def marginalized_analysis(): sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1c.out', 'w')) x, y = make_data() prior = gv.gvar(91 * ['0(1)']) # prior for the fit ymod = y - (f(x, prior) - f(x, prior[:1])) priormod = prior[:1] fit = lsqfit.nonlinear_fit(data=(x, ymod), prior=priormod, fcn=f) print fit.format(maxline=True) sys.stdout = STDOUT print lsqfit.wavg(list(ymod) + list(priormod)) make_plot(x, ymod, fit, 'ymod(x)') inputs = dict(prior=prior, y0=y[0], y1=y[1], y2=y[2], y3=y[3], y4=y[4]) outputs = dict(p0=fit.p[0]) print gv.fmt_errorbudget(inputs=inputs, outputs=outputs) return fit
def marginalized_analysis():
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1c.out', 'w'))
x, y = make_data()
prior = gv.gvar(91 * ['0(1)']) # prior for the fit
ymod = y - (f(x, prior) - f(x, prior[:1]))
priormod = prior[:1]
fit = lsqfit.nonlinear_fit(data=(x, ymod), prior=priormod, fcn=f)
print fit.format(maxline=True)
sys.stdout = STDOUT
print lsqfit.wavg(list(ymod) + list(priormod))
make_plot(x, ymod, fit, 'ymod(x)', name='eg-appendix1c')
inputs = dict(prior=prior, y0=y[0], y1=y[1], y2=y[2], y3=y[3], y4=y[4])
outputs = dict(p0=fit.p[0])
print gv.fmt_errorbudget(inputs=inputs, outputs=outputs)
return fit
def _fit_plateau(self, svdcut):
"""Fits the marginalized data to a constant"""
if self.tfit is not None:
tfit = self.tfit
else:
tfit = np.arange(self.t_snk)
# Average over the remaining plateau
yfit = self.marginalized_data[tfit]
return lsqfit.wavg(yfit, prior=self.r_guess, svdcut=svdcut)
def main():
gv.ranseed([2009,2010,2011,2012]) # initialize random numbers (opt.)
x,y = make_data() # make fit data
p0 = None # make larger fits go faster (opt.)
sys_stdout = sys.stdout
sys.stdout = tee.tee(sys.stdout, open("eg1.out","w"))
for nexp in range(3,20):
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,p0=p0) #, svdcut=SVDCUT)
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
if nexp in [8, 9, 10]:
print(".".center(73))
if nexp > 7 and nexp < 19:
continue
elif nexp not in [3]:
print("")
print '************************************* nexp =',nexp
print fit.format() # print the fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print 'E1/E0 =',E[1]/E[0],' E2/E0 =',E[2]/E[0]
print 'a1/a0 =',a[1]/a[0],' a2/a0 =',a[2]/a[0]
# extra data 1
print '\n--------------------- fit with extra information'
sys.stdout = tee.tee(sys_stdout, open("eg1a.out", "w"))
def ratio(p):
return p['a'][1] / p['a'][0]
newfit = lsqfit.nonlinear_fit(data=gv.gvar(1,1e-5), fcn=ratio, prior=fit.p)
print (newfit)
# print(newfit.p['a'][1] / newfit.p['a'][0])
# print(fit.p['a'][1] / fit.p['a'][0])
# alternate method for extra data
sys.stdout = tee.tee(sys_stdout, open("eg1b.out", "w"))
fit.p['a1/a0'] = fit.p['a'][1] / fit.p['a'][0]
new_data = {'a1/a0' : gv.gvar(1,1e-5)}
new_p = lsqfit.wavg([fit.p, new_data])
print 'chi2/dof = %.2f\n' % (new_p.chi2 / new_p.dof)
print 'E:', new_p['E'][:4]
print 'a:', new_p['a'][:4]
print 'a1/a0:', new_p['a1/a0']
# # extra data 2
# sys.stdout = tee.tee(sys_stdout, open("eg1b.out", "w"))
# newfit = fit
# for i in range(1):
# print '\n--------------------- fit with %d extra data sets' % (i+1)
# x, ynew = make_data()
# prior = newfit.p
# newfit = lsqfit.nonlinear_fit(data=(x,ynew), fcn=f, prior=prior) # , svdcut=SVDCUT)
# print newfit
sys.stdout = sys_stdout
# def fcn(x, p):
# return f(x, p), f(x, p)
# prior = make_prior(nexp)
# fit = lsqfit.nonlinear_fit(data=(x, [y, ynew]), fcn=fcn, prior=prior, p0=newfit.pmean) # , svdcut=SVDCUT)
# print(fit)
if DO_BOOTSTRAP:
Nbs = 40 # number of bootstrap copies
outputs = {'E1/E0':[], 'E2/E0':[], 'a1/a0':[],'a2/a0':[],'E1':[],'a1':[]} # results
for bsfit in fit.bootstrap_iter(n=Nbs):
E = bsfit.pmean['E'] # best-fit parameters
a = bsfit.pmean['a']
outputs['E1/E0'].append(E[1]/E[0]) # accumulate results
outputs['E2/E0'].append(E[2]/E[0])
outputs['a1/a0'].append(a[1]/a[0])
outputs['a2/a0'].append(a[2]/a[0])
outputs['E1'].append(E[1])
outputs['a1'].append(a[1])
# print E[:2]
# print a[:2]
# print bsfit.chi2/bsfit.dof
# extract means and standard deviations from the bootstrap output
for k in outputs:
outputs[k] = gv.gvar(np.mean(outputs[k]),np.std(outputs[k]))
print 'Bootstrap results:'
print 'E1/E0 =',outputs['E1/E0'],' E2/E1 =',outputs['E2/E0']
print 'a1/a0 =',outputs['a1/a0'],' a2/a0 =',outputs['a2/a0']
print 'E1 =',outputs['E1'],' a1 =',outputs['a1']
if DO_PLOT:
import pylab as plt
ratio = y/fit.fcn(x,fit.pmean)
plt.xlim(0,21)
plt.xlabel('x')
plt.ylabel('y/f(x,p)')
plt.errorbar(x=x,y=gv.mean(ratio),yerr=gv.sdev(ratio),fmt='ob')
plt.plot([0.0,21.0],[1.0,1.0])
plt.show()
def plot_corr_effective_mass(models,data,fit=None,req=[list(),list()],**kwargs):
"""
