def __init__(self,P,A,B,scale=100.0,amp=100.0*np.eye(2)):
""" Create instance of astrometric map from a background mapping
(Bgmap object P) and objects in each frame (Bivarg arrays A and B).
"""
from pyBA.distortion import astrometry_cov, d2
self.P = P
self.A = A
self.B = B
# Default GP hyperparameters
self.scale = scale
self.amp = amp
self.hyperparams = {'scale': self.scale, 'amp': self.amp}
# Gather locations of inputs and build distance matrix
self.xyarr = np.array([o.mu for o in self.A])
self.d2 = d2(self.xyarr,self.xyarr)
# Use measurement uncertainties of displacement as 'nugget'
self.V = np.array([a.sigma for a in A]) + np.array([b.sigma for b in B])
# Build covariance matrix for data points
self.C = astrometry_cov(self.d2, self.scale, self.amp, var = self.V)
# Don't compute cholesky decomposition of C until needed
self.chol = None
return
def __init__(self, P, A, B, scale=100.0, amp=100.0 * np.eye(2)):
""" Create instance of astrometric map from a background mapping
(Bgmap object P) and objects in each frame (Bivarg arrays A and B).
"""
from pyBA.distortion import astrometry_cov, d2
self.P = P
self.A = A
self.B = B
# Default GP hyperparameters
self.scale = scale
self.amp = amp
self.hyperparams = {'scale': self.scale, 'amp': self.amp}
# Gather locations of inputs and build distance matrix
self.xyarr = np.array([o.mu for o in self.A])
self.d2 = d2(self.xyarr, self.xyarr)
# Use measurement uncertainties of displacement as 'nugget'
self.V = np.array([a.sigma
for a in A]) + np.array([b.sigma for b in B])
# Build covariance matrix for data points
self.C = astrometry_cov(self.d2, self.scale, self.amp, var=self.V)
# Don't compute cholesky decomposition of C until needed
self.chol = None
return
def regression(self, xy):
"""Performs regression on a mapping object at some locations,
which can be points or distributions."""
from scipy.linalg import cho_solve
from pyBA.distortion import d2, astrometry_cov, compute_residual
# Convert list of inputs to array if needed
if type(xy) == list:
xy = np.array(xy)
# Parse input
if type(xy)==np.ndarray:
# Single point
if xy.size == 2 and type(xy)==np.ndarray:
XY = np.array([ Bivarg(mu=xy,sigma=0) ])
# Array of points
elif xy.ndim == 2 and type(xy[0])==np.ndarray:
XY = np.array([ Bivarg(mu=xy[i],sigma=0) for i in range(len(xy)) ])
# Array of query distributions
elif type(xy[0].__class__.__name__=='Bivarg'):
XY = xy
else:
raise TypeError('Regression input should be an nx2 array of coordinates, or an array of Bivarg distributions')
# Single query distribution
elif xy.__class__.__name__ == 'Bivarg':
XY = np.array([ xy ])
else:
raise TypeError('Regression input should be an nx2 array of coordinates, or an array of Bivarg distributions')
## Gaussian process regression
# Old grid coordinates
xyobs = np.array([o.mu for o in self.A])
# New grid coordinates
xynew = np.array([o.mu for o in XY])
# Get regression data (resdiual to background)
dx, dy = compute_residual(self.A, self.B, self.P)
dxy = np.array([dx, dy]).T.flatten()
# Build cross covariance between old and new locations
d2_grid = d2(xynew,xyobs)
Cs = astrometry_cov(d2_grid, self.scale, self.amp)
# Build covariance for new locations
d2_grid = d2(xynew, xynew)
Vnew = np.array([o.sigma for o in XY])
