def main():
gv.ranseed(4)
x = np.array([1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])
y_samples = [
[2.8409, 4.8393, 6.8403, 8.8377, 10.8356, 12.8389, 14.8356, 16.8362, 18.8351, 20.8341],
[2.8639, 4.8612, 6.8597, 8.8559, 10.8537, 12.8525, 14.8498, 16.8487, 18.8460, 20.8447],
[3.1048, 5.1072, 7.1071, 9.1076, 11.1090, 13.1107, 15.1113, 17.1134, 19.1145, 21.1163],
[3.0710, 5.0696, 7.0708, 9.0705, 11.0694, 13.0681, 15.0693, 17.0695, 19.0667, 21.0678],
[3.0241, 5.0223, 7.0198, 9.0204, 11.0191, 13.0193, 15.0198, 17.0163, 19.0154, 21.0155],
[2.9719, 4.9700, 6.9709, 8.9706, 10.9707, 12.9705, 14.9699, 16.9686, 18.9676, 20.9686],
[3.0688, 5.0709, 7.0724, 9.0730, 11.0749, 13.0776, 15.0790, 17.0800, 19.0794, 21.0795],
[3.1471, 5.1468, 7.1452, 9.1451, 11.1429, 13.1445, 15.1450, 17.1435, 19.1425, 21.1432],
[3.0233, 5.0233, 7.0225, 9.0224, 11.0225, 13.0216, 15.0224, 17.0217, 19.0208, 21.0222],
[2.8797, 4.8792, 6.8803, 8.8794, 10.8800, 12.8797, 14.8801, 16.8797, 18.8803, 20.8812],
[3.0388, 5.0407, 7.0409, 9.0439, 11.0443, 13.0459, 15.0455, 17.0479, 19.0493, 21.0505],
[3.1353, 5.1368, 7.1376, 9.1367, 11.1360, 13.1377, 15.1369, 17.1400, 19.1384, 21.1396],
[3.0051, 5.0063, 7.0022, 9.0052, 11.0040, 13.0033, 15.0007, 16.9989, 18.9994, 20.9995],
]
y = gv.dataset.avg_data(y_samples)
svd = gv.dataset.svd_diagnosis(y_samples)
y = gv.svd(y, svdcut=svd.svdcut)
if SHOW_PLOTS:
svd.plot_ratio(show=True)
def fcn(p):
return p['y0'] + p['s'] * x
prior = gv.gvar(dict(y0='0(5)', s='0(5)'))
fit = lsqfit.nonlinear_fit(data=y, fcn=fcn, prior=prior)
print(fit)
def main():
x, y = make_data() # collect fit data
p0 = None # make larger fits go faster (opt.)
for nexp in range(1, 7):
print('************************************* nexp =', nexp)
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x, y), fcn=fcn, prior=prior, p0=p0)
print(fit) # print the fit results
if nexp > 2:
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])
if fit.chi2 / fit.dof < 1.:
p0 = fit.pmean # starting point for next fit (opt.)
print()
# error budget analysis
# 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}
outputs = gv.BufferDict()
outputs['E2/E0'] = E[2] / E[0]
outputs['E1/E0'] = E[1] / E[0]
outputs['a2/a0'] = a[2] / a[0]
outputs['a1/a0'] = a[1] / a[0]
inputs = gv.BufferDict()
inputs['a'] = fit.prior['a']
inputs['y'] = y
inputs['E'] = fit.prior['E']
print('================= Error Budget Analysis')
print(gv.fmt_values(outputs))
print(gv.fmt_errorbudget(outputs, inputs))
def prep_plot(plt, data):
if not SHOW_PLOT or not ONE_W:
return plt
fit = lsqfit.nonlinear_fit(
data=gv.gvar(data.y, data.sig), prior=make_prior(), fcn=data.fitfcn
)
print(fit)
if False:
plt.rc('text',usetex=True)
plt.rc('font',family='serif', serif=['Times'])
ebargs = dict(
fmt='o', mfc='w', alpha=1.0, ms=1.5 * 2.5,
capsize=1.5 * 1.25, elinewidth=.5 * 1.5, mew=.5 * 1.5
)
fw = 3.3 # make bigger
fh = fw /1.61803399
# plt.figure(figsize=(fw,fh))
plt.rcParams["figure.figsize"] = (fw, fh)
else:
plt.rc('font',family='serif')
ebargs = dict(fmt='o', mfc='w', alpha=1.0)
plt.errorbar(x=data.x, y=data.y, yerr=data.sig, c='b', **ebargs)
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plot_fit(plt, fit.p, data, 'k:') # , color='0.8')
return plt
def main():
x, y = make_data()
prior = make_prior()
fit = lsqfit.nonlinear_fit(prior=prior, data=(x, y), fcn=fcn)
print(fit)
print('p1/p0 =', fit.p[1] / fit.p[0], 'p3/p2 =', fit.p[3] / fit.p[2])
print('corr(p0,p1) = {:.4f}'.format(gv.evalcorr(fit.p[:2])[1, 0]))
def do_fit_BsEtas(Fits,f,Nijk,Npow,addrho,svdnoise,priornoise,prior,fpf0same):
# have to define function in here so it only takes p as an argument (I think)
###############################
def fcn(p):
models = gv.BufferDict()
if 'f0_qsq{0}'.format(qsqmaxphys) in f:
models['f0_qsq{0}'.format(qsqmaxphys)] = make_f0_BsEtas(Nijk,Npow,addrho,p,Fits[0],0,p['qsq_qsq{0}'.format(qsqmaxphys)],p['z_qsq{0}'.format(qsqmaxphys)],Fits[0]['masses'][0],fpf0same,0,newdata=True)
if 'fp_qsq{0}'.format(qsqmaxphys) in f:
models['fp_qsq{0}'.format(qsqmaxphys)] = make_fp_BsEtas(Nijk,Npow,addrho,p,Fits[0],0,p['qsq_qsq{0}'.format(qsqmaxphys)],p['z_qsq{0}'.format(qsqmaxphys)],Fits[0]['masses'][0],fpf0same,0,newdata=True)
if 'f0_qsq{0}'.format(0) in f:
models['f0_qsq{0}'.format(0)] = make_f0_BsEtas(Nijk,Npow,addrho,p,Fits[0],0,0,p['z_qsq{0}'.format(0)],Fits[0]['masses'][0],fpf0same,0,newdata=True)
for Fit in Fits:
for mass in Fit['masses']:
for twist in Fit['twists']:
tag = '{0}_m{1}_tw{2}'.format(Fit['conf'],mass,twist)
#tag2 = '{0}_m{1}_tw{2}'.format(Fit['conf'],Fit['masses'][0],Fit['twists'][0])
#print(gv.evalcorr([f['f0_{0}'.format(tag)],f['f0_{0}'.format(tag2)]])[0][1])
if 'f0_{0}'.format(tag) in f:
models['f0_{0}'.format(tag)] = make_f0_BsEtas(Nijk,Npow,addrho,p,Fit,Fit['a'].mean,p['qsq_{0}'.format(tag)],p['z_{0}'.format(tag)],mass,fpf0same,float(mass)) #second mass is amh
if 'fp_{0}'.format(tag) in f:
models['fp_{0}'.format(tag)] = make_fp_BsEtas(Nijk,Npow,addrho,p,Fit,Fit['a'].mean,p['qsq_{0}'.format(tag)],p['z_{0}'.format(tag)],mass,fpf0same,float(mass)) #second mass is amh
return(models)
#################################
p0 = None
#if os.path.isfile('Fits/pmean{0}{1}{2}.pickle'.format(addrho,Npow,Nijk)):
# p0 = gv.load('Fits/pmean{0}{1}{2}.pickle'.format(addrho,Npow,Nijk))
fit = lsqfit.nonlinear_fit(data=f, prior=prior, p0=p0, fcn=fcn, svdcut=1e-5 ,add_svdnoise=svdnoise, add_priornoise=priornoise, maxit=500, tol=(1e-8,0.0,0.0),fitter='gsl_multifit', alg='subspace2D', solver='cholesky' ,debug=False)
gv.dump(fit.pmean,'Fits/pmean{0}{1}{2}.pickle'.format(addrho,Npow,Nijk))
print(fit.format(maxline=True))
return(fit.p)
def do_2st_3t_fit_combine2_jack(ratio1_,
ratio2_,
t2_,
ncut1_=1,
ncut2_=0,
dm_=gv.gvar(0.4, np.inf),
show=True):
nconf_ = ratio1_.coords['jackknife'].size
t_ = ratio1_.coords['t'].values
data1_ = ratio1_.sel(t2=t2_).squeeze().transpose(
'jackknife', 't2', 't').values.reshape(nconf_, t2_.size * t_.size)
data2_ = ratio2_.sel(t2=t2_).squeeze().transpose(
'jackknife', 't2', 't').values.reshape(nconf_, t2_.size * t_.size)
data1_fit = prep_data_ratio_new_jack(data1_, ncut1_, ncut2_, t2_, t_)
data2_fit = prep_data_ratio_new_jack(data2_, ncut1_, ncut2_, t2_, t_)
x_temp = {}
x_temp['1'] = data1_fit[0]
x_temp['2'] = data2_fit[0]
data_temp = {}
data_temp['1'] = data1_fit[1]
data_temp['2'] = data2_fit[1]
data_fit = (x_temp, data_temp)
prior0_2st_3t_combine2['dm'] = dm_
fit_ = lsqfit.nonlinear_fit(data=data_fit,
prior=prior0_2st_3t_combine2,
fcn=fcn_2st_3t_combine2,
debug=True)
if show:
print_fit(fit_)
print(fit_.p['c0_2'] - fit_.p['c0_1'])
return fit_
def main():
gv.ranseed([2009,2010,2011,2012,2013]) # initialize random numbers (opt.)
x,y = make_data() # make fit data
p0 = None # make larger fits go faster (opt.)