Get all data ready so that it can be plotted on command
Allows for dynamic cycling through plots
"""
_emNMod = len(models)
_emIdx = [0] ## -- index of plotted function, in array so it can be modified in functions
## -- objects to hold all plot data
## - Dat/Fit refers to the correlator data or the fit function
## - Central/Error are the central value and errors
_emLogRatio = []
_emLogRatioCentral = []
_emLogRatioError = []
_emLogRatioFit = []
_emFoldRatio = []
_emFoldRatioCentral= []
_emFoldRatioError = []
_emFoldRatioFit = []
_emRatioFit = []
_emRatioFitNonZero = []
_emFitCentral = []
_emFitError = []
## -- timeslice objects
_emTPosRatio = []
_emTPosFit = []
_emTPosFold = []
_emTPosFoldFit = []
#
## -- fitting options
_emFitMin = 0
_emFitMax = 0
_emSep = 0
fig,ax = plt.subplots(1,figsize=(10,8))
#
## -- setup plot function
def do_plot_corr_effective_mass(idx,fig=fig):
fig.clear()
#fig.set_size_inches(10,10) #doesn't work
ax = fig.add_subplot(111)
if print_quality:
plt.subplots_adjust(bottom=0.15,left=0.18,right=0.97,top=0.95)
else:
#plt.subplots_adjust(bottom=0.15,left=0.15,right=0.97,top=0.95)
pass
#fig.set_figheight(20) #doesn't work
#fig.set_figwidth(20)
key = models[idx[0]].datatag
ax.set_xlim([-1,df.cor_len/2])
ax.set_ylim(utp.get_option("y_limit",[0.0,1.4],**kwargs[key]))
#
# -- plot correlator data
if utp.get_option("meff_do_fold",False,**kwargs[key]):
## -- plot fit
ax.plot([t for t in _emTPosFit[idx[0]] if t < len(_emTData)/2],_emFitCentral[idx[0]],
color=utp.get_option("color3",'b',**kwargs[key]))
ax.plot([t for t in _emTPosFit[idx[0]] if t < len(_emTData)/2],_emFitError[idx[0]][0],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
ax.plot([t for t in _emTPosFit[idx[0]] if t < len(_emTData)/2],_emFitError[idx[0]][1],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
## -- _emTPosRatio not necessarily symmetric, get times correct
ax.errorbar(_emTPosFold[idx[0]],_emFoldRatioCentral[idx[0]],yerr=_emFoldRatioError[idx[0]],
mfc=utp.get_option("markerfacecolor1",'None',**kwargs[key]),
mec=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
color=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
ls=utp.get_option("linestyle1",'None',**kwargs[key]),
marker=utp.get_option("marker1",'o',**kwargs[key]),
ms=utp.get_option("markersize",10,**kwargs[key]))
ax.scatter(_emTPosFoldFit[idx[0]],gv.mean(_emFoldRatioFit[idx[0]]),
color=utp.get_option("color1",'r',**kwargs[key]),
marker=utp.get_option("marker",'o',**kwargs[key]),
s=utp.get_option("markersize",100,**kwargs[key]))
else:
## -- plot fit
ax.plot(_emTPosFit[idx[0]],_emFitCentral[idx[0]],
color=utp.get_option("color3",'b',**kwargs[key]))
ax.plot(_emTPosFit[idx[0]],_emFitError[idx[0]][0],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
ax.plot(_emTPosFit[idx[0]],_emFitError[idx[0]][1],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
## --
ax.errorbar(_emTPosRatio[idx[0]],_emLogRatioCentral[idx[0]],yerr=_emLogRatioError[idx[0]],
mfc=utp.get_option("markerfacecolor1",'None',**kwargs[key]),
mec=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
color=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
ls=utp.get_option("linestyle1",'None',**kwargs[key]),
marker=utp.get_option("marker1",'o',**kwargs[key]),
ms=utp.get_option("markersize",8,**kwargs[key]))
ax.scatter(_emTPosFit[idx[0]],gv.mean(_emLogRatioFit[idx[0]]),
color=utp.get_option("color1",'r',**kwargs[key]),
marker=utp.get_option("marker",'o',**kwargs[key]),
s=utp.get_option("markersize",64,**kwargs[key]))
fig.suptitle(utp.get_option("plottitleem",str(idx[0])+" default title "+str(key),**kwargs[key]),
fontsize=utp.get_option("titlesize",20,**kwargs[key]))
# -- modify some options
if print_quality:
ax.set_xlabel(r'$t$',fontsize=40)
if sn_ratio:
ax.set_ylabel(utp.get_option("yaxistitle",
r"$-\frac{1}{"+str(_emSep)+r"}v_{i}^{T}\,log\frac{C_{ij}(t+"+str(_emSep)+r")}{C_{ij}(t)}w_{j}$",
**kwargs[key]),fontsize=40)
else:
ax.set_ylabel(utp.get_option("yaxistitle",
r"$-\frac{1}{"+str(_emSep)+r"}\,log\frac{C_{ij}(t+"+str(_emSep)+r")}{C_{ij}(t)}$",
**kwargs[key]),fontsize=40)
plt.xticks(plt.xticks()[0],fontsize=24)
plt.yticks(plt.yticks()[0],fontsize=24)
else:
ax.set_xlabel(r'$t$')
ax.set_ylabel(utp.get_option("yaxistitle",
r"$-\frac{1}{"+str(_emSep)+r"}\,log\frac{C(t+"+str(_emSep)+r")}{C(t)}$",**kwargs[key]))
for item in ([ax.xaxis.label,ax.yaxis.label]):
# must be after setting label content (LaTeX ruins it)
item.set_fontsize(fontsize=utp.get_option("fontsize",20,**kwargs[key]))
rect =fig.patch
rect.set_facecolor('white')
if utp.get_option("to_file",False,**kwargs[key]):
save_dir = utp.get_option("em_save_dir","./plotdump",**kwargs[key])
save_name = utp.get_option("em_save_name","emplot-"+key+".pdf",**kwargs[key])
