def weighting_function(freq_vec, f_changeover, sharpness):
""" another weighting function, using tanh to prevent exp. overflow """
weight = .5 - .5 * tanh(
(freq_vec.squeeze()[1:] - f_changeover) * sharpness)
weight = (weight + weight[::-1]).squeeze()
weight = np.hstack([1., weight])
return weight
def feedforward(self):
# 검색 단어가 유일한 입력임
for i in range(len(self.wordids)):
self.ai[i] = 1.0
# 은닉 노드 활성화
for j in range(len(self.hiddenids)):
sum = 0.0
for i in range(len(self.wordids)):
sum = sum + self.ai[i] * self.wi[i][j]
self.ah[j] = tanh(sum)
# 출력 노드 활성화
for k in range(len(self.urlids)):
sum = 0.0
for j in range(len(self.hiddenids)):
sum = sum + self.ah[j] * self.wo[j][k]
self.ao[k] = tanh(sum)
return self.ao[:]
def feedforward(self):
# 검색 단어가 유일한 입력임
for i in range(len(self.wordids)):
self.ai[i] = 1.0
# 은닉 노드 활성화
for j in range(len(self.hiddenids)):
sum = 0.0
for i in range(len(self.wordids)):
sum = sum + self.ai[i] * self.wi[i][j]
self.ah[j] = tanh(sum)
# 출력 노드 활성화
for k in range(len(self.urlids)):
sum = 0.0
for j in range(len(self.hiddenids)):
sum = sum + self.ah[j] * self.wo[j][k]
self.ao[k] = tanh(sum)
return self.ao[:]
def f(x, amptan, ttan):
return amptan * pl.tanh(2 * (x / ttan)**4)
def phiPrime2(self,t):
return 0.5*M.pi*t*M.cosh(t)/M.cosh(0.5*M.pi*M.sinh(t))**2+M.tanh(0.5*M.pi*M.sinh(t))
def phi2(self,t):
return t*M.tanh(0.5*M.pi*M.sinh(t))
def main():
args = aTools.parseCMD()
# Check if our data file exists, if not: write one.
# Otherwise, open the file and plot.
check = glob.glob('*JackKnifeData_Cv.dat*')
fileNames = args.fileNames
skip = args.skip
# check which ensemble
canonical=True
if fileNames[0][0]=='g':
canonical=False
print fileNames
if check == []:
temps,Cvs,CvsErr = pl.array([]),pl.array([]),pl.array([])
Es, EsErr = pl.array([]), pl.array([])
rhos_rhos, rhos_rhoErr = pl.array([]), pl.array([])
# open energy/ specific heat data file, write headers
fout = open('JackKnifeData_Cv.dat', 'w')
fout.write('#%15s\t%16s\t%16s\t%16s\t%16s\n'% (
'T', 'E', 'Eerr', 'Cv', 'CvErr'))
# open superfluid stiffness data file, write headers
foutSup = open('JackKnifeData_super.dat','w')
foutSup.write('#%15s\t%16s\t%16s\n'%(
'T', 'rho_s/rho', 'rho_s/rhoErr'))
# perform jackknife analysis of data, writing to disk
if args.Crunched: # check if we have combined data
tempList = aTools.getHeadersFromFile(fileNames[0])
for temp in tempList:
temps = pl.append(temps,float(temp))
n,n2 = 0,0
for fileName in fileNames:
print '\n\n---',fileName,'---\n'
for temp in tempList:
print n
if 'Estimator' in fileName:
E, EEcv, Ecv, dEdB = pl.loadtxt(fileName,\
unpack=True, usecols=(n,n+1,n+2,n+3), delimiter=',')
EAve, Eerr = aTools.jackknife(E[skip:])
jkAve, jkErr = aTools.jackknife(
EEcv[skip:],Ecv[skip:],dEdB[skip:])
print 'T = ',float(temp),':'
print '<E> = ',EAve,' +/- ',Eerr
print '<Cv> = ',jkAve,' +/- ',jkErr
Es = pl.append(Es, EAve)
Cvs = pl.append(Cvs, jkAve)
EsErr = pl.append(EsErr, Eerr)
CvsErr = pl.append(CvsErr, jkErr)
fout.write('%16.8E\t%16.8E\t%16.8E\t%16.8E\t%16.8E\n' %(
float(temp), EAve, Eerr, jkAve, jkErr))
n += 4
elif 'Super' in fileName:
rhos_rho = pl.loadtxt(fileName, \
unpack=True, usecols=(n2,), delimiter=',')
