def do_lstsqr(dataroot='~/Data/AIA/',
ldirroot='~/ts/pickle/',
sfigroot='~/ts/img/',
scsvroot='~/ts/csv/',
corename='shutdownfun3_6hr',
sunlocation='disk',
fits_level='1.5',
waves=['171', '193', '211', '131'],
regions=['qs', 'loopfootpoints'],
windows=['no window'],
manip='none'):
five_min = 1.0 / 300.0
three_min = 1.0 / 180.0
# main loop
for iwave, wave in enumerate(waves):
# Which wavelength?
print('Wave: ' + wave + ' (%i out of %i)' % (iwave + 1, len(waves)))
# Now that the loading and saving locations are seot up, proceed with
# the analysis.
for iregion, region in enumerate(regions):
# Which region
print('Region: ' + region + ' (%i out of %i)' % (iregion + 1, len(regions)))
# Create the branches in order
branches = [corename, sunlocation, fits_level, wave, region]
# Set up the roots we are interested in
roots = {"pickle": ldirroot,
"image": sfigroot,
"csv": scsvroot}
# Data and save locations are based here
locations = aia_specific.save_location_calculator(roots,
branches)
# set the saving locations
sfig = locations["image"]
scsv = locations["csv"]
# Identifier
ident = aia_specific.ident_creator(branches)
# Go through all the windows
for iwindow, window in enumerate(windows):
# Which window
print('Window: ' + window + ' (%i out of %i)' % (iwindow + 1, len(windows)))
# Update the region identifier
region_id = '.'.join((ident, window, manip))
# Load the data
pkl_location = locations['pickle']
ifilename = ident + '.datacube'
pkl_file_location = os.path.join(pkl_location, ifilename + '.pickle')
print('Loading ' + pkl_file_location)
pkl_file = open(pkl_file_location, 'rb')
dc = pickle.load(pkl_file)
pkl_file.close()
# Get some properties of the datacube
ny = dc.shape[0]
nx = dc.shape[1]
nt = dc.shape[2]
tsdetails = tsDetails(nx, ny, nt)
# Define an array to store the analyzed data
dc_analysed = np.zeros_like(dc)
# calculate a window function
win, dummy_winname = DefineWindow(window, nt)
# Create the name for the data
#data_name = wave + ' (' + fits_level + winname + ', ' + manip + '), ' + region
data_name = region_id
# Create a location to save the figures
savefig = os.path.join(os.path.expanduser(sfig), window, manip)
if not(os.path.isdir(savefig)):
os.makedirs(savefig)
savefig = os.path.join(savefig, region_id)
# Create a time series object
dt = 12.0
t = dt * np.arange(0, nt)
tsdummy = TimeSeries(t, t)
freqs = tsdummy.PowerSpectrum.frequencies.positive
iobs = np.zeros(tsdummy.PowerSpectrum.Npower.shape)
logiobs = np.zeros(tsdummy.PowerSpectrum.Npower.shape)
nposfreq = len(iobs)
nfreq = tsdummy.PowerSpectrum.frequencies.nfreq
# storage
pwr = np.zeros((ny, nx, nposfreq))
logpwr = np.zeros_like(pwr)
doriginal = np.zeros_like(t)
dmanip = np.zeros_like(t)
fft_transform = np.zeros((ny, nx, nfreq), dtype=np.complex64)
for i in range(0, nx):
for j in range(0, ny):
# Get the next time-series
d = dc[j, i, :].flatten()
# Fix the data for any non-finite entries
d = tsutils.fix_nonfinite(d)
# Sum up all the original data
doriginal = doriginal + d
# Remove the mean
#if manip == 'submean':
# d = d - np.mean(d)
# Relative intensity
if manip == 'relative':
dmean = np.mean(d)
d = (d - dmean) / dmean
# Sum up all the manipulated data
dmanip = dmanip + d
# Multiply the data by the apodization window
d = d * win
# Keep the analyzed data cube
dc_analysed[j, i, :] = d
# Form a time series object. Handy for calculating the Fourier power at all non-zero frequencies
ts = TimeSeries(t, d)
# Define the Fourier power we are analyzing
this_power = ts.PowerSpectrum.ppower
# Get the total Fourier power
iobs = iobs + this_power
# Store the individual Fourier power
pwr[j, i, :] = this_power
# Sum up the log of the Fourier power - equivalent to doing the geometric mean
logiobs = logiobs + np.log(this_power)
# Store the individual log Fourier power
logpwr[j, i, :] = np.log(this_power)
# Get the FFT transform values and store them
fft_transform[j, i, :] = ts.fft_transform
###############################################################
# Post-processing of the data products
# Limits to the data
dc_analysed_minmax = (np.min(dc_analysed), np.max(dc_analysed))
# Average of the analyzed time-series and create a time series object
full_data = np.mean(dc_analysed, axis=(0, 1))
full_ts = TimeSeries(t, full_data)
full_ts.name = data_name
full_ts.label = 'average emission ' + tsdetails
# Fourier power: average over all the pixels
iobs = iobs / (1.0 * nx * ny)
# Fourier power: standard deviation over all the pixels
sigma = np.std(pwr, axis=(0, 1))
# Logarithmic power: average over all the pixels
logiobs = logiobs / (1.0 * nx * ny)
# Logarithmic power: standard deviation over all pixels
logsigma = np.std(logpwr, axis=(0, 1))
# Original data: average
doriginal = doriginal / (1.0 * nx * ny)
# Manipulated data: average
dmanip = dmanip / (1.0 * nx * ny)
