def gauss_cdf ( x , mu = 0.0 , sigma = 1.0 ) :
"""Standard gaussian CDF:
>>> x,mu, sigma = ....
>>> cdf = gauss_cdf ( x , mu , sigma )
"""
y = VE ( x )
return _gauss_cdf_ ( y if 0 < y.cov2() else y.value () , mu , sigma )
def __call__ ( self , x , y , cxy = 0 ) :
"""Evaluate the function
>>> func2 = lambda x,y : x*x + y*y
>>> eval2 = Eval2VE ( func2 )
>>> x = VE(1,0.1**2)
>>> y = VE(2,0.1**2)
>>> print eval2(x,y) ## treat x,y as uncorrelated
>>> print eval2(x,y, 0) ## ditto
>>> print eval2(x,y,+1) ## treat x,y as 100% correlated
>>> print eval2(x,y,-1) ## treat x,y as 100% anti-correlated
"""
assert isinstance ( cxy , num_types ) and \
( abs ( cxy ) <= 1 or isequal ( abs ( cxy ) , 1 ) ) , \
'Invalid correlation coefficient %s' % cxy
x = VE ( x )
y = VE ( y )
xv = x.value()
yv = y.value()
val = self.func ( xv , yv )
xc2 = x.cov2()
yc2 = x.cov2()
x_plain = xc2 <= 0 or iszero ( xc2 )
y_plain = yc2 <= 0 or iszero ( yc2 )
#
if x_plain and y_plain : return VE ( val , 0 )
#
## here we need to calculate the uncertainties
#
dx = self.partial[0] ( xv , yv ) if not x_plain else 0
dy = self.partial[1] ( xv , yv ) if not y_plain else 0
#
cov2 = dx * dx * xc2 + dy * dy * yc2
if cxy and xc2 and yc2 :
cov2 += 2 * cxy * dx * dy * math.sqrt ( xc2 * yc2 )
return VE ( val , cov2 )
def __call__(self, x, y, cxy=0):
"""Evaluate the function
>>> func2 = lambda x,y : x*x + y*y
>>> eval2 = Eval2VE ( func2 )
>>> x = VE(1,0.1**2)
>>> y = VE(2,0.1**2)
>>> print eval2(x,y) ## treat x,y as uncorrelated
>>> print eval2(x,y, 0) ## ditto
>>> print eval2(x,y,+1) ## treat x,y as 100% correlated
>>> print eval2(x,y,-1) ## treat x,y as 100% anti-correlated
"""
## evaluate the function
val = self._value_(x, y)
#
x = VE(x)
y = VE(y)
#
x_plain = x.cov2() <= 0 or iszero(x.cov2())
y_plain = y.cov2() <= 0 or iszero(y.cov2())
#
if x_plain and y_plain: return VE(val, 0)
#
## here we need to calculate the uncertainties
#
cov2 = 0.0
#
fx = self.dFdX(x, y.value()) if not x_plain else 0
fy = self.dFdY(x.value(), y) if not y_plain else 0
#
if not x_plain: cov2 += fx * fx * x.cov2()
if not y_plain: cov2 += fy * fy * y.cov2()
#
if not x_plain and not y_plain:
## adjust the correlation coefficient:
cxy = min(max(-1, cxy), 1)
if not iszero(cxy):
cov2 += 2 * cxy * fx * fy * x.error() * y.error()
return VE(val, cov2)
def pretty_ve ( value , width = 8 , precision = 6 , parentheses = True ) :
"""Nice printout of the ValueWithError object ( string + exponent)
- return nice stirng and the separate exponent
>>> s , n = pretty_ve ( number )
"""
from ostap.math.ve import VE
value = VE ( value )
fmt , fmtv , fmte , n = fmt_pretty_ve ( value , width , precision , parentheses )
v = value.value ()
e = max ( 0 , value.error () )
return fmt % ( v / 10**n , e / 10**n ) , n
def dFdY(self, x, y):
"""Get a partial derivatives d(func)/d(Y)"""
y = VE(y)
return self._partial_(self._dFdY, x, y.value(), y.cov2())
def dFdX(self, x, y):
"""Get a partial derivatives d(func)/d(X)"""
x = VE(x)
return self._partial_(self._dFdX, x.value(), y, x.cov2())