superAve, superErr = aTools.jackknife(rhos_rho[skip:])
print 'rho_s/rho = ', superAve,' +/- ',superErr
rhos_rhos = pl.append(rhos_rhos, superAve)
rhos_rhoErr = pl.append(rhos_rhoErr, superErr)
foutSup.write('%16.8E\t%16.8E\t%16.8E\n' %(
float(temp), superAve, superErr))
n2 += 1
else: # otherwise just read in individual (g)ce-estimator files
for fileName in fileNames:
if canonical:
temp = float(fileName[13:19])
else:
temp = float(fileName[14:20])
temps = pl.append(temps, temp)
E, EEcv, Ecv, dEdB = pl.loadtxt(fileName, unpack=True,
usecols=(4,11,12,13))
jkAve, jkErr = aTools.jackknife(
EEcv[skip:],Ecv[skip:],dEdB[skip:])
EAve, Eerr = aTools.jackknife(E[skip:])
print 'T = ',temp
print '<Cv> = ',jkAve,' +/- ',jkErr
print '<E> = ',EAve,' +/- ',Eerr
Es = pl.append(Es, EAve)
Cvs = pl.append(Cvs, jkAve)
EsErr = pl.append(EsErr, Eerr)
CvsErr = pl.append(CvsErr, jkErr)
fout.write('%16.8E\t%16.8E\t%16.8E\t%16.8E\t%16.8E\n' %(
float(temp), EAve, Eerr, jkAve, jkErr))
fout.close()
else:
print 'Found existing data file in CWD.'
temps, Es, EsErr, Cvs, CvsErr = pl.loadtxt('JackKnifeData_Cv.dat',
unpack=True)
temps, rhos_rhos, rhos_rhoErr = pl.loadtxt('JackKnifeData_super.dat',
unpack=True)
errCheck = False
if errCheck:
EsNorm, EsErrNorm = pl.array([]), pl.array([])
for fileName in args.fileNames:
#Ecv,Eth = pl.loadtxt(fileName, unpack=True, usecols=(4,-5))
Ecv = pl.loadtxt(fileName, unpack=True, usecols=(4,))
EsNorm = pl.append(EsNorm,pl.average(Ecv))
#ET = pl.append(ET, pl.average(Eth))
EsErrNorm = pl.append(EsErrNorm, pl.std(Ecv)/pl.sqrt(float(len(Ecv))))
#ETerr = pl.append(ETerr, pl.std(Eth)/pl.sqrt(float(len(Eth))))
pl.scatter(temps, EsErrNorm, label='Standard Error', color='Navy')
pl.scatter(temps, EsErr, label='Jackknife Error', color='Orange')
pl.grid()
pl.legend()
pl.show()
QHO = False
if QHO:
# analytical solutions for 1D QHO with one particle
tempRange = pl.arange(0.01,1.0,0.01)
Eanalytic = 0.5/pl.tanh(1.0/(2.0*tempRange))
CvAnalytic = 1.0/(4.0*(tempRange*pl.sinh(1.0/(2.0*tempRange)))**2)
ShareAxis=True # shared x-axis for Cv and Energy
# plot the specific heat vs. temperature
if ShareAxis:
ax1 = pl.subplot(211)
else:
pl.figure(1)
if QHO: # plot analytic result
pl.plot(tempRange,CvAnalytic, label='Exact')
pl.errorbar(temps,Cvs,CvsErr, label='PIMC',color='Violet',fmt='o')
if not ShareAxis:
pl.xlabel('Temperature [K]')
pl.ylabel('Specific Heat', fontsize=20)
pl.grid(True)
pl.legend(loc=2)
# plot the energy vs. temperature
if ShareAxis:
pl.setp(ax1.get_xticklabels(), visible=False)
ax2 = pl.subplot(212, sharex=ax1)
else:
pl.figure(2)
if QHO: # plot analytic result
pl.plot(tempRange,Eanalytic, label='Exact')
pl.errorbar(temps,Es,EsErr, label='PIMC virial',color='Lime',fmt='o')
pl.xlabel('Temperature [K]', fontsize=20)
pl.ylabel('Energy [K]', fontsize=20)
pl.grid(True)
pl.legend(loc=2)
pl.savefig('Helium_critical_CVest.pdf', format='pdf',
bbox_inches='tight')
if ShareAxis:
pl.figure(2)
else:
pl.figure(3)
pl.errorbar(temps, rhos_rhos, rhos_rhoErr)
pl.xlabel('Temperature [K]', fontsize=20)
pl.ylabel('Superfluid Stiffness', fontsize=20)
pl.grid(True)
pl.show()
def sigmoid(x, H=.5, Q=1, G=60, P=1, T=0.5):
'''Sigmoidal thresholding function.'''
