best-fit line.
x,y assumed to be Numpy arrays. a,b scalars.
Returns the float sd with the mean deviation.
Author: Rodrigo Nemmen
"""
if a == None:
print("err, pls input fitted parameters.")
return -1
# Std. deviation of an individual measurement (Bevington, eq. 6.15)
N = np.size(x)
yHat = np.multiply(np.power(x, a), np.power(10, b))
sd = 1. / (N - 2.) * np.sum((y - yHat) ** 2)
sd = np.sqrt(sd)
return sd
def confband_scaling(xd, yd, a, b, conf=0.95, x=None):
"""
Calculates the confidence band of the linear regression model at the desired confidence
level, using analytical methods. The 2sigma confidence interval is 95% sure to contain
the best-fit regression line. This is not the same as saying it will contain 95% of
the data points.
Arguments:
- conf: desired confidence level, by default 0.95 (2 sigma)
- xd,yd: data arrays
- a,b: linear fit parameters as in y=ax+b
- x: (optional) array with x values to calculate the confidence band. If none is provided, will
by default generate 100 points in the original x-range of the data.
Returns:
Sequence (lcb,ucb,x) with the arrays holding the lower and upper confidence bands
corresponding to the [input] x array.
Usage:
>>> lcb,ucb,x=nemmen.confband(all.kp,all.lg,a,b,conf=0.95)
calculates the confidence bands for the given input arrays
>>> pylab.fill_between(x, lcb, ucb, alpha=0.3, facecolor='gray')
plots a shaded area containing the confidence band
References:
1. http://en.wikipedia.org/wiki/Simple_linear_regression, see Section Confidence intervals
2. http://www.weibull.com/DOEWeb/confidence_intervals_in_simple_linear_regression.htm
Author: Rodrigo Nemmen
v1 Dec. 2011
v2 Jun. 2012: corrected bug in computing dy
"""
alpha = 1. - conf # significance
n = xd.size # data sample size
# if x == None:
# x = np.linspace(xd.min(), xd.max(), 100)
# Predicted values (best-fit model)
# y = a * x + b
y = np.multiply(np.power(x, a), np.power(10, b))
# Auxiliary definitions
sd = scatterfit_scaling(xd, yd, a, b) # Scatter of data about the model
sxd = np.sum((xd - xd.mean()) ** 2)
sx = (x - xd.mean()) ** 2 # array
# Quantile of Student's t distribution for p=1-alpha/2
q = stats.t.ppf(1. - alpha / 2., n - 2)
# Confidence band
dy = q * sd * np.sqrt(1. / n + sx / sxd)
ucb = y + dy # Upper confidence band
lcb = y - dy # Lower confidence band
return lcb, ucb, x
# plot the CDF of two lognormal distribuionts for Fig. 2D
def plotKSTest_beta():
a1, b1 = 2, 4
a2, b2 = 2, 2
a3, b3 = 1, 3
x = np.linspace(0, 1, 100)
y1 = beta.cdf(x, a1, b1)
y2 = beta.cdf(x, a2, b2)
y3 = beta.cdf(x, a3, b3)
fig = plt.figure(figsize=(4,3))
# plt.plot(x, y1, lw=2, c='#f15a29', label="y1")
# plt.plot(x, y2, lw=2, c='#1c75bc', label="y2")
plt.plot(x, y3, lw=2, c='#eb008b')
plt.xlabel('Performance')
plt.xlim(0,1)
# plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + 'results/revision/KStest_CDFs_2F.pdf')
plt.close()
# variant distance metrics between two sets of samples
def distanceComparison():
a = [0.2, 1, 3]
b = [5, 6, 8]
c = [5, 6, 8.1]
a1 = np.asarray(a)
a1.sort()
b1 = np.asarray(b)
b1.sort()
c1 = np.asarray(c)
c1.sort()
