def test_covtransform1():
logger.info('Descartes to polar tranformation')
## Descartes coordinates
X = 1, 4
## their covarinac ematrix
C = Ostap.SymMatrix(2)()
C[0, 0] = 0.20
C[0, 1] = 0.05
C[1, 1] = 0.30
R = C.correlations()
## Polar coordinated
r = lambda x, y: math.sqrt(x * x + y * y)
phi = lambda x, y: math.atan2(y, x)
C_polar = transform(C, X, r, phi)
R_polar = C_polar.correlations()
logger.info('Descartes Covariance :\n%s' % C)
logger.info('Descartes Correlation :\n%s' % R)
logger.info('Polar Covariance :\n%s' % C_polar)
logger.info('Polar Correlation :\n%s' % R_polar)
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()