def _h1_cmp_dist_ ( h1 ,
h2 ,
rescale = False ) :
"""Calculate the norm of difference of scaled histograms/functions
|f1-f2|, such |f1|=1 and |f2|=1
>>> h1 = ... ## the first histo
>>> h2 = ... ## the second histo
>>> diff = h1.cmp_dist ( h2 )
"""
if rescale :
h1_ = h1.rescale_bins ( 1.0 )
h2_ = h2.rescale_bins ( 1.0 )
res = _h1_cmp_dist_ ( h1_ , h2_ , rescale = False )
del h1_, h2_
return res
f1 = h1.asFunc ()
f2 = h2.asFunc ()
lims = h1.xminmax()
from ostap.math.integral import integral as _integral_
r1 = _integral_ ( lambda x : f1 ( x )**2 , lims[0] , lims[1] , limit = 200 , err = True )
r2 = _integral_ ( lambda x : f2 ( x )**2 , lims[0] , lims[1] , limit = 200 , err = True )
import math
sf1 = 1.0 / math.sqrt ( r1.value() )
sf2 = 1.0 / math.sqrt ( r2.value() )
d12 = _integral_ ( lambda x : (sf1*f1(x)-sf2*f2(x))**2 , lims[0] , lims[1] , limit = 200 , err = True )
return d12
def _h1_cmp_costheta_(h1, h2, density=False):
"""Compare the 1D-historgams (as functions)
Calculate scalar product and get ``the angle'' from it
>>> h1 = ... ## the first histo
>>> h2 = ... ## the second histo
>>> cos_theta = h1.cmp_costheta ( h2 )
"""
if density:
h1_ = h1.density()
h2_ = h2.density()
cmp = _h1_cmp_costheta_(h1_, h2_, density=False)
del h1_
del h2_
return cmp
f1 = h1.asFunc()
f2 = h2.asFunc()
lims = h1.xminmax()
from ostap.math.integral import integral as _integral_
vr1 = _integral_(lambda x: f1(x)**2, lims[0], lims[1], limit=200, err=True)
vr2 = _integral_(lambda x: f2(x)**2, lims[0], lims[1], limit=200, err=True)
vr12 = _integral_(lambda x: f1(x) * f2(x),
lims[0],
lims[1],
limit=200,
err=True)
return vr12 / (vr1 * vr2)**0.5
def _h1_cmp_dist_(h1, h2, density=False):
"""Calculate the norm of difference of scaled histograms/functions
|f1-f2|, such |f1|=1 and |f2|=1
>>> h1 = ... ## the first histo
>>> h2 = ... ## the second histo
>>> diff = h1.cmp_dist ( h2 )
"""
assert isinstance ( h1 , ROOT.TH1 ) and not isinstance ( h1 , ROOT.TH2 ) , \
"cmp_dist: invalid type of h1 %s/%s" % ( h1 , type ( h1 ) )
assert isinstance ( h2 , ROOT.TH1 ) and not isinstance ( h2 , ROOT.TH2 ) , \
"cmp_dist: invalid type of h2 %s/%s" % ( h2 , type ( h2 ) )
if density:
h1_ = h1.density()
h2_ = h2.density()
cmp = _h1_cmp_dist_(h1_, h2_, density=False)
del h1_
del h2_
return cmp
f1 = h1.asFunc()
f2 = h2.asFunc()
lims = h1.xminmax()
from ostap.math.integral import integral as _integral_
r1 = _integral_(lambda x: f1(x)**2, lims[0], lims[1], limit=200, err=True)
r2 = _integral_(lambda x: f2(x)**2, lims[0], lims[1], limit=200, err=True)
import math
sf1 = 1.0 / math.sqrt(r1.value())
sf2 = 1.0 / math.sqrt(r2.value())
d12 = _integral_(lambda x: (sf1 * f1(x) - sf2 * f2(x))**2,
lims[0],
lims[1],
limit=200,
err=True)
volume = (lims[1] - lims[0])
return d12 / volume
def _h1_cmp_dist2_(h1, h2, density=False):
"""Calculate the norm of difference of scaled histograms/functions
|(f1-f2)**2/(f1*f2)|, such |f1|=1 and |f2|=1
>>> h1 = ... ## the first histo
>>> h2 = ... ## the second histo
>>> diff = h1.cmp_dist2 ( h2 )
"""
if density:
h1_ = h1.density()
h2_ = h2.density()
cmp = _h1_cmp_dist2_(h1_, h2_, density=False)
del h1_
del h2_
return cmp
f1 = h1.asFunc()
f2 = h2.asFunc()
lims = h1.xminmax()
from ostap.math.integral import integral as _integral_
r1 = _integral_(lambda x: f1(x)**2, lims[0], lims[1], limit=200, err=True)
r2 = _integral_(lambda x: f2(x)**2, lims[0], lims[1], limit=200, err=True)
import math
sf1 = 1.0 / math.sqrt(r1.value())
sf2 = 1.0 / math.sqrt(r2.value())
def _func_(x):
v1 = sf1 * f1(x)
v2 = sf2 * f2(x)
v = (v1 - v2) * (v1 - v2) / abs(v1 * v2)
return v * v
d12 = _integral_(_func_, lims[0], lims[1], limit=200, err=True)
return d12
def _h1_chi2_cmp_ ( h1 ,
func ,
integral = False ,
select = lambda x,y,v : True ,
chi2 = lambda v1,v2 : v1.chi2(v2) ) :
"""Calculate chi2 for histogram and ``function''
>>> h1 = ... ## the first histo
>>> func = ... ## the the function
>>> chi2ndf,prob = h1.chi2_cmp ( func , integral = False )
"""
c2 = 0
ndf = 0
_func_ = lambda x,xl,xr : func(x)
if integral and hasattr ( func , 'integral' ) :
_func_ = lambda x,xl,xr : func.integral(xl,xr)/(xr-xl)
elif integral and hasattr ( func , 'Integral' ) :
_func_ = lambda x,xl,xr : func.Integral(xl,xr)/(xr-xl)
elif integral :
## use numerical integration from scipy
from ostap.math.intergal import integral as _integral_
_func_ = lambda x,xl,xr : _integral_ ( func , xl , xr )/(xr-xl)
for entry in h1.iteritems() :
x = entry[1]
y1 = entry[2]
xv = x.value()
xe = x.error()
xl = xv - xe
xr = xv + xe
y2 = _func_ ( x , xl , xr )
if not select ( x, y1 , y2 ) : continue
c2 += chi2 ( y1 , y2 )
ndf += 1
c2ndf = c2/ndf
return c2ndf, ROOT.TMath.Prob( c2 , ndf )