return H * (Q + tanh(G * (P * x - T)))
def weighting_function(freq_vec, f_changeover, sharpness):
""" another weighting function, using tanh to prevent exp. overflow """
weight = .5 - .5*tanh((freq_vec.squeeze()[1:] - f_changeover) * sharpness)
weight = (weight + weight[::-1]).squeeze()
weight = np.hstack([1., weight])
return weight
def hfunc(x):
"Nonlinearity used for output."
return tanh(x)
def main():
args = parseCMD()
# Check if our data file exists, if not: write one.
# Otherwise, open the file and plot.
check = glob.glob('*JackKnifeData_Cv.dat*')
if check == []:
fileNames = args.fileNames
skip = args.skip
temps,Cvs,CvsErr = pl.array([]),pl.array([]),pl.array([])
Es, EsErr = pl.array([]),pl.array([])
ET, ETerr = pl.array([]),pl.array([])
# open new data file, write headers
fout = open('JackKnifeData_Cv.dat', 'w')
fout.write('#%15s\t%16s\t%16s\t%16s\t%16s\t%16s\t%16s\n'% (
'T', 'Ecv', 'EcvErr', 'Et', 'EtErr','Cv', 'CvErr'))
# perform jackknife analysis of data, writing to disk
for fileName in fileNames:
temp = float(fileName[-40:-34])
temps = pl.append(temps, temp)
# grab and analyze energy data
Ecv,Eth = pl.loadtxt(fileName, unpack=True, usecols=(4,-5))
E = pl.average(Ecv)
Et = pl.average(Eth)
EErr = pl.std(Ecv)/pl.sqrt(float(len(Ecv)))
EtErr = pl.std(Eth)/pl.sqrt(float(len(Eth)))
Es = pl.append(Es,E)
ET = pl.append(ET, Et)
EsErr = pl.append(EsErr, EErr)
ETerr = pl.append(ETerr, EtErr)
# grab and analyze specific heat data
EEcv, Ecv, dEdB = pl.loadtxt(fileName, unpack=True, usecols=(11,12,13))
jkAve, jkErr = jk.jackknife(EEcv[skip:],Ecv[skip:],dEdB[skip:])
Cvs = pl.append(Cvs,jkAve)
CvsErr = pl.append(CvsErr,jkErr)
fout.write('%16.8E\t%16.8E\t%16.8E\t%16.8E\t%16.8E\t%16.8E\t%16.8E\n' %(
temp, E, EErr, Et, EtErr, jkAve, jkErr))
print 'T = ',str(temp),' complete.'
fout.close()
else:
print 'Found existing data file in CWD.'
temps,Es,EsErr,ET,ETerr,Cvs,CvsErr = pl.loadtxt(
'JackKnifeData_Cv.dat', unpack=True)
# plot specific heat for QHO
tempRange = pl.arange(0.01,1.0,0.01)
Eanalytic = 0.5/pl.tanh(1.0/(2.0*tempRange))
CvAnalytic = 1.0/(4.0*(tempRange*pl.sinh(1.0/(2.0*tempRange)))**2)
pl.figure(1)
ax1 = pl.subplot(211)
pl.plot(tempRange,CvAnalytic, label='Exact')
pl.errorbar(temps,Cvs,CvsErr, label='PIMC',color='Violet',fmt='o')
pl.ylabel('Specific Heat',fontsize=20)
pl.title('1D QHO -- 1 boson',fontsize=20)
pl.legend(loc=2)
pl.setp(ax1.get_xticklabels(), visible=False)
ax2 = pl.subplot(212, sharex=ax1)
pl.plot(tempRange,Eanalytic, label='Exact')
pl.errorbar(temps,Es,EsErr, label='PIMC virial',color='Lime',fmt='o')
pl.errorbar(temps,ET,ETerr, label='PIMC therm.',color='k',fmt='o')
#pl.scatter(temps,Es, label='PIMC')
pl.xlabel('Temperature [K]',fontsize=20)
pl.ylabel('Energy [K]',fontsize=20)
pl.legend(loc=2)
pl.savefig('1Dqho_largerCOM_800000bins_CvANDenergy.pdf',
format='pdf', bbox_inches='tight')
pl.show()
import pylab as pl
sr = 44100.
fc = 500.