plt.savefig(save_dir+'/'+save_name)
if utp.get_option("to_terminal",True,**kwargs[key]):
plt.draw()
pass
#
## -- setup button press action function
def press_effective_mass(event,idx=_emIdx):
#print('press_effective_mass', event.key)
try:
## -- manually indicate index
idx[0] = int(event.key) + (idx[0])*10
except ValueError:
if event.key==' ': ## -- space
## -- allows for replotting when changing index by typing number keys
idx[0] = idx[0] % _emNMod
do_plot_corr_effective_mass(idx)
elif event.key=='left':
idx[0] = (idx[0] - 1) % _emNMod
do_plot_corr_effective_mass(idx)
elif event.key=='right':
idx[0] = (idx[0] + 1) % _emNMod
do_plot_corr_effective_mass(idx)
elif event.key=='backspace':
## -- reset index so can manually flip through using number keys
idx[0] = 0
elif event.key=='d':
## -- dump plots into ./plotdump directory
for ix,model in zip(range(len(models)),models):
key = model.datatag
save_dir = utp.get_option("em_save_dir","./plotdump",**kwargs[key])
save_name = utp.get_option("em_save_name","emplot-"+key+".png",**kwargs[key])
do_plot_corr_effective_mass([ix])
plt.savefig(save_dir+'/'+save_name)
do_plot_corr_effective_mass(idx)
#
## --
fig.canvas.mpl_connect('key_press_event',press_effective_mass)
## -- save plot data
for idx,model in zip(range(len(models)),models):
key = model.datatag
## -- parameters used in fitting
## default = 2
_emSep = utp.get_option("meff_sep",2,**kwargs[key])
## default = smallest t not included in fit
_emFitMin = utp.get_option("meff_fit_min",model.tfit[-1]+1,**kwargs[key])
## default = midpoint - sep
_emFitMax = utp.get_option("meff_fit_max",
model.tdata[-1]/2-_emSep-int(model.tdata[-1]/12),**kwargs[key])
_emTData = model.tdata
_emTFit = range(_emFitMin,_emFitMax)
_emTFit = np.append(_emTFit,list(sorted([len(_emTData) - t for t in _emTFit])))
if not(fit is None) and (len(req[0]) > 0 or len(req[1]) > 0):
_emSubFcn = utp.mask_fit_fcn(model,fit,req,invert=False)
_emSub = np.array(_emSubFcn(np.array(_emTData)))
else:
_emSub = 0
_emDataFold = utf.fold_data(data[key]-_emSub,(model.tp < 0))
#_emTDataNonZero = [t for t in _emTData if np.abs(gv.mean(data[key])[t]) > 1e-20]
#_emTDataNonZero = [t for t in range(len(_emDataFold)) if np.mean(_emDataFold[t]) > 1e-20]
#
## -- data
_emRatio = np.array(_emDataFold[_emSep:])/np.array(_emDataFold[:-_emSep])
_emTDataRatio = np.array(range(len(_emRatio)))
_emTDataNonZero = np.array([t for t in range(len(_emRatio)) if _emRatio[t] > 1e-20])
#_emRatio = np.array([-gv.log(x)/_emSep for x in _emRatio if x > 1e-20])
#_emTDataRatio =\
# [t for t in _emTData
# if (t in _emTDataNonZero) and (t <= _emTData[-1]/2 +1 - _emSep) ] # first half
#_emTDataRatio = np.append(_emTDataRatio,
# [t for t in _emTData
# if (t in _emTDataNonZero) and (t >= _emTData[-1]/2 +1 + _emSep) ] ) # second half
#_emRatio =\
# [data[key][t+_emSep]/data[key][t] for t in _emTData
# if (t in _emTDataNonZero) and (t <= _emTData[-1]/2 +1 - _emSep) ] # first half
#_emRatio = np.append(_emRatio,
# [data[key][t-_emSep]/data[key][t] for t in _emTData
# if (t in _emTDataNonZero) and (t >= _emTData[-1]/2 +1 + _emSep) ] ) # second half
## -- times
_emTPosRatio.append(
[_emTDataRatio[t] for t in range(len(_emTDataRatio)) if _emRatio[t] > 0] )
_emTPosFit.append(
[_emTDataRatio[t] for t in range(len(_emTDataRatio))
if _emRatio[t] > 0 and _emTDataRatio[t] in _emTFit] )
## -- ratios
_emLogRatio.append(
[-gv.log(_emRatio[t])/_emSep for t in range(len(_emTDataRatio)) if _emRatio[t] > 0] )
_emLogRatioFit.append(
[-gv.log(_emRatio[t])/_emSep for t in range(len(_emTDataRatio))
if (gv.mean(_emRatio[t]) > 0) and (_emTDataRatio[t] in _emTPosFit[-1])] )
_emFoldRatio.append(_emLogRatio[-1])
_emFoldRatioFit.append(_emLogRatioFit[-1])
_emTPosFold.append(_emTPosRatio[-1])
_emTPosFoldFit.append(_emTPosFit[-1])
## -- folding
#_emFoldRatio.append(list())
#_emFoldRatioFit.append(list())
#_emTPosFold.append(list())
#_emTPosFoldFit.append(list())
#for t in range(1,len(_emTData)/2):
# if not(t in _emTPosRatio[-1]) or not(len(_emTData)-t in _emTPosRatio[-1]):
# continue
# _emFoldRatio[-1].append((_emLogRatio[-1][list(_emTPosRatio[-1]).index(t)]
# +_emLogRatio[-1][list(_emTPosRatio[-1]).index(len(_emTData)-t)])/2)
# _emTPosFold[-1].append(t)
# if not(t in _emTPosFit[-1]) or not(len(_emTData)-t in _emTPosFit[-1]):
# continue
# _emFoldRatioFit[-1].append((_emLogRatio[-1][list(_emTPosRatio[-1]).index(t)]
# +_emLogRatio[-1][list(_emTPosRatio[-1]).index(len(_emTData)-t)])/2)
# _emTPosFoldFit[-1].append(t)
#for t in range(len(_emTPosFold[-1])):
# print t,_emTPosFold[-1][t],_emFoldRatio[-1][t]
#for t in range(len(_emTPosFoldFit[-1])):
