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_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_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