sys_stdout = sys.stdout
for nexp in range(3,6):
prior = make_prior(nexp,x)
fit = lsqfit.nonlinear_fit(data=y,fcn=f,prior=prior,p0=p0) # ,svdcut=SVDCUT)
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
fit.check_roundoff()
if nexp == 4:
sys.stdout = tee.tee(sys.stdout,open("eg2.out","w"))
print '************************************* nexp =',nexp
print fit # 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]
sys.stdout = sys_stdout
print
#
if DO_BOOTSTRAP:
Nbs = 10 # 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:
print fit.format(100) # print the fit results
import pylab as pp
from gvar import mean,sdev
fity = f(x,fit.pmean)
ratio = y/fity
pp.xlim(0,21)
pp.xlabel('x')
pp.ylabel('y/f(x,p)')
pp.errorbar(x=gv.mean(x),y=gv.mean(ratio),yerr=gv.sdev(ratio),fmt='ob')
pp.plot([0.0,21.0],[1.0,1.0])
pp.show()
def bad_analysis(): sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1a.out', 'w')) x, y = make_data() p0 = np.ones(5.) # starting value for chi**2 minimization fit = lsqfit.nonlinear_fit(data=(x, y), p0=p0, fcn=f) print fit.format(maxline=True) make_plot(x, y, fit) return fit
def bad_analysis():
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1a.out', 'w'))
x, y = make_data()
p0 = np.ones(5.) # starting value for chi**2 minimization
fit = lsqfit.nonlinear_fit(data=(x, y), p0=p0, fcn=f)
print fit.format(maxline=True)
make_plot(x, y, fit, name='eg-appendix1a')
return fit
def fitscript_v2(trange,T,data,priors,fcn,init=None,basak=None):
sets = len(data)/T
#print "sets:", sets
pmean = []
psdev = []
post = []
p0 = []
prior = []
tmintbl = []
tmaxtbl = []
chi2 = []
dof = []
Q = []
lgbftbl = []
rawoutput = []
for tmin in range(trange['tmin'][0], trange['tmin'][1]+1):
for tmax in range(trange['tmax'][0], trange['tmax'][1]+1):
x = x_indep(tmin, tmax)
xlist, y = y_dep(x, data, sets)
if basak is not None:
x = {'indep': x, 'basak': basak}
else: pass
fit = lsqfit.nonlinear_fit(data=(x,y),prior=priors,fcn=fcn,p0=init,maxit=1000000) #,svdcut=1E-3)
pmean.append(fit.pmean)
psdev.append(fit.psdev)
post.append(fit.p)
p0.append(fit.p0)
prior.append(fit.prior)
tmintbl.append(tmin)
tmaxtbl.append(tmax)
chi2.append(fit.chi2)
dof.append(fit.dof)
lgbftbl.append(fit.logGBF)
Q.append(fit.Q)
rawoutput.append(fit)
#fcnname = str(fcn.__name__)
#fitline = fcn(x,fit.p)
#print "%s_%s_t, %s_%s_y, +-, %s_%s_fit, +-" %(fcnname, basak[0], fcnname, basak[0], fcnname, basak[0])
#for i in range(len(xlist)):
# print xlist[i], ',', y[i].mean, ',', y[i].sdev, ',', fitline[i].mean, ',', fitline[i].sdev
#print '======'
#print fcn.__name__, basak
#print fit
#print '======'
fittbl = dict()
fittbl['tmin'] = tmintbl
fittbl['tmax'] = tmaxtbl
fittbl['pmean'] = pmean
fittbl['psdev'] = psdev
fittbl['post'] = post
fittbl['p0'] = p0
fittbl['prior'] = prior
fittbl['chi2'] = chi2
fittbl['dof'] = dof
fittbl['logGBF'] = lgbftbl
fittbl['Q'] = Q
fittbl['rawoutput'] = rawoutput
return fittbl
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.)
for nexp in range(3,8):
print('************************************* nexp =',nexp)
prior = make_prior(nexp)
# eps = gv.gvar(1,1e-300) # use svdcut to make it independent
# prior['a'] *= eps
# y *= eps
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,
p0=p0,svdcut=SVDCUT)
print(fit) # print the fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print('E1/E0 =',(E[1]/E[0]).fmt(),' E2/E0 =',(E[2]/E[0]).fmt())
print('a1/a0 =',(a[1]/a[0]).fmt(),' a2/a0 =',(a[2]/a[0]).fmt())
print()
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
if DO_BOOTSTRAP:
Nbs = 10 # 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.dataset.avg_data(outputs[k],bstrap=True).fmt(3)
# gv.gvar(np.mean(outputs[k]),
# np.std(outputs[k])).fmt(3)
print('Bootstrap results:')
print('E1/E0 =',outputs['E1/E0'],' E2/E0 =',outputs['E2/E0'])
print('a1/a0 =',outputs['a1/a0'],' a2/a0 =',outputs['a2/a0'])
print('E1 =',outputs['E1'],' a1 =',outputs['a1'])
if DO_PLOT:
print(fit.format(100)) # print the fit results
import pylab as plt
ratio = y/f(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 fit_data(data):
nstates = 2
x = np.arange(5, 10)
y = data[x]
p = priors(nstates)
fitc = fit_functions(T=len(data) + 1, nstates=nstates)
fit = lsqfit.nonlinear_fit(data=(x, y), prior=p, fcn=fitc.twopt)
print fit
return fit
def __call__(self, nstates, times, **fitter_kwargs):
""" Run the fit. """
x, y = self.build_xy(times.tmin_src, times.tmin_snk, times.t_step)
prior = self.build_prior(nstates.n, nstates.m)
if self.correlated:
fit = lsqfit.nonlinear_fit(data=(x, y),
fcn=ratio_model,
prior=prior,
**fitter_kwargs)
else:
fit = lsqfit.nonlinear_fit(udata=(x, y),
fcn=ratio_model,
prior=prior,
**fitter_kwargs)
fit = serialize.SerializableRatioAnalysis(fit, nstates, times,
self.ds.m_src, self.ds.m_snk)
self._fit = fit
return fit
def prior_analysis(): x, y = make_data() # loose prior sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1d.out', 'w')) prior = gv.gvar(91 * ['0(3)']) # prior for the fit fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f) print fit.format(maxline=True) # really loose prior sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1h.out', 'w')) prior = gv.gvar(91 * ['0(20)']) # prior for the fit fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f) print fit.format(maxline=True) make_plot(x, y, fit, xmax=0.96) # tight prior sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1e.out', 'w')) prior = gv.gvar(91 * ['0.0(3)']) # prior for the fit fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f) print fit.format(maxline=True)
def prior_analysis():
x, y = make_data()
# loose prior
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1d.out', 'w'))
prior = gv.gvar(91 * ['0(3)']) # prior for the fit
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f)
print fit.format(maxline=True)
# really loose prior
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1h.out', 'w'))
prior = gv.gvar(91 * ['0(20)']) # prior for the fit
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f)
print fit.format(maxline=True)
make_plot(x, y, fit, xmax=0.96, name='eg-appendix1d')
# tight prior
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1e.out', 'w'))
prior = gv.gvar(91 * ['0.0(3)']) # prior for the fit
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f)
print fit.format(maxline=True)
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.)
for nexp in range(3,8):
print('************************************* nexp =',nexp)
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,p0=p0,svdcut=SVDCUT)
print(fit) # print the fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print('E1/E0 =',(E[1]/E[0]).fmt(),' E2/E0 =',(E[2]/E[0]).fmt())
print('a1/a0 =',(a[1]/a[0]).fmt(),' a2/a0 =',(a[2]/a[0]).fmt())
print()
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
if DO_ERRORBUDGET:
outputs = OrderedDict([
('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 = OrderedDict([
('E', fit.prior['E']), ('a', fit.prior['a']),
('y', y), ('svd', fit.svdcorrection)
])
print(fit.fmt_values(outputs))
print(fit.fmt_errorbudget(outputs,inputs))
if DO_EMPBAYES:
def fitargs(z,nexp=nexp,prior=prior,f=f,data=(x,y),p0=p0):
z = gv.exp(z)
prior['a'] = [gv.gvar(0.5,0.5*z[0]) for i in range(nexp)]
