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 scintillation_parameters(self,plotbound=1.0):
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())
rslice = self.acf[centerrind:,centercind]
maxr = np.where(rslice<=MIN)[0][0]
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)
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.array(list(map(np.sqrt,np.diagonal(pcov)))) #multiply by s_sq!!!!!
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
SHAPE = np.shape(plotacf)
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
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 self.verbose:
print("dnu/dt %0.3f MHz/min" % ((dF/dT)*np.tan(rotation)))#((dF/dT)*np.tan(rotation))
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)
plt.show()
return delta_t_d,delta_nu_d,rotation #need to report errors
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