KSD, pvalue = stats.ks_2samp(a1, c1)
print(KSD)
a = [float(i)/sum(a) for i in a]
b = [float(i)/sum(b) for i in b]
c = [float(i)/sum(c) for i in c]
# print(a,b,c)
WD = stats.wasserstein_distance(a, c)
print(WD)
KLD = stats.entropy(a, c)
print(KLD)
KLD = stats.entropy(c, a)
print(KLD)
JSD = distance.jensenshannon(a, c)
print(JSD)
JSD = distance.jensenshannon(c, a)
print(JSD)
return 0
# variant distance metrics between two sets of samples
def distanceComparison_realData():
# load the Rg for the three cities
# Boston, LA, Bogota
return 0
# relation between rg and income
def RgAndIncome():
return 0
# group Rgs into rings in city
def groupingRgsIntoRings(city="Boston"):
city_lower = city.lower()
cityInfo = pickle.load(open(dataPath + "results/cityInfo_all.pkl", "rb"))
cityRadius, _, _, _, _, _, _, _ = cityInfo[city]
if city == "Lisbon": # the map of Lisbon is too large, we limit the radius to 36km
cityRadius = 36
# load distance to CBD
distanceToCBD = pickle.load(open(dataPath + "Luis/" + city + "/distanceToCBD_tract.pkl", "rb"))
towerLoc, towerToCBD = step0_dataPreparation.towerDistanceToCBD(city, cityRadius)
towerLocToId = dict()
for tid in towerLoc:
towerLocToId[towerLoc[tid]] = tid
towersInCity = set(towerLoc.keys())
# load the Rgs of all mobile phone users
gyData = open(dataPath + "Luis/" + city + "/rgy_" + city_lower + "_info.csv", "r")
gyData.readline()
Rgs = [] # group the popualtion into 3km rings, g0:0-3km. g1:3-6km, ...
gyrationsInGroups = {}
count = 0
for row in gyData:
count += 1
row = row.rstrip().split(",")
if city=="Rio":
if 'NA' in row[:4]:
# print(row)
continue
homeGeoID = row[0]
lon = float(row[1])
lat = float(row[2])
mean_gyration = float(row[3]) # mean gyration in km
if mean_gyration == 19.4460297117887:
continue
elif city == "Atlanta":
if 'NA' in row[:4]:
# print(row)
continue
homeGeoID = row[0]
lon = float(row[2])
lat = float(row[1])
mean_gyration = float(row[3]) # mean gyration in km
elif city == "Shanghai":
if 'NA' in row:
# print(row)
continue
homeGeoID = row[0]
lon = float(row[1])
lat = float(row[2])
gyrations = [float(g) for g in row[3:] if float(g)>0]
# if 0 in gyrations:
# continue
if len(gyrations) == 0:
continue
mean_gyration = np.mean(gyrations) # mean gyration in km
elif city in ["Shenzhen", "Wuhan"]:
if 'NA' in row[:4]:
# print(row)
continue
homeGeoID = row[0]
lon = float(row[3])
lat = float(row[2])
mean_gyration = float(row[1]) # mean gyration in km
else:
if 'NA' in row[:6]:
# print(row)
continue
homeGeoID = row[0]
lon = float(row[4])
lat = float(row[5])
mean_gyration = float(row[2]) # mean gyration in km
'''
# Only keep population in city bondaries
try:
homeGeoID_fromLoc = towerLocToId[(lon, lat)] # int(row[0])
except:
continue
if homeGeoID_fromLoc not in towersInCity:
continue
d = towerToCBD[homeGeoID_fromLoc]
'''
d = distanceToCBD[homeGeoID]
if d >= cityRadius+1:
# print(d, cityRadius)
continue
group = int(d)//3
Rgs.append([mean_gyration, group])
if group not in gyrationsInGroups:
gyrationsInGroups[group] = [mean_gyration]
else:
gyrationsInGroups[group].append(mean_gyration)
