def run_rmsynth(data,
polyOrd=3,
phiMax_radm2=None,
dPhi_radm2=None,
nSamples=10.0,
weightType="variance",
fitRMSF=False,
noStokesI=False,
phiNoise_radm2=1e6,
nBits=32,
showPlots=False,
debug=False,
verbose=False,
log=print,
units='Jy/beam',
e_num=1):
"""Run RM synthesis on 1D data.
Args:
data (list): Contains frequency and polarization data as either:
[freq_Hz, I, Q, U, dI, dQ, dU]
freq_Hz (array_like): Frequency of each channel in Hz.
I (array_like): Stokes I intensity in each channel.
Q (array_like): Stokes Q intensity in each channel.
U (array_like): Stokes U intensity in each channel.
dI (array_like): Error in Stokes I intensity in each channel.
dQ (array_like): Error in Stokes Q intensity in each channel.
dU (array_like): Error in Stokes U intensity in each channel.
or
[freq_Hz, q, u, dq, du]
freq_Hz (array_like): Frequency of each channel in Hz.
q (array_like): Fractional Stokes Q intensity (Q/I) in each channel.
u (array_like): Fractional Stokes U intensity (U/I) in each channel.
dq (array_like): Error in fractional Stokes Q intensity in each channel.
du (array_like): Error in fractional Stokes U intensity in each channel.
Kwargs:
polyOrd (int): Order of polynomial to fit to Stokes I spectrum.
phiMax_radm2 (float): Maximum absolute Faraday depth (rad/m^2).
dPhi_radm2 (float): Faraday depth channel size (rad/m^2).
nSamples (float): Number of samples across the RMSF.
weightType (str): Can be "variance" or "uniform"
"variance" -- Weight by uncertainty in Q and U.
"uniform" -- Weight uniformly (i.e. with 1s)
fitRMSF (bool): Fit a Gaussian to the RMSF?
noStokesI (bool: Is Stokes I data provided?
phiNoise_radm2 (float): ????
nBits (int): Precision of floating point numbers.
showPlots (bool): Show plots?
debug (bool): Turn on debugging messages & plots?
verbose (bool): Verbosity.
log (function): Which logging function to use.
units (str): Units of data.
Returns:
mDict (dict): Summary of RM synthesis results.
aDict (dict): Data output by RM synthesis.
"""
# Default data types
dtFloat = "float" + str(nBits)
dtComplex = "complex" + str(2 * nBits)
# freq_Hz, I, Q, U, dI, dQ, dU
try:
if verbose: log("> Trying [freq_Hz, I, Q, U, dI, dQ, dU]", end=' ')
(freqArr_Hz, IArr, QArr, UArr, dIArr, dQArr, dUArr) = data
if verbose: log("... success.")
except Exception:
if verbose: log("...failed.")
# freq_Hz, q, u, dq, du
try:
if verbose: log("> Trying [freq_Hz, q, u, dq, du]", end=' ')
(freqArr_Hz, QArr, UArr, dQArr, dUArr) = data
if verbose: log("... success.")
noStokesI = True
except Exception:
if verbose: log("...failed.")
if debug:
log(traceback.format_exc())
sys.exit()
if verbose: log("Successfully read in the Stokes spectra.")
# If no Stokes I present, create a dummy spectrum = unity
if noStokesI:
if verbose: log("Warn: no Stokes I data in use.")
IArr = np.ones_like(QArr)
dIArr = np.zeros_like(QArr)
# Convert to GHz for convenience
freqArr_GHz = freqArr_Hz / 1e9
dQUArr = (dQArr + dUArr) / 2.0
# Fit the Stokes I spectrum and create the fractional spectra
IModArr, qArr, uArr, dqArr, duArr, fitDict = \
create_frac_spectra(freqArr = freqArr_GHz,
IArr = IArr,
QArr = QArr,
UArr = UArr,
dIArr = dIArr,
dQArr = dQArr,
dUArr = dUArr,
polyOrd = polyOrd,
verbose = True,
debug = debug)
# Plot the data and the Stokes I model fit
if showPlots:
if verbose: log("Plotting the input data and spectral index fit.")
freqHirArr_Hz = np.linspace(freqArr_Hz[0], freqArr_Hz[-1], 10000)
IModHirArr = poly5(fitDict["p"])(freqHirArr_Hz / 1e9)
specFig = plt.figure(figsize=(12.0, 8))
plot_Ipqu_spectra_fig(freqArr_Hz=freqArr_Hz,
IArr=IArr,
qArr=qArr,
uArr=uArr,
dIArr=dIArr,
dqArr=dqArr,
duArr=duArr,
freqHirArr_Hz=freqHirArr_Hz,
IModArr=IModHirArr,
fig=specFig,
units=units)
# Use the custom navigation toolbar (does not work on Mac OS X)
# try:
# specFig.canvas.toolbar.pack_forget()
# CustomNavbar(specFig.canvas, specFig.canvas.toolbar.window)
# except Exception:
# pass
# Display the figure
# if not plt.isinteractive():
# specFig.show()
# DEBUG (plot the Q, U and average RMS spectrum)
if debug:
rmsFig = plt.figure(figsize=(12.0, 8))
ax = rmsFig.add_subplot(111)
ax.plot(freqArr_Hz / 1e9,
dQUArr,
marker='o',
color='k',
lw=0.5,
label='rms <QU>')
ax.plot(freqArr_Hz / 1e9,
dQArr,
marker='o',
color='b',
lw=0.5,
label='rms Q')
ax.plot(freqArr_Hz / 1e9,
dUArr,
marker='o',
color='r',
lw=0.5,
label='rms U')
xRange = (np.nanmax(freqArr_Hz) - np.nanmin(freqArr_Hz)) / 1e9
ax.set_xlim(
np.min(freqArr_Hz) / 1e9 - xRange * 0.05,
np.max(freqArr_Hz) / 1e9 + xRange * 0.05)
ax.set_xlabel('$\\nu$ (GHz)')
ax.set_ylabel('RMS ' + units)
ax.set_title("RMS noise in Stokes Q, U and <Q,U> spectra")
# rmsFig.show()
#-------------------------------------------------------------------------#
# Calculate some wavelength parameters
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
dFreq_Hz = np.nanmin(np.abs(np.diff(freqArr_Hz)))
lambdaSqRange_m2 = (np.nanmax(lambdaSqArr_m2) - np.nanmin(lambdaSqArr_m2))
dLambdaSqMin_m2 = np.nanmin(np.abs(np.diff(lambdaSqArr_m2)))
dLambdaSqMax_m2 = np.nanmax(np.abs(np.diff(lambdaSqArr_m2)))
# Set the Faraday depth range
fwhmRMSF_radm2 = 2.0 * m.sqrt(3.0) / lambdaSqRange_m2
if dPhi_radm2 is None:
dPhi_radm2 = fwhmRMSF_radm2 / nSamples
if phiMax_radm2 is None:
phiMax_radm2 = m.sqrt(3.0) / dLambdaSqMax_m2
phiMax_radm2 = max(phiMax_radm2, 600.0) # Force the minimum phiMax
# Faraday depth sampling. Zero always centred on middle channel
nChanRM = int(round(abs((phiMax_radm2 - 0.0) / dPhi_radm2)) * 2.0 + 1.0)
startPhi_radm2 = -(nChanRM - 1.0) * dPhi_radm2 / 2.0
stopPhi_radm2 = +(nChanRM - 1.0) * dPhi_radm2 / 2.0
phiArr_radm2 = np.linspace(startPhi_radm2, stopPhi_radm2, nChanRM)
phiArr_radm2 = phiArr_radm2.astype(dtFloat)
if verbose:
log("PhiArr = %.2f to %.2f by %.2f (%d chans)." %
(phiArr_radm2[0], phiArr_radm2[-1], float(dPhi_radm2), nChanRM))
# Calculate the weighting as 1/sigma^2 or all 1s (uniform)
if weightType == "variance":
weightArr = 1.0 / np.power(dQUArr, 2.0)
else:
weightType = "uniform"
weightArr = np.ones(freqArr_Hz.shape, dtype=dtFloat)
if verbose: log("Weight type is '%s'." % weightType)
startTime = time.time()
# Perform RM-synthesis on the spectrum
dirtyFDF, lam0Sq_m2, mylist = do_rmsynth_planes(
dataQ=qArr,
dataU=uArr,
lambdaSqArr_m2=lambdaSqArr_m2,
phiArr_radm2=phiArr_radm2,
weightArr=weightArr,
nBits=nBits,
verbose=verbose,
log=log,
e_num=e_num)
# Calculate the Rotation Measure Spread Function
RMSFArr, phi2Arr_radm2, fwhmRMSFArr, fitStatArr = \
get_rmsf_planes(lambdaSqArr_m2 = lambdaSqArr_m2,
phiArr_radm2 = phiArr_radm2,
weightArr = weightArr,
mskArr = ~np.isfinite(qArr),
lam0Sq_m2 = lam0Sq_m2,
double = True,
fitRMSF = fitRMSF,
fitRMSFreal = False,
nBits = nBits,
verbose = verbose,
log = log)
fwhmRMSF = float(fwhmRMSFArr)
# ALTERNATE RM-SYNTHESIS CODE --------------------------------------------#
#dirtyFDF, [phi2Arr_radm2, RMSFArr], lam0Sq_m2, fwhmRMSF = \
# do_rmsynth(qArr, uArr, lambdaSqArr_m2, phiArr_radm2, weightArr)
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
if verbose: log("> RM-synthesis completed in %.2f seconds." % cputime)
# Determine the Stokes I value at lam0Sq_m2 from the Stokes I model
# Multiply the dirty FDF by Ifreq0 to recover the PI
freq0_Hz = C / m.sqrt(lam0Sq_m2)
Ifreq0 = poly5(fitDict["p"])(freq0_Hz / 1e9)
dirtyFDF *= (Ifreq0
) # FDF is in fracpol units initially, convert back to flux
# Calculate the theoretical noise in the FDF !!Old formula only works for wariance weights!
weightArr = np.where(np.isnan(weightArr), 0.0, weightArr)
dFDFth = np.sqrt(
np.sum(weightArr**2 * np.nan_to_num(dQUArr)**2) /
(np.sum(weightArr))**2)
# Measure the parameters of the dirty FDF
# Use the theoretical noise to calculate uncertainties
mDict = measure_FDF_parms(FDF=dirtyFDF,
phiArr=phiArr_radm2,
fwhmRMSF=fwhmRMSF,
dFDF=dFDFth,
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=lam0Sq_m2)
mDict["Ifreq0"] = toscalar(Ifreq0)
mDict["polyCoeffs"] = ",".join([str(x) for x in fitDict["p"]])
mDict["IfitStat"] = fitDict["fitStatus"]
mDict["IfitChiSqRed"] = fitDict["chiSqRed"]
mDict["lam0Sq_m2"] = toscalar(lam0Sq_m2)
mDict["freq0_Hz"] = toscalar(freq0_Hz)
mDict["fwhmRMSF"] = toscalar(fwhmRMSF)
mDict["dQU"] = toscalar(nanmedian(dQUArr))
mDict["dFDFth"] = toscalar(dFDFth)
mDict["units"] = units
mDict['dQUArr'] = dQUArr
if fitDict["fitStatus"] >= 128:
log("WARNING: Stokes I model contains negative values!")
elif fitDict["fitStatus"] >= 64:
log("Caution: Stokes I model has low signal-to-noise.")