return dict(prior=prior,data=data,fcn=f,p0=p0)
##
z0 = [0.0]
fit,z = lsqfit.empbayes_fit(z0,fitargs,tol=1e-3)
print(fit) # print the optimized fit results
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print('E1/E0 =',(E[1]/E[0]).fmt(),' E2/E0 =',(E[2]/E[0]).fmt())
print('a1/a0 =',(a[1]/a[0]).fmt(),' a2/a0 =',(a[2]/a[0]).fmt())
print("prior['a'] =",fit.prior['a'][0].fmt())
print()
if DO_PLOT:
import pylab as pp
from gvar import mean,sdev
fity = f(x,fit.pmean)
ratio = y/fity
pp.xlim(0,21)
pp.xlabel('x')
pp.ylabel('y/f(x,p)')
pp.errorbar(x=x,y=mean(ratio),yerr=sdev(ratio),fmt='ob')
pp.plot([0.0,21.0],[1.0,1.0])
pp.show()
def Analyse_NM():
def f_pot_NM(x, p):
xt = (x - p['n_sat']) / (3 * p['n_sat'])
v0 = p['E_sat+E_sym'] - T_SM(
p['n_sat']) - T_SM(p['n_sat']) * (2**(2 / 3) - 1)
v1 = p['L_sym'] - 2 * T_SM(p['n_sat']) - 2 * T_SM(
p['n_sat']) * (2**(2 / 3) - 1)
v2 = p['K_sat+K_sym'] + 2 * T_SM(p['n_sat']) - 2 * T_SM(
p['n_sat']) * (-1 * 2**(2 / 3) + 1)
v3 = p['Q_sat+Q_sym'] - 8 * T_SM(p['n_sat']) - 2 * T_SM(
p['n_sat']) * (4 * 2**(2 / 3) - 4)
v4 = p['Z_sat+Z_sym'] + 56 * T_SM(p['n_sat']) - 8 * T_SM(
p['n_sat']) * (-7 * 2**(2 / 3) + 7)
ans = v0 + v1 * xt + (v2 / 2.) * xt**2 + (v3 / 6.) * xt**3 + (
v4 / 24.) * (xt)**4
return ans
def f_pot_NM_c(x, p):
xt = (x - p['n_sat']) / (3 * p['n_sat'])
lam = f_pot_NM(0, p) * 3.**5
beta = 3
return f_pot_NM(x, p) + lam * xt**5 * np.exp(-42 *
(x / 0.16)**(beta / 3))
def f_NM(x, p):
return T_NM(x) + f_pot_NM_c(x, p)
# prior_eNM = {} # Drischler prior
# prior_eNM['n_sat'] = SM3_par['n_sat']
# prior_eNM['E_sat+E_sym'] = gv.gvar(16.85, 3.33)
# prior_eNM['L_sym'] = gv.gvar(48.1, 3.6)
# prior_eNM['K_sat+K_sym'] = gv.gvar(42,62)
# prior_eNM['Q_sat+Q_sym'] = gv.gvar(-303, 338)
# prior_eNM['Z_sat+Z_sym'] = gv.gvar(-1011, 593)
prior_eNM = {} # Jerome priors
prior_eNM['n_sat'] = SM3_par['n_sat']
prior_eNM['E_sat+E_sym'] = gv.gvar(16.0, 3.0)
prior_eNM['L_sym'] = gv.gvar(50, 10)
prior_eNM['K_sat+K_sym'] = gv.gvar(100, 100)
prior_eNM['Q_sat+Q_sym'] = gv.gvar(0, 400)
prior_eNM['Z_sat+Z_sym'] = gv.gvar(-500, 500)
x = td
y = te_NM_av
fit = lsqfit.nonlinear_fit(data=(x, y),
prior=prior_eNM,
fcn=f_NM,
debug=True,
svdcut=ts_NM.svdcut)
NM3_par = fit.p
return f_NM, NM3_par
def fit_data(data,
fit_range,
particles,
Pcm,
nstates,
nsinks,
cov=None,
print_fit=True):
if nsinks == 1:
if print_fit:
print "fitting with " + str(nstates) + " states and smeared data"
else:
pass
else:
if print_fit:
print "fitting with " + str(
nstates) + " states and point and smeared data"
else:
pass
x = fit_range
y = data
if cov is None:
cov_matrix = gv.evalcov(y)
#cov_matrix = gv.evalcov(y)/len(y)
#cov_matrix = np.identity(len(x))
if print_fit:
print np.shape(cov_matrix)
else:
pass
else:
cov_matrix = cov
y = gv.mean(y)
#you'll need to update the pipi function to deal with number of sinks as well as nstates
if particles == "pipi":
p = pipi_priors(nstates, nsinks, Pcm)
#fitc = pipi_fit_function(nstates=nstates,T=len(data))
if nsinks == 1:
fitc = pipi_fit_function(nstates=nstates, T=48, sinks=["s"])
else:
fitc = pipi_fit_function(nstates=nstates, T=48, sinks=["s", "p"])
elif particles == "pion":
p = pion_priors(nstates, nsinks, Pcm)
p0 = pion_priors(nstates, nsinks, Pcm)
if nsinks == 1:
fitc = pion_fit_function(nstates=nstates, T=48, sinks=["s"])
else:
fitc = pion_fit_function(nstates=nstates, T=48, sinks=["s", "p"])
#fit = lsqfit.nonlinear_fit(data=(x,y,cov_matrix),prior=p0,fcn=fitc.full_func)
fit = lsqfit.nonlinear_fit(data=(x, y, cov_matrix),
prior=p,
fcn=fitc.full_func)
if print_fit:
print fit
else:
pass
return fit
def main():
p0 = [0.5, 0.4, 0.7]
N = 50000 # takes 2min to do 2000000; scales linearly
x = np.linspace(0.2, 2., N)
y = make_fake_data(x, p0, f)
print('y = [{} {} ... {}]\n'.format(y[0], y[1], y[-1]))
prior = gv.gvar(['0(1)', '0(1)', '0(1)'])
fit = lsqfit.nonlinear_fit(udata=(x, y), prior=prior, fcn=f)
print(fit)
def xval_wrapper(pen, win, parameter_file_path, splines, spline_power,
data_file_path, data_error_file_path, k):
try:
parameters = read_parameters(parameter_file_path)
data = read_data(data_file_path)
tr = data[:win]
val = data[win:(win + 7)]
mi = SEIRModel(fit_columns=["hospital_census", "vent_census"],
update_parameters=flexible_beta)
xx, pp = prepare_model_parameters(parameters=parameters,
data=tr,
beta_fun='flexible_beta',
splines=splines,
spline_power=spline_power)
pp['beta_splines'] = gvar([0 for i in range(k)],
[pen for i in range(k)])
mi.fit_start_date = xx["day0"]
xx["error_infos"] = (read_csv(data_error_file_path).set_index("param")
["value"].to_dict())
fit = nonlinear_fit(
data=(xx, get_yy(tr, **xx["error_infos"])),
prior=pp,
fcn=mi.fit_fcn,
debug=False,
)
# detect and handle degenerate fits
# THIS IS A TEMPORARY HACK
splinecoefvec = np.array([
fit.p['beta_splines'][i].mean
for i in range(len(fit.p['beta_splines']))
])
cv = np.std(splinecoefvec) / np.mean(splinecoefvec)
if cv < .1:
MSE = -9999
error = "degenerate fit"
else:
xx = fit.x.copy()
xx["dates"] = xx["dates"].union(
date_range(xx["dates"].max(), freq="D", periods=8))
prediction_df = mi.propagate_uncertainties(xx, fit.p)
prediction_df.index = prediction_df.index.round("H")
mg = val.merge(prediction_df, left_index=True, right_index=True)
# scaling
hosp = (mg.hosp - np.mean(mg.hosp)) / np.std(mg.hosp)
hosp_hat = (mg.hospital_census.apply(lambda x: x.mean) -
np.mean(mg.hosp)) / np.std(mg.hosp)
vent = (mg.vent - np.mean(mg.vent)) / np.std(mg.vent)
vent_hat = (mg.vent_census.apply(lambda x: x.mean) -
np.mean(mg.vent)) / np.std(mg.vent)
MSE = mse(hosp, hosp_hat) + mse(vent, vent_hat)
error = ""
return dict(mse=MSE, pen=pen, win=win, error=error)
except Exception as e:
return dict(mse=-9999, pen=pen, win=win, error=e)
def jackknife_fitting_prior(data_, func_, prior0_, ncut1, ncut2, t1, t2):
jk_res = []
for ij in range(data_.shape[0]):
data_new_ = np.delete(data_, ij, 0)
data_fit = prep_data_ratio(data_new_, ncut1, ncut2, t1, t2)
fit = lsqfit.nonlinear_fit(data=data_fit,
prior=prior0_,
fcn=func_,
debug=True)
jk_res.append(fit.p)
return jk_res
def minfcn(z, save=save):
args = fitargs(z)
if save['lastp0'] is not None:
args['p0'] = save['lastp0']
fit = lsqfit.nonlinear_fit(**args)
if numpy.isnan(fit.logGBF):
raise ValueError
else:
save['lastz'] = z
save['lastp0'] = fit.pmean
return -fit.logGBF
def bootstrap_fitting(nbs_, data_, func_, p0_, ncut1, ncut2, t1, t2):
bs_res = []
for ib in range(nbs_):
xb_ = get_boot_sample(np.arange(0, data_.shape[0], 1))
data_new_ = data_[xb_, ...]
data_fit = prep_data_ratio(data_new_, ncut1, ncut2, t1, t2)
fit = lsqfit.nonlinear_fit(data=data_fit,
p0=p0_,
fcn=func_,
debug=True)
bs_res.append(fit.p)
return bs_res
def f_perform_fit(all_dta,
x,
y,
par,
f_func,
verbose=True,
concise=False,
plot=True,
full_data=False,
error_band=False,
semilog=False):
'''
Function wrapper to perform correlator fit for mesons.
Reads dictionary dta with x and y data.
Performs both cosh and sinh fits.
'''
# Performing meson fit
p0 = f_make_p0(par)
fit = lsqfit.nonlinear_fit(data=(x, y['y']),
fcn=f_func,
p0=p0,
extend=True,
svdcut=1e-8)
# Print the fit results
if concise:
pass
else:
print "*****************************", '\n'
if verbose:
print f_func.__doc__.strip('\n').strip(
' ') # Prints the functional form of fit function.