# print t,_emTPosFoldFit[-1][t],_emFoldRatioFit[-1][t]
_emLogRatioCentral.append(gv.mean(_emLogRatio[-1]))
_emLogRatioError.append([ list(gv.sdev(_emLogRatio[-1])), list(gv.sdev(_emLogRatio[-1])) ])
_emFoldRatioCentral.append(gv.mean(_emFoldRatio[-1]))
_emFoldRatioError.append([ list(gv.sdev(_emFoldRatio[-1])), list(gv.sdev(_emFoldRatio[-1])) ])
## -- fit
_emRatioFit.append(lsq.wavg(_emLogRatioFit[-1]))
if utp.get_option("meff_do_fold",False,**kwargs[key]):
_emFitCentral.append([gv.mean(_emRatioFit[-1]) for t in _emTPosFit[-1] if t < len(_emTData)/2])
_emFitError.append(
[list(np.array(_emFitCentral[-1])-np.array([gv.sdev(_emRatioFit[-1])
for t in _emTPosFit[-1] if t < len(_emTData)/2])),
list(np.array(_emFitCentral[-1])+np.array([gv.sdev(_emRatioFit[-1])
for t in _emTPosFit[-1] if t < len(_emTData)/2]))])
else:
_emFitCentral.append([gv.mean(_emRatioFit[-1]) for t in _emTPosFit[-1]])
_emFitError.append(
[list(np.array(_emFitCentral[-1])-np.array([gv.sdev(_emRatioFit[-1])
for t in _emTPosFit[-1]])),
list(np.array(_emFitCentral[-1])+np.array([gv.sdev(_emRatioFit[-1])
for t in _emTPosFit[-1]]))])
print "Best plateau fits: "
for key,rfit in zip([model.datatag for model in models],_emRatioFit):
print " ",key," : ",rfit
print " ----------------- "
_emRatioFitNonZero = [x for x in _emRatioFit if not(x is None)]
print " avg : ",lsq.wavg(_emRatioFitNonZero)
## -- done saving data
if not(utp.get_option("to_terminal",True,**kwargs[key])) and\
utp.get_option("to_file",False,**kwargs[key]):
for ix in range(len(models)):
## -- loops and saves all without creating window
do_plot_corr_effective_mass([ix])
else:
do_plot_corr_effective_mass(_emIdx)
def main():
x, y = make_data() # make fit data
# y = gv.gvar(gv.mean(y), 0.75**2 * gv.evalcov(y))
p0 = None # make larger fits go faster (opt.)
sys_stdout = sys.stdout
sys.stdout = tee.tee(sys.stdout, open("eg1.out", "w"))
for nexp in range(1, 7):
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x, y), fcn=fcn, prior=prior, p0=p0)
if fit.chi2 / fit.dof < 1.:
p0 = fit.pmean # starting point for next fit (opt.)
print '************************************* nexp =', nexp
print fit.format() # print the fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
if nexp > 2:
print 'E1/E0 =', E[1] / E[0], ' E2/E0 =', E[2] / E[0]
print 'a1/a0 =', a[1] / a[0], ' a2/a0 =', a[2] / a[0]
print
# error budget
outputs = {
'E1/E0': E[1] / E[0],
'E2/E0': E[2] / E[0],
'a1/a0': a[1] / a[0],
'a2/a0': a[2] / a[0]
}
inputs = {'E': fit.prior['E'], 'a': fit.prior['a'], 'y': y}
inputs = collections.OrderedDict()
inputs['a'] = fit.prior['a']
inputs['E'] = fit.prior['E']
inputs['y'] = fit.data[1]
print '================= Error Budget Analysis'
print fit.fmt_values(outputs)
print fit.fmt_errorbudget(outputs, inputs)
sys.stdout = sys_stdout
# print(gv.gvar(str(a[1])) / gv.gvar(str(a[0])) )
# print(gv.evalcorr([fit.p['a'][1], fit.p['E'][1]]))
# print(fit.format(True))
# redo fit with 4 parameters since that is enough
prior = make_prior(4)
fit = lsqfit.nonlinear_fit(data=(x, y), fcn=fcn, prior=prior, p0=fit.pmean)
sys.stdout = tee.tee(sys_stdout, open("eg1a.out", "w"))
print '--------------------- original fit'
print fit.format()
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print 'E1/E0 =', E[1] / E[0], ' E2/E0 =', E[2] / E[0]
print 'a1/a0 =', a[1] / a[0], ' a2/a0 =', a[2] / a[0]
print
# extra data 1
print '\n--------------------- new fit to extra information'
def ratio(p):
return p['a'][1] / p['a'][0]
newfit = lsqfit.nonlinear_fit(data=gv.gvar(1, 1e-5),
fcn=ratio,
prior=fit.p)
print(newfit.format())
E = newfit.p['E']
a = newfit.p['a']
print 'E1/E0 =', E[1] / E[0], ' E2/E0 =', E[2] / E[0]
print 'a1/a0 =', a[1] / a[0], ' a2/a0 =', a[2] / a[0]
if DO_PLOT:
import matplotlib.pyplot as plt
ratio = y / fit.fcn(x, fit.pmean)
plt.xlim(4, 15)
plt.ylim(0.95, 1.05)
plt.xlabel('x')
plt.ylabel('y / f(x,p)')
plt.yticks([0.96, 0.98, 1.00, 1.02, 1.04],
['0.96', '0.98', '1.00', '1.02', '1.04'])
plt.errorbar(x=x, y=gv.mean(ratio), yerr=gv.sdev(ratio), fmt='ob')
plt.plot([4.0, 21.0], [1.0, 1.0], 'b:')
plt.savefig('eg1.png', bbox_inches='tight')
plt.show()
# alternate method for extra data
sys.stdout = tee.tee(sys_stdout, open("eg1b.out", "w"))
fit.p['a1/a0'] = fit.p['a'][1] / fit.p['a'][0]
new_data = {'a1/a0': gv.gvar(1, 1e-5)}
new_p = lsqfit.wavg([fit.p, new_data])
print 'chi2/dof = %.2f\n' % (new_p.chi2 / new_p.dof)
print 'E:', new_p['E'][:4]
print 'a:', new_p['a'][:4]
print 'a1/a0:', new_p['a1/a0']
if DO_BAYES:
# Bayesian Fit
gv.ranseed([123])
prior = make_prior(4)
fit = lsqfit.nonlinear_fit(data=(x, y),
fcn=f,
prior=prior,
p0=fit.pmean)
sys.stdout = tee.tee(sys_stdout, open("eg1c.out", "w"))
# print fit
expval = lsqfit.BayesIntegrator(fit, limit=10.)
