def scintillation_parameters(self,
plotbound=1.0,
maxr=None,
maxc=None,
savefig=None,
show=True,
full_output=False,
simple=False,
eta=0.2,
cmap=cm.binary,
finitescintleerrors=True):
if self.acf is None:
self.acf2d()
if self.dT is None:
dT = 1
else:
dT = self.dT
if self.dF is None:
dF = 1
else:
dF = self.dF
acfshape = np.shape(self.acf)
centerrind = acfshape[0] // 2
centercind = acfshape[1] // 2
if simple: # Do 1D slices
NF = len(self.F)
Faxis = (np.arange(-(NF - 1), NF, dtype=np.float) * np.abs(dF)
) #why abs?
NT = len(self.T)
Taxis = (np.arange(-(NT - 1), NT, dtype=np.float) *
np.abs(dT))[1:-1] #???
#try:
pout, errs = ffit.gaussianfit(Taxis[NT // 2:3 * NT // 2],
self.acf[centerrind,
NT // 2:3 * NT // 2],
baseline=True)
f = interpolate.interp1d(
Taxis,
ffit.funcgaussian(pout, Taxis, baseline=True) -
(pout[3] + pout[0] / np.e))
delta_t_d = optimize.brentq(f, 0, Taxis[-1])
#except:
# delta_t_d = 0.0
# print "dtd",pout
# plt.plot(Taxis,self.acf[centerrind,:])
# plt.plot(Taxis,f(Taxis))
# plt.show()
#try:
pout, errs = ffit.gaussianfit(Faxis[NF // 2:3 * NF // 2],
self.acf[NF // 2:3 * NF // 2,
centercind],
baseline=True)
f = interpolate.interp1d(
Faxis,
ffit.funcgaussian(pout, Faxis, baseline=True) -
(pout[3] + pout[0] / 2))
delta_nu_d = optimize.brentq(f, 0, Faxis[-1])
#except:
# delta_nu_d = 0
#print "dnud",pout,Faxis[-1],dF
#print Faxis
#raise SystemExit
#plt.plot(Faxis,self.acf[:,centercind])
#plt.plot(Faxis,f(Faxis))
#plt.show()
#following Glenn's code and Cordes 1986 (Space Velocities...)
# Errors from finite scintle effect:
bw = self.getBandwidth()
T = self.getTspan()
if delta_t_d == 0.0:
N_d = (1 + eta * bw / delta_nu_d)
elif delta_nu_d == 0.0:
N_d = (1 + eta * T / delta_t_d)
else:
N_d = (1 + eta * bw / delta_nu_d) * (1 + eta * T / delta_t_d)
fse_nu_d = delta_nu_d / (2 * np.log(2) * np.sqrt(N_d)
) #log because of FWHM?
fse_t_d = delta_t_d / (2 * np.sqrt(N_d))
err_nu_d = fse_nu_d
err_t_d = fse_t_d #need to add in fitting errors
if full_output:
return delta_t_d, err_t_d, delta_nu_d, err_nu_d
return delta_t_d, delta_nu_d
# Look for the central peak in the ACF
MIN = np.min(self.acf)
if MIN < 0: #The min value is approximately from a gaussian distribution
MIN = np.abs(MIN)
else:
#center,hist = u.histogram(acf.flatten(),interval=0.001) #relies on 0.001
#MIN = center[np.argmax(hist)]
MIN = u.RMS(self.acf.flatten())
if maxr is None:
rslice = self.acf[centerrind:, centercind]
maxr = np.where(rslice <= MIN)[0][0]
if maxc is None:
cslice = self.acf[centerrind, centercind:]
maxc = np.where(cslice <= MIN)[0][0]
plotacf = self.acf[int(centerrind - plotbound * maxr +
1):int(centerrind + plotbound * maxr),
int(centercind - plotbound * maxc +
1):int(centercind + plotbound * maxc + 1)]
params, pcov = ffit.fitgaussian2d(
plotacf) #pcov already takes into account s_sq issue
SHAPE = np.shape(plotacf)
fit = ffit.gaussian2d(*params)
amplitude, center_x, center_y, width_x, width_y, rotation, baseline = params