print(fit.format(maxline=True)), "\n\n"
else:
print fit, "\n\n"
# Plot fit
if plot:
f_fit_plot(x,
y,
all_dta,
fit,
full_data=full_data,
error_band=error_band,
semilog=semilog)
return fit
def main():
param, data = collect_data('spline.p')
F, prior = make_fcn_prior(param)
fit = lsqfit.nonlinear_fit(data=data, prior=prior, fcn=F)
print(fit)
# create f(m)
f = gv.cspline.CSpline(fit.p['mknot'], fit.p['fknot'])
# create error budget
outputs = {'f(1)':f(1), 'f(5)':f(5), 'f(9)':f(9)}
inputs = {'data':data}
inputs.update(prior)
print(gv.fmt_values(outputs))
print(gv.fmt_errorbudget(outputs=outputs, inputs=inputs))
make_plot(param, data, fit)
def main():
x, y = make_data()
prior = make_prior(100) # 100 exponential terms in all
p0 = None
for nexp in range(1, 6):
# marginalize the last 100 - nexp terms (in ymod_prior)
fit_prior = gv.BufferDict() # part of prior used in fit
ymod_prior = gv.BufferDict() # part of prior absorbed in ymod
for k in prior:
fit_prior[k] = prior[k][:nexp]
ymod_prior[k] = prior[k][nexp:]
ymod = y - fcn(x, ymod_prior) # remove temrs in ymod_prior
# fit modified data with just nexp terms (in fit_prior)
fit = lsqfit.nonlinear_fit(
data=(x, ymod),
prior=fit_prior,
fcn=fcn,
p0=p0,
tol=1e-15,
svdcut=1e-4,
)
# print fit information
print('************************************* nexp =', nexp)
print(fit.format(True))
p0 = fit.pmean
# print summary information and error budget
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
# 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 prior':prior['E'], 'a prior':prior['a'],
# 'svd cut':fit.svdcorrection,
# }
outputs = gv.BufferDict()
outputs['E2/E0'] = E[2] / E[0]
outputs['E1/E0'] = E[1] / E[0]
outputs['a2/a0'] = a[2] / a[0]
outputs['a1/a0'] = a[1] / a[0]
inputs = gv.BufferDict()
inputs['E prior'] = prior['E']
inputs['svd cut'] = fit.svdcorrection
inputs['a prior'] = prior['a']
print(fit.fmt_values(outputs))
print(fit.fmt_errorbudget(outputs, inputs))
def Analyse_SM():
def f_pot_SM(x, p):
xt = (x - p['n_sat']) / (3 * p['n_sat'])
v0 = p['E_sat'] - T_SM(p['n_sat'])
v1 = -2 * T_SM(p['n_sat'])
v2 = p['K_sat'] + 2 * T_SM(p['n_sat'])
v3 = p['Q_sat'] - 8 * T_SM(p['n_sat'])
v4 = p['Z_sat'] + 56 * T_SM(p['n_sat'])
ans = v0 + v1 * xt + (v2 / 2.) * xt**2 + (v3 / 6.) * xt**3 + (
v4 / 24.) * (xt)**4
return ans
def f_pot_SM_c(x, p):
xt = (x - p['n_sat']) / (3 * p['n_sat'])
lam = f_pot_SM(0, p) * 3.**5
beta = 3
return f_pot_SM(x, p) + lam * xt**5 * np.exp(-17 *
(x / 0.16)**(beta / 3))
def f_SM(x, p):
return T_SM(x) + f_pot_SM_c(x, p)
# prior_e_SM = {} # Drischler prior
# prior_e_SM['n_sat'] = gv.gvar(0.171, 0.016)
# prior_e_SM['E_sat'] = gv.gvar(-15.16, 1.24)
# prior_e_SM['K_sat'] = gv.gvar(214, 22)
# prior_e_SM['Q_sat'] = gv.gvar(-139, 104)
# prior_e_SM['Z_sat'] = gv.gvar(1306, 214)
prior_e_SM = {} # Jerome priors
prior_e_SM['n_sat'] = gv.gvar(0.16, 0.01)
prior_e_SM['E_sat'] = gv.gvar(-15.5, 1.0)
prior_e_SM['K_sat'] = gv.gvar(230, 20)
prior_e_SM['Q_sat'] = gv.gvar(-300, 400)
prior_e_SM['Z_sat'] = gv.gvar(1300, 500)
x = td
y = te_SM_av
fit = lsqfit.nonlinear_fit(data=(x, y),
prior=prior_e_SM,
fcn=f_SM,
debug=True,
svdcut=ts_SM.svdcut)
SM3_par = fit.p
return f_SM, SM3_par
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 good_analysis(): sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1b.out', 'w')) x, y = make_data() prior = gv.gvar(N * ['0(1)']) # prior for the fit fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f) print fit.format(maxline=True) make_plot(x, y, fit) inputs = gv.BufferDict(prior=prior) for xi, yi in zip(x, y): inputs['y(%.2f)' % xi] = yi sys.stdout = tee.tee(STDOUT, open(OUTDIR+'eg-appendix1g.out', 'w')) inputs = dict(prior=prior, y=y) outputs = dict(p0=fit.p[0]) print gv.fmt_errorbudget(inputs=inputs, outputs=outputs) return fit
def good_analysis(plot=MAKE_PLOTS):
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1b.out', 'w'))
x, y = make_data()
prior = gv.gvar(N * ['0(1)']) # prior for the fit
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f)
print fit.format(maxline=True)
if plot:
make_plot(x, y, fit, name='eg-appendix1b')
inputs = gv.BufferDict(prior=prior)
for xi, yi in zip(x, y):
inputs['y(%.2f)' % xi] = yi
sys.stdout = tee.tee(STDOUT, open(OUTDIR + 'eg-appendix1g.out', 'w'))
inputs = dict(prior=prior, y=y)
outputs = dict(p0=fit.p[0])
print gv.fmt_errorbudget(inputs=inputs, outputs=outputs)
return fit
def main():
# pendulum data exhibits experimental error in ability to measure theta
t = gv.gvar([
'0.10(1)', '0.20(1)', '0.30(1)', '0.40(1)', '0.50(1)',
'0.60(1)', '0.70(1)', '0.80(1)', '0.90(1)', '1.00(1)'
])
theta = gv.gvar([
'1.477(79)', '0.791(79)', '-0.046(79)', '-0.852(79)',
'-1.523(79)', '-1.647(79)', '-1.216(79)', '-0.810(79)',
'0.185(79)', '0.832(79)'
])
for t_n, theta_n in zip(t, theta):
print("{} {:>10}".format(t_n.fmt(2), theta_n.fmt(3)))
# prior: assume experimental error in ability to specify theta(0)
prior = gv.BufferDict()
prior['g/l'] = gv.gvar('40(20)')
prior['theta(0)'] = gv.gvar('1.571(50)')
prior['t'] = t
# fit function: use class Pendulum object to integrate pendulum motion
def fitfcn(p, t=None):
if t is None:
t = p['t']
pendulum = Pendulum(p['g/l'])
return pendulum(p['theta(0)'], t)
# do the fit and print results
fit = lsqfit.nonlinear_fit(data=theta, prior=prior, fcn=fitfcn)
sys.stdout = tee.tee(STDOUT, open('case-pendulum.out', 'w'))
print(fit.format(maxline=True))
sys.stdout = STDOUT
print('fit/exact for (g/l) =', fit.p['g/l'] / (2*np.pi) ** 2)
print('fit/exact for theta(0) =', fit.p['theta(0)'] / (np.pi / 2.))
if MAKE_PLOT:
# make figure (saved to file pendulum.pdf)
plt.figure(figsize=(4,3))
# start plot with data
plt.errorbar(
x=gv.mean(t), xerr=gv.sdev(t), y=gv.mean(theta), yerr=gv.sdev(theta),
fmt='k.',
)
# use best-fit function to add smooth curve for 100 points
t = np.linspace(0., 1.1, 100)
th = fitfcn(fit.p, t)
show_plot(t, th)
def main():
# pendulum data exhibits experimental error in ability to measure theta
t = gv.gvar([
'0.10(1)', '0.20(1)', '0.30(1)', '0.40(1)', '0.50(1)',
'0.60(1)', '0.70(1)', '0.80(1)', '0.90(1)', '1.00(1)'
])
theta = gv.gvar([
'1.477(79)', '0.791(79)', '-0.046(79)', '-0.852(79)',
'-1.523(79)', '-1.647(79)', '-1.216(79)', '-0.810(79)',
'0.185(79)', '0.832(79)'
])
for t_n, theta_n in zip(t, theta):
print("{} {:>10}".format(t_n.fmt(2), theta_n.fmt(3)))
# prior: assume experimental error in ability to specify theta(0)
prior = gv.BufferDict()
prior['g/l'] = gv.gvar('40(20)')
prior['theta(0)'] = gv.gvar('1.571(50)')
prior['t'] = t
# fit function: use class Pendulum object to integrate pendulum motion
def fitfcn(p, t=None):
if t is None:
t = p['t']
pendulum = Pendulum(p['g/l'])
return pendulum(p['theta(0)'], t)
# do the fit and print results
fit = lsqfit.nonlinear_fit(data=theta, prior=prior, fcn=fitfcn)
sys.stdout = tee.tee(STDOUT, open('case-pendulum.out', 'w'))
print(fit.format(maxline=True))
sys.stdout = STDOUT
print('fit/exact for (g/l) =', fit.p['g/l'] / (2*np.pi) ** 2)
print('fit/exact for theta(0) =', fit.p['theta(0)'] / (np.pi / 2.))
if MAKE_PLOT:
# make figure (saved to file pendulum.pdf)
plt.figure(figsize=(4,3))
# start plot with data
plt.errorbar(
x=gv.mean(t), xerr=gv.sdev(t), y=gv.mean(theta), yerr=gv.sdev(theta),
fmt='b.',
)
# use best-fit function to add smooth curve for 100 points
t = np.linspace(0., 1.1, 100)
th = fitfcn(fit.p, t)
show_plot(t, th)
def fit_data(x, y, p):
prior = make_priors(y, p)
corr = gv.evalcorr(prior)
#for k1 in prior:
# for k2 in prior:
# c = np.squeeze(corr[(k1,k2)])
# if c not in [1.0,0.0]:
# print k1, k2, c
# else: pass
p['fv']['mpiL'] = y['mpiL']
p['ma']['mpiL'] = y['mmaL']
fitc = fit_functions(fv=p['fv'], ma=p['ma'])
fit = lsqfit.nonlinear_fit(data=(x, y['y']),
prior=prior,
fcn=fitc.fit_switch,
maxit=1000000)
print fit.format('v')
return {'fit': fit, 'prior': prior, 'fitc': fitc}
def Fit_e_sym4_eta():
e_sym4_eta_av = []
for h in range(6):
e_sym4_eta_av.append(esym4_eta[:, h])
s4_eta = gv.dataset.svd_diagnosis(e_sym4_eta_av)
e_sym4_eta_av = gv.dataset.avg_data(e_sym4_eta_av, spread=True)
prior_esym4 = {
} # comes from posterior of (e_sym - e_sym2) fit subtraction
prior_esym4['n_sat'] = gv.gvar('0.1606(74)')
prior_esym4['E_sym4'] = gv.gvar('1.3(1.5)')
prior_esym4['L_sym4'] = gv.gvar('0.7(5.7)')
prior_esym4['K_sym4'] = gv.gvar('-20(57)')
prior_esym4['Q_sym4'] = gv.gvar('107(432)')
prior_esym4['Z_sym4'] = gv.gvar('101(1058)')
def f_esym4(x, p):
xt = (x - p['n_sat']) / (3 * p['n_sat'])
ans = p['E_sym4'] + (p['K_sym4']/2)*xt**2 \
+ (p['Q_sym4']/6)*xt**3 + (p['Z_sym4']/24)*(xt)**4 \
+ p['L_sym4']*xt
return ans
# def f_esym4_c(x,p):
# xt = (x-p['n_sat'])/(3*p['n_sat'])
# b = 6.93
# lam = f_esym4(0,p) * 3.**5
# return f_esym4(x,p) + lam * xt**5 * np.exp(-b*x/0.16)
x = td
y = e_sym4_eta_av
fit = lsqfit.nonlinear_fit(data=(x, y),
prior=prior_esym4,
fcn=f_esym4,
debug=True,
svdcut=0.1)
e_sym4_eta_par = fit.p
return e_sym4_eta_par
def fitscript_v2(trange, T, data, priors, fcn, result_flag='off'):
if trange['tmax'][1] > T/2:
sets = len(data)/T
else:
sets = len(data)/(T/2)
posterior = []
tmintbl = []
tmaxtbl = []
chi2tbl = []
lgbftbl = []
lgpostd = []
for tmin in range(trange['tmin'][0], trange['tmin'][1]+1):
for tmax in range(trange['tmax'][0], trange['tmax'][1]+1):
x = x_indep(tmin, tmax)
y = y_dep(x, data, sets)
fit = lsqfit.nonlinear_fit(data=(x,y), prior=priors, fcn=fcn)
if result_flag=='on':
print tmin, tmax,
print fit
posterior.append(fit.p)
tmintbl.append(tmin)
tmaxtbl.append(tmax)
chi2tbl.append(fit.chi2/fit.dof)
lgbftbl.append(fit.logGBF)
# log posterior probability
# factor of log 2pi**k/2
pifactor = ((tmax-tmin+1)/2.0) * np.log(2*np.pi)
# log det data covariance
datacov = gv.evalcov(y) # data covariance
L = np.linalg.cholesky(datacov) # cholesky decomposition
#logdetA = 2.*np.trace(np.log(L))
logsqrtdetA = np.trace(np.log(L))
chi2factor = -0.5*fit.chi2
lgpostd.append(-pifactor-0.5*fit.chi2)
fittbl = dict()
fittbl['tmin'] = tmintbl
fittbl['tmax'] = tmaxtbl
fittbl['post'] = posterior
fittbl['chi2dof'] = chi2tbl
fittbl['logGBF'] = lgbftbl
fittbl['logposterior'] = lgpostd
fittbl['rawoutput'] = fit
return fittbl
def empbayes_fit(z0, fitargs, **minargs):
""" Call ``lsqfit.nonlinear_fit(**fitargs(z))`` varying ``z``,
starting at ``z0``, to maximize ``logGBF`` (empirical Bayes procedure).