# adapt integrator to PDF
expval(neval=40000, nitn=10)
# calculate expectation value of function g(p)
fit_hist = gv.PDFHistogram(fit.p['E'][0])
def g(p):
parameters = [p['a'][0], p['E'][0]]
return dict(
mean=parameters,
outer=np.outer(parameters, parameters),
hist=fit_hist.count(p['E'][0]),
)
r = expval(g, neval=40000, nitn=10, adapt=False)
# print results
print r.summary()
means = r['mean']
cov = r['outer'] - np.outer(r['mean'], r['mean'])
print 'Results from Bayesian Integration:'
print 'a0: mean =', means[0], ' sdev =', cov[0, 0]**0.5
print 'E0: mean =', means[1], ' sdev =', cov[1, 1]**0.5
print 'covariance from Bayesian integral =', np.array2string(
cov, prefix=36 * ' ')
print
print 'Results from Least-Squares Fit:'
print 'a0: mean =', fit.p['a'][0].mean, ' sdev =', fit.p['a'][0].sdev
print 'E0: mean =', fit.p['E'][0].mean, ' sdev =', fit.p['E'][0].sdev
print 'covariance from least-squares fit =', np.array2string(
gv.evalcov([fit.p['a'][0], fit.p['E'][0]]),
prefix=36 * ' ',
precision=3)
sys.stdout = sys_stdout
# make histogram of E[0] probabilty
plt = fit_hist.make_plot(r['hist'])
plt.xlabel('$E_0$')
plt.ylabel('probability')
plt.savefig('eg1c.png', bbox_inches='tight')
# plt.show()
if DO_BOOTSTRAP:
Nbs = 40 # number of bootstrap copies
outputs = {
'E1/E0': [],
'E2/E0': [],
'a1/a0': [],
'a2/a0': [],
'E1': [],
'a1': []
} # results
for bsfit in fit.bootstrap_iter(n=Nbs):
E = bsfit.pmean['E'] # best-fit parameters
a = bsfit.pmean['a']
outputs['E1/E0'].append(E[1] / E[0]) # accumulate results
outputs['E2/E0'].append(E[2] / E[0])
outputs['a1/a0'].append(a[1] / a[0])
outputs['a2/a0'].append(a[2] / a[0])
outputs['E1'].append(E[1])
outputs['a1'].append(a[1])
# print E[:2]
# print a[:2]
# print bsfit.chi2/bsfit.dof
# extract means and standard deviations from the bootstrap output
for k in outputs:
outputs[k] = gv.gvar(np.mean(outputs[k]), np.std(outputs[k]))
print 'Bootstrap results:'
print 'E1/E0 =', outputs['E1/E0'], ' E2/E1 =', outputs['E2/E0']
print 'a1/a0 =', outputs['a1/a0'], ' a2/a0 =', outputs['a2/a0']
print 'E1 =', outputs['E1'], ' a1 =', outputs['a1']
def __init__(self, data, ampl='0(1)', dE='1(1)', E=None, s=(1, -1),
tp=None, tmin=6, svdcut=1e-6, osc=False, nterm=10):
"""
Args:
data: list / array of correlator data
ampl: str, the prior for the amplitude. Default is '0(1)'
dE: str, the prior for the energy splitting. Default is '1(1)'
E0: str, the prior for the ground state energy. Default is None,
which corresponds to taking the value for dE for the ground
state as well
s: tuple (s, so) with the signs for the towers of decay and
oscillating states, repsectively. Default is (1, -1)
tp: int, the periodicity of the data. Negative tp denotes
antiperiodic "sinh-like" data. Default is None, corresponding
to exponential decay
tmin: int, the smallest tmin to include in the "averaging"
svdcut: float, the desired svd cut for the "averaging"
osc: bool, whether to estimate the lowest-lying oscillating state
instead of the decay state
nterms: the number of terms to include in the towers of decaying
and oscillating states.
Raises:
RuntimeError: Can't estimate energy when cosh(E) < 1.