###############################################################
# Power spectrum analysis: arithmetic mean approach
# Normalize the frequency.
xnorm = tsdummy.PowerSpectrum.frequencies.positive[0]
x = freqs / xnorm
# Fourier power: fit a power law to the arithmetic mean of the
# Fourier power
# Generate a guess
pguess = [iobs[0], 1.8, iobs[-1]]
# 5 minute power bump
#gguess = [1.0, five_min, 0.0025]
# Final guess
#p0 = [np.sqrt(iobs[0]), 1.8, iobs[-1],
# 0.01, 1.4, 0.25]
#p0 = pguess
#bff = ObservedPowerSpectrumModel(x, p0[0], p0[1], p0[2], p0[3], p0[4], p0[5])
# do the fit
p0 = pguess
answer = curve_fit(PowerLawPlusConstant, x, iobs, sigma=sigma, p0=pguess)
#answer = curve_fit(ObservedPowerSpectrumModel, x, iobs, p0=p0)
# Get the fit parameters out and calculate the best fit
param = answer[0]
bf = PowerLawPlusConstant(x, param[0], param[1], param[2])
#bf = ObservedPowerSpectrumModel(x, param[0], param[1], param[2], param[3], param[4], param[5])
# Error estimate for the power law index
nerr = np.sqrt(answer[1][1, 1])
# Fourier powerr: get a Time series from the arithmetic sum of
# all the time-series at every pixel, find the Fourier power
# and do the fit
full_ts_iobs = full_ts.PowerSpectrum.ppower / np.mean(full_ts.PowerSpectrum.ppower)
answer_full_ts = curve_fit(LogPowerLawPlusConstant, x, np.log(full_ts_iobs), p0=answer[0])
#answer_full_ts = fmin_tnc(LogPowerLawPlusConstant, x, approx_grad=True)
# Get the fit parameters out and calculate the best fit
param_fts = answer_full_ts[0]
bf_fts = np.exp(LogPowerLawPlusConstant(x, param_fts[0], param_fts[1], param_fts[2]))
nerr_fts = np.sqrt(answer[1][1, 1])
# Plots of power spectra: arithmetic means of summed emission
# and summed power spectra
plt.figure(1)
plt.loglog(freqs, full_ts_iobs, color='r', label='power spectrum from summed emission (exponential distributed)')
plt.loglog(freqs, bf_fts, color='r', linestyle="--", label='fit to power spectrum of summed emission n=%4.2f +/- %4.2f' % (param_fts[1], nerr_fts))
plt.loglog(freqs, iobs, color='b', label='arithmetic mean of power spectra from each pixel (Erlang distributed)')
plt.loglog(freqs, bf, color='b', linestyle="--", label='fit to arithmetic mean of power spectra from each pixel n=%4.2f +/- %4.2f' % (param[1], nerr))
plt.axvline(five_min, color='k', linestyle='-.', label='5 mins.')
plt.axvline(three_min, color='k', linestyle='--', label='3 mins.')
plt.axhline(1.0, color='k', label='average power')
plt.xlabel('frequency (Hz)')
plt.ylabel('normalized power [%i time series, %i samples each]' % (nx * ny, nt))
plt.title(data_name + ' - aPS')
plt.legend(loc=1, fontsize=10)
plt.text(freqs[0], 500, 'note: least-squares fit used, but data is not Gaussian distributed', fontsize=8)
#plt.ylim(0.0001, 1000.0)
plt.savefig(savefig + '.arithmetic_mean_power_spectra.png')
###############################################################
# Power spectrum analysis: geometric mean approach
# ------------------------------------------------------------------------
# Do the same thing over again, this time working with the log of the
# normalized power. This is effectively the geometric mean
# Fit the function to the log of the mean power
answer2 = curve_fit(LogPowerLawPlusConstant, x, logiobs, sigma=logsigma, p0=answer[0])
# Get the fit parameters out and calculate the best fit
param2 = answer2[0]
bf2 = np.exp(LogPowerLawPlusConstant(x, param2[0], param2[1], param2[2]))
# Error estimate for the power law index
nerr2 = np.sqrt(answer2[1][1, 1])
# Create the histogram of all the log powers. Histograms look normal-ish if
# you take the logarithm of the power. This suggests a log-normal distribution
# of power in all frequencies
# number of histogram bins
bins = 100
hpwr = np.zeros((nposfreq, bins))
for f in range(0, nposfreq):
h = np.histogram(logpwr[:, :, f], bins=bins, range=[np.min(logpwr), np.max(logpwr)])
hpwr[f, :] = h[0] / (1.0 * np.sum(h[0]))
