def spline_smoothing(self, sigma=None, lam=None, **kwargs):
""" Cubic Spline Interplation
sigma: phase bin error bars
lam: (0,1], 1 = maximize fitting through control points (knots), 0 = minimize curvature of spline
"""
tdata = self.bins
ydata = u.normalize(self.data, simple=True)
N = len(ydata)
noise = self.getOffpulseNoise()
if lam is None or (lam > 1 or lam <= 0):
lam = 1 - noise**2
mu = 2 * float(1 - lam) / (3 * lam)
### Define knot locations
# Rotate the pulse so the peak is at the edges of the spline
shift = -np.argmax(ydata)
yshift = np.roll(ydata, shift)
# Add periodic point
tdata = np.concatenate((tdata, [tdata[-1] + np.diff(tdata)[0]]))
yshift = np.concatenate((yshift, [yshift[0]]))
knots = u.subdivide(tdata, yshift, noise, **kwargs)
knots = np.array(np.sort(knots), dtype=np.int)
knots = np.concatenate(([0], knots, [N])) #Add endpoints
if sigma is None:
setsigma = True
#for passnum in range(2):
while True:
Nknots = len(knots)
Narcs = Nknots - 1
t = np.array(tdata[knots], dtype=np.float)
# Determine the knot y-values.
y = np.zeros_like(t)
y[0] = yshift[0]
y[-1] = yshift[-1]
for i in range(1, len(knots) - 1):
knotL = knots[i - 1]
knotR = knots[i + 1]
dt = tdata[knotL:knotR]
dy = yshift[knotL:knotR]
p = np.polyfit(
dt, dy, 3
) #Fit a preliminary cubic over the data to place the point.
f = np.poly1d(p)
y[i] = f(tdata[knots[i]])
if setsigma:
sigma = np.ones(len(y), dtype=np.float)
Sigma = np.diag(sigma[:-1]) #matrix
# Smoothing with Cubic Splines by D.S.G. Pollock 1999
h = t[1:] - t[:-1]
r = 3.0 / h
f = np.zeros_like(h)
p = np.zeros_like(h)
#q = np.zeros_like(h)
p[0] = 2 * (h[0] + h[-1])
#q[0] = 3*(y[1] - y[0])/h[0] - 3*(y[-1] - y[-2])/h[-1] #note the indices
f[0] = -(r[-1] + r[0])
for i in range(1, Narcs):
p[i] = 2 * (h[i] + h[i - 1])
#q[i] = 3*(y[i+1] - y[i])/h[i] - 3*(y[i] - y[i-1])/h[i-1]
f[i] = -(r[i - 1] + r[i])
# Build projection matrices
R = np.zeros((Narcs, Narcs))
Qp = np.zeros((Narcs, Narcs))
for i in range(Narcs):
#for j in range(Narcs):
# if i == j:
R[i, i] = p[i]
Qp[i, i] = f[i]
if i != Narcs - 1:
R[i + 1, i] = h[i]
R[i, i + 1] = h[i]
Qp[i + 1, i] = r[i]
Qp[i, i + 1] = r[i]
R[0, -1] = h[-1]
R[-1, 0] = h[-1]
Qp[0, -1] = r[-1]
Qp[-1, 0] = r[-1]
Q = np.transpose(Qp)
A = mu * np.dot(np.dot(Qp, Sigma), Q) + R
b = np.linalg.solve(A, np.dot(Qp, y[:-1]))
d = y[:-1] - mu * np.dot(np.dot(Sigma, Q), b)
a = np.zeros(Narcs)
c = np.zeros(Narcs)
i = Narcs - 1
a[i] = (b[0] - b[i]) / (3 * h[i])
for i in range(Narcs - 1):
a[i] = (b[i + 1] - b[i]) / (3 * h[i])
i = Narcs - 1
c[i] = (d[0] - d[i]) / h[i] - a[i] * h[i]**2 - b[i] * h[i]
for i in range(Narcs - 1):
c[i] = (d[i + 1] - d[i]) / h[i] - a[i] * h[i]**2 - b[i] * h[i]
# Build polynomials
S = []
for i in range(Narcs):
S.append(np.poly1d([a[i], b[i], c[i], d[i]]))
ytemp = np.zeros_like(yshift)
for i in range(Narcs):
ts = np.arange(t[i], t[i + 1])
hs = ts - t[i]
yS = S[i](hs)
ytemp[int(t[i]):int(t[i + 1])] = yS
ytemp[-1] = ytemp[0]
resids = yshift - ytemp
#print resids,noise
rms_resids = u.RMS(resids)
#inds = np.where(np.abs(resids)>4*rms_resids)[0]
inds = np.where(
np.logical_and(yshift > 3 * noise,
np.abs(resids) > 4 * rms_resids)
)[0] #require the intensity to be "significant", and the residuals
if len(inds) == 0:
break
#newinds = np.sort(np.abs(resids))
newinds = np.argsort(np.abs(resids))
#print np.argmax(np.abs(resids))
#print newinds
#raise SystemExit
#newind = np.argmax(np.abs(resids))
newind = newinds[-1]
i = 1
addknot = True
while newind in knots and np.any(np.abs(knots - newind) <= 4):
if i == N:
addknot = False
break
i += 1
newind = newinds[-i]
'''
for newind in newinds:
if newind in knots:
continue
elif np.all(np.abs(newind-knots)<=1):
continue
print newind
break
'''
if addknot:
#print newind
knots = np.sort(np.concatenate((knots, [newind])))
else:
break
resids = yshift - ytemp
rms_resids = u.RMS(resids)
tdata = tdata[:-1]
#yshift = yshift[:-1]
ytemp = ytemp[:-1]
#yshift = np.roll(yshift,-shift)
ytemp = np.roll(ytemp, -shift)
ytemp /= np.max(ytemp)
return ytemp
def spline_smoothing(self,sigma=None,lam=None,**kwargs):
""" Cubic Spline Interplation
sigma: phase bin error bars
lam: (0,1], 1 = maximize fitting through control points (knots), 0 = minimize curvature of spline
"""
tdata = self.bins
ydata = u.normalize(self.data,simple=True)
N = len(ydata)
noise = self.getOffpulseNoise()
if lam is None or (lam > 1 or lam <= 0):
lam = 1-noise**2
mu = 2*float(1-lam)/(3*lam)
### Define knot locations
# Rotate the pulse so the peak is at the edges of the spline
shift = -np.argmax(ydata)
yshift = np.roll(ydata,shift)
# Add periodic point
tdata = np.concatenate((tdata,[tdata[-1] + np.diff(tdata)[0]]))
yshift = np.concatenate((yshift,[yshift[0]]))
knots = u.subdivide(tdata,yshift,noise,**kwargs)
knots = np.array(np.sort(knots),dtype=np.int)
knots = np.concatenate(([0],knots,[N])) #Add endpoints
if sigma is None:
setsigma = True
#for passnum in range(2):
while True:
Nknots = len(knots)
Narcs = Nknots-1
t = np.array(tdata[knots],dtype=np.float)