#Add information on nature of channels:
good_channels = np.where(np.logical_and(weightArr != 0,
np.isfinite(qArr)))[0]
mDict["min_freq"] = float(np.min(freqArr_Hz[good_channels]))
mDict["max_freq"] = float(np.max(freqArr_Hz[good_channels]))
mDict["N_channels"] = good_channels.size
mDict["median_channel_width"] = float(np.median(np.diff(freqArr_Hz)))
# Measure the complexity of the q and u spectra
mDict["fracPol"] = mDict["ampPeakPIfit"] / (Ifreq0)
mD, pD = measure_qu_complexity(freqArr_Hz=freqArr_Hz,
qArr=qArr,
uArr=uArr,
dqArr=dqArr,
duArr=duArr,
fracPol=mDict["fracPol"],
psi0_deg=mDict["polAngle0Fit_deg"],
RM_radm2=mDict["phiPeakPIfit_rm2"])
mDict.update(mD)
# Debugging plots for spectral complexity measure
if debug:
tmpFig = plot_complexity_fig(xArr=pD["xArrQ"],
qArr=pD["yArrQ"],
dqArr=pD["dyArrQ"],
sigmaAddqArr=pD["sigmaAddArrQ"],
chiSqRedqArr=pD["chiSqRedArrQ"],
probqArr=pD["probArrQ"],
uArr=pD["yArrU"],
duArr=pD["dyArrU"],
sigmaAdduArr=pD["sigmaAddArrU"],
chiSqReduArr=pD["chiSqRedArrU"],
probuArr=pD["probArrU"],
mDict=mDict)
tmpFig.show()
#add array dictionary
aDict = dict()
aDict["phiArr_radm2"] = phiArr_radm2
aDict["phi2Arr_radm2"] = phi2Arr_radm2
aDict["RMSFArr"] = RMSFArr
aDict["freqArr_Hz"] = freqArr_Hz
aDict["weightArr"] = weightArr
aDict["dirtyFDF"] = dirtyFDF
if verbose:
# Print the results to the screen
log()
log('-' * 80)
log('RESULTS:\n')
log('FWHM RMSF = %.4g rad/m^2' % (mDict["fwhmRMSF"]))
log('Pol Angle = %.4g (+/-%.4g) deg' %
(mDict["polAngleFit_deg"], mDict["dPolAngleFit_deg"]))
log('Pol Angle 0 = %.4g (+/-%.4g) deg' %
(mDict["polAngle0Fit_deg"], mDict["dPolAngle0Fit_deg"]))
log('Peak FD = %.4g (+/-%.4g) rad/m^2' %
(mDict["phiPeakPIfit_rm2"], mDict["dPhiPeakPIfit_rm2"]))
log('freq0_GHz = %.4g ' % (mDict["freq0_Hz"] / 1e9))
log('I freq0 = %.4g %s' % (mDict["Ifreq0"], units))
log('Peak PI = %.4g (+/-%.4g) %s' %
(mDict["ampPeakPIfit"], mDict["dAmpPeakPIfit"], units))
log('QU Noise = %.4g %s' % (mDict["dQU"], units))
log('FDF Noise (theory) = %.4g %s' % (mDict["dFDFth"], units))
log('FDF Noise (Corrected MAD) = %.4g %s' %
(mDict["dFDFcorMAD"], units))
log('FDF Noise (rms) = %.4g %s' % (mDict["dFDFrms"], units))
log('FDF SNR = %.4g ' % (mDict["snrPIfit"]))
log('sigma_add(q) = %.4g (+%.4g, -%.4g)' %
(mDict["sigmaAddQ"], mDict["dSigmaAddPlusQ"],
mDict["dSigmaAddMinusQ"]))
log('sigma_add(u) = %.4g (+%.4g, -%.4g)' %
(mDict["sigmaAddU"], mDict["dSigmaAddPlusU"],
mDict["dSigmaAddMinusU"]))
log()
log('-' * 80)
myfig = plotmylist(mylist)
plt.show()
myfig.show()
# Plot the RM Spread Function and dirty FDF
if showPlots:
fdfFig = plt.figure(figsize=(12.0, 8))
plot_rmsf_fdf_fig(phiArr=phiArr_radm2,
FDF=dirtyFDF,
phi2Arr=phi2Arr_radm2,
RMSFArr=RMSFArr,
fwhmRMSF=fwhmRMSF,
vLine=mDict["phiPeakPIfit_rm2"],
fig=fdfFig,
units=units)
# Use the custom navigation toolbar
# try:
# fdfFig.canvas.toolbar.pack_forget()
# CustomNavbar(fdfFig.canvas, fdfFig.canvas.toolbar.window)
# except Exception:
# pass
# Display the figure
# fdfFig.show()
# Pause if plotting enabled
if showPlots or debug:
plt.show()
# #if verbose: print "Press <RETURN> to exit ...",
# input()
return mDict, aDict, mylist
def run_rmclean(mDictS,
aDict,
cutoff,
maxIter=1000,
gain=0.1,
nBits=32,
showPlots=False,
verbose=False,
log=print):
"""Run RM-CLEAN on a complex FDF spectrum given a RMSF.
Args:
mDictS (dict): Summary of RM synthesis results.
aDict (dict): Data output by RM synthesis.
cutoff (float): CLEAN cutoff in flux units
Kwargs:
maxIter (int): Maximum number of CLEAN iterations per pixel.
gain (float): CLEAN loop gain.
nBits (int): Precision of floating point numbers.
showPlots (bool): Show plots?
verbose (bool): Verbosity.
log (function): Which logging function to use.
Returns:
mDict (dict): Summary of RMCLEAN results.
arrdict (dict): Data output by RMCLEAN.
"""
phiArr_radm2 = aDict["phiArr_radm2"]
freqArr_Hz = aDict["freqArr_Hz"]
weightArr = aDict["weightArr"]
dirtyFDF = aDict["dirtyFDF"]
phi2Arr_radm2 = aDict["phi2Arr_radm2"]
RMSFArr = aDict["RMSFArr"]
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
# If the cutoff is negative, assume it is a sigma level
if verbose:
log("Expected RMS noise = %.4g flux units" % (mDictS["dFDFth"]))
if cutoff < 0:
if verbose: log("Using a sigma cutoff of %.1f." % (-1 * cutoff))
cutoff = -1 * mDictS["dFDFth"] * cutoff
if verbose: log("Absolute value = %.3g" % cutoff)
else:
if verbose:
log("Using an absolute cutoff of %.3g (%.1f x expected RMS)." %
(cutoff, cutoff / mDictS["dFDFth"]))
startTime = time.time()
# Perform RM-clean on the spectrum
cleanFDF, ccArr, iterCountArr, residFDF = \
do_rmclean_hogbom(dirtyFDF = dirtyFDF,
phiArr_radm2 = phiArr_radm2,
RMSFArr = RMSFArr,
phi2Arr_radm2 = phi2Arr_radm2,
fwhmRMSFArr = np.array(mDictS["fwhmRMSF"]),
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
verbose = verbose,
doPlots = showPlots)
# ALTERNATIVE RM_CLEAN CODE ----------------------------------------------#
'''
cleanFDF, ccArr, fwhmRMSF, iterCount = \
do_rmclean(dirtyFDF = dirtyFDF,
phiArr = phiArr_radm2,
lamSqArr = lamSqArr_m2,
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
weight = weightArr,
RMSFArr = RMSFArr,
RMSFphiArr = phi2Arr_radm2,
fwhmRMSF = mDictS["fwhmRMSF"],
doPlots = True)
'''
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
if verbose: log("> RM-CLEAN completed in %.4f seconds." % cputime)
# Measure the parameters of the deconvolved FDF
mDict = measure_FDF_parms(
FDF=cleanFDF,
phiArr=phiArr_radm2,
fwhmRMSF=mDictS["fwhmRMSF"],
#dFDF = mDictS["dFDFth"],
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=mDictS["lam0Sq_m2"])
mDict["cleanCutoff"] = cutoff
mDict["nIter"] = int(iterCountArr)
# Measure the complexity of the clean component spectrum
mDict["mom2CCFDF"] = measure_fdf_complexity(phiArr=phiArr_radm2, FDF=ccArr)
#Calculating observed errors (based on dFDFcorMAD)
mDict["dPhiObserved_rm2"] = mDict["dPhiPeakPIfit_rm2"] * mDict[
"dFDFcorMAD"] / mDictS["dFDFth"]
mDict["dAmpObserved"] = mDict["dFDFcorMAD"]
mDict["dPolAngleFitObserved_deg"] = mDict["dPolAngleFit_deg"] * mDict[
"dFDFcorMAD"] / mDictS["dFDFth"]
nChansGood = np.sum(np.where(lambdaSqArr_m2 == lambdaSqArr_m2, 1.0, 0.0))
varLamSqArr_m2 = (np.sum(lambdaSqArr_m2**2.0) -
np.sum(lambdaSqArr_m2)**2.0 / nChansGood) / (nChansGood -
1)
mDict["dPolAngle0ChanObserved_deg"] = \
np.degrees(np.sqrt( mDict["dFDFcorMAD"]**2.0 / (4.0*(nChansGood-2.0)*mDict["ampPeakPIfit"]**2.0) *
((nChansGood-1)/nChansGood + mDictS["lam0Sq_m2"]**2.0/varLamSqArr_m2) ))
if verbose:
# Print the results to the screen
log()
log('-' * 80)
log('RESULTS:\n')
log('FWHM RMSF = %.4g rad/m^2' % (mDictS["fwhmRMSF"]))
log('Pol Angle = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict["polAngleFit_deg"], mDict["dPolAngleFitObserved_deg"],
mDict["dPolAngleFit_deg"]))
log('Pol Angle 0 = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict["polAngle0Fit_deg"], mDict["dPolAngle0ChanObserved_deg"],
mDict["dPolAngle0Fit_deg"]))
log('Peak FD = %.4g (+/-%.4g observed, +- %.4g theoretical) rad/m^2' %
(mDict["phiPeakPIfit_rm2"], mDict["dPhiObserved_rm2"],
mDict["dPhiPeakPIfit_rm2"]))
log('freq0_GHz = %.4g ' % (mDictS["freq0_Hz"] / 1e9))
log('I freq0 = %.4g %s' % (mDictS["Ifreq0"], mDictS["units"]))
log('Peak PI = %.4g (+/-%.4g observed, +- %.4g theoretical) %s' %
(mDict["ampPeakPIfit"], mDict["dAmpObserved"],
mDict["dAmpPeakPIfit"], mDictS["units"]))
log('QU Noise = %.4g %s' % (mDictS["dQU"], mDictS["units"]))
log('FDF Noise (theory) = %.4g %s' %
(mDictS["dFDFth"], mDictS["units"]))
log('FDF Noise (Corrected MAD) = %.4g %s' %
(mDict["dFDFcorMAD"], mDictS["units"]))
log('FDF Noise (rms) = %.4g %s' %
(mDict["dFDFrms"], mDictS["units"]))
log('FDF SNR = %.4g ' % (mDict["snrPIfit"]))
log()
log('-' * 80)
# Pause to display the figure
if showPlots:
plot_clean_spec(phiArr_radm2, dirtyFDF, cleanFDF, ccArr, residFDF,
cutoff, mDictS["units"])
print("Press <RETURN> to exit ...", end=' ')
input()
#add array dictionary
arrdict = dict()
arrdict["phiArr_radm2"] = phiArr_radm2
arrdict["freqArr_Hz"] = freqArr_Hz
arrdict["cleanFDF"] = cleanFDF
arrdict["ccArr"] = ccArr
arrdict["iterCountArr"] = iterCountArr
arrdict["residFDF"] = residFDF
return mDict, arrdict
def pixelwise_peak_fitting(FDF,
phiArr,
fwhmRMSF,
lamSqArr_m2,
lam0Sq,
product_list,
noiseArr=None,
stokesIcube=None):
"""
Performs the 1D FDF peak fitting used in RMsynth/RMclean_1D, pixelwise on
all pixels in a 3D FDF cube.