gyData.close()
# write data
outData = open(dataPath + "Luis/" + city + "/rgy_" + city_lower + "_groups.csv", "w")
outData.writelines("Rg,group\n")
for row in Rgs:
row = ','.join([str(i) for i in row]) + "\n"
outData.writelines(row)
outData.close()
return 0
# distribution of gyrations in groups
fig = plt.figure(figsize=(3.6,2.7))
linestyles = ['solid', 'dashed', 'dotted', 'dashdot', \
(0, (5, 1)), (0, (5, 10)), (0, (3, 1, 1, 1))]
groupNames = ['0-3 km', '3-6 km', '6-9 km', '9-12 km', '12-15 km', '15-18 km', '18-21 km']
for g in range(7):
# d_max is smaller than 21
if len(gyrationsInGroups[g]) == 0:
continue
bins = np.linspace(0, 50, 51)
usagesHist = np.histogram(np.array(gyrationsInGroups[g]), bins)
# bins = np.array(bins[:-1])
usagesHist = np.divide(usagesHist[0], float(np.sum(usagesHist[0])))
usagesHist = [0] + usagesHist.tolist()
# print(usagesHist)
plt.plot(bins.tolist(), usagesHist, linewidth=1, linestyle=linestyles[g],\
c=cityColors[city], label=groupNames[g])
plt.xlim(0, 51)
plt.ylim(0, 0.25)
# plt.ylim(0.001)
# plt.yscale("log")
plt.xticks(range(0, 51, 10), fontsize=12)
plt.yticks([0, 0.05, 0.1, 0.15, 0.2, 0.25], fontsize=12)
plt.xlabel(r'$Rg$ [km]', fontsize=14)
plt.ylabel(r"$P(Rg)$ [km$^{-1}$]", fontsize=14)
plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + "Luis/" + city + '/Rgs_byGroup_' + city + '.png', dpi=200)
plt.savefig(dataPath + "Luis/" + city + '/Rgs_byGroup_' + city + '.pdf')
plt.close()
# group Rgs into rings in city
def groupingRgsIntoRings_city(city="Boston", gapWidth=3):
city_lower = city.lower()
# load the Rgs of all mobile phone users
ringGyrations, gyrationsInSevenGroups = pickle.load(open(dataPath + "results/Rgs_" + city + ".pkl", "rb"))
# keep in 50 km
if len(ringGyrations) > 50:
ringGyrations = ringGyrations[:51]
if city == "Lisbon":
ringGyrations = ringGyrations[:36]
Rgs = [] # group the popualtion into 3km rings, g0:0-3km. g1:3-6km, ...
gyrationsInGroups = {}
numUsers = 0
for d in range(len(ringGyrations)):
rgys = ringGyrations[d]
numUsers += len(rgys)
group = int(d)//gapWidth
# group= int(np.floor(d/3.0))
for rg in rgys:
Rgs.append([rg, group])
if group not in gyrationsInGroups:
gyrationsInGroups[group] = rgys
else:
gyrationsInGroups[group] += rgys
print(city + " No. users : %d" % numUsers)
# write data
outData = open(dataPath + "Luis/" + city + "/rgy_" + city_lower + "_groups_" + str(gapWidth) + "km.csv", "w")
outData.writelines("Rg,group\n")
for row in Rgs:
row = ','.join([str(i) for i in row]) + "\n"
outData.writelines(row)
outData.close()
# we remove ZERO Rg when calcualte the KS
def distanceComparison_city(city="Boston", numBins=150):
city_lower = city.lower()
# load city Rg groups
inData = open(dataPath + "Luis/" + city + "/rgy_" + city_lower + "_groups_1km.csv", "r")
header = inData.readline()
gyrationsInGroups = {}
for row in inData:
row = row.rstrip().split(",")
rgy = float(row[0])
group = int(row[1])
if group not in gyrationsInGroups:
gyrationsInGroups[group] = [rgy]
else:
gyrationsInGroups[group].append(rgy)
inData.close()
maxR = np.max(list(gyrationsInGroups.keys())) + 1