The fit is redone for each value of ``z`` that is tried, in order
to determine ``logGBF``.
:param z0: Starting point for search.
:type z0: array
:param fitargs: Function of array ``z`` that determines which fit
parameters to use. The function returns these as an argument
dictionary for :func:`lsqfit.nonlinear_fit`.
:type fitargs: function
:param minargs: Optional argument dictionary, passed on to
:class:`lsqfit.multiminex`, which finds the minimum.
:type minargs: dictionary
:returns: A tuple containing the best fit (object of type
:class:`lsqfit.nonlinear_fit`) and the optimal value for parameter ``z``.
"""
if minargs == {}: # default
minargs = dict(tol=1e-3, step=math.log(1.1), maxit=30, analyzer=None)
save = dict(lastz=None, lastp0=None)
def minfcn(z, save=save):
args = fitargs(z)
if save['lastp0'] is not None:
args['p0'] = save['lastp0']
fit = lsqfit.nonlinear_fit(**args)
if numpy.isnan(fit.logGBF):
raise ValueError
else:
save['lastz'] = z
save['lastp0'] = fit.pmean
return -fit.logGBF
try:
z = multiminex(numpy.array(z0), minfcn, **minargs).x
except ValueError:
print('*** empbayes_fit warning: null logGBF')
z = save['lastz']
args = fitargs(z)
if save['lastp0'] is not None:
args['p0'] = save['lastp0']
return lsqfit.nonlinear_fit(**args), z
def fit_data(params,data):
result = dict()
result['tmin'] = []
result['tmax'] = []
result['Ns'] = []
result['fit'] = []
T = len(data)/len(params['corrs'])
Ncorr = len(params['corrs'])
for tmin in range(params['tmin'][0],params['tmin'][1]+1):
for tmax in range(params['tmax'][0],params['tmax'][1]+1):
for n in range(params['Ns'][0],params['Ns'][1]+1):
print "trange: [%s,%s] Ns: %s" %(tmin,tmax,n)
x = dict()
x['t'] = np.array(range(tmin, tmax+1))
x['corrs'] = params['corrs']
tmask = [i+j*T for j in range(Ncorr) for i in x['t']]
y = data[tmask]
try:
#f = open('./nucleon_p0/%s_%s_%s.yml' %(tmin,tmax,n),'r')
f = open('./nucleon_p0/boot0.yml','r')
p0 = yml.load(f)
f.close()
except:
p0 = None
fcn = fit_function(T,n)
priors = set_priors(params,n)
fit = lsqfit.nonlinear_fit(data=(x,y),prior=priors,p0=p0,fcn=fcn.twopt_fit,maxit=100000)
result['tmin'].append(tmin)
result['tmax'].append(tmax)
result['Ns'].append(n)
result['fit'].append(fit)
if params['update_boot0']:
#f = open('./nucleon_p0/%s_%s_%s.yml' %(tmin,tmax,n),'w+')
f = open('./nucleon_p0/boot0.yml', 'w+')
boot0 = dict()
for k in fit.p.keys():
boot0[k] = fit.p[k].mean
yml.dump(boot0,f)
f.flush()
f.close()
return result
def main(self, pt2_t, ra_tseq, ra_t, fh_t1, fh_t2, pt2, ra_re, ra_im,
fh_re, fh_im):
'''
pt2_t：2pt 的自变量
ra_tseq：3pt 的 tseq
ra_t：3pt 的插入流时间
fh_t1 和 fh_t2：因为 FH 需要 ( sum(tseq=t2) - sum(tseq=t1) ) / (t2 - t1)，所以需要两组自变量，不过现在这个 fit function 用不到 fh_t2
pt2：2pt 的因变量
ra_re, ra_im：ratio 因变量的实虚部
fh_re, fh_im：fh 因变量的实虚部
'''
priors = self.pri()
x = {}
y = gv.BufferDict()
if self.fit_2pt == True:
x['2pt'] = pt2_t
y['2pt'] = pt2
if self.fit_ratio == True:
x['ra_re'] = [ra_tseq, ra_t]
y['ra_re'] = ra_re
x['ra_im'] = [ra_tseq, ra_t]
y['ra_im'] = ra_im
if self.fit_fh == True:
x['fh_re'] = fh_t1
y['fh_re'] = fh_re
x['fh_im'] = fh_t1
y['fh_im'] = fh_im
fit_result = lsf.nonlinear_fit(data=(x, y),
prior=priors,
fcn=self.fcn,
maxit=10000,
svdcut=1e-100,
fitter='scipy_least_squares')
return fit_result
def do_2st_3t_fit(ratio_,
t2_,
ncut1_=1,
ncut2_=0,
dm_=gv.gvar(0.4, np.inf),
show=True):
nconf_ = ratio_.coords['conf'].size
t_ = ratio_.coords['t'].values
data_ = ratio_.sel(t2=t2_).squeeze().transpose(
'conf', 't2', 't').values.reshape(nconf_, t2_.size * t_.size)
data_fit = prep_data_ratio_new(data_, ncut1_, ncut2_, t2_, t_)
# print(data_fit[0].shape)
# print(data_fit[1].shape)
prior0_2st_3t['dm'] = dm_
fit_ = lsqfit.nonlinear_fit(data=data_fit,
prior=prior0_2st_3t,
fcn=fcn_2st_3t,
debug=True)
if show:
print_fit(fit_)
return fit_
def do_fit(options, paramlabel, icorre, data):
xmin = options.xrange[0]
xmax = options.xrange[1]
choose_t = options.choose
rmin = options.rmin
rmax = options.rmax
paramout = {}
chi2dof = []
Q = []
for i in paramlabel:
paramout[i] = []
newtmin = choose_t.copy()
for tmin in range(rmin[icorre], rmin[icorre] + 8):
print("*" * 25 + "tmin = " + str(tmin) + ", tmax = " +
str(rmax[icorre]) + "*" * 25)
newtmin[icorre] = tmin
x, y = make_data_all(data, newtmin, rmax)
prior = make_prior_all_twostate()
fit = lsqfit.nonlinear_fit(data=(x, y),
fcn=fcn_all_twostate,
prior=prior,
p0=None)
print(fit)
if tmin == choose_t[icorre]:
print("-" * 25 + "choosed tmin = " + str(tmin) + "-" * 25)
print("\n")
choose_fit = fit
for i in paramlabel:
paramout[i].append(fit.p[i])
chi2dof.append(fit.chi2 / fit.dof)
Q.append(fit.Q)
return (chi2dof, Q, paramout), choose_fit
def main():
# pendulum data exhibits experimental error in ability to measure theta
t = [ 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.]
theta = gv.gvar([
'1.477(79)', '0.791(79)', '-0.046(79)', '-0.852(79)',
'-1.523(79)', '-1.647(79)', '-1.216(79)', '-0.810(79)',
'0.185(79)', '0.832(79)'
])
# prior: assume experimental error in ability to specify theta(0)
prior = gv.BufferDict()
prior['g/l'] = (2 * math.pi) ** 2 * gv.gvar(1, 0.1)
prior['theta(0)'] = gv.gvar(math.pi / 2., 0.05)
# fit function: use class Pendulum object to integrate pendulum motion
def fitfcn(p, t=t):
pendulum = Pendulum(p['g/l'])
return pendulum(p['theta(0)'], t)
# do the fit and print results
fit = lsqfit.nonlinear_fit(data=theta, prior=prior, fcn=fitfcn)
print(fit.format(maxline=True))
print('fit/exact for (g/l) =', fit.p['g/l'] / (2*math.pi) ** 2)
print('fit/exact for theta(0) =', fit.p['theta(0)'] / (math.pi / 2.))
if MAKE_PLOT:
# make figure (saved to file pendulum.pdf)
plt.figure(figsize=(4,3))
# start plot with data
plt.errorbar(
x=t, y=gv.mean(theta), yerr=gv.sdev(theta),
fmt='k.',
)
# use best-fit function to add smooth curve for 100 points
t = np.linspace(0., 1.1, 100)
th = fitfcn(fit.p, t)
show_plot(t, th)
def fitscript(trange, data, prior, fcn, sets=1, result_flag='off'):
print "depricated to v2 I think?"
posterior = []
tmintbl = []
tmaxtbl = []
for tmin in range(trange['tmin'][0], trange['tmin'][1]+1):
for tmax in range(trange['tmax'][0], trange['tmax'][1]+1):
x = x_indep(tmin, tmax)
y = y_dep(x, data, sets)
fit = lsqfit.nonlinear_fit(data=(x,y), prior=prior, fcn=fcn)
if result_flag=='on':
print tmin, tmax,
#for n in prior.keys():
# print fit.p[n].mean,'(',fit.p[n].sdev,')',
#print '\n'
print fit
posterior.append(fit.p)
tmintbl.append(tmin)
tmaxtbl.append(tmax)
fittbl = dict()
fittbl['tmin'] = tmintbl
fittbl['tmax'] = tmaxtbl
fittbl['post'] = posterior
return fittbl
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
for nexp in range(3, 8):
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x, y), fcn=f, prior=prior, p0=p0, svdcut=1e-15) # ,svdcut=SVDCUT)
if fit.chi2 / fit.dof < 1.0:
p0 = fit.pmean # starting point for next fit (opt.)