Inputs:
FDF: FDF cube (3D array). This is assumed to be in astropy axis ordering
(Phi, dec, ra)
phiArr: (1D) array of phi values
fwhmRMSF: 2D array of RMSF FWHM values
lamSqArr_m2: 1D array of channel lambda^2 values.
lam0Sq: scalar value for lambda^2_0, the reference wavelength squared.
product_list: list containing the names of the fitting products to save.
dFDF: 2D array of theoretical noise values. If not supplied, the
peak fitting will default to using the measured noise.
Outputs: dictionary of 2D maps, 1 per fit output
"""
#FDF: output by synth3d or clean3d
#phiArr: can be generated from FDF cube
#fwhm: 2D map produced synth3D
#dFDFth: not currently produced (default mode not to input noise!)
# If not present, measure_FDF_parms uses the corMAD noise.
#
#lamSqArr is only needed for computing errors in derotated angles
# This could be compressed to a map or single value from RMsynth?
#lam0Sq is necessary for de-rotation
map_size = FDF.shape[1:]
#Create pixel location arrays:
xarr, yarr = np.meshgrid(range(map_size[0]), range(map_size[1]))
xarr = xarr.ravel()
yarr = yarr.ravel()
#Create empty maps:
map_dict = {}
for parameter in product_list:
map_dict[parameter] = np.zeros(map_size)
freqArr_Hz = C / np.sqrt(lamSqArr_m2)
freq0_Hz = C / np.sqrt(lam0Sq)
if stokesIcube is not None:
idx = np.abs(freqArr_Hz - freq0_Hz).argmin()
if freqArr_Hz[idx] < freq0_Hz:
Ifreq0Arr = interp_images(stokesIcube[idx, :, :],
stokesIcube[idx + 1, :, :],
f=0.5)
elif freqArr_Hz[idx] > freq0_Hz:
Ifreq0Arr = interp_images(stokesIcube[idx - 1, :, :],
stokesIcube[idx, :, :],
f=0.5)
else:
Ifreq0Arr = stokesIcube[idx, :, :]
else:
Ifreq0Arr = np.ones(map_size)
stokesIcube = np.ones((freqArr_Hz.size, map_size[0], map_size[1]))
#compute weights if needed:
if noiseArr is not None:
weightArr = 1.0 / np.power(noiseArr, 2.0)
weightArr = np.where(np.isnan(weightArr), 0.0, weightArr)
dFDF = Ifreq0Arr * np.sqrt(
np.sum(weightArr**2 * np.nan_to_num(noiseArr)**2) /
(np.sum(weightArr))**2)
else:
weightArr = np.ones(lamSqArr_m2.shape, dtype=np.float32)
dFDF = None
#Run fitting pixel-wise:
progress(40, 0)
for i in range(xarr.size):
FDF_pix = FDF[:, xarr[i], yarr[i]]
fwhmRMSF_pix = fwhmRMSF[xarr[i], yarr[i]]
if type(dFDF) == type(None):
dFDF_pix = None
else:
dFDF_pix = dFDF[xarr[i], yarr[i]]
try:
mDict = measure_FDF_parms(FDF_pix,
phiArr,
fwhmRMSF_pix,
dFDF=dFDF_pix,
lamSqArr_m2=lamSqArr_m2,
lam0Sq=lam0Sq,
snrDoBiasCorrect=5.0)
#Add keywords not included by the above function:
mDict['lam0Sq_m2'] = lam0Sq
mDict['freq0_Hz'] = freq0_Hz
mDict['fwhmRMSF'] = fwhmRMSF_pix
mDict['Ifreq0'] = Ifreq0Arr[xarr[i], yarr[i]]
mDict['fracPol'] = mDict["ampPeakPIfit"] / mDict['Ifreq0']
mDict["min_freq"] = float(np.min(freqArr_Hz))
mDict["max_freq"] = float(np.max(freqArr_Hz))
mDict["N_channels"] = lamSqArr_m2.size
mDict["median_channel_width"] = float(
np.median(np.diff(freqArr_Hz)))
if dFDF_pix is not None:
mDict['dFDFth'] = dFDF_pix
else:
mDict['dFDFth'] = np.nan
for parameter in product_list:
map_dict[parameter][xarr[i], yarr[i]] = mDict[parameter]
except:
for parameter in product_list:
map_dict[parameter][xarr[i], yarr[i]] = np.nan
if i % 100 == 0:
progress(40, i / xarr.size * 100)
return map_dict
def run_rmclean(mDictS,
aDict,
cutoff,
maxIter=1000,
gain=0.1,
prefixOut="",
outDir="",
nBits=32,
showPlots=False,
doAnimate=False,
verbose=False,
log=print):
"""
Run RM-CLEAN on a complex FDF spectrum given a RMSF.
"""
phiArr_radm2 = aDict["phiArr_radm2"]
freqArr_Hz = aDict["freqArr_Hz"]
weightArr = aDict["weightArr"]
dirtyFDF = aDict["dirtyFDF"]
phi2Arr_radm2 = aDict["phi2Arr_radm2"]
RMSFArr = aDict["RMSFArr"]
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
# If the cutoff is negative, assume it is a sigma level
if verbose:
log("Expected RMS noise = %.4g mJy/beam/rmsf" %
(mDictS["dFDFth_Jybm"] * 1e3))
if cutoff < 0:
log("Using a sigma cutoff of %.1f." % (-1 * cutoff))
cutoff = -1 * mDictS["dFDFth_Jybm"] * cutoff
log("Absolute value = %.3g" % cutoff)
else:
log("Using an absolute cutoff of %.3g (%.1f x expected RMS)." %
(cutoff, cutoff / mDictS["dFDFth_Jybm"]))
startTime = time.time()
# Perform RM-clean on the spectrum
cleanFDF, ccArr, iterCountArr = \
do_rmclean_hogbom(dirtyFDF = dirtyFDF,
phiArr_radm2 = phiArr_radm2,
RMSFArr = RMSFArr,
phi2Arr_radm2 = phi2Arr_radm2,
fwhmRMSFArr = np.array(mDictS["fwhmRMSF"]),
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
verbose = verbose,
doPlots = showPlots,
doAnimate = doAnimate)
# ALTERNATIVE RM_CLEAN CODE ----------------------------------------------#
'''
cleanFDF, ccArr, fwhmRMSF, iterCount = \
do_rmclean(dirtyFDF = dirtyFDF,
phiArr = phiArr_radm2,
lamSqArr = lamSqArr_m2,
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
weight = weightArr,
RMSFArr = RMSFArr,
RMSFphiArr = phi2Arr_radm2,
fwhmRMSF = mDictS["fwhmRMSF"],
doPlots = True)
'''
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
log("> RM-CLEAN completed in %.4f seconds." % cputime)
# Measure the parameters of the deconvolved FDF
mDict = measure_FDF_parms(
FDF=cleanFDF,
phiArr=phiArr_radm2,
fwhmRMSF=mDictS["fwhmRMSF"],
#dFDF = mDictS["dFDFth_Jybm"],
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=mDictS["lam0Sq_m2"])
mDict["cleanCutoff"] = cutoff
mDict["nIter"] = int(iterCountArr)
# Measure the complexity of the clean component spectrum
mDict["mom2CCFDF"] = measure_fdf_complexity(phiArr=phiArr_radm2, FDF=ccArr)
#Calculating observed errors (based on dFDFcorMAD)
mDict["dPhiObserved_rm2"] = mDict["dPhiPeakPIfit_rm2"] * mDict[
"dFDFcorMAD_Jybm"] / mDictS["dFDFth_Jybm"]
mDict["dAmpObserved_Jybm"] = mDict["dFDFcorMAD_Jybm"]
mDict["dPolAngleFitObserved_deg"] = mDict["dPolAngleFit_deg"] * mDict[
"dFDFcorMAD_Jybm"] / mDictS["dFDFth_Jybm"]
nChansGood = np.sum(np.where(lambdaSqArr_m2 == lambdaSqArr_m2, 1.0, 0.0))
varLamSqArr_m2 = (np.sum(lambdaSqArr_m2**2.0) -
np.sum(lambdaSqArr_m2)**2.0 / nChansGood) / (nChansGood -
1)
mDict["dPolAngle0ChanObserved_deg"] = \
np.degrees(np.sqrt( mDict["dFDFcorMAD_Jybm"]**2.0 / (4.0*(nChansGood-2.0)*mDict["ampPeakPIfit_Jybm"]**2.0) *
((nChansGood-1)/nChansGood + mDictS["lam0Sq_m2"]**2.0/varLamSqArr_m2) ))
# Save the deconvolved FDF and CC model to ASCII files
log("Saving the clean FDF and component model to ASCII files.")
outFile = prefixOut + "_FDFclean.dat"
log("> %s" % outFile)
np.savetxt(outFile, list(zip(phiArr_radm2, cleanFDF.real, cleanFDF.imag)))
outFile = prefixOut + "_FDFmodel.dat"
log("> %s" % outFile)
np.savetxt(outFile, list(zip(phiArr_radm2, ccArr.real, ccArr.imag)))
# Save the RM-clean measurements to a "key=value" text file
log("Saving the measurements on the FDF in 'key=val' and JSON formats.")
outFile = prefixOut + "_RMclean.dat"
log("> %s" % outFile)
FH = open(outFile, "w")
for k, v in mDict.items():
FH.write("%s=%s\n" % (k, v))
FH.close()
outFile = prefixOut + "_RMclean.json"
log("> %s" % outFile)
json.dump(mDict, open(outFile, "w"))
# Print the results to the screen
log()
log('-' * 80)
log('RESULTS:\n')
log('FWHM RMSF = %.4g rad/m^2' % (mDictS["fwhmRMSF"]))
log('Pol Angle = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict["polAngleFit_deg"], mDict["dPolAngleFitObserved_deg"],
mDict["dPolAngleFit_deg"]))
log('Pol Angle 0 = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict["polAngle0Fit_deg"], mDict["dPolAngle0ChanObserved_deg"],
mDict["dPolAngle0Fit_deg"]))
log('Peak FD = %.4g (+/-%.4g observed, +- %.4g theoretical) rad/m^2' %
(mDict["phiPeakPIfit_rm2"], mDict["dPhiObserved_rm2"],
mDict["dPhiPeakPIfit_rm2"]))
log('freq0_GHz = %.4g ' % (mDictS["freq0_Hz"] / 1e9))
log('I freq0 = %.4g mJy/beam' % (mDictS["Ifreq0_mJybm"]))
log('Peak PI = %.4g (+/-%.4g observed, +- %.4g theoretical) mJy/beam' %
(mDict["ampPeakPIfit_Jybm"] * 1e3, mDict["dAmpObserved_Jybm"] * 1e3,
mDict["dAmpPeakPIfit_Jybm"] * 1e3))
log('QU Noise = %.4g mJy/beam' % (mDictS["dQU_Jybm"] * 1e3))
log('FDF Noise (theory) = %.4g mJy/beam' % (mDictS["dFDFth_Jybm"] * 1e3))
log('FDF Noise (Corrected MAD) = %.4g mJy/beam' %
(mDict["dFDFcorMAD_Jybm"] * 1e3))
log('FDF Noise (rms) = %.4g mJy/beam' % (mDict["dFDFrms_Jybm"] * 1e3))
log('FDF SNR = %.4g ' % (mDict["snrPIfit"]))
log()
log('-' * 80)
# Pause to display the figure
if showPlots or doAnimate:
print("Press <RETURN> to exit ...", end=' ')
input()
return mDict
def run_rmsynth(dataFile,
polyOrd=3,
phiMax_radm2=None,
dPhi_radm2=None,
nSamples=10.0,
weightType="variance",
fitRMSF=False,
noStokesI=False,
phiNoise_radm2=1e6,
nBits=32,
showPlots=False,
debug=False):
"""
Read the I, Q & U data from the ASCII file and run RM-synthesis.
