def _median_ ( self , func , xmin , xmax , *args ) :
## need to know the integral
from ostap.math.integral import IntegralCache
iint = IntegralCache ( func , xmin , False , *args )
half = 2.0 / iint ( xmax )
from scipy import optimize
ifun = lambda x : iint( x ) * half - 1.0
## @see https://en.wikipedia.org/wiki/Median#Inequality_relating_means_and_medians
try:
meanv = Mean . __call__ ( self , func , *args )
sigma = RMS . __call__ ( self , func , *args )
import math
xmn = meanv - 2 * sigma ## use 2 instead of 1
xmx = meanv + 2 * sigma ## use 2 instead of 1
#
if isinstance ( xmin , float ) : xmn = max ( xmn , xmin )
if isinstance ( xmax , float ) : xmx = min ( xmx , xmax )
#
result = optimize.brentq ( ifun , xmn , xmx )
except :
result = optimize.brentq ( ifun , xmin , xmax )
return result
def __call__(self, func, *args):
##
if 0.5 == self.Q: return Median.__call__(self, func, *args)
elif 0.0 == self.Q: return self.xmin
elif 1.0 == self.Q: return self.xmax
## need to know the integral
from ostap.math.integral import IntegralCache
iint = IntegralCache(func, self.xmin, err=False, args=args)
quan = 1.0 / iint(self.xmax) / self.Q
ifun = lambda x: iint(x) * quan - 1.0
xmn = self.xmin
xmx = self.xmax
p = 0.5
l = 0.5
## make some bracketing before next step
while (not isinstance(xmn, float)) or (not isinstance(
xmx, float)) or l > 0.1:
l /= 2
m = self._median_(func, xmn, xmx, *args)
if self.Q < p:
xmn = xmn
xmx = float(m)
p -= l
elif self.Q > p:
xmn = float(m)
xmx = xmx
p += l
else:
return m ## RETURN
## finally, calculate quantile
from ostap.math.rootfinder import findroot
result = findroot(ifun, xmn, xmx)
return result
def _integral_(self, func, xmn, xmx, *args):
from ostap.math.integral import IntegralCache
integrator = IntegralCache(func, xmn, err=self.err, args=args)
return integrator(xmx, *args)