# Calculate the probability density in each frequency bin.
p = [0.68, 0.95]
lim = np.zeros((len(p), 2, nposfreq))
for i, thisp in enumerate(p):
tailp = 0.5 * (1.0 - thisp)
for f in range(0, nposfreq):
lo = 0
while np.sum(hpwr[f, 0:lo]) <= tailp:
lo = lo + 1
hi = 0
while np.sum(hpwr[f, 0:hi]) <= 1.0 - tailp:
hi = hi + 1
lim[i, 0, f] = np.exp(h[1][lo])
lim[i, 1, f] = np.exp(h[1][hi])
# Give the best plot we can under the circumstances. Since we have been
# looking at the log of the power, plots are slightly different
plt.figure(2)
plt.loglog(freqs, np.exp(logiobs), label='geometric mean of power spectra at each pixel')
plt.loglog(freqs, bf2, color='k', label='best fit n=%4.2f +/- %4.2f' % (param2[1], nerr2))
plt.loglog(freqs, lim[0, 0, :], linestyle='--', label='lower 68%')
plt.loglog(freqs, lim[0, 1, :], linestyle='--', label='upper 68%')
plt.loglog(freqs, lim[1, 0, :], linestyle=':', label='lower 95%')
plt.loglog(freqs, lim[1, 1, :], linestyle=':', label='upper 95%')
plt.axvline(five_min, color='k', linestyle='-.', label='5 mins.')
plt.axvline(three_min, color='k', linestyle='--', label='3 mins.')
plt.xlabel('frequency (Hz)')
plt.ylabel('power [%i time series, %i samples each]' % (nx * ny, nt))
plt.title(data_name + ' - gPS')
plt.legend(loc=1, fontsize=10)
plt.savefig(savefig + '.geometric_mean_power_spectra.png')
# plot some histograms of the log power at a small number of equally spaced
# frequencies
findex = [0, 11, 19, 38, 76]
plt.figure(3)
plt.xlabel('$\log_{10}(power)$')
plt.ylabel('proportion found at given frequency')
plt.title(data_name + ' - power distributions')
for f in findex:
plt.plot(h[1][1:] / np.log(10.0), hpwr[f, :], label='%7.5f Hz' % (freqs[f]))
plt.legend(loc=3, fontsize=10)
plt.savefig(savefig + '.power_spectra_distributions.png')
# plot out the time series
plt.figure(4)
full_ts.peek()
plt.savefig(savefig + '.full_ts_timeseries.png')
plt.close('all')
###############################################################
# Time series plots
# Plot all the analyzed time series
plt.figure(10)
for i in range(0, nx):
for j in range(0, ny):
plt.plot(t, dc_analysed[j, i, :])
plt.xlabel('time (seconds)')
plt.ylabel('analyzed emission ' + tsdetails)
plt.title(data_name)
plt.ylim(dc_analysed_minmax)
plt.xlim((t[0], t[-1]))
plt.savefig(savefig + '.all_analyzed_ts.png')
# Plot a histogram of the studied data at each time
bins = 50
hist_dc_analysed = np.zeros((bins, nt))
for this_time in range(0, nt):
hist_dc_analysed[:, this_time], bin_edges = np.histogram(dc_analysed[:, :, this_time], bins=bins, range=dc_analysed_minmax)
hist_dc_analysed = hist_dc_analysed / (1.0 * nx * ny)
plt.figure(12)
plt.xlabel('time (seconds)')
plt.ylabel('analyzed emission ' + tsdetails)
plt.imshow(hist_dc_analysed, aspect='auto', origin='lower',
extent=(t[0], t[-1], dc_analysed_minmax[0], dc_analysed_minmax[1]))
plt.colorbar()
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_ts_histogram.png')
###############################################################
# Fourier power plots
# Plot all the analyzed FFTs
plt.figure(11)
for i in range(0, nx):
for j in range(0, ny):
ts = TimeSeries(t, dc_analysed[j, i, :])
ts.peek_ps()
plt.loglog()
plt.axvline(five_min, color='k', linestyle='-.', label='5 mins.')