"""
self.osc = osc
self.nterm = nterm
s = self._to_tuple(s)
a, ao = self._build(ampl)
dE, dEo = self._build(dE, E)
s, so = s
tmax = None
if tp is None:
# Data is not periodic
# Model data with exponential decay
def g(E, t):
return gv.exp(-E * t)
elif tp > 0:
# Data is periodic
# Model with a cosh
def g(E, t):
return gv.exp(-E * t) + gv.exp(-E * (tp - t))
if tmin > 1:
tmax = -tmin + 1
else:
tmax = None
elif tp < 0:
# Data is antiperiodic
# Model with a sinh
def g(E, t):
return gv.exp(-E * t) - gv.exp(-E * (-tp - t))
# Reflect and fold the data around the midpoint
tmid = int((-tp + 1) // 2)
data_rest = lsqfit.wavg(
[data[1:tmid], -data[-1:-tmid:-1]], svdcut=svdcut)
data = np.array([data[0]] + list(data_rest))
else:
raise ValueError('FastFit: bad tp')
t = np.arange(len(data))[tmin:tmax]
data = data[tmin:tmax]
if not t.size:
raise ValueError(
'FastFit: tmin too large? No t values left. '
f'(tmin, tmax, tp)=({tmin}, {tmax}, {tp}).'
)
self.tmin = tmin
self.tmax = tmax
if osc:
data *= (-1) ** t * so
a, ao = ao, a
dE, dEo = dEo, dE
s, so = so, s
d_data = 0.
E = np.cumsum(dE)
# Sum the tower of decaying states, excluding the ground state
for aj, Ej in list(zip(a, E))[1:]:
d_data += s * aj * g(Ej, t)
# Sum the full tower of oscillating states
if ao is not None and dEo is not None:
Eo = np.cumsum(dEo)
for aj, Ej in zip(ao, Eo):
d_data += so * aj * g(Ej, t) * (-1) ** t
# Marginalize over the exicted states
data = data - d_data
self.marginalized_data = data
# Average over the remaining plateau
meff = 0.5 * (data[2:] + data[:-2]) / data[1:-1]
ratio = lsqfit.wavg(meff, prior=gv.cosh(E[0]), svdcut=svdcut)
if ratio >= 1:
self.E = type(ratio)(gv.arccosh(ratio), ratio.fit)
self.ampl = lsqfit.wavg(data / g(self.E, t) / s,
svdcut=svdcut, prior=a[0])
else:
LOGGER.warn(
'Cannot estiamte energy in FastFit: cosh(E) = %s',
str(ratio)
)
self.E = None
self.ampl = None
def main():
gv.ranseed([2009,2010,2011,2012]) # initialize random numbers (opt.)
x,y = make_data() # make fit data
p0 = None # make larger fits go faster (opt.)
sys_stdout = sys.stdout
sys.stdout = tee.tee(sys.stdout, open("eg1.out","w"))
for nexp in range(1, 11):
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,p0=p0) #, svdcut=SVDCUT)
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
if nexp > 5 and nexp < 10:
print(".".center(73))
continue
elif nexp not in [1]:
print("")
print '************************************* nexp =',nexp
print fit.format() # print the fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
if nexp > 2:
print 'E1/E0 =',E[1]/E[0],' E2/E0 =',E[2]/E[0]
print 'a1/a0 =',a[1]/a[0],' a2/a0 =',a[2]/a[0]
# redo fit with 4 parameters since that is enough
prior = make_prior(4)
fit = lsqfit.nonlinear_fit(data=(x,y), fcn=f, prior=prior, p0=fit.pmean)
sys.stdout = sys_stdout
print fit
# extra data 1
print '\n--------------------- fit with extra information'
sys.stdout = tee.tee(sys_stdout, open("eg1a.out", "w"))
def ratio(p):
return p['a'][1] / p['a'][0]
newfit = lsqfit.nonlinear_fit(data=gv.gvar(1,1e-5), fcn=ratio, prior=fit.p)
print (newfit)
E = newfit.p['E']
a = newfit.p['a']
print 'E1/E0 =',E[1]/E[0],' E2/E0 =',E[2]/E[0]
print 'a1/a0 =',a[1]/a[0],' a2/a0 =',a[2]/a[0]
# alternate method for extra data
sys.stdout = tee.tee(sys_stdout, open("eg1b.out", "w"))
fit.p['a1/a0'] = fit.p['a'][1] / fit.p['a'][0]
new_data = {'a1/a0' : gv.gvar(1,1e-5)}
new_p = lsqfit.wavg([fit.p, new_data])
print 'chi2/dof = %.2f\n' % (new_p.chi2 / new_p.dof)
print 'E:', new_p['E'][:4]
print 'a:', new_p['a'][:4]
print 'a1/a0:', new_p['a1/a0']
if DO_BAYES:
# Bayesian Fit
gv.ranseed([123])
prior = make_prior(4)
fit = lsqfit.nonlinear_fit(data=(x,y), fcn=f, prior=prior, p0=fit.pmean)
sys.stdout = tee.tee(sys_stdout, open("eg1c.out", "w"))
# print fit
expval = lsqfit.BayesIntegrator(fit, limit=10.)