t = pl.arange(0, sr)
w = 2 * pl.pi * fc * t / sr
k = 10000. / (fc * pl.log10(fc))
scal = 1. / pl.tanh(k)
s = scal * pl.tanh(k * pl.sin(w))
pl.figure(figsize=(8, 5))
pl.subplot(211)
pl.ylim(-1.1, 1.1)
pl.plot(t[0:440] / sr, s[0:440], 'k-')
pl.xlabel("time (s)")
sig = s
N = 32768
start = 0
x = pl.arange(0, N / 2)
bins = x * sr / N
win = pl.hanning(N)
scal = N * pl.sqrt(pl.mean(win**2))
sig1 = sig[start:N + start]
window = pl.fft(sig1 * win / max(sig1))
mags = abs(window / scal)
spec = 20 * pl.log10(mags / max(mags))
def hprime(x, y=None):
if y is None:
y = tanh(x)
return 1 - y**2
def hfunc(x):
return tanh(x)
def gfunc(x):
return tanh(x)
def thresholding(self, x):
'''Thresholding definition depending on threshold_type: 0 for tanh ; 1 for Brunel's function.'''
return 0.5 * (1. + tanh(self.gamma * (x - self.theta)))
def thresholding(self, x, theta):
'''Thresholding definition depending on threshold_type: 0 for tanh ; 1 for Brunel's function.'''
return 0.5 * (1. + tanh(self.G * (self.P * x - theta)))
'blue': [(0.0, 0.0, 0.0),
(xlo, 0.1, 0.1),
((1-whiterange)/gmax, 1.0, 1.0),
((1+whiterange)/gmax, 1.0, 1.0),
(xhi, 1.0, 1.0),
(xhier,0.0, 0.0),
(1.0, 0.0, 0.0)]}
cmap = matplotlib.colors.LinearSegmentedColormap('mine', cdict)
return Z, R, g2mc, cmap, gmax
pylab.figure(figsize=(21,15 + 10*dx))
pylab.subplot(1,1,1).set_aspect('equal')
Z, R, g2mc, cmap, gmax = read_g2_and_prepare_plot(zmin, 21, 15.0)
rbins = Z.shape[0]
nrmin = round(rbins/2) + 10
levels = pylab.concatenate([pylab.linspace(0, .85, 10),
pylab.linspace(.855, 0.99, 10),
pylab.linspace(1.01, 1.15, 10),
pylab.linspace(1.2, gmax, 10)])
g2mc = (1+pylab.tanh((R+10)/2))/2*(g2mc-1) + 1
pylab.contourf(Z[:nrmin,:], R[:nrmin,:], g2mc[:nrmin,:], levels, vmax=gmax*.5, vmin=0, cmap=cmap)
pylab.axes().get_xaxis().set_visible(False)
pylab.axes().get_yaxis().set_visible(False)
pylab.title('')
pylab.subplots_adjust(left=-0.01, right=1.02, top=1.02, bottom=-0.02)
pylab.savefig("figs/pretty-%d.svg" % (int(ff*10)))
pylab.show()
def f(x, amptan, ttan, amplog, tlog, sigma):
return amptan * pl.tanh(
2 * (x / ttan)**4) + amplog * stats.lognorm.pdf(
x, scale=pl.exp(tlog), s=sigma)
def gfunc(x):
"Nonlinearity used for input to state."
return tanh(x)
def gfunc(x):
"Nonlinearity used for input to state."
return tanh(x)
def hfunc(x):
"Nonlinearity used for output."
return tanh(x)
def main():
args = parseCMD()
# Check if our data file exists, if not: write one.
# Otherwise, open the file and plot.
check = glob.glob('*JackKnifeData_Cv.dat*')
if check == []:
fileNames = args.fileNames
skip = args.skip
temps, Cvs, CvsErr = pl.array([]), pl.array([]), pl.array([])
timeSteps = pl.array([])
# open new data file, write headers
fout = open('JackKnifeData_Cv.dat', 'w')
fout.write('#%09s\t%10s\t%10s\t%10s\n' % ('T', 'tau', 'Cv', 'CvErr'))
# perform jackknife analysis of data, writing to disk
for fileName in fileNames:
tau = float(fileName[-21:-14])
temp = float(fileName[-40:-34])
timeSteps = pl.append(timeSteps, tau)
temps = pl.append(temps, temp)
EEcv, Ecv, dEdB = pl.loadtxt(fileName,
unpack=True,
usecols=(11, 12, 13))
jkAve, jkErr = aTools.jackknife(EEcv[skip:], Ecv[skip:],
dEdB[skip:])
print '<est> = ', jkAve, ' +/- ', jkErr
Cvs = pl.append(Cvs, jkAve)
CvsErr = pl.append(CvsErr, jkErr)
fout.write('%10s\t%10s\t%10s\t%10s\n' % (temp, tau, jkAve, jkErr))
fout.close()
else:
print 'Found existing data file in CWD.'