if nexp == 5:
sys.stdout = tee.tee(sys_stdout, open("eg3.out", "w"))
print "************************************* nexp =", nexp
print fit # 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]
# print E[1]-E[0], E[-1]-E[-2]
# print (E[1]/E[0]).partialsdev(fit.prior['E'])
# print (E[1]/E[0]).partialsdev(fit.prior['a'])
# print (E[1]/E[0]).partialsdev(fit.y)
sys.stdout = sys_stdout
print
# sys.stdout = tee.tee(sys_stdout, open("eg3a.out", "w"))
# for i in range(1):
# print '--------------------- fit with %d extra data sets' % (i+1)
# x, y = make_data(1)
# prior = fit.p
# fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f1,prior=prior, svdcut=SVDCUT)
# print fit
sys.stdout = sys_stdout
if DO_BOOTSTRAP:
Nbs = 10 # 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:
print fit.format(100) # print the fit results
import pylab as pp
from gvar import mean, sdev
fity = f(x, fit.pmean)
ratio = y / fity
pp.xlim(0, 21)
pp.xlabel("x")
pp.ylabel("y/f(x,p)")
pp.errorbar(x=x, y=mean(ratio), yerr=sdev(ratio), fmt="ob")
pp.plot([0.0, 21.0], [1.0, 1.0])
pp.show()
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 main():
gd.ranseed([2009,2010,2011,2012]) # initialize random numbers (opt.)
max_prior = make_prior(20) # maximum sized prior
p0 = None # make larger fits go faster (opt.)
sys_stdout = sys.stdout
if USE_SVD:
sys.stdout = tee.tee(sys_stdout,open("eg5a.out","w"))
for nexp in range(1,5):
print '************************************* nexp =',nexp
fit_prior = lsqfit.GPrior() # prior used in fit
ymod_prior = lsqfit.GPrior() # part of max_prior absorbed in ymod
for k in max_prior:
fit_prior[k] = max_prior[k][:nexp]
ymod_prior[k] = max_prior[k][nexp:]
x,y = make_data(ymod_prior) # make fit data
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=fit_prior,p0=p0,svdcut=SVDCUT,maxit=10000)
if nexp==4 and not USE_SVD:
sys.stdout = tee.tee(sys_stdout, open("eg5b.out", "w"))
print fit.format(100) # print the fit results
# if nexp>3:
# 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]
# E = fit.palt['E'] # best-fit parameters
# a = fit.palt['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
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
E = fit.p['E'] # best-fit parameters
a = fit.p['a']
print 'E1/E0 =',(E[1]/E[0]).fmt(),' E2/E0 =',(E[2]/E[0]).fmt()
print 'a1/a0 =',(a[1]/a[0]).fmt(),' a2/a0 =',(a[2]/a[0]).fmt()
sys.stdout = sys_stdout
if DO_ERRORBUDGET:
if USE_SVD:
sys.stdout = tee.tee(sys_stdout,open("eg5d.out","w"))
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':max_prior['E'],'a':max_prior['a'],'svd':fit.svdcorrection}
print fit.fmt_values(outputs)
print fit.fmt_errorbudget(outputs,inputs)
sys.stdout = sys_stdout
outputs = {''}
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
# extract means and "standard deviations" from the bootstrap output
outputs = gd.dataset.avg_data(outputs,bstrap=True)
# for k in outputs:
# outputs[k] = gd.gvar(np.mean(outputs[k]),np.std(outputs[k]))
if USE_SVD:
sys.stdout = tee.tee(sys_stdout,open("eg5e.out","w"))
print 'Bootstrap results:'
print 'E1/E0 =',outputs['E1/E0'].fmt(),' E2/E1 =',outputs['E2/E0'].fmt()
print 'a1/a0 =',outputs['a1/a0'].fmt(),' a2/a0 =',outputs['a2/a0'].fmt()
print 'E1 =',outputs['E1'].fmt(),' a1 =',outputs['a1'].fmt()
def wavg(dataseq, prior=None, fast=False, **kargs):
""" Weighted average of |GVar|\s or arrays/dicts of |GVar|\s.
The weighted average of several |GVar|\s is what one obtains from
a least-squares fit of the collection of |GVar|\s to the
one-parameter fit function ::
def f(p):
return N * [p[0]]
where ``N`` is the number of |GVar|\s. The average is the best-fit
value for ``p[0]``. |GVar|\s with smaller standard deviations carry
more weight than those with larger standard deviations. The averages
computed by ``wavg`` take account of correlations between the |GVar|\s.
If ``prior`` is not ``None``, it is added to the list of data
used in the average. Thus ``wavg([x2, x3], prior=x1)`` is the
same as ``wavg([x1, x2, x3])``.
Typical usage is ::
x1 = gvar.gvar(...)
x2 = gvar.gvar(...)
x3 = gvar.gvar(...)
xavg = wavg([x1, x2, x3]) # weighted average of x1, x2 and x3
where the result ``xavg`` is a |GVar| containing the weighted average.
The individual |GVar|\s in the last example can be replaced by
multidimensional distributions, represented by arrays of |GVar|\s
or dictionaries of |GVar|\s (or arrays of |GVar|\s). For example, ::
x1 = [gvar.gvar(...), gvar.gvar(...)]
x2 = [gvar.gvar(...), gvar.gvar(...)]
x3 = [gvar.gvar(...), gvar.gvar(...)]
xavg = wavg([x1, x2, x3])
# xavg[i] is wgtd avg of x1[i], x2[i], x3[i]
where each array ``x1``, ``x2`` ... must have the same shape.
The result ``xavg`` in this case is an array of |GVar|\s, where
the shape of the array is the same as that of ``x1``, etc.
Another example is ::
x1 = dict(a=[gvar.gvar(...), gvar.gvar(...)], b=gvar.gvar(...))
x2 = dict(a=[gvar.gvar(...), gvar.gvar(...)], b=gvar.gvar(...))
x3 = dict(a=[gvar.gvar(...), gvar.gvar(...)])
xavg = wavg([x1, x2, x3])
# xavg['a'][i] is wgtd avg of x1['a'][i], x2['a'][i], x3['a'][i]
# xavg['b'] is gtd avg of x1['b'], x2['b']
where different dictionaries can have (some) different keys. Here the
result ``xavg`` is a :class:`gvar.BufferDict`` having the same keys as
``x1``, etc.
Weighted averages can become costly when the number of random samples being
averaged is large (100s or more). In such cases it might be useful to set
parameter ``fast=True``. This causes ``wavg`` to estimate the weighted
average by incorporating the random samples one at a time into a
running average::
result = prior
for dataseq_i in dataseq:
result = wavg([result, dataseq_i], ...)
This method is much faster when ``len(dataseq)`` is large, and gives the
exact result when there are no correlations between different elements
of list ``dataseq``. The results are approximately correct when
``dataseq[i]`` and ``dataseq[j]`` are correlated for ``i!=j``.
:param dataseq: The |GVar|\s to be averaged. ``dataseq`` is a one-dimensional
sequence of |GVar|\s, or of arrays of |GVar|\s, or of dictionaries
containing |GVar|\s or arrays of |GVar|\s. All ``dataseq[i]`` must
have the same shape.
:param prior: Prior values for the averages, to be included in the weighted
average. Default value is ``None``, in which case ``prior`` is ignored.
:type prior: |GVar| or array/dictionary of |GVar|\s
:param fast: Setting ``fast=True`` causes ``wavg`` to compute an
approximation to the weighted average that is much faster to calculate
when averaging a large number of samples (100s or more). The default is
``fast=False``.
:type fast: bool
:param kargs: Additional arguments (e.g., ``svdcut``) to the fitter
used to do the averaging.
:type kargs: dict
Results returned by :func:`gvar.wavg` have the following extra
attributes describing the average:
.. attribute:: chi2
``chi**2`` for weighted average.
.. attribute:: dof
Effective number of degrees of freedom.
.. attribute:: Q
The probability that the ``chi**2`` could have been larger,
by chance, assuming that the data are all Gaussain and consistent
with each other. Values smaller than 0.1 or suggest that the
data are not Gaussian or are inconsistent with each other. Also
called the *p-value*.
Quality factor `Q` (or *p-value*) for fit.
.. attribute:: time
Time required to do average.
.. attribute:: svdcorrection
The *svd* corrections made to the data when ``svdcut`` is not ``None``.
.. attribute:: fit
Fit output from average.
"""
if len(dataseq) <= 0:
if prior is None:
return None
wavg.Q = 1
wavg.chi2 = 0
wavg.dof = 0
wavg.time = 0
wavg.fit = None
wavg.svdcorrection = None
if hasattr(prior, 'keys'):
return BufferDictWAvg(dataseq[0], wavg)
if numpy.shape(prior) == ():
return GVarWAvg(prior, wavg)
else:
return ArrayWAvg(numpy.asarray(prior), wavg)
elif len(dataseq) == 1 and prior is None:
wavg.Q = 1
wavg.chi2 = 0
wavg.dof = 0
wavg.time = 0
wavg.fit = None
wavg.svdcorrection = None
if hasattr(dataseq[0], 'keys'):
return BufferDictWAvg(dataseq[0], wavg)
if numpy.shape(dataseq[0]) == ():
return GVarWAvg(dataseq[0], wavg)
else:
return ArrayWAvg(numpy.asarray(dataseq[0]), wavg)
if fast:
chi2 = 0
dof = 0
time = 0
ans = prior
svdcorrection = gvar.BufferDict()
for i, dataseq_i in enumerate(dataseq):
if ans is None:
ans = dataseq_i
else:
ans = wavg([ans, dataseq_i], fast=False, **kargs)
chi2 += wavg.chi2
dof += wavg.dof
time += wavg.time
if wavg.svdcorrection is not None:
for k in wavg.svdcorrection:
svdcorrection[str(i) + ':' + k] = wavg.svdcorrection[k]
wavg.chi2 = chi2
wavg.dof = dof
wavg.time = time
wavg.Q = gammaQ(dof / 2., chi2 / 2.)
