def _rfr_sum_ ( self , var1 , var2 , *vars ) :
"""Get correct estimate of sum of two or more variables,
taking into account correlations
>>> r = ...
>>> print r.sum( 'S' , 'B' ) ## S+B
"""
allvars = ( var1 , var2 ) + vars
n = len ( allvars )
s = 0.0
c2 = 0.0
for i in range ( n ) :
vi = allvars [ i ]
if isinstance ( vi , str ) : vi = self.param ( vi ) [1]
v = vi.value
v = VE ( v )
s += v . value ()
vc = v.cov2()
if 0 >= vc or vi in self.constPars() : continue
c2 += vc
for j in range ( i ) :
vj = allvars [ j ]
if isinstance ( vj , str ) : vj = self.param ( vj ) [1]
if vj in self.constPars() : continue
c2 += 2 * self.covariance ( vi , vj )
return VE ( s , c2 )
def _rfr_multiply_ ( self , var1 , var2 , *vars ) :
"""Get correct estimate of product of two variables,
taking into account correlations
>>> r = ...
>>> print r.multiply( 'S' , 'B' ) ## S*B
"""
allvars = ( var1 , var2 ) + vars
n = len ( allvars )
m = 1.0
c2 = 0
for i in range ( n ) :
vi = allvars[i]
if isinstance ( vi , str ) : vi = self.param ( vi )[1]
v = vi.value
v = VE ( v )
vv = v.value ()
if iszero ( vv ) or iszero ( m ) : return VE ( 0.0 , 0.0 ) ## RETURN HERE
m *= vv
vc = v.cov2()
if 0 >= vc or vi in self.constPars() : continue
c2 += vc / ( vv * vv )
for j in range ( i ) :
vj = allvars [ j ]
if isinstance ( vj , str ) : vj = self.param( vj )[1]
if vj in self.constPars() : continue
w = vj . value
w = VE ( w )
ww = w.value()
c2 += 2 * self.covariance ( vi , vj ) / ( vv * ww )
return VE ( m , c2 * m * m )
def transform(C, X, *Y):
""" Transform the covariance nmatrix C at point X to the variables Y(X)
>>> X = 1 , 2
>>> C = Ostap.SymMatrix(2)()
>>> C [ 0 , 0 ] = 0.20
>>> C [ 0 , 1 ] = 0.05
>>> C [ 1 , 1 ] = 0.30
>>> r = lambda x , y : (x*x+y*y)**2
>>> phi = lambda x , y : math.atan2 ( y , x )
>>> C_polar = transform ( C , X , r , phi )
"""
ny = len(Y)
assert 1 <= ny, 'Invalid size of Y!'
nx = len(X)
if C is None and 1 <= nx:
C = Ostap.SymMatrix(nx)()
for i, x in enumerate(X):
xx = VE(x)
C[i, i] = xx.cov2()
shape = C.shape
assert shape[0] == shape[1] and shape[0] == nx, 'Invalid shape of matrix C!'
CC = Ostap.SymMatrix(nx)()
for i in range(CC.kRows):
CC[i, i] = C(i, i)
for j in range(i + 1, CC.kCols):
v = 0.5 * (C(i, j) + C(j, i))
CC[i, j] = v
XX = Ostap.Vector(nx)()
for i, x in enumerate(X):
XX[i] = float(x)
## get vector-with-errors
XX = Ostap.VectorE(nx)(XX, CC)
R = XX.transform(*Y)
return R.cov2()