"""
# Default data types
dtFloat = "float" + str(nBits)
dtComplex = "complex" + str(2 * nBits)
# Output prefix is derived from the input file name
prefixOut, ext = os.path.splitext(dataFile)
# Read the data-file. Format=space-delimited, comments="#".
print "Reading the data file '%s':" % dataFile
# freq_Hz, I_Jy, Q_Jy, U_Jy, dI_Jy, dQ_Jy, dU_Jy
try:
print "> Trying [freq_Hz, I_Jy, Q_Jy, U_Jy, dI_Jy, dQ_Jy, dU_Jy]",
(freqArr_Hz, IArr_Jy, QArr_Jy, UArr_Jy,
dIArr_Jy, dQArr_Jy, dUArr_Jy) = \
np.loadtxt(dataFile, unpack=True, dtype=dtFloat)
print "... success."
except Exception:
print "...failed."
# freq_Hz, q_Jy, u_Jy, dq_Jy, du_Jy
try:
print "> Trying [freq_Hz, q_Jy, u_Jy, dq_Jy, du_Jy]",
(freqArr_Hz, QArr_Jy, UArr_Jy, dQArr_Jy, dUArr_Jy) = \
np.loadtxt(dataFile, unpack=True, dtype=dtFloat)
print "... success."
noStokesI = True
except Exception:
print "...failed."
if debug:
print traceback.format_exc()
sys.exit()
print "Successfully read in the Stokes spectra."
# If no Stokes I present, create a dummy spectrum = unity
if noStokesI:
print "Warn: no Stokes I data in use."
IArr_Jy = np.ones_like(QArr_Jy)
dIArr_Jy = np.zeros_like(QArr_Jy)
# Convert to GHz and mJy for convenience
freqArr_GHz = freqArr_Hz / 1e9
IArr_mJy = IArr_Jy * 1e3
QArr_mJy = QArr_Jy * 1e3
UArr_mJy = UArr_Jy * 1e3
dIArr_mJy = dIArr_Jy * 1e3
dQArr_mJy = dQArr_Jy * 1e3
dUArr_mJy = dUArr_Jy * 1e3
dQUArr_mJy = (dQArr_mJy + dUArr_mJy) / 2.0
dQUArr_Jy = dQUArr_mJy / 1e3
# Fit the Stokes I spectrum and create the fractional spectra
IModArr, qArr, uArr, dqArr, duArr, fitDict = \
create_frac_spectra(freqArr = freqArr_GHz,
IArr = IArr_mJy,
QArr = QArr_mJy,
UArr = UArr_mJy,
dIArr = dIArr_mJy,
dQArr = dQArr_mJy,
dUArr = dUArr_mJy,
polyOrd = polyOrd,
verbose = True,
debug = debug)
# Plot the data and the Stokes I model fit
if showPlots:
print "Plotting the input data and spectral index fit."
freqHirArr_Hz = np.linspace(freqArr_Hz[0], freqArr_Hz[-1], 10000)
IModHirArr_mJy = poly5(fitDict["p"])(freqHirArr_Hz / 1e9)
specFig = plt.figure(figsize=(12.0, 8))
plot_Ipqu_spectra_fig(freqArr_Hz=freqArr_Hz,
IArr_mJy=IArr_mJy,
qArr=qArr,
uArr=uArr,
dIArr_mJy=dIArr_mJy,
dqArr=dqArr,
duArr=duArr,
freqHirArr_Hz=freqHirArr_Hz,
IModArr_mJy=IModHirArr_mJy,
fig=specFig)
# Use the custom navigation toolbar (does not work on Mac OS X)
try:
specFig.canvas.toolbar.pack_forget()
CustomNavbar(specFig.canvas, specFig.canvas.toolbar.window)
except Exception:
pass
# Display the figure
specFig.show()
# DEBUG (plot the Q, U and average RMS spectrum)
if debug:
rmsFig = plt.figure(figsize=(12.0, 8))
ax = rmsFig.add_subplot(111)
ax.plot(freqArr_Hz / 1e9,
dQUArr_mJy,
marker='o',
color='k',
lw=0.5,
label='rms <QU>')
ax.plot(freqArr_Hz / 1e9,
dQArr_mJy,
marker='o',
color='b',
lw=0.5,
label='rms Q')
ax.plot(freqArr_Hz / 1e9,
dUArr_mJy,
marker='o',
color='r',
lw=0.5,
label='rms U')
xRange = (np.nanmax(freqArr_Hz) - np.nanmin(freqArr_Hz)) / 1e9
ax.set_xlim(
np.min(freqArr_Hz) / 1e9 - xRange * 0.05,
np.max(freqArr_Hz) / 1e9 + xRange * 0.05)
ax.set_xlabel('$\\nu$ (GHz)')
ax.set_ylabel('RMS (mJy bm$^{-1}$)')
ax.set_title("RMS noise in Stokes Q, U and <Q,U> spectra")
rmsFig.show()
#-------------------------------------------------------------------------#
# Calculate some wavelength parameters
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
dFreq_Hz = np.nanmin(np.abs(np.diff(freqArr_Hz)))
lambdaSqRange_m2 = (np.nanmax(lambdaSqArr_m2) - np.nanmin(lambdaSqArr_m2))
dLambdaSqMin_m2 = np.nanmin(np.abs(np.diff(lambdaSqArr_m2)))
dLambdaSqMax_m2 = np.nanmax(np.abs(np.diff(lambdaSqArr_m2)))
# Set the Faraday depth range
fwhmRMSF_radm2 = 2.0 * m.sqrt(3.0) / lambdaSqRange_m2
if dPhi_radm2 is None:
dPhi_radm2 = fwhmRMSF_radm2 / nSamples
if phiMax_radm2 is None:
phiMax_radm2 = m.sqrt(3.0) / dLambdaSqMax_m2
phiMax_radm2 = max(phiMax_radm2, 600.0) # Force the minimum phiMax
# Faraday depth sampling. Zero always centred on middle channel
nChanRM = round(abs((phiMax_radm2 - 0.0) / dPhi_radm2)) * 2.0 + 1.0
startPhi_radm2 = -(nChanRM - 1.0) * dPhi_radm2 / 2.0
stopPhi_radm2 = +(nChanRM - 1.0) * dPhi_radm2 / 2.0
phiArr_radm2 = np.linspace(startPhi_radm2, stopPhi_radm2, nChanRM)
phiArr_radm2 = phiArr_radm2.astype(dtFloat)
print "PhiArr = %.2f to %.2f by %.2f (%d chans)." % (
phiArr_radm2[0], phiArr_radm2[-1], float(dPhi_radm2), nChanRM)
# Calculate the weighting as 1/sigma^2 or all 1s (natural)
if weightType == "variance":
weightArr = 1.0 / np.power(dQUArr_mJy, 2.0)
else:
weightType = "natural"
weightArr = np.ones(freqArr_Hz.shape, dtype=dtFloat)
print "Weight type is '%s'." % weightType
startTime = time.time()
# Perform RM-synthesis on the spectrum
dirtyFDF, lam0Sq_m2 = do_rmsynth_planes(dataQ=qArr,
dataU=uArr,
lambdaSqArr_m2=lambdaSqArr_m2,
phiArr_radm2=phiArr_radm2,
weightArr=weightArr,
nBits=nBits,
verbose=True)
# Calculate the Rotation Measure Spread Function
RMSFArr, phi2Arr_radm2, fwhmRMSFArr, fitStatArr = \
get_rmsf_planes(lambdaSqArr_m2 = lambdaSqArr_m2,
phiArr_radm2 = phiArr_radm2,
weightArr = weightArr,
mskArr = np.isnan(qArr),
lam0Sq_m2 = lam0Sq_m2,
double = True,
fitRMSF = fitRMSF,
fitRMSFreal = False,
nBits = nBits,
verbose = True)
fwhmRMSF = float(fwhmRMSFArr)
# ALTERNATE RM-SYNTHESIS CODE --------------------------------------------#
#dirtyFDF, [phi2Arr_radm2, RMSFArr], lam0Sq_m2, fwhmRMSF = \
# do_rmsynth(qArr, uArr, lambdaSqArr_m2, phiArr_radm2, weightArr)
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
print "> RM-synthesis completed in %.2f seconds." % cputime
# Determine the Stokes I value at lam0Sq_m2 from the Stokes I model
# Multiply the dirty FDF by Ifreq0 to recover the PI in Jy
freq0_Hz = C / m.sqrt(lam0Sq_m2)
Ifreq0_mJybm = poly5(fitDict["p"])(freq0_Hz / 1e9)
dirtyFDF *= (Ifreq0_mJybm / 1e3) # FDF is in Jy
# Calculate the theoretical noise in the FDF
dFDFth_Jybm = np.sqrt(1. / np.sum(1. / dQUArr_Jy**2.))
# Measure the parameters of the dirty FDF
# Use the theoretical noise to calculate uncertainties
mDict = measure_FDF_parms(FDF=dirtyFDF,
phiArr=phiArr_radm2,
fwhmRMSF=fwhmRMSF,
dFDF=dFDFth_Jybm,
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=lam0Sq_m2)
mDict["Ifreq0_mJybm"] = toscalar(Ifreq0_mJybm)
mDict["polyCoeffs"] = ",".join([str(x) for x in fitDict["p"]])
mDict["IfitStat"] = fitDict["fitStatus"]
mDict["IfitChiSqRed"] = fitDict["chiSqRed"]
mDict["lam0Sq_m2"] = toscalar(lam0Sq_m2)
mDict["freq0_Hz"] = toscalar(freq0_Hz)
mDict["fwhmRMSF"] = toscalar(fwhmRMSF)
mDict["dQU_Jybm"] = toscalar(nanmedian(dQUArr_Jy))
mDict["dFDFth_Jybm"] = toscalar(dFDFth_Jybm)
# Measure the complexity of the q and u spectra
mDict["fracPol"] = mDict["ampPeakPIfit_Jybm"] / (Ifreq0_mJybm / 1e3)
mD, pD = measure_qu_complexity(freqArr_Hz=freqArr_Hz,
qArr=qArr,
uArr=uArr,
dqArr=dqArr,
duArr=duArr,
fracPol=mDict["fracPol"],
psi0_deg=mDict["polAngle0Fit_deg"],
RM_radm2=mDict["phiPeakPIfit_rm2"])
mDict.update(mD)
# Debugging plots for spectral complexity measure
if debug:
tmpFig = plot_complexity_fig(xArr=pD["xArrQ"],
qArr=pD["yArrQ"],
dqArr=pD["dyArrQ"],
sigmaAddqArr=pD["sigmaAddArrQ"],
chiSqRedqArr=pD["chiSqRedArrQ"],
probqArr=pD["probArrQ"],
uArr=pD["yArrU"],
duArr=pD["dyArrU"],
sigmaAdduArr=pD["sigmaAddArrU"],
chiSqReduArr=pD["chiSqRedArrU"],
probuArr=pD["probArrU"],
mDict=mDict)
tmpFig.show()
# Save the dirty FDF, RMSF and weight array to ASCII files
print "Saving the dirty FDF, RMSF weight arrays to ASCII files."