plt.axvline(three_min, color='k', linestyle='--', label='3 mins.')
plt.xlabel('frequency (Hz)')
plt.ylabel('FFT power ' + tsdetails)
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_fft.png')
# Plot a histogram of the studied FFTs at each time
bins = 50
minmax = [np.min(logpwr), np.max(logpwr)]
hist_dc_analysed_logpwr = np.zeros((bins, nposfreq))
for this_freq in range(0, nposfreq):
hist_dc_analysed_logpwr[:, this_freq], bin_edges = np.histogram(logpwr[:, :, this_freq], bins=bins, range=minmax)
hist_dc_analysed_logpwr = hist_dc_analysed_logpwr / (1.0 * nx * ny)
plt.figure(13)
plt.xlabel('frequency (Hz)')
plt.ylabel('FFT power ' + tsdetails)
plt.imshow(hist_dc_analysed_logpwr, aspect='auto', origin='lower',
extent=(freqs[0], freqs[-1], np.exp(minmax[0]), np.exp(minmax[1])))
plt.semilogy()
plt.colorbar()
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_fft_histogram.png')
###############################################################
# Save various data products
# Fourier Power of the analyzed data
ofilename = region_id
pkl_write(pkl_location,
'OUT.' + ofilename + '.fourier_power.pickle',
(freqs, pwr))
# Analyzed data
pkl_write(pkl_location,
'OUT.' + ofilename + '.dc_analysed.pickle',
(t, dc_analysed))
# Fourier transform
pkl_write(pkl_location,
'OUT.' + ofilename + '.fft_transform.pickle',
(freqs, fft_transform))
# Save the full time series to a CSV file
csv_timeseries_write(os.path.join(os.path.expanduser(scsv), window, manip),
'.'.join((data_name, 'average_analyzed_ts.csv')),
(t, full_data))
# Original data
csv_timeseries_write(os.path.join(os.path.expanduser(scsv)),
'.'.join((ident, 'average_original_ts.csv')),
(t, doriginal))
def do_lstsqr(dataroot='~/Data/AIA/',
ldirroot='~/ts/pickle/',
sfigroot='~/ts/img/',
scsvroot='~/ts/csv/',
corename='shutdownfun3_6hr',
sunlocation='disk',
fits_level='1.5',
waves=['171', '193', '211', '131'],
regions=['qs', 'loopfootpoints'],
windows=['no window'],
manip='none',
savefig_format='eps',
freqfactor=[1000.0, 'mHz'],
sunday_name={"qs": "quiet Sun", "loopfootpoints": "loop footpoints"}):
five_min = freqfactor[0] * 1.0 / 300.0
three_min = freqfactor[0] * 1.0 / 180.0
# main loop
for iwave, wave in enumerate(waves):
# Which wavelength?
print('Wave: ' + wave + ' (%i out of %i)' % (iwave + 1, len(waves)))
# Now that the loading and saving locations are seot up, proceed with
# the analysis.
for iregion, region in enumerate(regions):
# Which region
print('Region: ' + region + ' (%i out of %i)' % (iregion + 1, len(regions)))
# Create the branches in order
branches = [corename, sunlocation, fits_level, wave, region]
# Set up the roots we are interested in
roots = {"pickle": ldirroot,
"image": sfigroot,
"csv": scsvroot}
# Data and save locations are based here
locations = aia_specific.save_location_calculator(roots,
branches)
# set the saving locations
sfig = locations["image"]
scsv = locations["csv"]
# Identifier
ident = aia_specific.ident_creator(branches)
# Go through all the windows
for iwindow, window in enumerate(windows):
# Which window
print('Window: ' + window + ' (%i out of %i)' % (iwindow + 1, len(windows)))
# Update the region identifier
region_id = '.'.join((ident, window, manip))
# Load the data
pkl_location = locations['pickle']
ifilename = ident + '.datacube'
pkl_file_location = os.path.join(pkl_location, ifilename + '.pickle')
print('Loading ' + pkl_file_location)
pkl_file = open(pkl_file_location, 'rb')
dc = pickle.load(pkl_file)
pkl_file.close()
# Get some properties of the datacube
ny = dc.shape[0]
nx = dc.shape[1]
nt = dc.shape[2]
tsdetails = tsDetails(nx, ny, nt)
# Define an array to store the analyzed data
dc_analysed = np.zeros_like(dc)
# calculate a window function
win, dummy_winname = DefineWindow(window, nt)
# Create the name for the data
#data_name = wave + ' (' + fits_level + winname + ', ' + manip + '), ' + region
#data_name = region_id