# adapt integrator to PDF
expval(neval=10000, nitn=10)
# calculate expectation value of function g(p)
fit_hist = gv.PDFHistogram(fit.p['E'][0])
def g(p):
parameters = [p['a'][0], p['E'][0]]
return dict(
mean=parameters,
outer=np.outer(parameters, parameters),
hist=fit_hist.count(p['E'][0]),
)
r = expval(g, neval=10000, nitn=10, adapt=False)
# print results
print r.summary()
means = r['mean']
cov = r['outer'] - np.outer(r['mean'], r['mean'])
print 'Results from Bayesian Integration:'
print 'a0: mean =', means[0], ' sdev =', cov[0,0]**0.5
print 'E0: mean =', means[1], ' sdev =', cov[1,1]**0.5
print 'covariance from Bayesian integral =', np.array2string(cov, prefix=36 * ' ')
print
print 'Results from Least-Squares Fit:'
print 'a0: mean =', fit.p['a'][0].mean, ' sdev =', fit.p['a'][0].sdev
print 'E0: mean =', fit.p['E'][0].mean, ' sdev =', fit.p['E'][0].sdev
print 'covariance from least-squares fit =', np.array2string(gv.evalcov([fit.p['a'][0], fit.p['E'][0]]), prefix=36*' ',precision=3)
sys.stdout = sys_stdout
# make histogram of E[0] probabilty
plt = fit_hist.make_plot(r['hist'])
plt.xlabel('$E_0$')
plt.ylabel('probability')
plt.savefig('eg1c.png', bbox_inches='tight')
# plt.show()
# # extra data 2
# sys.stdout = tee.tee(sys_stdout, open("eg1b.out", "w"))
# newfit = fit
# for i in range(1):
# print '\n--------------------- fit with %d extra data sets' % (i+1)
# x, ynew = make_data()
# prior = newfit.p
# newfit = lsqfit.nonlinear_fit(data=(x,ynew), fcn=f, prior=prior) # , svdcut=SVDCUT)
# print newfit
sys.stdout = sys_stdout
# def fcn(x, p):
# return f(x, p), f(x, p)
# prior = make_prior(nexp)
# fit = lsqfit.nonlinear_fit(data=(x, [y, ynew]), fcn=fcn, prior=prior, p0=newfit.pmean) # , svdcut=SVDCUT)
# print(fit)
if DO_BOOTSTRAP:
Nbs = 40 # number of bootstrap copies
outputs = {'E1/E0':[], 'E2/E0':[], 'a1/a0':[],'a2/a0':[],'E1':[],'a1':[]} # results
for bsfit in fit.bootstrap_iter(n=Nbs):
E = bsfit.pmean['E'] # best-fit parameters
a = bsfit.pmean['a']
outputs['E1/E0'].append(E[1]/E[0]) # accumulate results
outputs['E2/E0'].append(E[2]/E[0])
outputs['a1/a0'].append(a[1]/a[0])
outputs['a2/a0'].append(a[2]/a[0])
outputs['E1'].append(E[1])
outputs['a1'].append(a[1])
# print E[:2]
# print a[:2]
# print bsfit.chi2/bsfit.dof
# extract means and standard deviations from the bootstrap output
for k in outputs:
outputs[k] = gv.gvar(np.mean(outputs[k]),np.std(outputs[k]))
print 'Bootstrap results:'
print 'E1/E0 =',outputs['E1/E0'],' E2/E1 =',outputs['E2/E0']
print 'a1/a0 =',outputs['a1/a0'],' a2/a0 =',outputs['a2/a0']
print 'E1 =',outputs['E1'],' a1 =',outputs['a1']
if DO_PLOT:
import matplotlib.pyplot as plt
ratio = y / fit.fcn(x,fit.pmean)
plt.xlim(4, 21)
plt.xlabel('x')
plt.ylabel('y / f(x,p)')
plt.errorbar(x=x,y=gv.mean(ratio),yerr=gv.sdev(ratio),fmt='ob')
plt.plot([4.0, 21.0], [1.0, 1.0], 'b:')
plt.savefig('eg1.png', bbox_inches='tight')
plt.show()
def plot_corr_effective_mass_check(models,data,fit=None,**kwargs):
"""
Get all data ready so that it can be plotted on command
Allows for dynamic cycling through plots
"""
_emNMod = len(models)
_emIdx = [0] ## -- index of plotted function, in array so it can be modified in functions
## -- objects to hold all plot data
## - Dat/Fit refers to the correlator data or the fit function
## - Central/Error are the central value and errors
_emLogRatio = []
_emLogRatioCentral = []
_emLogRatioError = []
_emLogRatioFit = []
_emRatioFit = []
_emRatioFitNonZero = []
_emFitCentral = []
_emFitError = []
## -- timeslice objects
_emTPosRatio = []
_emTPosFit = []
#
## -- fitting options
_emFitMin = 0
_emFitMax = 0
_emSep = 0
fig,ax = plt.subplots(1)
#
## -- setup plot function
def do_plot_corr_effective_mass_check(idx,fig=fig):
fig.clear()
ax = fig.add_subplot(111)
key = models[idx[0]].datatag
ax.set_ylim(utp.get_option("y_limit",[0.0,1.2],**kwargs[key]))
#
## -- plot fit
ax.plot(_emTPosFit[idx[0]],_emFitCentral[idx[0]],
color=utp.get_option("color3",'b',**kwargs[key]))
ax.plot(_emTPosFit[idx[0]],_emFitError[idx[0]][0],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
ax.plot(_emTPosFit[idx[0]],_emFitError[idx[0]][1],
color=utp.get_option("color3",'b',**kwargs[key]),
ls=utp.get_option("linestyle2",'--',**kwargs[key]))
## -- plot reference
for val in df.ec_reference_lines:
vt = [val for t in _emTPosFit[idx[0]]]
ax.plot(_emTPosFit[idx[0]],vt,
color=utp.get_option("color2",'g',**kwargs[key]))
# -- plot correlator data
ax.errorbar(_emTPosRatio[idx[0]],_emLogRatioCentral[idx[0]],yerr=_emLogRatioError[idx[0]],
mfc=utp.get_option("markerfacecolor1",'None',**kwargs[key]),
mec=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
color=utp.get_option("markeredgecolor1",'k',**kwargs[key]),
ls=utp.get_option("linestyle1",'None',**kwargs[key]),
marker=utp.get_option("marker1",'o',**kwargs[key]),
ms=utp.get_option("markersize",6,**kwargs[key]))
ax.scatter(_emTPosFit[idx[0]],gv.mean(_emLogRatioFit[idx[0]]),
