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 = y.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 , args , cor = None ) :
"""Calcualte the value of the scalar function of N arguments
with uncertainties and correlations
>>> fun2 = lambda x , y : ...
>>> fun2e = EvalNVEcor ( fun2 , 2 )
>>> cor = ... # 2x2 symmetric correlation matrix
>>> x = ...
>>> y = ...
>>> result = fun2e ( (x,y) , cor ) ##
"""
n = self.N
assert len ( args ) == n , 'Invalid argument size'
## get value of the function
val = self.func ( *args )
c2 = 0
x = n * [ 0 ] ## argument
g = n * [ 0 ] ## gradient
for i in range ( n ) :
xi = VE ( args[i] )
x [i] = x
ci = xi.cov2()
if ci < 0 or iszero ( ci ) : continue
di = self.partial[i] ( *args )
if iszero ( di ) : continue
ei = xi.error()
g [i] = di
e [i] = ei
## diagonal correlation coefficients are assumed to be 1 and ignored!
c2 += ci * di * di
for j in range ( i ) :
xj = x [ j ]
cj = xj.cov2 ()
if cj < 0 or iszero ( cj ) : continue
dj = d [ j ]
if iszero ( dj ) : continue
ej = e [ j ]
rij = self.__corr ( cor , i , j ) if cor else 0
assert -1 <= rij <= 1 or isequal ( abs ( rij ) , 1 ) ,\
'Invalid correlaation coefficient (%d,%d)=%s ' % ( i , j , rij )
c2 += 2.0 * di * dj * rij * ei * ej
return VE ( val , c2 )
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 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())