outFile = prefixOut + "_FDFdirty.dat"
print "> %s" % outFile
np.savetxt(outFile, zip(phiArr_radm2, dirtyFDF.real, dirtyFDF.imag))
outFile = prefixOut + "_RMSF.dat"
print "> %s" % outFile
np.savetxt(outFile, zip(phi2Arr_radm2, RMSFArr.real, RMSFArr.imag))
outFile = prefixOut + "_weight.dat"
print "> %s" % outFile
np.savetxt(outFile, zip(freqArr_Hz, weightArr))
# Save the measurements to a "key=value" text file
print "Saving the measurements on the FDF in 'key=val' and JSON formats."
outFile = prefixOut + "_RMsynth.dat"
print "> %s" % outFile
FH = open(outFile, "w")
for k, v in mDict.iteritems():
FH.write("%s=%s\n" % (k, v))
FH.close()
outFile = prefixOut + "_RMsynth.json"
print "> %s" % outFile
json.dump(dict(mDict), open(outFile, "w"))
# Print the results to the screen
print
print '-' * 80
print 'RESULTS:\n'
print 'FWHM RMSF = %.4g rad/m^2' % (mDict["fwhmRMSF"])
print 'Pol Angle = %.4g (+/-%.4g) deg' % (mDict["polAngleFit_deg"],
mDict["dPolAngleFit_deg"])
print 'Pol Angle 0 = %.4g (+/-%.4g) deg' % (mDict["polAngle0Fit_deg"],
mDict["dPolAngle0Fit_deg"])
print 'Peak FD = %.4g (+/-%.4g) rad/m^2' % (mDict["phiPeakPIfit_rm2"],
mDict["dPhiPeakPIfit_rm2"])
print 'freq0_GHz = %.4g ' % (mDict["freq0_Hz"] / 1e9)
print 'I freq0 = %.4g mJy/beam' % (mDict["Ifreq0_mJybm"])
print 'Peak PI = %.4g (+/-%.4g) mJy/beam' % (
mDict["ampPeakPIfit_Jybm"] * 1e3, mDict["dAmpPeakPIfit_Jybm"] * 1e3)
print 'QU Noise = %.4g mJy/beam' % (mDict["dQU_Jybm"] * 1e3)
print 'FDF Noise (theory) = %.4g mJy/beam' % (mDict["dFDFth_Jybm"] * 1e3)
print 'FDF SNR = %.4g ' % (mDict["snrPIfit"])
print 'sigma_add(q) = %.4g (+%.4g, -%.4g)' % (
mDict["sigmaAddQ"], mDict["dSigmaAddPlusQ"], mDict["dSigmaAddMinusQ"])
print 'sigma_add(u) = %.4g (+%.4g, -%.4g)' % (
mDict["sigmaAddU"], mDict["dSigmaAddPlusU"], mDict["dSigmaAddMinusU"])
print
print '-' * 80
# Plot the RM Spread Function and dirty FDF
if showPlots:
fdfFig = plt.figure(figsize=(12.0, 8))
plot_rmsf_fdf_fig(phiArr=phiArr_radm2,
FDF=dirtyFDF,
phi2Arr=phi2Arr_radm2,
RMSFArr=RMSFArr,
fwhmRMSF=fwhmRMSF,
vLine=mDict["phiPeakPIfit_rm2"],
fig=fdfFig)
# Use the custom navigation toolbar
try:
fdfFig.canvas.toolbar.pack_forget()
CustomNavbar(fdfFig.canvas, fdfFig.canvas.toolbar.window)
except Exception:
pass
# Display the figure
fdfFig.show()
# Pause if plotting enabled
if showPlots or debug:
print "Press <RETURN> to exit ...",
raw_input()
def run_rmclean(mDict,
aDict,
cutoff,
maxIter=1000,
gain=0.1,
nBits=32,
showPlots=False,
prefixOut="",
verbose=False,
log=print,
saveFigures=False,
window=None):
"""Run RM-CLEAN on a complex FDF spectrum given a RMSF.
Args:
mDict (dict): Summary of RM synthesis results.
aDict (dict): Data output by RM synthesis.
cutoff (float): CLEAN cutoff in flux units (positive)
or as multiple of theoretical noise (negative)
(i.e. -8 = clean to 8 sigma threshold)
Kwargs:
maxIter (int): Maximum number of CLEAN iterations per pixel.
gain (float): CLEAN loop gain.
nBits (int): Precision of floating point numbers.
showPlots (bool): Show plots?
verbose (bool): Verbosity.
log (function): Which logging function to use.
window (float): Threshold for deeper windowed cleaning
Returns:
mDict_cl (dict): Summary of RMCLEAN results.
aDict_cl (dict): Data output by RMCLEAN.
"""
phiArr_radm2 = aDict["phiArr_radm2"]
freqArr_Hz = aDict["freqArr_Hz"]
weightArr = aDict["weightArr"]
dirtyFDF = aDict["dirtyFDF"]
phi2Arr_radm2 = aDict["phi2Arr_radm2"]
RMSFArr = aDict["RMSFArr"]
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
# If the cutoff is negative, assume it is a sigma level
if verbose: log("Expected RMS noise = %.4g flux units" % (mDict["dFDFth"]))
if cutoff < 0:
if verbose: log("Using a sigma cutoff of %.1f." % (-1 * cutoff))
cutoff = -1 * mDict["dFDFth"] * cutoff
if verbose: log("Absolute value = %.3g" % cutoff)
else:
if verbose:
log("Using an absolute cutoff of %.3g (%.1f x expected RMS)." %
(cutoff, cutoff / mDict["dFDFth"]))
if window is None:
window = np.nan
else:
if window < 0:
if verbose:
log("Using a window sigma cutoff of %.1f." % (-1 * window))
window = -1 * mDict["dFDFth"] * window
if verbose: log("Absolute value = %.3g" % window)
else:
if verbose:
log("Using an absolute window cutoff of %.3g (%.1f x expected RMS)."
% (window, window / mDict["dFDFth"]))
startTime = time.time()
# Perform RM-clean on the spectrum
cleanFDF, ccArr, iterCountArr, residFDF = \
do_rmclean_hogbom(dirtyFDF = dirtyFDF,
phiArr_radm2 = phiArr_radm2,
RMSFArr = RMSFArr,
phi2Arr_radm2 = phi2Arr_radm2,
fwhmRMSFArr = np.array(mDict["fwhmRMSF"]),
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
verbose = verbose,
doPlots = showPlots,
window = window
)
# ALTERNATIVE RM_CLEAN CODE ----------------------------------------------#
'''
cleanFDF, ccArr, fwhmRMSF, iterCount = \
do_rmclean(dirtyFDF = dirtyFDF,
phiArr = phiArr_radm2,
lamSqArr = lamSqArr_m2,
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
weight = weightArr,
RMSFArr = RMSFArr,
RMSFphiArr = phi2Arr_radm2,
fwhmRMSF = mDict["fwhmRMSF"],
doPlots = True)
'''
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
if verbose: log("> RM-CLEAN completed in %.4f seconds." % cputime)
# Measure the parameters of the deconvolved FDF
mDict_cl = measure_FDF_parms(FDF=cleanFDF,
phiArr=phiArr_radm2,
fwhmRMSF=mDict["fwhmRMSF"],
dFDF=mDict["dFDFth"],
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=mDict["lam0Sq_m2"])
mDict_cl["cleanCutoff"] = cutoff
mDict_cl["nIter"] = int(iterCountArr)
# Measure the complexity of the clean component spectrum
mDict_cl["mom2CCFDF"] = measure_fdf_complexity(phiArr=phiArr_radm2,
FDF=ccArr)
#Calculating observed errors (based on dFDFcorMAD)
mDict_cl["dPhiObserved_rm2"] = mDict_cl["dPhiPeakPIfit_rm2"] * mDict_cl[
"dFDFcorMAD"] / mDict["dFDFth"]
mDict_cl["dAmpObserved"] = mDict_cl["dFDFcorMAD"]
mDict_cl["dPolAngleFitObserved_deg"] = mDict_cl[
"dPolAngleFit_deg"] * mDict_cl["dFDFcorMAD"] / mDict["dFDFth"]
mDict_cl["dPolAngleFit0Observed_deg"] = mDict_cl[
"dPolAngle0Fit_deg"] * mDict_cl["dFDFcorMAD"] / mDict["dFDFth"]
if verbose:
# Print the results to the screen
log()
log('-' * 80)
log('RESULTS:\n')
log('FWHM RMSF = %.4g rad/m^2' % (mDict["fwhmRMSF"]))
log('Pol Angle = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict_cl["polAngleFit_deg"], mDict_cl["dPolAngleFitObserved_deg"],
mDict_cl["dPolAngleFit_deg"]))
log('Pol Angle 0 = %.4g (+/-%.4g observed, +- %.4g theoretical) deg' %
(mDict_cl["polAngle0Fit_deg"],
mDict_cl["dPolAngleFit0Observed_deg"],
mDict_cl["dPolAngle0Fit_deg"]))
log('Peak FD = %.4g (+/-%.4g observed, +- %.4g theoretical) rad/m^2' %
(mDict_cl["phiPeakPIfit_rm2"], mDict_cl["dPhiObserved_rm2"],
mDict_cl["dPhiPeakPIfit_rm2"]))
log('freq0_GHz = %.4g ' % (mDict["freq0_Hz"] / 1e9))
log('I freq0 = %.4g %s' % (mDict["Ifreq0"], mDict["units"]))
log('Peak PI = %.4g (+/-%.4g observed, +- %.4g theoretical) %s' %
(mDict_cl["ampPeakPIfit"], mDict_cl["dAmpObserved"],
mDict_cl["dAmpPeakPIfit"], mDict["units"]))
log('QU Noise = %.4g %s' % (mDict["dQU"], mDict["units"]))
log('FDF Noise (theory) = %.4g %s' %
(mDict["dFDFth"], mDict["units"]))
log('FDF Noise (Corrected MAD) = %.4g %s' %
(mDict_cl["dFDFcorMAD"], mDict["units"]))
log('FDF Noise (rms) = %.4g %s' %
(mDict_cl["dFDFrms"], mDict["units"]))
log('FDF SNR = %.4g ' % (mDict_cl["snrPIfit"]))
log()
log('-' * 80)
# Pause to display the figure
if showPlots or saveFigures:
fdfFig = plot_clean_spec(phiArr_radm2, dirtyFDF, cleanFDF, ccArr,
residFDF, cutoff, window, mDict["units"])
# Pause if plotting enabled
if showPlots:
plt.show()
if saveFigures:
if verbose: print("Saving CLEAN FDF plot:")
outFilePlot = prefixOut + "_cleanFDF-plots.pdf"
if verbose: print("> " + outFilePlot)
fdfFig.savefig(outFilePlot, bbox_inches='tight')
# print("Press <RETURN> to exit ...", end=' ')
# input()
#add array dictionary
aDict_cl = dict()
aDict_cl["phiArr_radm2"] = phiArr_radm2
aDict_cl["freqArr_Hz"] = freqArr_Hz
aDict_cl["cleanFDF"] = cleanFDF
aDict_cl["ccArr"] = ccArr
aDict_cl["iterCountArr"] = iterCountArr
aDict_cl["residFDF"] = residFDF
return mDict_cl, aDict_cl
def run_rmsynth(data,
polyOrd=3,
phiMax_radm2=None,
dPhi_radm2=None,
nSamples=10.0,
weightType="variance",
fitRMSF=False,
noStokesI=False,
phiNoise_radm2=1e6,
nBits=32,
showPlots=False,
debug=False,
verbose=False,
log=print):
"""
Read the I, Q & U data and run RM-synthesis.