print("Max No. of rings : %d" % maxR)
# remove abnormal and zero values
allGyrations = list(gyrationsInGroups.values())
allGyrations = list(itertools.chain(*allGyrations))
allGyrations = sorted(allGyrations)
RgThres = np.percentile(allGyrations, 95)
for group in gyrationsInGroups:
values = gyrationsInGroups[group]
values = [rg for rg in values if rg < RgThres]
values = [rg for rg in values if rg < 100]
values = [rg for rg in values if rg > 0]
gyrationsInGroups[group] = values
# maxR = min(maxR, 17) # 3km
# maxR = min(maxR, 26) # 2km
maxR = min(maxR, 51) # 1km
# calculate distribution distance between groups
rgyGaps = {"KS":[0], "WD":[0], "KL":[0], "JSD":[0], "relativeRg":[0]}
CBDRgs = gyrationsInGroups[0]
CBDRgs_mean = np.mean(CBDRgs)
bins = np.linspace(0, 50, numBins+1)
usagesHist_0 = np.histogram(np.asarray(CBDRgs), bins)
usagesHist_0 = np.divide(usagesHist_0[0], float(np.sum(usagesHist_0[0])))
distToCBD = [0]
for g in range(1,maxR):
try:
ringRgs = gyrationsInGroups[g]
except:
continue
# print("min V :%.2f" % np.min(ringRgs))
dist_ks = step0_dataPreparation.KSTest(ringRgs, CBDRgs)
# relative change of avgRg
ringRgs_mean = np.mean(ringRgs)
dist_rg = np.abs(ringRgs_mean-CBDRgs_mean) / CBDRgs_mean
# prepare the histogram for other distance metrics
usagesHist_d = np.histogram(np.asarray(ringRgs), bins)
usagesHist_d = np.divide(usagesHist_d[0], float(np.sum(usagesHist_d[0])))
# replace zero by small value
eps = 1e-10
usagesHist_d[usagesHist_d == 0] = eps
dist_wd = stats.wasserstein_distance(usagesHist_0, usagesHist_d)
dist_kl = stats.entropy(usagesHist_0, usagesHist_d)
dist_jsd = distance.jensenshannon(usagesHist_0, usagesHist_d)
rgyGaps["KS"].append(dist_ks)
rgyGaps["WD"].append(dist_wd)
rgyGaps["KL"].append(dist_kl)
rgyGaps["JSD"].append(dist_jsd)
rgyGaps["relativeRg"].append(dist_rg)
distToCBD.append(g/maxR)
# print(rgyGaps)
'''
# scatter plot
fig = plt.figure(figsize=(3.6,2.7))
distNames = ["JSD", "KL", "WD", "KS"]
for d in range(4):
dn = distNames[d]
dv = np.asarray(rgyGaps[dn])
# plt.scatter(dv, [d for i in range(7)], lw=0, s=30, c=cityColors[city], alpha=dv/0.4)
for i in range(maxR):
plt.scatter(dv[i], d, lw=1, s=50, c=cityColors[city], alpha=(i+1)/7)
# plt.xlim(0, 0.4)
plt.ylim(-0.5, 3.5)
# plt.ylim(0.001)
# plt.yscale("log")
# plt.xticks(range(0, 51, 10), fontsize=12)
plt.yticks(range(4), distNames, fontsize=12)
plt.xlabel(r'Divergence of $Rg$', fontsize=14)
plt.ylabel("Divergence metrics", fontsize=14)
# plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + "Luis/" + city + '/distComp_' + city + '.png', dpi=200)
plt.savefig(dataPath + "Luis/" + city + '/distComp_' + city + '.pdf')
plt.close()
'''
# linear and exponential fitting and plot
fig = plt.figure(figsize=(3.6,2.7))
# distNames = ["JSD", "KL", "WD", "KS"]
# lineStyles = ["dashdot", "dashed", "dotted", "solid"]
distNames = ["relativeRg", "JSD", "KL", "KS"]
lineStyles = ["dashed", "dotted", "solid", "dashdot"]
res = []
for d in range(len(distNames)):
dn = distNames[d]
dv = np.asarray(rgyGaps[dn])
X = np.asarray(distToCBD)