color=utp.get_option("color1",'r',**kwargs[key]),
marker=utp.get_option("marker",'o',**kwargs[key]),
s=utp.get_option("markersize",36,**kwargs[key]))
fig.suptitle(utp.get_option("plottitle",str(idx[0])+" default title "+str(key),**kwargs[key]),
fontsize=utp.get_option("titlesize",20,**kwargs[key]))
# -- modify some options
ax.set_xlabel(r'$t$ slice')
ax.set_ylabel(utp.get_option("yaxistitle",
r"$-\frac{1}{"+str(_emSep)+r"}\,log\frac{C(t+"+str(_emSep)+r")}{C(t)}$",**kwargs[key]))
for item in ([ax.xaxis.label,ax.yaxis.label]):
# must be after setting label content (LaTeX ruins it)
item.set_fontsize(fontsize=utp.get_option("fontsize",20,**kwargs[key]))
rect =fig.patch
rect.set_facecolor('white')
if utp.get_option("to_file",False,**kwargs[key]):
save_dir = utp.get_option("ec_save_dir","./plotdump",**kwargs[key])
save_name = utp.get_option("ec_save_name","ecplot-"+key+".pdf",**kwargs[key])
plt.savefig(save_dir+'/'+save_name)
if utp.get_option("to_terminal",True,**kwargs[key]):
plt.draw()
pass
#
## -- setup button press action function
def press_effective_mass(event,idx=_emIdx):
#print('press_effective_mass', event.key)
try:
## -- manually indicate index
idx[0] = int(event.key) + (idx[0])*10
except ValueError:
if event.key==' ': ## -- space
## -- allows for replotting when changing index by typing number keys
idx[0] = idx[0] % _emNMod
do_plot_corr_effective_mass_check(idx)
elif event.key=='left':
idx[0] = (idx[0] - 1) % _emNMod
do_plot_corr_effective_mass_check(idx)
elif event.key=='right':
idx[0] = (idx[0] + 1) % _emNMod
do_plot_corr_effective_mass_check(idx)
elif event.key=='backspace':
## -- reset index so can manually flip through using number keys
idx[0] = 0
elif event.key=='d':
## -- dump plots into ./plotdump directory
for ix,model in zip(range(len(models)),models):
key = model.datatag
save_dir = utp.get_option("ec_save_dir","./plotdump",**kwargs[key])
save_name = utp.get_option("ec_save_name","ecplot-"+key+".png",**kwargs[key])
do_plot_corr_effective_mass_check([ix])
plt.savefig(save_dir+'/'+save_name)
do_plot_corr_effective_mass_check(idx)
#
## --
fig.canvas.mpl_connect('key_press_event',press_effective_mass)
## -- save plot data
for idx,model in zip(range(len(models)),models):
key = model.datatag
## -- parameters used in fitting
## default = 2
_emSep = utp.get_option("meff_sep",2,**kwargs[key])
## default = smallest t not included in fit
_emFitMin = utp.get_option("meff_fit_min",model.tfit[-1]+1,**kwargs[key])
## default = midpoint - sep
_emFitMax = utp.get_option("meff_fit_max",
model.tdata[-1]/2-_emSep-int(model.tdata[-1]/12),**kwargs[key])
_emTData = model.tdata
_emTFit = range(_emFitMin,_emFitMax)
_emTFit = np.append(_emTFit,list(sorted([len(_emTData) - t for t in _emTFit])))
_emTDataNonZero = [t for t in _emTData if np.abs(gv.mean(data[key])[t]) > 1e-20]
#
## -- data
_emTDataRatio =\
[t for t in _emTData
if (t in _emTDataNonZero) and (t <= _emTData[-1]/2 +1 - _emSep) ] # first half
_emTDataRatio = np.append(_emTDataRatio,
[t for t in _emTData
if (t in _emTDataNonZero) and (t >= _emTData[-1]/2 +1 + _emSep) ] ) # second half
_emRatio =\
[data[key][t+_emSep]/data[key][t] for t in _emTData
if (t in _emTDataNonZero) and (t <= _emTData[-1]/2 +1 - _emSep) ] # first half
_emRatio = np.append(_emRatio,
[data[key][t-_emSep]/data[key][t] for t in _emTData
if (t in _emTDataNonZero) and (t >= _emTData[-1]/2 +1 + _emSep) ] ) # second half
_emTPosRatio.append(
[_emTDataRatio[t] for t in range(len(_emTDataRatio)) if _emRatio[t] > 0] )
_emTPosFit.append(
[_emTDataRatio[t] for t in range(len(_emTDataRatio))
if _emRatio[t] > 0 and _emTDataRatio[t] in _emTFit] )
_emLogRatio.append(
[-gv.log(_emRatio[t])/_emSep for t in range(len(_emTDataRatio)) if _emRatio[t] > 0] )
_emLogRatioFit.append(
[-gv.log(_emRatio[t])/_emSep for t in range(len(_emTDataRatio))
if (gv.mean(_emRatio[t]) > 0) and (_emTDataRatio[t] in _emTPosFit[-1])] )
_emLogRatioCentral.append(gv.mean(_emLogRatio[-1]))
_emLogRatioError.append([ list(gv.sdev(_emLogRatio[-1])), list(gv.sdev(_emLogRatio[-1])) ])
## -- fit
_emRatioFit.append(lsq.wavg(_emLogRatioFit[-1]))
_emFitCentral.append([gv.mean(_emRatioFit[-1]) for t in _emTPosFit[-1]])
_emFitError.append(
[list(np.array(_emFitCentral[-1])-np.array([gv.sdev(_emRatioFit[-1]) for t in _emTPosFit[-1]])),
list(np.array(_emFitCentral[-1])+np.array([gv.sdev(_emRatioFit[-1]) for t in _emTPosFit[-1]]))]
)
print "Best plateau fits: "
for key,rfit in zip([model.datatag for model in models],_emRatioFit):
print " ",key," : ",rfit
print " ----------------- "
_emRatioFitNonZero = [x for x in _emRatioFit if not(x is None)]
print " avg : ",lsq.wavg(_emRatioFitNonZero)
## -- done saving data
if not(utp.get_option("to_terminal",True,**kwargs[key])) and\
utp.get_option("to_file",False,**kwargs[key]):
for ix in range(len(models)):
## -- loops and saves all without creating window
do_plot_corr_effective_mass_check([ix])
else:
do_plot_corr_effective_mass_check(_emIdx)