wavg.svdcorrection = svdcorrection
wavg.fit = None
ans.dof = wavg.dof
ans.Q = wavg.Q
ans.chi2 = wavg.chi2
ans.time = wavg.time
ans.svdcorrection = wavg.svdcorrection
ans.fit = wavg.fit
return ans
if hasattr(dataseq[0], 'keys'):
data = {}
keys = []
if prior is not None:
dataseq = [prior] + list(dataseq)
for dataseq_i in dataseq:
for k in dataseq_i:
if k in data:
data[k].append(dataseq_i[k])
else:
data[k] = [dataseq_i[k]]
keys.append(k)
data = gvar.BufferDict(data, keys=keys)
p0 = gvar.BufferDict()
for k in data:
p0[k] = gvar.mean(data[k][0]) + gvar.sdev(data[k][0]) / 10.
def fcn(p):
ans = gvar.BufferDict()
for k in data:
ans[k] = len(data[k]) * [p[k]]
return ans
else:
p = numpy.asarray(dataseq[0])
data = [] if prior is None else [prior]
data += [dataseqi for dataseqi in dataseq]
p0 = numpy.asarray(gvar.mean(data[0]) + gvar.sdev(data[0]) / 10.)
data = numpy.array(data)
def fcn(p):
return len(data) * [p]
fit = lsqfit.nonlinear_fit(data=data, fcn=fcn, p0=p0, **kargs)
# wavg.Q = fit.Q
# wavg.chi2 = fit.chi2
# wavg.dof = fit.dof
# wavg.time = fit.time
# wavg.svdcorrection = fit.svdcorrection
# wavg.fit = fit
if p0.shape is None:
return BufferDictWAvg(gvar.BufferDict(p0, buf=fit.p.flat), fit)
elif p0.shape == ():
return GVarWAvg(fit.p.flat[0], fit)
else:
return ArrayWAvg(fit.p.reshape(p0.shape), fit)
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.)
for nexp in range(3,5):
print '************************************* nexp =',nexp
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,p0=p0)
print fit # 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]
print
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
sys_stdout = sys.stdout
if DO_ERRORBUDGET:
lines = [
"E = fit.p['E']",
"a = fit.p['a']",
"print(E[1] / E[0])",
"print((E[1] / E[0]).partialsdev(fit.prior['E']))",
"print((E[1] / E[0]).partialsdev(fit.prior['a']))",
"print((E[1] / E[0]).partialsdev(y))"
]
sys.stdout = tee.tee(sys_stdout, open("eg4c.out","w"))
for line in lines:
print ">>>", line
if line[:5] == "print":
print(eval(line[5:]))
# print E[1]/E[0]
# print (E[1]/E[0]).partialsdev(fit.prior['E'])
# print (E[1]/E[0]).partialsdev(fit.prior['a'])
# print (E[1]/E[0]).partialsdev(y)
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}
sys.stdout = tee.tee(sys_stdout, open("eg4b.out","w"))
print fit.fmt_values(outputs)
print fit.fmt_errorbudget(outputs,inputs)
sys.stdout = sys_stdout
if DO_SIMULATIONS:
# fit simulations
sys.stdout = tee.tee(sys_stdout, open("eg4d.out","w"))
for sfit in fit.simulated_fit_iter(3):
print '************************************* simulation'
print(sfit)
sE = sfit.p['E'] # best-fit parameters
sa = sfit.p['a']
E = sfit.pexact['E']
a = sfit.pexact['a']
print 'E1/E0 =', sE[1] / sE[0], ' E2/E0 =', sE[2] / sE[0]
print 'a1/a0 =', sa[1] / sa[0], ' a2/a0 =', sa[2] / sa[0]
print '\nSimulated Fit Values - Exact Values:'
print 'E1/E0:', (sE[1] / sE[0]) - (E[1] / E[0]),\
' E2/E0:', (sE[2] / sE[0]) - (E[2] / E[0])
print 'a1/a0:', (sa[1] / sa[0]) - (a[1] / a[0]),\
' a2/a0:', (sa[2] / sa[0]) - (a[2] / a[0])
# compute chi**2 comparing fit results to exact results
sim_results = [sE[0], sE[1], sa[0], sa[1]]
exact_results = [E[0], E[1], a[0], a[1]]
chi2 = gv.chi2(sim_results, exact_results, svdcut=1e-8)
print '\nParameter chi2/dof [dof] = %.2f' % (chi2/chi2.dof), '[%d]' % chi2.dof, ' Q = %.1f' % chi2.Q
print
sys.stdout = sys_stdout
if DO_EMPBAYES:
def fitargs(z,nexp=nexp,prior=prior,f=f,data=(x,y),p0=p0):
z = gv.exp(z)
prior['a'] = [gv.gvar(0.5,0.5*z[0]) for i in range(nexp)]
return dict(prior=prior,data=data,fcn=f,p0=p0)
##
z0 = [0.0]
fit,z = lsqfit.empbayes_fit(z0,fitargs,tol=1e-3)
sys.stdout = tee.tee(sys_stdout, open("eg4a.out","w"))
print fit # print the optimized 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]
# print "prior['a'] =",fit.prior['a'][0]
sys.stdout = sys_stdout
print
if DO_PLOT:
import pylab as pp
from gvar import mean,sdev
fity = f(x,fit.pmean)
ratio = y/fity
pp.xlim(0,21)
pp.xlabel('x')
pp.ylabel('y/f(x,p)')
pp.errorbar(x=x,y=mean(ratio),yerr=sdev(ratio),fmt='ob')
pp.plot([0.0,21.0],[1.0,1.0])
pp.show()
from gvar import *
from lsqfit import nonlinear_fit
import functools
import inspect
import sys
ranseed([123])
ygen = gvar(0.02, 0.2) - 0.005
print (ygen)
y = [gvar(ygen(), ygen.sdev) for i in range(20)]
ystr = [yi.fmt(2) for yi in y]
y = gvar(ystr)
print (ystr[:])
print
log_prior = BufferDict(loga = log(gvar(0.02, 0.02)))
sqrt_prior = BufferDict(sqrta = sqrt(gvar(0.02, 0.02)))
prior = BufferDict(a = gvar(0.02, 0.02))
stdout = sys.stdout
for p in [prior, log_prior, sqrt_prior]:
key = list(p.keys())[0]
sys.stdout = open("eg6-{}.out".format(key), "w")
def fcn(p, N=len(y)):
return N*[p['a']]
f = nonlinear_fit(prior=p, fcn=fcn, data=(y), extend=True)
print (f)
print ("a =", f.p['a'].fmt())
sys.stdout = stdout
PLOT = False
RESULTS = False
# least-squares fit
x = np.array([0.1, 1.2, 1.9, 3.5])
y = gv.gvar(["1.2(1.0)", "2.4(1)", "2.0(1.2)", "5.2(3.2)"])
prior = gv.BufferDict()
prior["a"] = "0(5)"
prior["s"] = "0(2)"
prior["g"] = "2(2)"
prior = gv.gvar(prior)
def f(x, p):
return p["a"] + p["s"] * x ** p["g"]
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=f, debug=True)
print(fit)
hist = gv.PDFHistogram(fit.p["s"] * fit.p["g"])
# Bayesian integral to evaluate expectation value of s*g
def g(p):
sg = p["s"] * p["g"]
return dict(moments=[sg, sg ** 2, sg ** 3, sg ** 4], histogram=hist.count(sg))
expval = lsqfit.BayesIntegrator(fit, limit=20.0)
warmup = expval(neval=2000, nitn=10)
results = expval(g, neval=2000, nitn=10, adapt=False)
if RESULTS:
print(results.summary())
stats = hist.analyze(results["histogram"]).stats
def fitscript_v3(trange,fhtrange,T,data,priors,fcn,init=None,basak=None):
sets = len(data)/T
#print "sets:", sets
pmean = []
psdev = []
post = []
p0 = []
prior = []
tmintbl = []
tmaxtbl = []
fhtmintbl = []
fhtmaxtbl = []
chi2 = []
chi2f = []
dof = []
lgbftbl = []
Q = []
rawoutput = []
for tmin in range(trange['tmin'][0], trange['tmin'][1]+1):
for tmax in range(trange['tmax'][0], trange['tmax'][1]+1):
for fhtmin in range(fhtrange['tmin'][0], fhtrange['tmin'][1]+1):
for fhtmax in range(fhtrange['tmax'][0], fhtrange['tmax'][1]+1):
x2 = x_indep(tmin, tmax)
fhx = x_indep(fhtmin, fhtmax)
x = [x2,fhx]
xlist, y = y_dep_v2(x, data, sets)
if basak is not None:
x = {'indep': x, 'basak': basak}
else: pass
fit = lsqfit.nonlinear_fit(data=(x,y),prior=priors,fcn=fcn,p0=init,maxit=1000000) #,svdcut=1E-5)
print fhtmin, fhtmax, fit.p['gA00'].mean, fit.p['gA00'].sdev, fit.p['E0'].mean, fit.p['E0'].sdev, fit.chi2/fit.dof, fit.Q, fit.logGBF
pmean.append(fit.pmean)
psdev.append(fit.psdev)
post.append(fit.p)
p0.append(fit.p0)
prior.append(fit.prior)
tmintbl.append(tmin)
tmaxtbl.append(tmax)
fhtmintbl.append(fhtmin)
fhtmaxtbl.append(fhtmax)
chi2.append(fit.chi2)
dof.append(fit.dof)
lgbftbl.append(fit.logGBF)
Q.append(fit.Q)
rawoutput.append(fit)
chi2f.append(chi2freq(fit.chi2,fit.prior,fit.p))
## print correlation matrix of data
#corr = gv.evalcorr(fit.y)
#string = ''
#for i in range(len(corr)):
# for j in range(len(corr)):
# string +='%s,%s,%s\n' %(str(i),str(j),str(corr[i,j]))
#f = open('./temp.csv','w')
#f.write(string)
#f.flush()
#f.close()
## end corr
#fitline = fcn(x,fit.p)
#print "t, y, +-, fit, +-"
#for i in range(len(xlist)):
# print xlist[i], ',', y[i].mean, ',', y[i].sdev, ',', fitline[i].mean, ',', fitline[i].sdev
#print fit
#print '======'
#print fcn.__name__, basak
#print fit
#print '======'
fittbl = dict()
fittbl['tmin'] = tmintbl
fittbl['tmax'] = tmaxtbl
fittbl['fhtmin'] = fhtmintbl
fittbl['fhtmax'] = fhtmaxtbl