# plt.plot(X, dv, lw=1.5, linestyle=lineStyles[d], c=cityColors[city], label=dn)
plt.scatter(X, dv, lw=1.5, edgecolor=cityColors[city], marker="s",
s = 20, c="#ffffff")
# fit the dv with linear regression
(a_lin, b_lin, r_lin, tt_lin, stderr_lin) = stats.linregress(X, dv)
# print(r_lin**2, tt_lin, stderr_lin)
Y_pred = a_lin*X + b_lin
r2_lin = r2_score(dv, Y_pred)
plt.plot(X, Y_pred, lw=1.5, linestyle=lineStyles[d], c=cityColors[city], label=dn)
# fit the dv with scaling law
X_log = np.log10(X[1:])
dv_log = np.log10(dv[1:])
(a_scal, b_scal, r_scal, tt_scal, stderr_scal) = stats.linregress(X_log, dv_log)
# print(dn, r_scal, tt_scal, stderr_scal)
# Y_pred = np.multiply(np.power(X[1:], a_scal), b_scal)
# r2_scal = r2_score(dv[1:], Y_pred)
# print(a_scal)
print("%s,%s,%.4f,%.4f,%.4f,%.4f" % (city, dn, a_lin, r_lin**2, a_scal, r_scal**2))
res.append([city, dn, a_lin, r_lin**2, tt_lin, stderr_lin, a_scal, r_scal**2])
# plt.xlim(1)
# plt.ylim(-0.5, 3.5)
# plt.ylim(0.001)
# plt.yscale("log")
# plt.xticks(range(0, 51, 10), fontsize=12)
# plt.yticks(range(4), distNames, fontsize=12)
# plt.xscale('log', nonpositive='clip')
plt.xlabel("Distance to CBD [km]", fontsize=14)
plt.ylabel("Divergence", fontsize=14)
plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + "Luis/" + city + '/distComp_' + city + '_fit_1km.png', dpi=200)
plt.savefig(dataPath + "Luis/" + city + '/distComp_' + city + '_fit_1km.pdf')
plt.close()
return res
def multiCitiesDistComp():
outData = open(dataPath + "results/revision/multiCitiesDistComp_1km.csv", "w")
outData.writelines("city,metric,slopeLinear,r2Linear,ttLinear,stderrLinear,slopeScaling,r2Scaling\n")
for city in cities_Luis + cities_Spain:
# groupingRgsIntoRings_city(city, gapWidth=1) # run only one time
res = distanceComparison_city(city, numBins=100)
for row in res:
row = "%s,%s,%.4f,%.4f,%.6f,%.4f,%.4f,%.4f\n" % tuple(row)
outData.writelines(row)
outData.close()
# relation between KS(d,0) and d/d_max
def KSIndexVSdistance_comp(cities):
gapDistance = 3 # width of ring
cityInfo = pickle.load(open(dataPath + "results/cityInfo_all.pkl", "rb"))
numBins = 100
bins = np.linspace(0, 50, numBins+1)
outData = open(dataPath + "results/revision/multiCitiesDistComp_old.csv", "w")
outData.writelines("city,metric,slopeLinear,r2Linear,ttLinear,stderrLinear,slopeScaling,r2Scaling\n")
cityKSindex = {}
cityRingRgs = {}
cityLinearPara = {}
cityPowerLawPara = {}
for city in cities:
cityKSindex[city] = [[], []]
cityRingRgs[city] = [[], [], [], []] # relative r, distance, avgRg, medianRg
ringGyrations, gyrationsInGroups = pickle.load(open(dataPath + "results/Rgs_" + city + ".pkl", "rb"))
# keep in 50 km
print(city, "dmax = %d " % len(ringGyrations), "Gini = %.2f" % cityInfo[city][3])
if len(ringGyrations) > 50:
ringGyrations = ringGyrations[:51]
if city == "Lisbon":
ringGyrations = ringGyrations[:36]
dmax = len(ringGyrations)
dmax = dmax//3 * 3 + int(np.ceil((dmax%3)/3.0))*3
X = []
Dist = []
distNames = ["JSD", "KL", "KS"]
Y = {}
Y["JSD"] = []
Y["KL"] = []
Y["KS"] = []
Y["avgRgs"] = []
Y["medianRgs"] = []
