def test_simulation(self):
""" CorrFitter.simulated_data_iter """
models = [ self.mkcorr(a="a", b="a", dE="dE", tp=None) ]
fitter = self.dofit(models)
data = self.data
diter = gv.BufferDict()
k = list(data.keys())[0]
# make n config dataset corresponding to data
n = 100
diter = gv.raniter(
g = gv.gvar(gv.mean(self.data[k]), gv.evalcov(self.data[k]) * n),
n = n
)
dataset = gv.dataset.Dataset()
for d in diter:
dataset.append(k, d)
pexact = fitter.fit.pmean
covexact = gv.evalcov(gv.dataset.avg_data(dataset)[k])
for sdata in fitter.simulated_data_iter(n=2, dataset=dataset):
sfit = fitter.lsqfit(
data=sdata, prior=self.prior, p0=pexact, print_fit=False
)
diff = dict()
for i in ['a', 'logdE']:
diff[i] = sfit.p[i][0] - pexact[i][0]
c2 = gv.chi2(diff)
self.assertLess(c2/c2.dof, 15.)
self.assert_arraysclose(gv.evalcov(sdata[k]), covexact)
def main():
data, basis = make_data('etab.h5')
fitter = cf.CorrFitter(models=make_models())
p0 = None
for N in range(1, 8):
print(30 * '=', 'nterm =', N)
prior = make_prior(N, basis)
fit = fitter.lsqfit(data=data, prior=prior, p0=p0, svdcut=SVDCUT)
print(fit.format(pstyle=None if N < 7 else 'v'))
p0 = fit.pmean
print_results(fit, basis, prior, data)
if SHOWPLOTS:
fit.show_plots(save='etab.{}.png', view='ratio')
# check fit quality by adding noise
print('\n==================== add svd, prior noise')
noisy_fit = fitter.lsqfit(
data=data,
prior=prior,
p0=fit.pmean,
svdcut=SVDCUT,
noise=True,
)
print(noisy_fit.format(pstyle=None))
dE = fit.p['etab.dE'][:3]
noisy_dE = noisy_fit.p['etab.dE'][:3]
print(' dE:', dE)
print('noisy dE:', noisy_dE)
print(' ', gv.fmt_chi2(gv.chi2(dE - noisy_dE)))
if SHOWPLOTS:
fit.qqplot_residuals().show()
def main():
data, basis = make_data('etab.h5')
fitter = cf.CorrFitter(models=make_models())
p0 = None
for N in range(1, 8):
print(30 * '=', 'nterm =', N)
prior = make_prior(N, basis)
fit = fitter.lsqfit(data=data, prior=prior, p0=p0, svdcut=SVDCUT)
print(fit.format(pstyle=None if N < 7 else 'm'))
p0 = fit.pmean
print_results(fit, basis, prior, data)
if DISPLAYPLOTS:
fitter.display_plots()
print('\n==================== add svd, prior noise')
noisy_fit = fitter.lsqfit(
data=data,
prior=prior,
p0=fit.pmean,
svdcut=SVDCUT,
noise=True,
)
print(noisy_fit.format(pstyle=None))
dE = fit.p['etab.dE'][:3]
noisy_dE = noisy_fit.p['etab.dE'][:3]
print(' dE:', dE)
print('noisy dE:', noisy_dE)
print(' ', gv.fmt_chi2(gv.chi2(dE - noisy_dE)))
def main():
data = make_data('etas-Ds.h5')
models = make_models() # 1a
models = [
models[0], models[1], # 1b
dict(nterm=(2, 1), svdcut=6.3e-5), # 1c
(models[2], models[3]) # 1d
]
fitter = cf.CorrFitter(models=models) # 1e
p0 = None
for N in [1, 2, 3, 4]:
print(30 * '=', 'nterm =', N)
prior = make_prior(N)
fit = fitter.chained_lsqfit(data=data, prior=prior, p0=p0) # 2
print(fit.format(pstyle=None if N < 4 else 'm'))
p0 = fit.pmean
print_results(fit, prior, data)
if DISPLAYPLOTS:
fit.show_plots()
# check fit quality by adding noise
print('\n==================== add svd, prior noise')
noisy_fit = fitter.chained_lsqfit(
data=data, prior=prior, p0=fit.pmean, svdcut=SVDCUT,
noise=True,
)
print(noisy_fit.format(pstyle=None))