# Don't need to add variances for input points here, they will be propagated
# through the background transformation.
#Css = astrometry_cov(d2_grid, self.scale, self.amp, var=Vnew)
Css = astrometry_cov(d2_grid, self.scale, self.amp)
# Regression: mean function evaluated at new locations
vxy = Cs.dot(cho_solve(self.chol, dxy)).reshape( (len(XY),2) )
# Regression: uncertainties at new locations
S = Css - Cs.dot(cho_solve(self.chol, Cs.T))
## Package output
# Background (mean function) mapping
R = np.array([o.transform(self.P) for o in XY])
# Add regression residuals to mean function
munew = np.array([o.mu for o in R]) + vxy
# Get regression uncertainty from background mapping
S_P = self.P.uncertainty(XY)
# Get regression uncertainty from gaussian process
S_gp = np.array([S[i:i+2,i:i+2] for i in range(0,len(S),2)])
# Combine uncertainties into single covariance matrix
sigmanew = np.array([o.sigma for o in R]) + S_gp + S_P
# Construct output array of Bivargs
O = np.array([ Bivarg(mu=munew[i], sigma=sigmanew[i]) for i in range(len(R)) ])
return O, S_gp, S_P
def regression(self, xy):
"""Performs regression on a mapping object at some locations,
which can be points or distributions."""
from scipy.linalg import cho_solve
from pyBA.distortion import d2, astrometry_cov, compute_residual
# Convert list of inputs to array if needed
if type(xy) == list:
xy = np.array(xy)
# Parse input
if type(xy) == np.ndarray:
# Single point
if xy.size == 2 and type(xy) == np.ndarray:
XY = np.array([Bivarg(mu=xy, sigma=0)])
# Array of points
elif xy.ndim == 2 and type(xy[0]) == np.ndarray:
XY = np.array(
[Bivarg(mu=xy[i], sigma=0) for i in range(len(xy))])
# Array of query distributions
elif type(xy[0].__class__.__name__ == 'Bivarg'):
XY = xy
else:
raise TypeError(
'Regression input should be an nx2 array of coordinates, or an array of Bivarg distributions'
)
# Single query distribution
elif xy.__class__.__name__ == 'Bivarg':
XY = np.array([xy])
else:
raise TypeError(
'Regression input should be an nx2 array of coordinates, or an array of Bivarg distributions'
)
## Gaussian process regression
# Old grid coordinates
xyobs = np.array([o.mu for o in self.A])
# New grid coordinates
xynew = np.array([o.mu for o in XY])
# Get regression data (resdiual to background)
dx, dy = compute_residual(self.A, self.B, self.P)
dxy = np.array([dx, dy]).T.flatten()
# Build cross covariance between old and new locations
d2_grid = d2(xynew, xyobs)
Cs = astrometry_cov(d2_grid, self.scale, self.amp)
# Build covariance for new locations
d2_grid = d2(xynew, xynew)
Vnew = np.array([o.sigma for o in XY])
# Don't need to add variances for input points here, they will be propagated
# through the background transformation.
#Css = astrometry_cov(d2_grid, self.scale, self.amp, var=Vnew)
Css = astrometry_cov(d2_grid, self.scale, self.amp)
# Regression: mean function evaluated at new locations
vxy = Cs.dot(cho_solve(self.chol, dxy)).reshape((len(XY), 2))
# Regression: uncertainties at new locations
S = Css - Cs.dot(cho_solve(self.chol, Cs.T))
## Package output
# Background (mean function) mapping
R = np.array([o.transform(self.P) for o in XY])
# Add regression residuals to mean function
munew = np.array([o.mu for o in R]) + vxy
# Get regression uncertainty from background mapping
S_P = self.P.uncertainty(XY)
# Get regression uncertainty from gaussian process
S_gp = np.array([S[i:i + 2, i:i + 2] for i in range(0, len(S), 2)])
# Combine uncertainties into single covariance matrix
sigmanew = np.array([o.sigma for o in R]) + S_gp + S_P
# Construct output array of Bivargs
O = np.array(
[Bivarg(mu=munew[i], sigma=sigmanew[i]) for i in range(len(R))])
return O, S_gp, S_P