# remove abnormal gyrations
ringGyrations = step0_dataPreparation.removeLargeRgs_100(ringGyrations)
ringGyrations_d = ringGyrations[:gapDistance]
allGyrations_0 = list(itertools.chain(*ringGyrations_d))
# remove zero
allGyrations_0 = [g for g in allGyrations_0 if g > 0]
usagesHist_0 = np.histogram(np.asarray(allGyrations_0), bins)
usagesHist_0 = np.divide(usagesHist_0[0], float(np.sum(usagesHist_0[0])))
# maxDist = 21
for d in range(len(ringGyrations)):
# if d >= maxDist:
# continue
if d%gapDistance != 0:
continue
x = d / dmax
ringGyrations_d = ringGyrations[d:d+gapDistance]
allGyrations_d = list(itertools.chain(*ringGyrations_d))
# remove zero
allGyrations_d = [g for g in allGyrations_d if g > 0]
# average and median values
avgRg = np.mean(allGyrations_d)
medianRg = np.median(allGyrations_d)
dist_ks = step0_dataPreparation.KSTest(allGyrations_d, allGyrations_0)
dist_ks = np.abs(dist_ks)
# we also calculate other metrics, like JSD and KL
# prepare the histogram for other distance metrics
usagesHist_d = np.histogram(np.asarray(allGyrations_d), bins)
usagesHist_d = np.divide(usagesHist_d[0], float(np.sum(usagesHist_d[0])))
# replace zero by small value
eps = 1e-10
usagesHist_d[usagesHist_d == 0] = eps
dist_kl = stats.entropy(usagesHist_0, usagesHist_d)
dist_jsd = distance.jensenshannon(usagesHist_0, usagesHist_d)
X.append(x)
Dist.append(d)
Y["KS"].append(dist_ks)
Y["JSD"].append(dist_jsd)
Y["KL"].append(dist_kl)
Y["avgRgs"].append(avgRg)
Y["medianRgs"].append(medianRg)
cityKSindex[city][0] = X
cityKSindex[city][1] = Y["KS"]
cityRingRgs[city][0] = X # Dist
cityRingRgs[city][1] = Dist
cityRingRgs[city][2] = Y["avgRgs"]
cityRingRgs[city][3] = Y["medianRgs"]
res = []
for d in range(3):
dn = distNames[d]
(a_lin, b_lin, r_lin, tt_lin, stderr_lin) = stats.linregress(X, Y[dn])
# print('City: %s, regression: a=%.2f b=%.2f, std error= %.3f' % (city, a_lin, b_lin, stderr_lin))
# we also test power-law fitting here
# fit the dv with scaling law
X_log = np.log10(X[1:])
dv_log = np.log10(Y[dn][1:])
(a_scal, b_scal, r_scal, tt_scal, stderr_scal) = stats.linregress(X_log, dv_log)
print(" ---------- ")
print("%s,%s,%.4f,%.4f,%.6f,%.4f,%.4f,%.4f" % (city, dn, a_lin, r_lin**2, tt_lin, stderr_lin, a_scal, r_scal**2))
res.append([city, dn, a_lin, r_lin**2, tt_lin, stderr_lin, a_scal, r_scal**2])
# save results for each city
for row in res:
row = "%s,%s,%.4f,%.4f,%.6f,%.4f,%.4f,%.4f\n" % tuple(row)
outData.writelines(row)
outData.close()
# save cityKSindex
# pickle.dump(cityKSindex, open(dataPath + "results/revision/cityKSindex.pkl", "wb"), pickle.HIGHEST_PROTOCOL)
pickle.dump(cityRingRgs, open(dataPath + "results/revision/cityRingRgs_allRings.pkl", "wb"), pickle.HIGHEST_PROTOCOL)
def compMetricsResVis():
inData = open(dataPath + "results/revision/multiCitiesDistComp_B100.csv", "r")
header = inData.readline().rstrip().split(",")
metricData_slope = [] # metric,function,value
metricData_r2 = [] # metric,function,value
cityData = {}
for row in inData:
row = row.rstrip().split(",")
city, metric = row[:2]
slopeLinear,r2Linear,ttLinear,stdrrLinear,slopeScaling,r2Scaling = [float(i) for i in row[2:]]