if region in sunday_name:
data_name = 'AIA ' + str(wave) + ', ' + sunday_name[region]
else:
data_name = 'AIA ' + str(wave) + ', ' + region
# Create a location to save the figures
savefig = os.path.join(os.path.expanduser(sfig), window, manip)
if not(os.path.isdir(savefig)):
os.makedirs(savefig)
savefig = os.path.join(savefig, region_id)
# Create a time series object
dt = 12.0
t = dt * np.arange(0, nt)
tsdummy = TimeSeries(t, t)
freqs = freqfactor[0] * tsdummy.PowerSpectrum.frequencies.positive
iobs = np.zeros(tsdummy.PowerSpectrum.Npower.shape)
logiobs = np.zeros(tsdummy.PowerSpectrum.Npower.shape)
nposfreq = len(iobs)
nfreq = tsdummy.PowerSpectrum.frequencies.nfreq
# storage
pwr = np.zeros((ny, nx, nposfreq))
logpwr = np.zeros_like(pwr)
doriginal = np.zeros_like(t)
dmanip = np.zeros_like(t)
fft_transform = np.zeros((ny, nx, nfreq), dtype=np.complex64)
for i in range(0, nx):
for j in range(0, ny):
# Get the next time-series
d = dc[j, i, :].flatten()
# Fix the data for any non-finite entries
d = tsutils.fix_nonfinite(d)
# Sum up all the original data
doriginal = doriginal + d
# Remove the mean
#if manip == 'submean':
# d = d - np.mean(d)
# Basic rescaling of the time-series
d = ts_manip(d, manip)
# Sum up all the manipulated data
dmanip = dmanip + d
# Multiply the data by the apodization window
d = ts_apply_window(d, win)
# Keep the analyzed data cube
dc_analysed[j, i, :] = d
# Form a time series object. Handy for calculating the Fourier power at all non-zero frequencies
ts = TimeSeries(t, d)
# Define the Fourier power we are analyzing
this_power = ts.PowerSpectrum.ppower
# Get the total Fourier power
iobs = iobs + this_power
# Store the individual Fourier power
pwr[j, i, :] = this_power
# Sum up the log of the Fourier power - equivalent to doing the geometric mean
logiobs = logiobs + np.log(this_power)
# Store the individual log Fourier power
logpwr[j, i, :] = np.log(this_power)
# Get the FFT transform values and store them
fft_transform[j, i, :] = ts.fft_transform
###############################################################
# Post-processing of the data products
# Limits to the data
dc_analysed_minmax = (np.min(dc_analysed), np.max(dc_analysed))
# Original data: average
doriginal = doriginal / (1.0 * nx * ny)
# Manipulated data: average
dmanip = dmanip / (1.0 * nx * ny)
# Average of the analyzed time-series and create a time series
# object
full_data = np.mean(dc_analysed, axis=(0, 1))
full_ts = TimeSeries(t, full_data)
full_ts.name = data_name
full_ts.label = 'average analyzed emission ' + tsdetails
# Time series of the average original data
doriginal = ts_manip(doriginal, manip)
doriginal = ts_apply_window(d, win)
doriginal_ts = TimeSeries(t, doriginal)
doriginal_ts.name = data_name
doriginal_ts.label = 'average summed emission ' + tsdetails
# Fourier power: average over all the pixels
iobs = iobs / (1.0 * nx * ny)
# Fourier power: standard deviation over all the pixels
sigma = np.std(pwr, axis=(0, 1))
# Logarithmic power: average over all the pixels
logiobs = logiobs / (1.0 * nx * ny)
# Logarithmic power: standard deviation over all pixels
logsigma = np.std(logpwr, axis=(0, 1))
###############################################################
# Power spectrum analysis: arithmetic mean approach
# Normalize the frequency.
xnorm = tsdummy.PowerSpectrum.frequencies.positive[0]
x = freqs / (xnorm * freqfactor[0])
# Fourier power: fit a power law to the arithmetic mean of the
# Fourier power
#answer = curve_fit(aia_plaw_fit.PowerLawPlusConstant, x, iobs, sigma=sigma, p0=pguess)
answer, error = aia_plaw.do_fit(x, iobs, aia_plaw.PowerLawPlusConstant, sigma=sigma)
# Get the fit parameters out and calculate the best fit
param = answer[0, 0, :]
bf = aia_plaw.PowerLawPlusConstant(x,
answer[0, 0, 0],
answer[0, 0, 1],
answer[0, 0, 2])
# Error estimate for the power law index
nerr = np.sqrt(error[0, 0, 1])