fittbl['pmean'] = pmean
fittbl['psdev'] = psdev
fittbl['post'] = post
fittbl['p0'] = p0
fittbl['prior'] = prior
fittbl['chi2'] = chi2
fittbl['chi2f'] = chi2f
fittbl['dof'] = dof
fittbl['logGBF'] = lgbftbl
fittbl['Q'] = Q
fittbl['rawoutput'] = rawoutput
return fittbl
"data1" : np.array([0.1,1.0]),
"data2" : np.array([0.1,0.5])
}
# a priori values for fit parameters
prior = dict(a=gv.gvar(0.5,0.5),b=gv.gvar(0.5,0.5))
# print(y["data1"][0].mean,"+-",y["data1"][0].sdev)
# print(gv.evalcov(y["data1"]))
def fcn(x,p): # fit function of x and parameters p
ans = {}
for k in ["data1","data2"]:
ans[k] = gv.exp(p['a'] + x[k]*p['b'])
ans['b/a'] = p['b']/p['a']
return ans
# do the fit
fit = lsqfit.nonlinear_fit(data=(x,y),prior=prior,fcn=fcn)
sys.stdout = open("eg0.out","w")
print(fit.format(maxline=True)) # print standard summary of fit
p = fit.p # best-fit values for parameters
outputs = dict(a=p['a'],b=p['b'])
outputs['b/a'] = p['b']/p['a']
inputs = dict(y=y,prior=prior)
print(fit.fmt_values(outputs)) # tabulate outputs
print(fit.fmt_errorbudget(outputs,inputs)) # print error budget for outputs
# save best-fit values in file "outputfile.p" for later use
import pickle
pickle.dump(fit.p,open("outputfile.p","wb"))
def main():
### 1) least-squares fit to the data
x = np.array([
0.2, 0.4, 0.6, 0.8, 1.,
1.2, 1.4, 1.6, 1.8, 2.,
2.2, 2.4, 2.6, 2.8, 3.,
3.2, 3.4, 3.6, 3.8
])
y = gv.gvar([
'0.38(20)', '2.89(20)', '0.85(20)', '0.59(20)', '2.88(20)',
'1.44(20)', '0.73(20)', '1.23(20)', '1.68(20)', '1.36(20)',
'1.51(20)', '1.73(20)', '2.16(20)', '1.85(20)', '2.00(20)',
'2.11(20)', '2.75(20)', '0.86(20)', '2.73(20)'
])
prior = make_prior()
fit = lsqfit.nonlinear_fit(data=(x, y), prior=prior, fcn=fitfcn, extend=True)
if LSQFIT_ONLY:
sys.stdout = tee.tee(STDOUT, open('case-outliers-lsq.out', 'w'))
elif not MULTI_W:
sys.stdout = tee.tee(STDOUT, open('case-outliers.out', 'w'))
print(fit)
# plot data
plt.errorbar(x, gv.mean(y), gv.sdev(y), fmt='o', c='b')
# plot fit function
xline = np.linspace(x[0], x[-1], 100)
yline = fitfcn(xline, fit.p)
plt.plot(xline, gv.mean(yline), 'k:')
yp = gv.mean(yline) + gv.sdev(yline)
ym = gv.mean(yline) - gv.sdev(yline)
plt.fill_between(xline, yp, ym, color='0.8')
plt.xlabel('x')
plt.ylabel('y')
plt.savefig('case-outliers1.png', bbox_inches='tight')
if LSQFIT_ONLY:
return
### 2) Bayesian integral with modified PDF
pdf = ModifiedPDF(data=(x, y), fcn=fitfcn, prior=prior)
# integrator for expectation values with modified PDF
expval = lsqfit.BayesIntegrator(fit, pdf=pdf)
# adapt integrator to pdf
expval(neval=1000, nitn=15)
# evaluate expectation value of g(p)
def g(p):
w = 0.5 + 0.5 * p['2w-1']
c = p['c']
return dict(w=[w, w**2], mean=c, outer=np.outer(c,c))
results = expval(g, neval=1000, nitn=15, adapt=False)
print(results.summary())
# expval.map.show_grid(15)
if MULTI_W:
sys.stdout = tee.tee(STDOUT, open('case-outliers-multi.out', 'w'))
# parameters c[i]
mean = results['mean']
cov = results['outer'] - np.outer(mean, mean)
c = mean + gv.gvar(np.zeros(mean.shape), gv.mean(cov))
print('c =', c)
print(
'corr(c) =',
np.array2string(gv.evalcorr(c), prefix=10 * ' '),
'\n',
)
# parameter w
wmean, w2mean = results['w']
wsdev = gv.mean(w2mean - wmean ** 2) ** 0.5
w = wmean + gv.gvar(np.zeros(np.shape(wmean)), wsdev)
print('w =', w, '\n')
# Bayes Factor
print('logBF =', np.log(expval.norm))
sys.stdout = STDOUT
if MULTI_W:
return
# add new fit to plot
yline = fitfcn(xline, dict(c=c))
plt.plot(xline, gv.mean(yline), 'r--')
yp = gv.mean(yline) + gv.sdev(yline)
ym = gv.mean(yline) - gv.sdev(yline)
plt.fill_between(xline, yp, ym, color='r', alpha=0.2)
plt.savefig('case-outliers2.png', bbox_inches='tight')
def main():
gd.ranseed([2009,2010,2011,2012]) # initialize random numbers (opt.)
x,y = make_data() # make fit data
p0 = None # make larger fits go faster (opt.)
for nexp in range(2,8):
if nexp == 2:
sys_stdout = sys.stdout
sys.stdout = tee.tee(sys_stdout, open("eg4GBF.out","w"))
print '************************************* nexp =',nexp
prior = make_prior(nexp)
fit = lsqfit.nonlinear_fit(data=(x,y),fcn=f,prior=prior,p0=p0)
print fit # 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]
print
if nexp == 3:
sys.stdout = sys_stdout
if fit.chi2/fit.dof<1.:
p0 = fit.pmean # starting point for next fit (opt.)
if DO_ERRORBUDGET:
print E[1]/E[0]
print (E[1]/E[0]).partialsdev(fit.prior['E'])
print (E[1]/E[0]).partialsdev(fit.prior['a'])
print (E[1]/E[0]).partialsdev(y)
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}
sys.stdout = tee.tee(sys_stdout, open("eg4GBFb.out","w"))
print fit.fmt_values(outputs)
print fit.fmt_errorbudget(outputs,inputs)
sys.stdout = sys_stdout
if DO_EMPBAYES:
def fitargs(z,nexp=nexp,prior=prior,f=f,data=(x,y),p0=p0):
z = gd.exp(z)
prior['a'] = [gd.gvar(0.5,0.5*z[0]) for i in range(nexp)]
return dict(prior=prior,data=data,fcn=f,p0=p0)
##
z0 = [0.0]
fit,z = lsqfit.empbayes_fit(z0,fitargs,tol=1e-3)
sys.stdout = tee.tee(sys_stdout, open("eg4GBFa.out","w"))
print fit # print the optimized 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]
print "prior['a'] =",fit.prior['a'][0]
sys.stdout = sys_stdout
print
if DO_PLOT:
import pylab as pp
from gvar import mean,sdev
fity = f(x,fit.pmean)
ratio = y/fity
pp.xlim(0,21)
pp.xlabel('x')
pp.ylabel('y/f(x,p)')
pp.errorbar(x=x,y=mean(ratio),yerr=sdev(ratio),fmt='ob')
pp.plot([0.0,21.0],[1.0,1.0])
pp.show()
def make_prior():
prior = {}
prior['a'] = gv.gvar(1.0, 1.0)
prior['E'] = gv.gvar(4.5, 100.0)
prior['b'] = gv.gvar(-10.0, 50.0)
return prior
if __name__ == '__main__':
gv.ranseed([2009, 2010, 2011, 2012])
p0 = None
prior = make_prior()
#p0 = {'a':0.1,'E':0.5} # ***** #
#print f(X,p0)
fit = lsqfit.nonlinear_fit(data = (X, Y), fcn=f, prior=prior, p0=p0)
print fit
print(fit.format(maxline=True))
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 fitscript_v2(trange,nstates,T,data,p,init=None,basak=None): # +++CHANGE+++
sets = len(data)/T
#print "sets:", sets
pmean = []
psdev = []
post = []
p0 = []
prior = []
tmintbl = []
tmaxtbl = []
nstatestbl = [] #+++CHANGE+++
chi2 = []
dof = []
lgbftbl = []
rawoutput = []
for n in nstates: #+++CHANGE+++
priors = dict_of_tuple_to_gvar(meson_priors(p,n)) #+++CHANGE+++
fitfcn = c51.fit_function(T) #+++CHANGE+++
fcn = fitfcn.twopt_baryon_ss_ps #+++CHANGE+++
for tmin in range(trange['tmin'][0], trange['tmin'][1]+1):
for tmax in range(trange['tmax'][0], trange['tmax'][1]+1):
x = x_indep(tmin, tmax)
xlist, y = y_dep(x, data, sets)
if basak is not None:
x = {'indep': x, 'basak': basak}
else: pass
fit = lsqfit.nonlinear_fit(data=(x,y),prior=priors,fcn=fcn,p0=init)
pmean.append(fit.pmean)
psdev.append(fit.psdev)
post.append(fit.p)
p0.append(fit.p0)
prior.append(fit.prior)
tmintbl.append(tmin)
tmaxtbl.append(tmax)
nstatestbl.append(n) #+++CHANGE+++
chi2.append(fit.chi2)
dof.append(fit.dof)
lgbftbl.append(fit.logGBF)
rawoutput.append(fit)
#fcnname = str(fcn.__name__)
#fitline = fcn(x,fit.p)
#print "%s_%s_t, %s_%s_y, +-, %s_%s_fit, +-" %(fcnname, basak[0], fcnname, basak[0], fcnname, basak[0])
#for i in range(len(xlist)):
# print xlist[i], ',', y[i].mean, ',', y[i].sdev, ',', fitline[i].mean, ',', fitline[i].sdev
print '======'
print fcn.__name__, basak
print fit
print '======'
fittbl = dict()
fittbl['nstates'] = nstatestbl #+++CHANGE+++
fittbl['tmin'] = tmintbl
fittbl['tmax'] = tmaxtbl
fittbl['pmean'] = pmean
fittbl['psdev'] = psdev
fittbl['post'] = post
fittbl['p0'] = p0
fittbl['prior'] = prior
fittbl['chi2'] = chi2
fittbl['dof'] = dof
fittbl['logGBF'] = lgbftbl
fittbl['rawoutput'] = rawoutput
return fittbl