paramnames = [
"amplitude", "center_x", "center_y", "width_x", "width_y",
"rotation", "baseline"
]
if pcov is not None:
paramerrors = np.sqrt(np.diagonal(pcov))
else:
paramerrors = np.zeros_like(params)
if self.verbose:
for i, param in enumerate(params):
print("%s: %0.2e+/-%0.2e" %
(paramnames[i], param, paramerrors[i]))
#Solve for scintillation parameters numerically
try:
delta_t_d = (optimize.brentq(
lambda y: fit(SHAPE[0] // 2, y) - baseline - amplitude / np.e,
(SHAPE[1] - 1) // 2, SHAPE[1] * 2) -
(SHAPE[1] - 1) // 2) * dT #FWHM test
if self.verbose:
print("delta_t_d %0.3f %s" % (delta_t_d, self.Tunit))
except ValueError:
if self.verbose:
print("ERROR in delta_t_d")
delta_t_d = SHAPE[1] * dT
if pcov is not None:
err_t_d = paramerrors[3] * dT #assume no rotaton for now
else:
err_t_d = None
try:
delta_nu_d = (optimize.brentq(
lambda x: fit(x, SHAPE[1] // 2) - baseline - amplitude / 2.0,
(SHAPE[0] - 1) // 2, SHAPE[0]) - (SHAPE[0] - 1) // 2) * dF
if self.verbose:
print("delta_nu_d %0.3f %s" % (delta_nu_d, self.Funit))
except ValueError:
if self.verbose:
print("ERROR in delta_nu_d")
delta_nu_d = SHAPE[0] * dF
if pcov is not None:
err_nu_d = paramerrors[4] * dF #assume no rotaton for now
else:
err_nu_d = None
err_rot = paramerrors[5]
#finite-scintle errors
if finitescintleerrors:
bw = self.getBandwidth()
T = self.getTspan()
if delta_t_d == 0.0:
N_d = (1 + eta * bw / delta_nu_d)
elif delta_nu_d == 0.0:
N_d = (1 + eta * T / delta_t_d)
else:
N_d = (1 + eta * bw / delta_nu_d) * (1 + eta * T / delta_t_d)
fse_nu_d = delta_nu_d / (2 * np.log(2) * np.sqrt(N_d)
) #log because of FWHM?
fse_t_d = delta_t_d / (2 * np.sqrt(N_d))
fse_rot = rotation * np.sqrt((fse_nu_d / delta_nu_d)**2 +
(fse_t_d / delta_t_d)**2)
err_nu_d = np.sqrt(err_nu_d**2 + fse_nu_d**2)
err_t_d = np.sqrt(err_t_d**2 + fse_t_d**2)
err_rot = np.sqrt(err_rot**2 + fse_rot**2)
if self.verbose:
f = (dF / dT) * np.tan(rotation)
df = (dF / dT) * np.cos(rotation)**2 * err_rot
print("dnu/dt %0.3e+/-%0.3e %s/%s" %
(f, df, self.Funit, self.Tunit)) #((dF/dT)*np.tan(rotation))
if show or savefig is not None:
fig = plt.figure()
ax = fig.add_subplot(211)
u.imshow(self.data, cmap=cmap)
ax = fig.add_subplot(212)
u.imshow(plotacf, cmap=cmap)
plt.colorbar()
levels = (amplitude * np.array([1.0, 0.5, 1.0 / np.e])) + baseline
levels = (amplitude * np.array([0.5])) + baseline
#print(levels)
ax.contour(fit(*np.indices(plotacf.shape)), levels, colors='k')
#ax.set_xlim(len(xs)-20,len(xs)+20)
#ax.set_ylim(len(ys)-10,len(ys)+10)
if savefig is not None:
plt.savefig(savefig)
if show:
plt.show()
if full_output:
return delta_t_d, err_t_d, delta_nu_d, err_nu_d, rotation, err_rot
return delta_t_d, delta_nu_d, rotation
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 scintillation_parameters(self,
plotbound=1.0,
maxr=None,
maxc=None,
savefig=None,
show=True,
full_output=False):
if self.acf is None:
self.acf2d()
if self.dT is None:
dT = 1
else:
dT = self.dT