"""
# Default data types
dtFloat = "float" + str(nBits)
dtComplex = "complex" + str(2 * nBits)
# freq_Hz, I_Jy, Q_Jy, U_Jy, dI_Jy, dQ_Jy, dU_Jy
try:
if verbose:
log("> Trying [freq_Hz, I_Jy, Q_Jy, U_Jy, dI_Jy, dQ_Jy, dU_Jy]",
end=' ')
(freqArr_Hz, IArr_Jy, QArr_Jy, UArr_Jy, dIArr_Jy, dQArr_Jy,
dUArr_Jy) = data
if verbose: log("... success.")
except Exception:
if verbose: log("...failed.")
# freq_Hz, q_Jy, u_Jy, dq_Jy, du_Jy
try:
if verbose:
log("> Trying [freq_Hz, q_Jy, u_Jy, dq_Jy, du_Jy]", end=' ')
(freqArr_Hz, QArr_Jy, UArr_Jy, dQArr_Jy, dUArr_Jy) = data
if verbose: log("... success.")
noStokesI = True
except Exception:
if verbose: log("...failed.")
if debug:
log(traceback.format_exc())
sys.exit()
if verbose: log("Successfully read in the Stokes spectra.")
# If no Stokes I present, create a dummy spectrum = unity
if noStokesI:
log("Warn: no Stokes I data in use.")
IArr_Jy = np.ones_like(QArr_Jy)
dIArr_Jy = np.zeros_like(QArr_Jy)
# Convert to GHz and mJy for convenience
freqArr_GHz = freqArr_Hz / 1e9
IArr_mJy = IArr_Jy * 1e3
QArr_mJy = QArr_Jy * 1e3
UArr_mJy = UArr_Jy * 1e3
dIArr_mJy = dIArr_Jy * 1e3
dQArr_mJy = dQArr_Jy * 1e3
dUArr_mJy = dUArr_Jy * 1e3
dQUArr_mJy = (dQArr_mJy + dUArr_mJy) / 2.0
dQUArr_Jy = dQUArr_mJy / 1e3
# Fit the Stokes I spectrum and create the fractional spectra
IModArr, qArr, uArr, dqArr, duArr, fitDict = \
create_frac_spectra(freqArr = freqArr_GHz,
IArr = IArr_mJy,
QArr = QArr_mJy,
UArr = UArr_mJy,
dIArr = dIArr_mJy,
dQArr = dQArr_mJy,
dUArr = dUArr_mJy,
polyOrd = polyOrd,
verbose = True,
debug = debug)
# Plot the data and the Stokes I model fit
if showPlots:
if verbose: log("Plotting the input data and spectral index fit.")
freqHirArr_Hz = np.linspace(freqArr_Hz[0], freqArr_Hz[-1], 10000)
IModHirArr_mJy = poly5(fitDict["p"])(freqHirArr_Hz / 1e9)
specFig = plt.figure(figsize=(12.0, 8))
plot_Ipqu_spectra_fig(freqArr_Hz=freqArr_Hz,
IArr_mJy=IArr_mJy,
qArr=qArr,
uArr=uArr,
dIArr_mJy=dIArr_mJy,
dqArr=dqArr,
duArr=duArr,
freqHirArr_Hz=freqHirArr_Hz,
IModArr_mJy=IModHirArr_mJy,
fig=specFig)
# Use the custom navigation toolbar (does not work on Mac OS X)
# try:
# specFig.canvas.toolbar.pack_forget()
# CustomNavbar(specFig.canvas, specFig.canvas.toolbar.window)
# except Exception:
# pass
# Display the figure
# if not plt.isinteractive():
# specFig.show()
# DEBUG (plot the Q, U and average RMS spectrum)
if debug:
rmsFig = plt.figure(figsize=(12.0, 8))
ax = rmsFig.add_subplot(111)
ax.plot(freqArr_Hz / 1e9,
dQUArr_mJy,
marker='o',
color='k',
lw=0.5,
label='rms <QU>')
ax.plot(freqArr_Hz / 1e9,
dQArr_mJy,
marker='o',
color='b',
lw=0.5,
label='rms Q')
ax.plot(freqArr_Hz / 1e9,
dUArr_mJy,
marker='o',
color='r',
lw=0.5,
label='rms U')
xRange = (np.nanmax(freqArr_Hz) - np.nanmin(freqArr_Hz)) / 1e9
ax.set_xlim(
np.min(freqArr_Hz) / 1e9 - xRange * 0.05,
np.max(freqArr_Hz) / 1e9 + xRange * 0.05)
ax.set_xlabel('$\\nu$ (GHz)')
ax.set_ylabel('RMS (mJy bm$^{-1}$)')
ax.set_title("RMS noise in Stokes Q, U and <Q,U> spectra")
# rmsFig.show()
#-------------------------------------------------------------------------#
# Calculate some wavelength parameters
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
dFreq_Hz = np.nanmin(np.abs(np.diff(freqArr_Hz)))
lambdaSqRange_m2 = (np.nanmax(lambdaSqArr_m2) - np.nanmin(lambdaSqArr_m2))
dLambdaSqMin_m2 = np.nanmin(np.abs(np.diff(lambdaSqArr_m2)))
dLambdaSqMax_m2 = np.nanmax(np.abs(np.diff(lambdaSqArr_m2)))
# Set the Faraday depth range
fwhmRMSF_radm2 = 2.0 * m.sqrt(3.0) / lambdaSqRange_m2
if dPhi_radm2 is None:
dPhi_radm2 = fwhmRMSF_radm2 / nSamples
if phiMax_radm2 is None:
phiMax_radm2 = m.sqrt(3.0) / dLambdaSqMax_m2
phiMax_radm2 = max(phiMax_radm2, 600.0) # Force the minimum phiMax
# Faraday depth sampling. Zero always centred on middle channel
nChanRM = int(round(abs((phiMax_radm2 - 0.0) / dPhi_radm2)) * 2.0 + 1.0)
startPhi_radm2 = -(nChanRM - 1.0) * dPhi_radm2 / 2.0
stopPhi_radm2 = +(nChanRM - 1.0) * dPhi_radm2 / 2.0
phiArr_radm2 = np.linspace(startPhi_radm2, stopPhi_radm2, nChanRM)
phiArr_radm2 = phiArr_radm2.astype(dtFloat)
if verbose:
log("PhiArr = %.2f to %.2f by %.2f (%d chans)." %
(phiArr_radm2[0], phiArr_radm2[-1], float(dPhi_radm2), nChanRM))
# Calculate the weighting as 1/sigma^2 or all 1s (uniform)
if weightType == "variance":
weightArr = 1.0 / np.power(dQUArr_mJy, 2.0)
else:
weightType = "uniform"
weightArr = np.ones(freqArr_Hz.shape, dtype=dtFloat)
if verbose: log("Weight type is '%s'." % weightType)
startTime = time.time()
# Perform RM-synthesis on the spectrum
dirtyFDF, lam0Sq_m2 = do_rmsynth_planes(dataQ=qArr,
dataU=uArr,
lambdaSqArr_m2=lambdaSqArr_m2,
phiArr_radm2=phiArr_radm2,
weightArr=weightArr,
nBits=nBits,
verbose=True,
log=log)
# Calculate the Rotation Measure Spread Function
RMSFArr, phi2Arr_radm2, fwhmRMSFArr, fitStatArr = \
get_rmsf_planes(lambdaSqArr_m2 = lambdaSqArr_m2,
phiArr_radm2 = phiArr_radm2,
weightArr = weightArr,
mskArr = ~np.isfinite(qArr),
lam0Sq_m2 = lam0Sq_m2,
double = True,
fitRMSF = fitRMSF,
fitRMSFreal = False,
nBits = nBits,
verbose = True,
log = log)
fwhmRMSF = float(fwhmRMSFArr)
# ALTERNATE RM-SYNTHESIS CODE --------------------------------------------#
#dirtyFDF, [phi2Arr_radm2, RMSFArr], lam0Sq_m2, fwhmRMSF = \
# do_rmsynth(qArr, uArr, lambdaSqArr_m2, phiArr_radm2, weightArr)
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
if verbose: log("> RM-synthesis completed in %.2f seconds." % cputime)
# Determine the Stokes I value at lam0Sq_m2 from the Stokes I model
# Multiply the dirty FDF by Ifreq0 to recover the PI in Jy
freq0_Hz = C / m.sqrt(lam0Sq_m2)
Ifreq0_mJybm = poly5(fitDict["p"])(freq0_Hz / 1e9)
dirtyFDF *= (Ifreq0_mJybm / 1e3) # FDF is in Jy
# Calculate the theoretical noise in the FDF !!Old formula only works for wariance weights!
#dFDFth_Jybm = np.sqrt(1./np.sum(1./dQUArr_Jy**2.))
dFDFth_Jybm = np.sqrt(
np.sum(weightArr**2 * dQUArr_Jy**2) / (np.sum(weightArr))**2)
# Measure the parameters of the dirty FDF
# Use the theoretical noise to calculate uncertainties
mDict = measure_FDF_parms(FDF=dirtyFDF,
phiArr=phiArr_radm2,
fwhmRMSF=fwhmRMSF,
dFDF=dFDFth_Jybm,
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=lam0Sq_m2)
mDict["Ifreq0_mJybm"] = toscalar(Ifreq0_mJybm)
mDict["polyCoeffs"] = ",".join([str(x) for x in fitDict["p"]])
mDict["IfitStat"] = fitDict["fitStatus"]
mDict["IfitChiSqRed"] = fitDict["chiSqRed"]
mDict["lam0Sq_m2"] = toscalar(lam0Sq_m2)
mDict["freq0_Hz"] = toscalar(freq0_Hz)
mDict["fwhmRMSF"] = toscalar(fwhmRMSF)
mDict["dQU_Jybm"] = toscalar(nanmedian(dQUArr_Jy))
mDict["dFDFth_Jybm"] = toscalar(dFDFth_Jybm)
if mDict['phiPeakPIfit_rm2'] == None:
log('Peak is at edge of RM spectrum! Peak fitting failed!\n')
log('Rerunning with Phi_max twice as large.')