###############################################################
# Estimate the correlation distance in the region. This is
# done by calculating the cross-correlation coefficient between
# two randomly selected pixels in the region. If we do this
# often enough then we can estimate the distance at which the
# the cross-correlation between two pixels is zero. This
# length-scale is then squared to get the estimated area that
# contains a statistically independent time-series. If we
# divide the number of pixels in the region by this estimated
# area then we get an estimate of the number of independent
# time series in the region.
def cornorm(a, norm):
return (a - np.mean(a)) / (np.std(a) * norm)
def exponential_decay(x, A, tau):
return A * np.exp(-x / tau)
def exponential_decay2(x, A1, tau1, A2, tau2):
return A1 * np.exp(-x / tau1) + A2 * np.exp(-x / tau2)
def exponential_decay3(x, A1, tau1, const):
return A1 * np.exp(-x / tau1) + const
def linear(x, c, m):
return -m * x + c
nsample = 10000
npicked = 0
lag = 1
cc = []
distance = []
while npicked < nsample:
loc1 = (np.random.randint(0, ny), np.random.randint(0, nx))
loc2 = (np.random.randint(0, ny), np.random.randint(0, nx))
if loc1 != loc2:
# Calculate the distance between the two locations
distance.append(np.sqrt((loc1[0] - loc2[0]) ** 2 + (loc1[1] - loc2[1]) ** 2))
# Get the time series
ts1 = dc_analysed[loc1[0], loc1[1], :]
ts2 = dc_analysed[loc2[0], loc2[1], :]
# Calculate the cross-correlation coefficient
ccvalue = np.correlate(cornorm(ts1, np.size(ts1)), cornorm(ts2, 1.0), mode='full')
cc.append(ccvalue[nt - 1 + lag])
# Advance the counter
npicked = npicked + 1
distance = np.asarray(distance)
# Get a histogram of the distances
# What is the average correlation coefficient
cc = np.asarray(cc)
ccc = np.zeros(np.rint(np.max(distance)) + 1)
ccc_min = np.rint(np.min(distance))
xccc = np.arange(0.0, np.rint(np.max(distance)) + 1)
hist = np.zeros_like(ccc)
for jj, d in enumerate(distance):
dloc = np.rint(d)
hist[dloc] = hist[dloc] + 1
ccc[dloc] = ccc[dloc] + cc[jj]
ccc = ccc / hist
ccc[0] = 1.0
# Fit the positive part of the cross-correlation plot with an
# exponential decay curve to get an estimate of the decay
# decay constant. This can be used to estimate where exactly
# the cross-correlation falls below a certain level.
cccpos = ccc >= 0.0
if region != 'moss':
ccc_answer, ccc_error = curve_fit(exponential_decay, xccc[cccpos], ccc[cccpos])
amplitude = ccc_answer[0]
decay_constant = ccc_answer[1]
print('Model 0 ', amplitude, decay_constant)
# Estimated decorrelation lengths
decorr_length1 = decay_constant * (np.log(amplitude) - np.log(0.1))
decorr_length2 = decay_constant * (np.log(amplitude) - np.log(0.05))
ccc_best_fit = exponential_decay(xccc, amplitude, decay_constant)
else:
ccc_answer, ccc_error = curve_fit(exponential_decay3, xccc[cccpos], ccc[cccpos])
ccc_best_fit = exponential_decay(xccc, ccc_answer[0], ccc_answer[1])
plt.figure(3)
plt.xlabel('distance d (pixels)')
plt.ylabel('average cross correlation coefficient at lag %i [%i samples]' % (lag, nsample))
plt.title('Average cross correlation vs. distance')
plt.plot(xccc, ccc, label='data')
plt.plot(xccc, ccc_best_fit, label='Model 1 best fit')
#if region == 'moss':
# plt.plot(xccc, ccc_best_fit_orig, label='Model 0 best fit')
plt.axhline(0.1, color='k', linestyle='--')
plt.axhline(0.05, color='k', linestyle='-.')
plt.axhline(0.0, color='k')
#plt.axvline(decorr_length1, color='r', label='Length-scale (cc=0.1) = %3.2f pixels' % (decorr_length1), linestyle='--')
#plt.axvline(decorr_length2, color='r', label='Length-scale (cc=0.05) = %3.2f pixels' % (decorr_length2), linestyle='-.')