if self.dF is None:
dF = 1
else:
dF = self.dF
acfshape = np.shape(self.acf)
centerrind = acfshape[0] // 2
centercind = acfshape[1] // 2
# Look for the central peak in the ACF
MIN = np.min(self.acf)
if MIN < 0: #The min value is approximately from a gaussian distribution
MIN = np.abs(MIN)
else:
#center,hist = u.histogram(acf.flatten(),interval=0.001) #relies on 0.001
#MIN = center[np.argmax(hist)]
MIN = u.RMS(self.acf.flatten())
if maxr is None:
rslice = self.acf[centerrind:, centercind]
maxr = np.where(rslice <= MIN)[0][0]
if maxc is None:
cslice = self.acf[centerrind, centercind:]
maxc = np.where(cslice <= MIN)[0][0]
plotacf = self.acf[centerrind - plotbound * maxr + 1:centerrind +
plotbound * maxr, centercind - plotbound * maxc +
1:centercind + plotbound * maxc + 1]
params, pcov = ffit.fitgaussian2d(
plotacf) #pcov already takes into account s_sq issue
SHAPE = np.shape(plotacf)
fit = ffit.gaussian2d(*params)
amplitude, center_x, center_y, width_x, width_y, rotation, baseline = params
if self.verbose:
paramnames = [
"amplitude", "center_x", "center_y", "width_x", "width_y",
"rotation", "baseline"
]
if pcov is not None:
paramerrors = np.sqrt(np.diagonal(pcov))
else:
paramerrors = np.zeros_like(params)
for i, param in enumerate(params):
print("%s: %0.2e+/-%0.2e" %
(paramnames[i], param, paramerrors[i]))
#Solve for scintillation parameters numerically
try:
delta_t_d = (optimize.brentq(
lambda y: fit(SHAPE[0] // 2, y) - baseline - amplitude / np.e,
(SHAPE[1] - 1) // 2, SHAPE[1] * 2) -
(SHAPE[1] - 1) // 2) * dT #FWHM test
if self.verbose:
print("delta_t_d %0.3f minutes" % delta_t_d)
except ValueError:
if self.verbose:
print("ERROR in delta_t_d")
delta_t_d = SHAPE[1] * dT
if pcov is not None:
err_t_d = paramerrors[3] * dT #assume no rotaton for now
else:
err_t_d = None
try:
delta_nu_d = (optimize.brentq(
lambda x: fit(x, SHAPE[1] // 2) - baseline - amplitude / 2.0,
(SHAPE[0] - 1) // 2, SHAPE[0]) - (SHAPE[0] - 1) // 2) * dF
if self.verbose:
print("delta_nu_d %0.3f MHz" % delta_nu_d)
except ValueError:
if self.verbose:
print("ERROR in delta_nu_d")
delta_nu_d = SHAPE[0] * dF
if pcov is not None:
err_nu_d = paramerrors[4] * dF #assume no rotaton for now
else:
err_nu_d = None
err_rot = paramerrors[5]
if self.verbose:
print("dnu/dt %0.3f MHz/min" %
((dF / dT) * np.tan(rotation))) #((dF/dT)*np.tan(rotation))
if show or savefig is not None:
fig = plt.figure()
ax = fig.add_subplot(211)
u.imshow(self.data)
ax = fig.add_subplot(212)
u.imshow(plotacf)
plt.colorbar()
levels = (amplitude * np.array([1.0, 0.5, 1.0 / np.e])) + baseline
levels = (amplitude * np.array([0.5])) + baseline
print(levels)
ax.contour(fit(*np.indices(plotacf.shape)), levels, colors='k')
#ax.set_xlim(len(xs)-20,len(xs)+20)
#ax.set_ylim(len(ys)-10,len(ys)+10)
if savefig is not None:
plt.savefig(savefig)
if show:
plt.show()
if full_output:
return delta_t_d, err_t_d, delta_nu_d, err_nu_d, rotation, err_rot
return delta_t_d, delta_nu_d, rotation