#The following code re-runs everything with higher phiMax,
#Then overwrite the appropriate variables so as to continue on without
#interuption.
mDict, aDict = run_rmsynth(data=data,
polyOrd=polyOrd,
phiMax_radm2=phiMax_radm2 * 2,
dPhi_radm2=dPhi_radm2,
nSamples=nSamples,
weightType=weightType,
fitRMSF=fitRMSF,
noStokesI=noStokesI,
nBits=nBits,
showPlots=False,
debug=debug,
verbose=verbose)
phiArr_radm2 = aDict["phiArr_radm2"]
phi2Arr_radm2 = aDict["phi2Arr_radm2"]
RMSFArr = aDict["RMSFArr"]
freqArr_Hz = aDict["freqArr_Hz"]
weightArr = aDict["weightArr"]
dirtyFDF = aDict["dirtyFDF"]
# Measure the complexity of the q and u spectra
mDict["fracPol"] = mDict["ampPeakPIfit_Jybm"] / (Ifreq0_mJybm / 1e3)
mD, pD = measure_qu_complexity(freqArr_Hz=freqArr_Hz,
qArr=qArr,
uArr=uArr,
dqArr=dqArr,
duArr=duArr,
fracPol=mDict["fracPol"],
psi0_deg=mDict["polAngle0Fit_deg"],
RM_radm2=mDict["phiPeakPIfit_rm2"])
mDict.update(mD)
# Debugging plots for spectral complexity measure
if debug:
tmpFig = plot_complexity_fig(xArr=pD["xArrQ"],
qArr=pD["yArrQ"],
dqArr=pD["dyArrQ"],
sigmaAddqArr=pD["sigmaAddArrQ"],
chiSqRedqArr=pD["chiSqRedArrQ"],
probqArr=pD["probArrQ"],
uArr=pD["yArrU"],
duArr=pD["dyArrU"],
sigmaAdduArr=pD["sigmaAddArrU"],
chiSqReduArr=pD["chiSqRedArrU"],
probuArr=pD["probArrU"],
mDict=mDict)
tmpFig.show()
#add array dictionary
aDict = dict()
aDict["phiArr_radm2"] = phiArr_radm2
aDict["phi2Arr_radm2"] = phi2Arr_radm2
aDict["RMSFArr"] = RMSFArr
aDict["freqArr_Hz"] = freqArr_Hz
aDict["weightArr"] = weightArr
aDict["dirtyFDF"] = dirtyFDF
if verbose:
# Print the results to the screen
log()
log('-' * 80)
log('RESULTS:\n')
log('FWHM RMSF = %.4g rad/m^2' % (mDict["fwhmRMSF"]))
log('Pol Angle = %.4g (+/-%.4g) deg' %
(mDict["polAngleFit_deg"], mDict["dPolAngleFit_deg"]))
log('Pol Angle 0 = %.4g (+/-%.4g) deg' %
(mDict["polAngle0Fit_deg"], mDict["dPolAngle0Fit_deg"]))
log('Peak FD = %.4g (+/-%.4g) rad/m^2' %
(mDict["phiPeakPIfit_rm2"], mDict["dPhiPeakPIfit_rm2"]))
log('freq0_GHz = %.4g ' % (mDict["freq0_Hz"] / 1e9))
log('I freq0 = %.4g mJy/beam' % (mDict["Ifreq0_mJybm"]))
log('Peak PI = %.4g (+/-%.4g) mJy/beam' %
(mDict["ampPeakPIfit_Jybm"] * 1e3,
mDict["dAmpPeakPIfit_Jybm"] * 1e3))
log('QU Noise = %.4g mJy/beam' % (mDict["dQU_Jybm"] * 1e3))
log('FDF Noise (theory) = %.4g mJy/beam' %
(mDict["dFDFth_Jybm"] * 1e3))
log('FDF Noise (Corrected MAD) = %.4g mJy/beam' %
(mDict["dFDFcorMAD_Jybm"] * 1e3))
log('FDF Noise (rms) = %.4g mJy/beam' %
(mDict["dFDFrms_Jybm"] * 1e3))
log('FDF SNR = %.4g ' % (mDict["snrPIfit"]))
log('sigma_add(q) = %.4g (+%.4g, -%.4g)' %
(mDict["sigmaAddQ"], mDict["dSigmaAddPlusQ"],
mDict["dSigmaAddMinusQ"]))
log('sigma_add(u) = %.4g (+%.4g, -%.4g)' %
(mDict["sigmaAddU"], mDict["dSigmaAddPlusU"],
mDict["dSigmaAddMinusU"]))
log()
log('-' * 80)
# Plot the RM Spread Function and dirty FDF
if showPlots:
fdfFig = plt.figure(figsize=(12.0, 8))
plot_rmsf_fdf_fig(phiArr=phiArr_radm2,
FDF=dirtyFDF,
phi2Arr=phi2Arr_radm2,
RMSFArr=RMSFArr,
fwhmRMSF=fwhmRMSF,
vLine=mDict["phiPeakPIfit_rm2"],
fig=fdfFig)
# Use the custom navigation toolbar
# try:
# fdfFig.canvas.toolbar.pack_forget()
# CustomNavbar(fdfFig.canvas, fdfFig.canvas.toolbar.window)
# except Exception:
# pass
# Display the figure
# fdfFig.show()
# Pause if plotting enabled
if showPlots or debug:
plt.show()
# #if verbose: print "Press <RETURN> to exit ...",
# input()
return mDict, aDict
def RM_synth(stokes,
weight=True, # weighting needs more testing. Fails on certain events
upchan=False,
RM_lim=None,
nSamples=None,
normed=False,
noise_type='theory',
diagnostic_plots=False,
cutoff=None):
""" Performs rotation measure synthesis to extract Faraday Dispersion Function and RM measurement
Parameters
__________
stokes : list (freq,I,Q,U,V,dI,dQ,dU,dV)
Stokes params.
weight : Bool.
Freq. channel std., used as to create array of weights for FDF
band_lo, band_hi : float
bottom and top freq. band limits of burst.
upchan: Bool
If true, sets nSamples=3
RM_lim: float (optional)
limits in Phi space to calculate the FDF
nSamples: int (optional)
sampling density in Phi space
diagnostic_plots: Bool.
outputs diagnostic plots of FDF
Returns
_______
FDF params, (phi, FDF_arr) : list, array_like
(RM,RM_err,PA,PA_err), FDF_arr
"""
freqArr=stokes[0].copy()
IArr=stokes[1].copy()
QArr=stokes[2].copy()
UArr=stokes[3].copy()
VArr=stokes[4].copy()
dIArr=stokes[5].copy()
dQArr=stokes[6].copy()
dUArr=stokes[7].copy()
dVArr=stokes[8].copy()
freqArr_Hz=freqArr*1e6
lamArr_m=phys_const.speed_of_light/freqArr_Hz # convert to wavelength in m
lambdaSqArr_m2=lamArr_m**2
if normed is True:
dQArr=IArr*np.sqrt((dQArr/QArr)**2+(dIArr/IArr)**2)
dUArr=IArr*np.sqrt((dUArr/UArr)**2+(dIArr/IArr)**2)
QArr/=IArr
UArr/=IArr
dQUArr = (dQArr + dUArr)/2.0
if weight is True:
weightArr = 1.0 / np.power(dQUArr, 2.0)
else:
weightArr = np.ones(freqArr_Hz.shape, dtype=float)
dFDFth = np.sqrt( np.sum(weightArr**2 * dQUArr**2) / (np.sum(weightArr))**2 ) # check this equation!!!
if nSamples is None:
if upchan:
nSamples=3 # sampling resolution of the FDF.
else:
nSamples=10
lambdaSqRange_m2 = (np.nanmax(lambdaSqArr_m2) - np.nanmin(lambdaSqArr_m2) )
fwhmRMSF_radm2 = 2.0 * np.sqrt(3.0) / lambdaSqRange_m2
# dLambdaSqMin_m2 = np.nanmin(np.abs(np.diff(lambdaSqArr_m2)))
# dLambdaSqMax_m2 = np.nanmax(np.abs(np.diff(lambdaSqArr_m2)))
dLambdaSqMed_m2 = np.nanmedian(np.abs(np.diff(lambdaSqArr_m2)))
dPhi_radm2 = fwhmRMSF_radm2 / nSamples
# phiMax_radm2 = np.sqrt(3.0) / dLambdaSqMax_m2
phiMax_radm2 = np.sqrt(3.0) / dLambdaSqMed_m2 # sets the RM limit that can be probed based on intrachannel depolarization
phiMax_radm2 = max(phiMax_radm2,600) # Force the minimum phiMax
if RM_lim is None:
# Faraday depth sampling. Zero always centred on middle channel
nChanRM = int(round(abs((phiMax_radm2 - 0.0) / dPhi_radm2)) * 2.0 + 1.0)
startPhi_radm2 = - (nChanRM-1.0) * dPhi_radm2 / 2.0
stopPhi_radm2 = + (nChanRM-1.0) * dPhi_radm2 / 2.0
phiArr_radm2 = np.linspace(startPhi_radm2, stopPhi_radm2, nChanRM)
else:
startPhi_radm2 = RM_lim[0]
stopPhi_radm2 = RM_lim[1]
nChanRM = int(round(abs((((stopPhi_radm2-startPhi_radm2)//2) - 0.0) / dPhi_radm2)) * 2.0 + 1.0)
phiArr_radm2 = np.linspace(startPhi_radm2, stopPhi_radm2, nChanRM)
phiArr_radm2 = phiArr_radm2.astype(np.float)
### constructing FDF ###
dirtyFDF, lam0Sq_m2 = do_rmsynth_planes(
QArr,
UArr,
lambdaSqArr_m2,
phiArr_radm2)
RMSFArr, phi2Arr_radm2, fwhmRMSFArr, fitStatArr = get_rmsf_planes(
lambdaSqArr_m2 = lambdaSqArr_m2,
phiArr_radm2 = phiArr_radm2,
weightArr=weightArr,
mskArr=None,
lam0Sq_m2=lam0Sq_m2,
double = True) # routine needed for RM-cleaning
FDF, lam0Sq_m2 = do_rmsynth_planes(
QArr,
UArr,
lambdaSqArr_m2,
phiArr_radm2,
weightArr=weightArr,
lam0Sq_m2=None,
nBits=32,
verbose=False)
FDF_max=np.argmax(abs(FDF))
FDF_med=np.median(abs(FDF))
dFDFobs=np.median(abs(abs(FDF)-FDF_med)) / np.sqrt(np.pi/2) #MADFM definition of noise
# dFDF_obs=np.nanstd(abs(FDF)) #std. definition of noise
if noise_type is 'observed':
FDF_snr=abs((abs(FDF)-FDF_med)/dFDFobs)/2
if noise_type is 'theory':
FDF_snr=abs((abs(FDF)-FDF_med)/dFDFth)/2
mDict = measure_FDF_parms(FDF = dirtyFDF,
phiArr = phiArr_radm2,
fwhmRMSF = fwhmRMSF_radm2,
dFDF = dFDFth, #FDF_noise
lamSqArr_m2 = lambdaSqArr_m2,
lam0Sq = lam0Sq_m2)
RM_radm2_fit=mDict["phiPeakPIfit_rm2"]
dRM_radm2_fit=mDict["dPhiPeakPIfit_rm2"]
RM_radm2=phiArr_radm2[FDF_max]
dRM_radm2=fwhmRMSF_radm2/(2*FDF_snr.max())
polAngle0Fit_deg=mDict["polAngle0Fit_deg"]
dPolAngle0Fit_deg=mDict["dPolAngle0Fit_deg"] * np.sqrt(freqArr.size) # np.sqrt(freqArr.size) term corrects for band-average noise
if cutoff is None:
if diagnostic_plots:
fig, ax = plt.subplots(2,1, figsize=(20,10))
plt.subplots_adjust(left=0.1, bottom=0.1, right=0.99, top=0.95, wspace=0)
ax[0].set_title('Faraday Dispersion Function')
ax[0].plot(phiArr_radm2,FDF_snr)
ax[0].set_xlim([phiArr_radm2.min(), phiArr_radm2.max()])
ax[1].plot(phiArr_radm2,FDF_snr)
# ax[1].axvline(RM_radm2, color='k', ls=':', label=r'RM=%.2f $\pm$ %0.2f rad/m$^2$' %(RM_radm2,dRM_radm2))
ax[1].set_xlim(phiArr_radm2[FDF_max]-300,phiArr_radm2[FDF_max]+300)