plt.legend()
plt.savefig(savefig + '.lag%i_cross_corr.%s' % (lag, savefig_format))
# Fourier power: get a Time series from the arithmetic sum of
# all the time-series at every pixel, then apply the
# manipulation and the window. Find the Fourier power
# and do the fit.
doriginal_ts_iobs = doriginal_ts.PowerSpectrum.ppower
answer_doriginal_ts = curve_fit(aia_plaw.LogPowerLawPlusConstant, x, np.log(doriginal_ts_iobs), p0=answer[0])
param_dts = answer_doriginal_ts[0]
bf_dts = np.exp(aia_plaw.LogPowerLawPlusConstant(x, param_dts[0], param_dts[1], param_dts[2]))
nerr_dts = np.sqrt(answer_doriginal_ts[1][1, 1])
# -------------------------------------------------------------
# Plots of power spectra: arithmetic means of summed emission
# and summed power spectra
ax = plt.subplot(111)
# Set the scale type on each axis
ax.set_xscale('log')
ax.set_yscale('log')
# Set the formatting of the tick labels
xformatter = plt.FuncFormatter(log_10_product)
ax.xaxis.set_major_formatter(xformatter)
# Arithmetic mean of all the time series, then analysis
ax.plot(freqs, doriginal_ts_iobs, color='r', label='sum over region')
ax.plot(freqs, bf_dts, color='r', linestyle="--", label='fit to sum over region n=%4.2f +/- %4.2f' % (param_dts[1], nerr_dts))
# Arithmetic mean of the power spectra from each pixel
ax.plot(freqs, iobs, color='b', label='arithmetic mean of power spectra from each pixel (Erlang distributed)')
ax.plot(freqs, bf, color='b', linestyle="--", label='fit to arithmetic mean of power spectra from each pixel n=%4.2f +/- %4.2f' % (param[1], nerr))
# Extra information for the plot
ax.axvline(five_min, color=s5min.color, linestyle=s5min.linestyle, label=s5min.label)
ax.axvline(three_min, color=s3min.color, linestyle=s3min.linestyle, label=s3min.label)
#plt.axhline(1.0, color='k', label='average power')
plt.xlabel('frequency (%s)' % (freqfactor[1]))
plt.ylabel('normalized power [%i time series, %i samples each]' % (nx * ny, nt))
plt.title(data_name + ' - arithmetic mean')
#plt.grid()
plt.legend(loc=3, fontsize=10, framealpha=0.5)
#plt.text(freqs[0], 1.0, 'note: least-squares fit used, but data is not Gaussian distributed', fontsize=8)
plt.savefig(savefig + '.arithmetic_mean_power_spectra.%s' % (savefig_format))
plt.close('all')
# -------------------------------------------------------------
###############################################################
# Power spectrum analysis: geometric mean approach
# ------------------------------------------------------------------------
# Do the same thing over again, this time working with the log of the
# normalized power. This is the geometric mean
# Fit the function to the log of the mean power
answer2 = curve_fit(aia_plaw.LogPowerLawPlusConstant, x, logiobs, sigma=logsigma, p0=answer[0])
# Get the fit parameters out and calculate the best fit
param2 = answer2[0]
bf2 = np.exp(aia_plaw.LogPowerLawPlusConstant(x, param2[0], param2[1], param2[2]))
# Error estimate for the power law index
nerr2 = np.sqrt(answer2[1][1, 1])
# Create the histogram of all the log powers. Histograms look normal-ish if
# you take the logarithm of the power. This suggests a log-normal distribution
# of power in all frequencies
# number of histogram bins
# Calculate the probability density in each frequency bin.
bins = 100
bin_edges, hpwr, lim = calculate_histograms(nposfreq, logpwr, bins)
histogram_loc = np.zeros(shape=(bins))
for kk in range(0, bins):
histogram_loc[kk] = 0.5 * (bin_edges[kk] + bin_edges[kk + 1])
# -------------------------------------------------------------
# plot some histograms of the log power at a small number of
# frequencies.
findex = []
f_of_interest = [0.5 * five_min, five_min, three_min, 2 * three_min, 3 * three_min]
hcolor = ['r', 'b', 'g', 'k', 'm']
for thisf in f_of_interest:
findex.append(np.unravel_index(np.argmin(np.abs(thisf - freqs)), freqs.shape)[0])
plt.figure(3)
plt.xlabel('$\log_{10}(power)$')
plt.ylabel('proportion found at given frequency')
plt.title(data_name + ' : power distributions')
for jj, f in enumerate(findex):
xx = histogram_loc / np.log(10.0)
yy = hpwr[f, :]
gfit = curve_fit(aia_plaw.GaussianShape2, xx, yy)
#print gfit[0]
plt.plot(xx, yy, color=hcolor[jj], label='%7.2f %s, $\sigma=$ %3.2f' % (freqs[f], freqfactor[1], np.abs(gfit[0][2])))
plt.plot(xx, aia_plaw.GaussianShape2(xx, gfit[0][0], gfit[0][1],gfit[0][2]), color=hcolor[jj], linestyle='--')
plt.legend(loc=3, fontsize=10, framealpha=0.5)
plt.savefig(savefig + '.power_spectra_distributions.%s' % (savefig_format))
plt.close('all')
