def invertbtilde(self,nx): ''' Get inverse of the transformation for btilde to get back b in the original space. ''' btilde = nx[:,self.split:] b = applyAffine(invAffine(self.gb),btilde) return(btilde,b)
def computebtilde(self,tx): ''' Computes the btilde portion after the transformation. ''' b = tx[:,self.split:] btilde = applyAffine(self.gb,b) return(btilde)
def inv(self,nx): ''' Inverse map, if the map has not been defined via the ellipse reflection then it will be. ''' btilde,b = self.invertbtilde(nx) atilde = nx[:,:self.split] ashift = self.f(btilde) a = applyAffine(invAffine(self.ga),atilde-ashift) tx = hstack([a,b]) return(tx)
def __call__(self,tx): ''' Apply the map. If this is the first time this has been called it will automatically generate the ellipse reflect transformation. ''' a = tx[:,:self.split] btilde = self.computebtilde(tx) ashift = self.f(btilde) atilde = applyAffine(self.ga,a) + ashift nx = hstack([atilde,btilde]) return(nx)
def plotHMapEffects(s,alpha=0.1,Nsamp=1000):
D = s.D
Htrans = s.Htrans
cpairs = zip(
(['r','b','k'][i%3] for i in count(0)),
zip(xrange(D),[j%D for j in xrange(1,D+1)])
)
x = sampleSCrossSD(r0=1.0,r1=0.3,D=D-1,N=Nsamp)
tmpx = array(x)
for h,A in zip(Htrans.H,Htrans.A):
f = h.f
figure(figsize=(12,12))
subplot(2,2,1)
for c,(i,j) in cpairs:
scatter(tmpx[:,i],tmpx[:,j],alpha=alpha,c=c)
subplot(2,2,2)
bt = h.computebtilde(tmpx)
if bt.shape[1]==1:
scatter(zeros(bt.shape[0]),bt[:,0],alpha=alpha)
lnes = f.getEllipse()
for l in lnes:
hlines(l,-1,1)
subplot(2,2,3)
a = applyAffine(h.ga,tmpx[:,:h.split])
if a.shape[1]>2:
scatter(a[:,0],a[:,1],alpha=alpha)
else:
scatter(zeros_like(a[:,0]),a[:,0],alpha=alpha)
else:
scatter(*bt.T,alpha=alpha)
plot(*f.getEllipse())
subplot(2,2,3)
a = applyAffine(h.ga,tmpx[:,:h.split])
scatter(zeros(a.shape[0]),a[:,0],alpha=alpha)
subplot(2,2,4)
tmpx = h(tmpx)
for c,(i,j) in cpairs:
scatter(tmpx[:,i],tmpx[:,j],alpha=alpha,c=c)
tmpx = dot(A,tmpx.T).T