def initialise(self,kal,pca=True,fd=False):
'''
Perform initialisation, applying the kalman filter kal, z-scoring and
doing a PCA
'''
if fd:
self._finitediff()
else:
self._kalfilt(kal)
if pca:
#self._pca()
self.dtran.addTransform(PCASpec.pcaspec,self.ytf.getFlatX())
self.ytp = TangentVectors(
self.dtran(self.ytf.getX()),
self.dtran.dapply(self.ytf.getdX())
)
self.ydp = TangentVectors(
self.dtran(self.ydf.getX()),
self.dtran.dapply(self.ydf.getdX())
)
else:
#self.Lda = ones((self.y.shape[-1]))
#self.U = eye(self.y.shape[-1])
self.ytp = self.ytf
self.ydp = self.ydf
self.dtran.addTransform(ZScoreSpec.zscorespec,self.ytp.getFlatX())
self.yt = TangentVectors(
self.dtran(self.ytp.getX()),
self.dtran.dapply(self.ytp.getdX())
)
self.yd = TangentVectors(
self.dtran(self.ydp.getX()),
self.dtran.dapply(self.ydp.getdX())
)
self._zscore()
def _pca(self):
y,self.Lda,self.U=PCA(self.ytf.getFlatX().T,True)
self.ytp = TangentVectors(
einsum('...ij,...jl->...il',self.U,self.ytf.getX()),
einsum('...ij,...jl->...il',self.U,self.ytf.getdX())
)
self.ydp = TangentVectors(
einsum('...ij,...jl->...il',self.U,self.ydf.getX()),
einsum('...ij,...jl->...il',self.U,self.ydf.getdX())
)
def _kalfilt(self,kal):
'''
Apply a Kalman filter
'''
self.ytf = self._kf(self.yt0,kal)
self.ytf = TangentVectors(
self.ytf[:,:,:self.ytf.shape[-1]/2].transpose(0,2,1),
self.ytf[:,:,self.ytf.shape[-1]/2:].transpose(0,2,1)
)
self.ydf = self._kf(self.yd0,kal)
self.ydf = TangentVectors(
self.ydf[:,:,:self.ydf.shape[-1]/2].transpose(0,2,1),
self.ydf[:,:,self.ydf.shape[-1]/2:].transpose(0,2,1)
)
def _finitediff(self):
'''
Calculate derivatives using finite differences. Use this if the kalman
filter is under performing due to non-linearities.
'''
self.ytf = self._fd(self.yt0)
self.ytf = TangentVectors(
self.ytf[:,:,:self.ytf.shape[-1]/2].transpose(0,2,1),
self.ytf[:,:,self.ytf.shape[-1]/2:].transpose(0,2,1)
)
self.ydf = self._fd(self.yd0)
self.ydf = TangentVectors(
self.ydf[:,:,:self.ydf.shape[-1]/2].transpose(0,2,1),
self.ydf[:,:,self.ydf.shape[-1]/2:].transpose(0,2,1)
)
class Trials(object):
def __init__(self,x,y,Ntrain,maxN=None,ytf=None,ydf=None,ytp=None,ydp=None,
yt=None,yd=None,dtran=None
):
if type(x)==str:
self.x = unserialiseArray(x)
self.y = unserialiseArray(y)
else:
self.x = array(x)
self.y = array(y)
self.Ntrain = Ntrain
self.maxN = maxN
self.yt0 = self.y[:Ntrain]
self.yd0 = self.y[Ntrain:self.maxN]
self.xt = self.x[:Ntrain]
self.xd = self.x[Ntrain:self.maxN]
# Filtered
self.ytf = ytf
self.ydf = ydf
# Z-scored (normalized)
self.yt = yt
self.yd = yd
# PCAed
self.ytp = ytp
self.ydp = ydp
if dtran is None:
self.dtran = DataTransformStack()
else:
self.dtran = dtran
@staticmethod
def _fd(y0):
'''
Calculate the derivative of y0 using finite differences and a univariate
spline.
'''
y = list()
for iy in y0:
diy = diff(iy,axis=0)
xint = arange(iy.shape[0])
x0 = xint[:-1]+0.5
diy = array([UnivariateSpline(x0,idiy,s=0)(xint) for idiy in diy.T]).T
y.append(hstack([iy,diy]))
return(array(y))
def _finitediff(self):
'''
Calculate derivatives using finite differences. Use this if the kalman
filter is under performing due to non-linearities.