p = key_parameters(fit.p)
noisy_p = key_parameters(noisy_fit.p)
print(' fit:', p)
print('noisy fit:', noisy_p)
print(' ', gv.fmt_chi2(gv.chi2(p - noisy_p)))
# simulated fit
for sim_pdata in fitter.simulated_pdata_iter(
n=2, dataset=cf.read_dataset('etas-Ds.h5'), p_exact=fit.pmean
):
print('\n==================== simulation')
sim_fit = fitter.chained_lsqfit(
pdata=sim_pdata, prior=prior, p0=fit.pmean, svdcut=SVDCUT,
)
print(sim_fit.format(pstyle=None))
p = key_parameters(fit.pmean)
sim_p = key_parameters(sim_fit.p)
print('simulated - exact:', sim_p - p)
print(' ', gv.fmt_chi2(gv.chi2(p - sim_p)))
def main():
data = make_data('etas-Ds.h5')
fitter = cf.CorrFitter(models=make_models())
p0 = None
prior = make_prior(8) # 1
for N in [1, 2]: # 2
print(30 * '=', 'nterm =', N)
fit = fitter.lsqfit(
data=data, prior=prior, p0=p0, nterm=(N, N), svdcut=SVDCUT # 3
)
print(fit) # 4
p0 = fit.pmean
print_results(fit, prior, data)
if DISPLAYPLOTS:
fit.show_plots()
# check fit quality by adding noise
print('\n==================== add svd, prior noise')
noisy_fit = fitter.lsqfit(
data=data, prior=prior, p0=fit.pmean, svdcut=SVDCUT, nterm=(N, N),
noise=True,
)
print(noisy_fit.format(pstyle=None))
p = key_parameters(fit.p)
noisy_p = key_parameters(noisy_fit.p)
print(' fit:', p)
print('noisy fit:', noisy_p)
print(' ', gv.fmt_chi2(gv.chi2(p - noisy_p)))
# simulated fit
for sim_pdata in fitter.simulated_pdata_iter(
n=2, dataset=cf.read_dataset('etas-Ds.h5'), p_exact=fit.pmean
):
print('\n==================== simulation')
sim_fit = fitter.lsqfit(
pdata=sim_pdata, prior=prior, p0=fit.pmean, svdcut=SVDCUT,
nterm=(N, N),
)
print(sim_fit.format(pstyle=None))
p = key_parameters(fit.pmean)
sim_p = key_parameters(sim_fit.p)
print('simulated - exact:', sim_p - p)
print(' ', gv.fmt_chi2(gv.chi2(p - sim_p)))
def main():
data = make_data('Ds-Ds.h5')
fitter = cf.CorrFitter(models=make_models())
p0 = None
for N in [1, 2, 3, 4]:
print(30 * '=', 'nterm =', N)
prior = make_prior(N)
fit = fitter.lsqfit(data=data, prior=prior, p0=p0, svdcut=SVDCUT)
print(fit.format(pstyle=None if N < 4 else 'v'))
p0 = fit.pmean
print_results(fit, prior, data)
if SHOWPLOTS:
fit.show_plots(save='Ds-Ds.{}.png', view='ratio')
# check fit quality by adding noise
print('\n==================== add svd, prior noise')
noisy_fit = fitter.lsqfit(
data=data, prior=prior, p0=fit.pmean, svdcut=SVDCUT,
noise=True,
)
print(noisy_fit.format(pstyle=None))
p = key_parameters(fit.p)
noisy_p = key_parameters(noisy_fit.p)
print(' fit:', p)
print('noisy fit:', noisy_p)
print(' ', gv.fmt_chi2(gv.chi2(p - noisy_p)))
# simulated fit
for sim_pdata in fitter.simulated_pdata_iter(
n=2, dataset=h5py.File('Ds-Ds.h5', 'r'), p_exact=fit.pmean
):
print('\n==================== simulation')
sim_fit = fitter.lsqfit(
pdata=sim_pdata, prior=prior, p0=fit.pmean, svdcut=SVDCUT,
)
print(sim_fit.format(pstyle=None))
p = key_parameters(fit.pmean)
sim_p = key_parameters(sim_fit.p)
print('simulated - exact:', sim_p - p)
print(' ', gv.fmt_chi2(gv.chi2(p - sim_p)))
def f_outlier_list(fit):
''' Code to find outliers in a fit
Reads fit and returns list of indices of outliers.