metricData_slope.append([metric, "Linear", slopeLinear])
metricData_slope.append([metric, "Scaling", slopeScaling])
metricData_r2.append([metric, "Linear", r2Linear])
metricData_r2.append([metric, "Scaling", r2Scaling])
if city not in cityData:
cityData[city] = [0 for i in range(12)]
if metric == "JSD":
cityData[city][0] = slopeLinear
cityData[city][3] = slopeScaling
cityData[city][6] = r2Linear
cityData[city][9] = r2Scaling
if metric == "KL":
cityData[city][1] = slopeLinear
cityData[city][4] = slopeScaling
cityData[city][7] = r2Linear
cityData[city][10] = r2Scaling
if metric == "KS":
cityData[city][2] = slopeLinear
cityData[city][5] = slopeScaling
cityData[city][8] = r2Linear
cityData[city][11] = r2Scaling
inData.close()
'''
outData = outData = open(dataPath + "results/revision/multiCitiesDistComp_latex.csv", "w")
header = ["City","JSD","KL","KS","JSD","KL","KS","JSD","KL","KS","JSD","KL","KS"]
outData.writelines(','.join(header) + "\n")
for city in cities_Luis + cities_Spain:
row = cityData[city]
row = [city] + ["%.3f" % i for i in row]
outData.writelines(",".join(row) + "\n")
avgValues = np.mean(list(cityData.values()),0)
meanRow = ",".join(["%.3f" % i for i in avgValues])
outData.writelines("Mean," + meanRow + "\n")
outData.close()
'''
metricData_slope = pd.DataFrame(data=metricData_slope, columns=["metric", "model", "slope"])
metricData_r2 = pd.DataFrame(data=metricData_r2, columns=["metric", "model", "r2"])
# sns.set_style('white')
pal = sns.color_palette('Paired')
fig = plt.figure(figsize=(4,3))
sns.boxplot(x="metric", y="slope", hue="model", data=metricData_slope,
palette=pal, fliersize=0)
sns.stripplot(x="metric", y="slope", hue="model", data=metricData_slope,
jitter=True, split=True, linewidth=0.5, palette=pal)
plt.legend(loc='upper left')
plt.xlabel("Divergence metrics", fontsize=14)
plt.ylabel("Slope", fontsize=14)
plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + 'results/revision/metricComp_slope_old.pdf')
plt.close()
fig = plt.figure(figsize=(4,3))
sns.boxplot(x="metric", y="r2", hue="model", data=metricData_r2,
palette=pal, fliersize=0)
sns.stripplot(x="metric", y="r2", hue="model", data=metricData_r2,
jitter=True, split=True, linewidth=0.5, palette=pal)
plt.legend(loc='upper left')
plt.xlabel("Divergence metrics", fontsize=14)
plt.ylabel(r"$r^2$", fontsize=14)
plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + 'results/revision/metricComp_r2_old.pdf')
plt.close()
# scatter plot between exponent and slope
fig = plt.figure(figsize=(4,3))
for city in cityData:
slopeLinear = cityData[city][2]
slopeScaling = cityData[city][5]
plt.scatter(slopeLinear, slopeScaling, s=40, facecolor=cityFaceColors[city], \
marker=cityMarkers[city], edgecolor=cityColors[city], lw=1, label=city, zorder=2)
plt.xlim(0, 0.55)
# plt.ylim(0, 0.55)
# plt.xticks(np.linspace(0, 1.0, 6), fontsize=16)
# plt.yticks(np.linspace(0, 2.0, 5), fontsize=16)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
# plt.grid(linestyle="dotted")
# plt.xlabel(r"Slop of $KS$ index", fontsize=14)
plt.xlabel(r"Slope of linear fitting", fontsize=14)