temps, timeSteps, Cvs, CvsErr = pl.loadtxt('JackKnifeData_Cv.dat',
unpack=True)
# make array of energies
Es, EsErr = pl.array([]), pl.array([])
ET, ETerr = pl.array([]), pl.array([])
for fileName in args.fileNames:
Ecv, Eth = pl.loadtxt(fileName, unpack=True, usecols=(4, -5))
Es = pl.append(Es, pl.average(Ecv))
ET = pl.append(ET, pl.average(Eth))
EsErr = pl.append(EsErr, pl.std(Ecv) / pl.sqrt(float(len(Ecv))))
ETerr = pl.append(ETerr, pl.std(Eth) / pl.sqrt(float(len(Eth))))
# plot specific heat for QHO
tempRange = pl.arange(0.01, 1.0, 0.01)
Eanalytic = 0.5 / pl.tanh(1.0 / (2.0 * tempRange))
CvAnalytic = 1.0 / (4.0 * (tempRange * pl.sinh(1.0 /
(2.0 * tempRange)))**2)
if args.timeStepScaling:
pl.figure(1)
pl.plot(timeSteps, 0.5 / pl.tanh(1.0 / (2.0 * (temps))), label='Exact')
pl.errorbar(timeSteps,
Es,
EsErr,
label='PIMC virial',
color='Lime',
fmt='o')
pl.errorbar(timeSteps,
ET,
ETerr,
label='PIMC therm.',
color='Navy',
fmt='o')
pl.xlabel('Time Step [1/K]')
pl.ylabel('Energy [K]')
pl.title('1D QHO -- 1 boson -- T=%s' % temps[0])
pl.legend(loc=1)
pl.figure(2)
pl.plot(timeSteps,
1.0 / (4.0 * (temps * pl.sinh(1.0 / (2.0 * temps)))**2),
label='Exact')
pl.errorbar(timeSteps,
Cvs,
CvsErr,
label='PIMC virial',
color='Navy',
fmt='o')
pl.xlabel('Time Step [1/K]')
pl.ylabel('Specific Heat [K]')
pl.title('1D QHO -- 1 boson -- T=%s' % temps[0])
pl.legend(loc=1)
else:
pl.figure(1)
pl.plot(tempRange, CvAnalytic, label='Exact')
pl.errorbar(temps, Cvs, CvsErr, label='PIMC', color='Violet', fmt='o')
pl.xlabel('Temperature [K]')
pl.ylabel('Specific Heat')
pl.title('1D QHO -- 1 boson')
pl.legend(loc=2)
pl.figure(2)
pl.plot(tempRange, Eanalytic, label='Exact')
pl.errorbar(temps,
Es,
EsErr,
label='PIMC virial',
color='Lime',
fmt='o')
pl.errorbar(temps, ET, ETerr, label='PIMC therm.', color='k', fmt='o')
#pl.scatter(temps,Es, label='PIMC')
pl.xlabel('Temperature [K]')
pl.ylabel('Energy [K]')
pl.title('1D QHO -- 1 boson')
pl.legend(loc=2)
pl.show()
'blue': [(0.0, 0.0, 0.0),
(xlo, 0.1, 0.1),
((1-whiterange)/gmax, 1.0, 1.0),
((1+whiterange)/gmax, 1.0, 1.0),
(xhi, 1.0, 1.0),
(xhier, 0.0, 0.0),
(1.0, 0.0, 0.0)]}
cmap = matplotlib.colors.LinearSegmentedColormap('mine', cdict)
return Z, R, g2mc, cmap, gmax
pylab.figure(figsize=(21, 15 + 10*dx))
pylab.subplot(1, 1, 1).set_aspect('equal')
Z, R, g2mc, cmap, gmax = read_g2_and_prepare_plot(zmin, 21, 15.0)
rbins = Z.shape[0]
nrmin = round(rbins/2) + 10
levels = pylab.concatenate([pylab.linspace(0, .85, 10),
pylab.linspace(.855, 0.99, 10),
pylab.linspace(1.01, 1.15, 10),
pylab.linspace(1.2, gmax, 10)])
g2mc = (1+pylab.tanh((R+10)/2))/2*(g2mc-1) + 1
pylab.contourf(Z[:nrmin,:], R[:nrmin,:], g2mc[:nrmin,:], levels, vmax=gmax*.5, vmin=0, cmap=cmap)
pylab.axes().get_xaxis().set_visible(False)
pylab.axes().get_yaxis().set_visible(False)
pylab.title('')
pylab.subplots_adjust(left=-0.01, right=1.02, top=1.02, bottom=-0.02)
pylab.savefig("figs/pretty-%d.svg" % (int(ff*10)))
pylab.show()