'''
y_th = fit.fcn(fit.x, fit.p)
y_exp = fit.y
outlier_list = []
for i, (j, k) in enumerate(zip(y_exp, y_th)):
# Find points with chi-square more than 3.
if gv.chi2(j, k) > 3.0:
outlier_list.append(i)
return outlier_list
def test_fit(fitter, datafile):
""" Test the fit with simulated data """
gv.ranseed((1487942813, 775399747, 906327435))
print('\nRandom seed:', gv.ranseed.seed)
dataset = cf.read_dataset(datafile)
pexact = fitter.fit.pmean
prior = fitter.fit.prior
for sdata in fitter.simulated_data_iter(n=2, dataset=dataset, pexact=pexact):
print('\n============================== simulation')
sfit = fitter.lsqfit(data=sdata, prior=prior, p0=pexact)
diff = []
# check chi**2 for leading parameters
for k in prior:
diff.append(sfit.p[k].flat[0] - pexact[k].flat[0])
chi2diff = gv.chi2(diff)
print(
'Leading parameter chi2/dof [dof] = %.2f' %
(chi2diff / chi2diff.dof),
'[%d]' % chi2diff.dof,
' Q = %.1f' % chi2diff.Q
)
def test_fit(fitter, datafile):
""" Test the fit with simulated data """
gv.ranseed((623738625, 435880512, 1745400596))
print('\nRandom seed:', gv.ranseed.seed)
dataset = read_dataset(datafile)
pexact = fitter.fit.pmean
prior = fitter.fit.prior
for sdata in fitter.simulated_data_iter(n=2, dataset=dataset, pexact=pexact):
print('\n============================== simulation')
sfit = fitter.lsqfit(data=sdata, prior=prior, p0=pexact, nterm=(2, 2))
diff = []
# check chi**2 for leading parameters
for k in prior:
diff.append(sfit.p[k].flat[0] - pexact[k].flat[0])
chi2_diff = gv.chi2(diff)
print(
'Leading parameter chi2/dof [dof] = %.2f' %
(chi2_diff / chi2_diff.dof),
'[%d]' % chi2_diff.dof,
' Q = %.1f' % chi2_diff.Q
)
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()
def main():
sys_stdout = sys.stdout
sys.stdout = tee.tee(sys.stdout, open("eg3a.out","w"))
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) =', gv.evalcorr(fit.p[:2])[1,0]
if DO_PLOT:
plt.semilogx()
plt.errorbar(
x=gv.mean(x), xerr=gv.sdev(x), y=gv.mean(y), yerr=gv.sdev(y),
fmt='ob'
)
# plot fit line
xx = np.linspace(0.99 * gv.mean(min(x)), 1.01 * gv.mean(max(x)), 100)
yy = fcn(xx, fit.pmean)
plt.xlabel('x')
plt.ylabel('y')
plt.plot(xx, yy, ':r')
plt.savefig('eg3.png', bbox_inches='tight')
plt.show()
sys.stdout = sys_stdout
if DO_BOOTSTRAP:
gv.ranseed(123)
sys.stdout = tee.tee(sys_stdout, open('eg3c.out', 'w'))
print fit
print 'p1/p0 =', fit.p[1] / fit.p[0], ' p3/p2 =', fit.p[3] / fit.p[2]
print 'corr(p0,p1) =', gv.evalcorr(fit.p[:2])[1,0]
Nbs = 40
outputs = {'p':[], 'p1/p0':[], 'p3/p2':[]}
for bsfit in fit.bootstrap_iter(n=Nbs):
p = bsfit.pmean
outputs['p'].append(p)
outputs['p1/p0'].append(p[1] / p[0])
outputs['p3/p2'].append(p[3] / p[2])
print '\nBootstrap Averages:'
outputs = gv.dataset.avg_data(outputs, bstrap=True)
print gv.tabulate(outputs)