'''
self.ytf = self._fd(self.yt0)
self.ytf = TangentVectors(
self.ytf[:,:,:self.ytf.shape[-1]/2].transpose(0,2,1),
self.ytf[:,:,self.ytf.shape[-1]/2:].transpose(0,2,1)
)
self.ydf = self._fd(self.yd0)
self.ydf = TangentVectors(
self.ydf[:,:,:self.ydf.shape[-1]/2].transpose(0,2,1),
self.ydf[:,:,self.ydf.shape[-1]/2:].transpose(0,2,1)
)
@staticmethod
def _kf(y0,kal):
'''
Apply a kalman kal filter to a specific set of trajectories in y0
'''
y = list()
for iy in y0:
K = kal.filter(flipud(iy).T,zeros(2*iy.shape[1]),eye(2*iy.shape[1]))
ix = K[0][:,-1]
iV = K[1][:,:,-1]
y.append(kal.smooth(iy.T,ix,iV)[0].T)
return(array(y))
def _kalfilt(self,kal):
'''
Apply a Kalman filter
'''
self.ytf = self._kf(self.yt0,kal)
self.ytf = TangentVectors(
self.ytf[:,:,:self.ytf.shape[-1]/2].transpose(0,2,1),
self.ytf[:,:,self.ytf.shape[-1]/2:].transpose(0,2,1)
)
self.ydf = self._kf(self.yd0,kal)
self.ydf = TangentVectors(
self.ydf[:,:,:self.ydf.shape[-1]/2].transpose(0,2,1),
self.ydf[:,:,self.ydf.shape[-1]/2:].transpose(0,2,1)
)
def _zscore(self):
self.muy = median(self.ytp.getFlatX(),1)
self.sigmay = std(self.ytp.getFlatX(),1)
self.yt = TangentVectors(
((self.ytp.getX().transpose(0,2,1)-self.muy)/self.sigmay).transpose(0,2,1),
(self.ytp.getdX().transpose(0,2,1)/self.sigmay).transpose(0,2,1)
)
self.yd = TangentVectors(
((self.ydp.getX().transpose(0,2,1)-self.muy)/self.sigmay).transpose(0,2,1),
(self.ydp.getdX().transpose(0,2,1)/self.sigmay).transpose(0,2,1)
)
def _pca(self):
y,self.Lda,self.U=PCA(self.ytf.getFlatX().T,True)
self.ytp = TangentVectors(
einsum('...ij,...jl->...il',self.U,self.ytf.getX()),
einsum('...ij,...jl->...il',self.U,self.ytf.getdX())
)
self.ydp = TangentVectors(
einsum('...ij,...jl->...il',self.U,self.ydf.getX()),
einsum('...ij,...jl->...il',self.U,self.ydf.getdX())
)
def initialise(self,kal,pca=True,fd=False):
'''
Perform initialisation, applying the kalman filter kal, z-scoring and
doing a PCA
'''
if fd:
self._finitediff()
else:
self._kalfilt(kal)
if pca:
#self._pca()
self.dtran.addTransform(PCASpec.pcaspec,self.ytf.getFlatX())
self.ytp = TangentVectors(
self.dtran(self.ytf.getX()),
self.dtran.dapply(self.ytf.getdX())
)
self.ydp = TangentVectors(
self.dtran(self.ydf.getX()),
self.dtran.dapply(self.ydf.getdX())
)
else:
#self.Lda = ones((self.y.shape[-1]))
#self.U = eye(self.y.shape[-1])
self.ytp = self.ytf
self.ydp = self.ydf
self.dtran.addTransform(ZScoreSpec.zscorespec,self.ytp.getFlatX())
self.yt = TangentVectors(
self.dtran(self.ytp.getX()),
self.dtran.dapply(self.ytp.getdX())
)
self.yd = TangentVectors(
self.dtran(self.ydp.getX()),
self.dtran.dapply(self.ydp.getdX())
)
self._zscore()
def __repr__(self):
return("Trials("+
"x="+repr(serialiseArray(self.x))+
",y="+repr(serialiseArray(self.y))+
",Ntrain="+repr(self.Ntrain)+
",maxN="+repr(self.maxN)+
",ytf="+repr(self.ytf)+
",ydf="+repr(self.ydf)+
",ytp="+repr(self.ytp)+
",ydp="+repr(self.ydp)+
",yt="+repr(self.yt)+
",yd="+repr(self.yd)+
",dtran="+repr(self.dtran)+
")")