# Determine the knot y-values.
y = np.zeros_like(t)
y[0] = yshift[0]
y[-1] = yshift[-1]
for i in range(1,len(knots)-1):
knotL = knots[i-1]
knotR = knots[i+1]
dt = tdata[knotL:knotR]
dy = yshift[knotL:knotR]
p = np.polyfit(dt,dy,3) #Fit a preliminary cubic over the data to place the point.
f = np.poly1d(p)
y[i] = f(tdata[knots[i]])
if setsigma:
sigma = np.ones(len(y),dtype=np.float)
Sigma = np.diag(sigma[:-1]) #matrix
# Smoothing with Cubic Splines by D.S.G. Pollock 1999
h = t[1:]-t[:-1]
r = 3.0/h
f = np.zeros_like(h)
p = np.zeros_like(h)
#q = np.zeros_like(h)
p[0] = 2*(h[0] + h[-1])
#q[0] = 3*(y[1] - y[0])/h[0] - 3*(y[-1] - y[-2])/h[-1] #note the indices
f[0] = -(r[-1]+r[0])
for i in range(1,Narcs):
p[i] = 2*(h[i] + h[i-1])
#q[i] = 3*(y[i+1] - y[i])/h[i] - 3*(y[i] - y[i-1])/h[i-1]
f[i] = -(r[i-1]+r[i])
# Build projection matrices
R = np.zeros((Narcs,Narcs))
Qp = np.zeros((Narcs,Narcs))
for i in range(Narcs):
#for j in range(Narcs):
# if i == j:
R[i,i] = p[i]
Qp[i,i] = f[i]
if i != Narcs -1:
R[i+1,i] = h[i]
R[i,i+1] = h[i]
Qp[i+1,i] = r[i]
Qp[i,i+1] = r[i]
R[0,-1] = h[-1]
R[-1,0] = h[-1]
Qp[0,-1] = r[-1]
Qp[-1,0] = r[-1]
Q = np.transpose(Qp)
A = mu*np.dot(np.dot(Qp,Sigma),Q) + R
b = np.linalg.solve(A,np.dot(Qp,y[:-1]))
d = y[:-1] - mu*np.dot(np.dot(Sigma,Q),b)
a = np.zeros(Narcs)
c = np.zeros(Narcs)
i = Narcs-1
a[i] = (b[0] - b[i])/(3*h[i])
for i in range(Narcs-1):
a[i] = (b[i+1] - b[i])/(3*h[i])
i = Narcs-1
c[i] = (d[0] - d[i])/h[i] - a[i]*h[i]**2 - b[i]*h[i]
for i in range(Narcs-1):
c[i] = (d[i+1] - d[i])/h[i] - a[i]*h[i]**2 - b[i]*h[i]
# Build polynomials
S = []
for i in range(Narcs):
S.append(np.poly1d([a[i],b[i],c[i],d[i]]))
ytemp = np.zeros_like(yshift)
for i in range(Narcs):
ts = np.arange(t[i],t[i+1])
hs = ts-t[i]
yS = S[i](hs)
ytemp[int(t[i]):int(t[i+1])] = yS
ytemp[-1] = ytemp[0]
resids = yshift-ytemp
#print resids,noise
rms_resids = u.RMS(resids)
#inds = np.where(np.abs(resids)>4*rms_resids)[0]
inds = np.where(np.logical_and(yshift>3*noise,np.abs(resids)>4*rms_resids))[0] #require the intensity to be "significant", and the residuals
if len(inds) == 0:
break
#newinds = np.sort(np.abs(resids))
newinds = np.argsort(np.abs(resids))
#print np.argmax(np.abs(resids))
#print newinds
#raise SystemExit
#newind = np.argmax(np.abs(resids))
newind = newinds[-1]
i = 1
addknot = True
while newind in knots and np.any(np.abs(knots-newind)<=4):
if i == N:
addknot = False
break
i+=1
newind = newinds[-i]
'''
for newind in newinds:
if newind in knots:
continue
elif np.all(np.abs(newind-knots)<=1):
continue
print newind
break
'''
if addknot:
#print newind
knots = np.sort(np.concatenate((knots,[newind])))
else:
break
resids = yshift-ytemp
rms_resids = u.RMS(resids)
tdata = tdata[:-1]
#yshift = yshift[:-1]
ytemp = ytemp[:-1]
#yshift = np.roll(yshift,-shift)
ytemp = np.roll(ytemp,-shift)
ytemp /= np.max(ytemp)
return ytemp