print 'corr(p0,p1) =', gv.evalcorr(outputs['p'][:2])[1,0]
# make histograms of p1/p0 and p3/p2
sys.stdout = sys_stdout
print
sys.stdout = tee.tee(sys_stdout, open('eg3d.out', 'w'))
print 'Histogram Analysis:'
count = {'p1/p0':[], 'p3/p2':[]}
hist = {
'p1/p0':gv.PDFHistogram(fit.p[1] / fit.p[0]),
'p3/p2':gv.PDFHistogram(fit.p[3] / fit.p[2]),
}
for bsfit in fit.bootstrap_iter(n=1000):
p = bsfit.pmean
count['p1/p0'].append(hist['p1/p0'].count(p[1] / p[0]))
count['p3/p2'].append(hist['p3/p2'].count(p[3] / p[2]))
count = gv.dataset.avg_data(count)
plt.rcParams['figure.figsize'] = [6.4, 2.4]
pltnum = 1
for k in count:
print k + ':'
print hist[k].analyze(count[k]).stats
plt.subplot(1, 2, pltnum)
plt.xlabel(k)
hist[k].make_plot(count[k], plot=plt)
if pltnum == 2:
plt.ylabel('')
pltnum += 1
plt.rcParams['figure.figsize'] = [6.4, 4.8]
plt.savefig('eg3d.png', bbox_inches='tight')
plt.show()
if DO_BAYESIAN:
gv.ranseed(123)
sys.stdout = tee.tee(sys_stdout, open('eg3e.out', 'w'))
print fit
expval = lsqfit.BayesIntegrator(fit)
# adapt integrator to PDF from fit
neval = 1000
nitn = 10
expval(neval=neval, nitn=nitn)
# <g(p)> gives mean and covariance matrix, and histograms
hist = [
gv.PDFHistogram(fit.p[0]), gv.PDFHistogram(fit.p[1]),
gv.PDFHistogram(fit.p[2]), gv.PDFHistogram(fit.p[3]),
]
def g(p):
return dict(
mean=p,
outer=np.outer(p, p),
count=[
hist[0].count(p[0]), hist[1].count(p[1]),
hist[2].count(p[2]), hist[3].count(p[3]),
],
)
# evaluate expectation value of g(p)
results = expval(g, neval=neval, nitn=nitn, adapt=False)
# analyze results
print('\nIterations:')
print(results.summary())
print('Integration Results:')
pmean = results['mean']
pcov = results['outer'] - np.outer(pmean, pmean)
print ' mean(p) =', pmean
print ' cov(p) =\n', pcov
# create GVars from results
p = gv.gvar(gv.mean(pmean), gv.mean(pcov))
print('\nBayesian Parameters:')
print(gv.tabulate(p))
# show histograms
print('\nHistogram Statistics:')
count = results['count']
for i in range(4):
print('p[{}] -'.format(i))
print(hist[i].analyze(count[i]).stats)
plt.subplot(2, 2, i + 1)
plt.xlabel('p[{}]'.format(i))
hist[i].make_plot(count[i], plot=plt)
if i % 2 != 0:
plt.ylabel('')
plt.savefig('eg3e.png', bbox_inches='tight')
plt.show()
if DO_SIMULATION:
gv.ranseed(1234)
sys.stdout = tee.tee(sys_stdout, open('eg3f.out', 'w'))
print(40 * '*' + ' real fit')
print(fit.format(True))
Q = []
p = []
for sfit in fit.simulated_fit_iter(n=3, add_priornoise=False):
print(40 * '=' + ' simulation')
print(sfit.format(True))
diff = sfit.p - sfit.pexact
print '\nsfit.p - pexact =', diff
print(gv.fmt_chi2(gv.chi2(diff)))
print
# omit constraint
sys.stdout = tee.tee(sys_stdout, open("eg3b.out", "w"))
prior = gv.gvar(4 * ['0(1)'])
prior[1] = gv.gvar('0(20)')
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) =', gv.evalcorr(fit.p[:2])[1,0]