ax[1].set_xlabel('$\phi$ [rad/m$^2$]')
fig.text(0.03, 0.5, 'Polarized Intensity [S/N]', va='center', rotation='vertical')
# plt.legend(fontsize=20)
# plt.tight_layout()
if isinstance(diagnostic_plots, bool):
plt.show()
else:
plot_name = "FDF.png"
plt.savefig(os.path.join(diagnostic_plots, plot_name))
plt.close("all")
return (RM_radm2_fit,RM_radm2,dRM_radm2_fit,dRM_radm2,polAngle0Fit_deg,dPolAngle0Fit_deg),(phiArr_radm2,FDF_snr)
else:
if noise_type is 'observed':
cutoff_abs = dFDFobs*cutoff
if noise_type is 'theory':
cutoff_abs = dFDFth*cutoff
cleanFDF, ccArr, iterCountArr, residFDF = do_rmclean_hogbom(dirtyFDF = FDF,
phiArr_radm2 = phiArr_radm2,
RMSFArr = RMSFArr,
phi2Arr_radm2 = phi2Arr_radm2,
fwhmRMSFArr = fwhmRMSF_radm2,
cutoff = cutoff_abs,
# maxIter = maxIter,
# gain = gain,
# verbose = verbose,
doPlots = True)
FDF_max=np.argmax(abs(cleanFDF))
FDF_med=np.median(abs(cleanFDF))
dFDFobs=np.median(abs(abs(cleanFDF)-FDF_med)) / np.sqrt(np.pi/2) #MADFM definition of noise # dFDF_obs=np.nanstd(abs(FDF)) #std. definition of noise
if noise_type is 'observed':
FDF_snr_clean=abs((abs(cleanFDF)-FDF_med)/dFDFobs)/2
ccArr_snr=(abs(ccArr)/dFDFobs)/2
if noise_type is 'theory':
FDF_snr_clean=abs((abs(cleanFDF)-FDF_med)/dFDFth)/2
ccArr_snr=(abs(ccArr)/dFDFth)/2
mDict = measure_FDF_parms(FDF = cleanFDF,
phiArr = phiArr_radm2,
fwhmRMSF = fwhmRMSF_radm2,
dFDF = dFDFth, #FDF_noise
lamSqArr_m2 = lambdaSqArr_m2,
lam0Sq = lam0Sq_m2)
RM_radm2_fit=mDict["phiPeakPIfit_rm2"]
dRM_radm2_fit=mDict["dPhiPeakPIfit_rm2"]
RM_radm2=phiArr_radm2[FDF_max]
dRM_radm2=fwhmRMSF_radm2/(2*FDF_snr_clean.max())
polAngle0Fit_deg=mDict["polAngle0Fit_deg"]
dPolAngle0Fit_deg=mDict["dPolAngle0Fit_deg"] * np.sqrt(freqArr.size) # np.sqrt(freqArr.size) term corrects for band-average noise
if diagnostic_plots:
fig, ax = plt.subplots(2,1, figsize=(20,10))
plt.subplots_adjust(left=0.1, bottom=0.1, right=0.99, top=0.95, wspace=0)
ax[0].set_title('Faraday Dispersion Function')
ax[0].plot(phiArr_radm2,FDF_snr_clean, label='clean FDF')
ax[0].plot(phiArr_radm2,FDF_snr, label='dirty FDF')
ax[0].axhline(cutoff, ls='--', color='k', label='clean cutoff')
ax[0].legend()
ax[0].set_xlim([phiArr_radm2.min(), phiArr_radm2.max()])
ax[1].plot(phiArr_radm2,FDF_snr_clean, label='clean FDF')
ax[1].plot(phiArr_radm2,FDF_snr, label='dirty FDF')
ax[1].axhline(cutoff, ls='--', color='k',label='clean cutoff')
ax[1].legend()
ax[1].set_xlim(phiArr_radm2[FDF_max]-300,phiArr_radm2[FDF_max]+300)
ax[1].set_xlabel('$\phi$ [rad/m$^2$]')
fig.text(0.03, 0.5, 'Polarized Intensity [S/N]', va='center', rotation='vertical')
if isinstance(diagnostic_plots, bool):
plt.show()
else:
plot_name = "FDF.png"
plt.savefig(os.path.join(diagnostic_plots, plot_name))
plt.close("all")
fig, ax = plt.subplots(2,1,figsize=(20,10))
plt.subplots_adjust(left=0.1, bottom=0.1, right=0.99, top=0.95, wspace=0, hspace=0.0)
ax[0].set_title('Faraday Dispersion Function')
ax[0].plot(phi2Arr_radm2,RMSFArr, label='RMTF')
ax[0].set_xlim([-300,300])
ax[0].xaxis.set_ticklabels([])
ax[0].legend()
ax[1].plot(phiArr_radm2,FDF_snr_clean, label='clean FDF')
ax[1].bar(phiArr_radm2,ccArr_snr, color='g', label='clean components')
ax[1].legend()
ax[1].set_xlim(phiArr_radm2[FDF_max]-300,phiArr_radm2[FDF_max]+300)
ax[1].set_xlabel('$\phi$ [rad/m$^2$]')
fig.text(0.03, 0.5, 'Polarized Intensity [S/N]', va='center', rotation='vertical')
# plt.legend(fontsize=20)
# plt.tight_layout()
if isinstance(diagnostic_plots, bool):
plt.show()
else:
plot_name = "FDF_clean.png"
plt.savefig(os.path.join(diagnostic_plots, plot_name))
plt.close("all")
return (RM_radm2_fit,RM_radm2,dRM_radm2_fit,dRM_radm2,polAngle0Fit_deg,dPolAngle0Fit_deg),(phiArr_radm2,FDF_snr_clean)
def run_rmclean(fdfFile,
rmsfFile,
weightFile,
rmSynthFile,
cutoff,
maxIter=1000,
gain=0.1,
prefixOut="",
outDir="",
nBits=32,
showPlots=False,
doAnimate=False):
"""
Run RM-CLEAN on a complex FDF spectrum given a RMSF.
"""
# Default data types
dtFloat = "float" + str(nBits)
dtComplex = "complex" + str(2 * nBits)
# Read the frequency vector for the lambda^2 array
freqArr_Hz, weightArr = np.loadtxt(weightFile, unpack=True, dtype=dtFloat)
lambdaSqArr_m2 = np.power(C / freqArr_Hz, 2.0)
# Read the FDF from the ASCII file
phiArr_radm2, FDFreal, FDFimag = np.loadtxt(fdfFile,
unpack=True,
dtype=dtFloat)
dirtyFDF = FDFreal + 1j * FDFimag
# Read the RMSF from the ASCII file
phi2Arr_radm2, RMSFreal, RMSFimag = np.loadtxt(rmsfFile,
unpack=True,
dtype=dtFloat)
RMSFArr = RMSFreal + 1j * RMSFimag
# Read the RM-synthesis parameters from the JSON file
mDictS = json.load(open(rmSynthFile, "r"))
# If the cutoff is negative, assume it is a sigma level
print "Expected RMS noise = %.4g mJy/beam/rmsf" % \
(mDictS["dFDFth_Jybm"]*1e3)
if cutoff < 0:
print "Using a sigma cutoff of %.1f." % (-1 * cutoff),
cutoff = -1 * mDictS["dFDFth_Jybm"] * cutoff
print "Absolute value = %.3g" % cutoff
else:
print "Using an absolute cutoff of %.3g (%.1f x expected RMS)." % \
(cutoff, cutoff/mDictS["dFDFth_Jybm"])
startTime = time.time()
# Perform RM-clean on the spectrum
cleanFDF, ccArr, iterCountArr = \
do_rmclean_hogbom(dirtyFDF = dirtyFDF,
phiArr_radm2 = phiArr_radm2,
RMSFArr = RMSFArr,
phi2Arr_radm2 = phi2Arr_radm2,
fwhmRMSFArr = np.array(mDictS["fwhmRMSF"]),
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
verbose = False,
doPlots = showPlots,
doAnimate = doAnimate)
cleanFDF #/= 1e3
ccArr #/= 1e3
# ALTERNATIVE RM_CLEAN CODE ----------------------------------------------#
'''
cleanFDF, ccArr, fwhmRMSF, iterCount = \
do_rmclean(dirtyFDF = dirtyFDF,
phiArr = phiArr_radm2,
lamSqArr = lamSqArr_m2,
cutoff = cutoff,
maxIter = maxIter,
gain = gain,
weight = weightArr,
RMSFArr = RMSFArr,
RMSFphiArr = phi2Arr_radm2,
fwhmRMSF = mDictS["fwhmRMSF"],
doPlots = True)
'''
#-------------------------------------------------------------------------#
endTime = time.time()
cputime = (endTime - startTime)
print "> RM-CLEAN completed in %.4f seconds." % cputime
# Measure the parameters of the deconvolved FDF
mDict = measure_FDF_parms(
FDF=cleanFDF,
phiArr=phiArr_radm2,
fwhmRMSF=mDictS["fwhmRMSF"],
#dFDF = mDictS["dFDFth_Jybm"],
lamSqArr_m2=lambdaSqArr_m2,
lam0Sq=mDictS["lam0Sq_m2"])
mDict["cleanCutoff"] = cutoff
mDict["nIter"] = int(iterCountArr)
# Measure the complexity of the clean component spectrum
mDict["mom2CCFDF"] = measure_fdf_complexity(phiArr=phiArr_radm2, FDF=ccArr)
# Save the deconvolved FDF and CC model to ASCII files
print "Saving the clean FDF and component model to ASCII files."
outFile = prefixOut + "_FDFclean.dat"
print "> %s" % outFile
np.savetxt(outFile, zip(phiArr_radm2, cleanFDF.real, cleanFDF.imag))
outFile = prefixOut + "_FDFmodel.dat"
print "> %s" % outFile
np.savetxt(outFile, zip(phiArr_radm2, ccArr))
# Save the RM-clean measurements to a "key=value" text file
print "Saving the measurements on the FDF in 'key=val' and JSON formats."
outFile = prefixOut + "_RMclean.dat"
print "> %s" % outFile
FH = open(outFile, "w")
for k, v in mDict.iteritems():
FH.write("%s=%s\n" % (k, v))
FH.close()
outFile = prefixOut + "_RMclean.json"
print "> %s" % outFile
json.dump(mDict, open(outFile, "w"))
# Print the results to the screen
print
print '-' * 80
print 'RESULTS:\n'
print 'FWHM RMSF = %.4g rad/m^2' % (mDictS["fwhmRMSF"])
print 'Pol Angle = %.4g (+/-%.4g) deg' % (mDict["polAngleFit_deg"],
mDict["dPolAngleFit_deg"])
print 'Pol Angle 0 = %.4g (+/-%.4g) deg' % (mDict["polAngle0Fit_deg"],
mDict["dPolAngle0Fit_deg"])
print 'Peak FD = %.4g (+/-%.4g) rad/m^2' % (mDict["phiPeakPIfit_rm2"],
mDict["dPhiPeakPIfit_rm2"])
print 'freq0_GHz = %.4g ' % (mDictS["freq0_Hz"] / 1e9)
print 'I freq0 = %.4g mJy/beam' % (mDictS["Ifreq0_mJybm"])
print 'Peak PI = %.4g (+/-%.4g) mJy/beam' % (
mDict["ampPeakPIfit_Jybm"] * 1e3, mDict["dAmpPeakPIfit_Jybm"] * 1e3)
print 'QU Noise = %.4g mJy/beam' % (mDictS["dQU_Jybm"] * 1e3)
print 'FDF Noise (measure) = %.4g mJy/beam' % (mDict["dFDFms_Jybm"] * 1e3)
print 'FDF SNR = %.4g ' % (mDict["snrPIfit"])
print
print '-' * 80
# Pause to display the figure
if showPlots or doAnimate:
print "Press <RETURN> to exit ...",
raw_input()