# plt.xlabel(r"$\Delta {KS}_{powerLaw}$", fontsize=14)
plt.ylabel(r"Power-law exponent", fontsize=14)
# plt.ylabel("UCI of population", fontsize=14)
# plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + 'results/revision/metricComp_exponent_slope.png', dpi=200)
plt.savefig(dataPath + 'results/revision/metricComp_exponent_slope.pdf')
plt.close()
# replot the Fig.3D with the updated dKS
def GiniVSdKS(cities):
cityInfo = pickle.load(open(dataPath + "results/cityInfo_all.pkl", "rb"))
# load dKS of cities
inData = open(dataPath + "results/revision/multiCitiesDistComp_B100.csv", "r") # 3km
# inData = open(dataPath + "results/revision/multiCitiesDistComp_pie.csv", "r")
header = inData.readline().rstrip().split(",")
cityDeltaKS = {}
for row in inData:
row = row.rstrip().split(",")
city, metric = row[:2]
if metric != "KS":
continue
dKS, r2, tt, stdrr, dKS_scaling, r2_scaling = [float(i) for i in row[2:]]
cityDeltaKS[city] = [dKS, stdrr]
# plot Gini of population vs. A2 values
# plot cities separatly in subplots
fig = plt.figure(figsize=(4, 3))
X = [cityDeltaKS[city][0] for city in cities]
Xerr = [cityDeltaKS[city][1] for city in cities]
Y = [cityInfo[city][3] for city in cities] # Gini
# Y = [cityInfo[city][5] for city in cities] # Crowding
meanDKS = np.mean(X)
meanGini = np.mean(Y)
print("mean of Gini : %.2f" % meanGini)
print("mean of dKS : %.2f" % meanDKS)
# return 0
# ax.scatter(X, Y, c=colors, s=30)
savedData = [] # data saved for paper publication
for i in range(len(cities)):
city = cities[i]
'''
plt.scatter([X[i]], [Y[i]], s=40, facecolor=cityFaceColors[city], \
marker=cityMarkers[city], edgecolor=cityColors[city], lw=1, label=city, zorder=2)
'''
plt.errorbar(X[i], Y[i], xerr=Xerr[i], ecolor=cityColors[city], capthick=2,
capsize=2, elinewidth=1, markeredgewidth=1,
markersize=4, markerfacecolor=cityFaceColors[city], \
marker=cityMarkers[city], markeredgecolor=cityColors[city], lw=1, label=city, zorder=2)
savedData.append([city, "%.2f" % Y[i], "%.2f" % X[i], "%.2f" % Xerr[i]])
# ax.scatter(X, Y, s=30, c=colors, lw=2)
# plt.plot([0.1, 0.5], [0.5, 0.5], lw=1.5, linestyle='--', c="k", zorder=1)
# plt.plot([0.30, 0.30], [0.2, 0.7], lw=1.5, linestyle='--', c="k", zorder=1)
# plt.xlim(0.08, 0.52)
plt.ylim(0.18, 0.72)
# plt.xticks(np.linspace(0, 1.0, 6), fontsize=16)
# plt.yticks(np.linspace(0, 2.0, 5), fontsize=16)
plt.xticks(fontsize=12)
plt.yticks(fontsize=12)
# plt.grid(linestyle="dotted")
# plt.xlabel(r"Slop of $KS$ index", fontsize=14)
plt.xlabel(r"$\Delta {KS}$", fontsize=14)
# plt.xlabel(r"Power-law exponent, $\beta$", fontsize=14)
plt.ylabel("Gini of population", fontsize=14)
# plt.ylabel("UCI of population", fontsize=14)
# plt.legend(frameon=False)
plt.tight_layout()
plt.savefig(dataPath + 'results/revision/Gini_KSslope_woZero_3km.png', dpi=200)
plt.savefig(dataPath + 'results/revision/Gini_KSslope_woZero_3km.pdf')
# plt.savefig(dataPath + 'results/revision/Gini_KSslope_woZero_pie_scaling.png', dpi=200)
# plt.savefig(dataPath + 'results/revision/Gini_KSslope_woZero_pie_scaling.pdf')
plt.close()