# Fit all the histogram curves to find the Gaussian width.
# Stick with natural units to get the fit values which are
# passed along to other programs
logiobs_distrib_width = np.zeros((nposfreq))
error_logiobs_distrib_width = np.zeros_like(logiobs_distrib_width)
iobs_peak = np.zeros_like(logiobs_distrib_width)
logiobs_peak_location = np.zeros_like(logiobs_distrib_width)
logiobs_std = np.zeros_like(logiobs_distrib_width)
for jj, f in enumerate(freqs):
all_logiobs_at_f = logpwr[:, :, jj]
logiobs_std[jj] = np.std(all_logiobs_at_f)
xx = histogram_loc
yy = hpwr[jj, :]
iobs_peak[jj] = xx[np.argmax(yy)]
try:
p0 = [0, 0, 0]
p0[0] = np.max(yy)
p0[1] = xx[np.argmax(yy)]
p0[2] = 0.5#np.sqrt(np.mean(((p0[1] - xx) * yy) ** 2))
gfit = curve_fit(aia_plaw.GaussianShape2, xx, yy, p0=p0)
logiobs_distrib_width[jj] = np.abs(gfit[0][2])
error_logiobs_distrib_width[jj] = np.sqrt(np.abs(gfit[1][2, 2]))
logiobs_peak_location[jj] = gfit[0][1]
except:
logiobs_distrib_width[jj] = None
error_logiobs_distrib_width[jj] = None
logiobs_peak_location[jj] = None
# -------------------------------------------------------------
# Plots of power spectra: geometric mean of power spectra at
# each pixel
ax = plt.subplot(111)
# Set the scale type on each axis
ax.set_xscale('log')
# Set the formatting of the tick labels
xformatter = plt.FuncFormatter(log_10_product)
ax.xaxis.set_major_formatter(xformatter)
# Geometric mean
ax.plot(freqs, logiobs / np.log(10.0), color='k', label='geometric mean of power spectra at each pixel')
#ax.plot(freqs, bf2, color='k', label='best fit n=%4.2f +/- %4.2f' % (param2[1], nerr2))
# Power at each frequency - distributions
ax.plot(freqs, np.log10(lim[0, 0, :]), label=s_L68.label, color=s_L68.color, linewidth=s_L68.linewidth, linestyle=s_L68.linestyle)
ax.plot(freqs, np.log10(lim[1, 0, :]), label=s_L95.label, color=s_L95.color, linewidth=s_L95.linewidth, linestyle=s_L95.linestyle)
ax.plot(freqs, np.log10(lim[0, 1, :]), label=s_U68.label, color=s_U68.color, linewidth=s_U68.linewidth, linestyle=s_U68.linestyle)
ax.plot(freqs, np.log10(lim[1, 1, :]), label=s_U95.label, color=s_U95.color, linewidth=s_U95.linewidth, linestyle=s_U95.linestyle)
# Position of the fitted peak in each distribution
ax.plot(freqs, logiobs_peak_location / np.log(10.0), color='m', label='fitted frequency')
# Extra information for the plot
ax.axvline(five_min, color=s5min.color, linestyle=s5min.linestyle, label=s5min.label)
ax.axvline(three_min, color=s3min.color, linestyle=s3min.linestyle, label=s3min.label)
plt.xlabel('frequency (%s)' % (freqfactor[1]))
plt.ylabel('power [%i time series, %i samples each]' % (nx * ny, nt))
plt.title(data_name + ' : geometric mean')
plt.legend(loc=3, fontsize=10, framealpha=0.5)
plt.savefig(savefig + '.geometric_mean_power_spectra.%s' % (savefig_format))
plt.close('all')
# -------------------------------------------------------------
# plot out the time series
plt.figure(4)
full_ts.peek()
plt.savefig(savefig + '.full_ts_timeseries.%s' % (savefig_format))
plt.close('all')
# -------------------------------------------------------------
# plot some histograms of the power at a small number of
# frequencies.
"""
histogram_loc2, hpwr2, lim2 = calculate_histograms(nposfreq, pwr, 100)
findex = []
f_of_interest = [0.5 * five_min, five_min, three_min, 2 * three_min, 3 * three_min]
for thisf in f_of_interest:
findex.append(np.unravel_index(np.argmin(np.abs(thisf - freqs)), freqs.shape)[0])
plt.figure(3)
plt.xlabel('power')
plt.ylabel('proportion found at given frequency')
plt.title(data_name + ' - power distributions')
for f in findex:
xx = histogram_loc2[1:] / np.log(10.0)
yy = hpwr2[f, :]
plt.loglog(xx, yy, label='%7.2f %s' % (freqs[f], freqfactor[1]))
plt.legend(loc=3, fontsize=10, framealpha=0.5)
plt.savefig(savefig + '.notlog_power_spectra_distributions.%s' % (savefig_format))
# plot out the time series
plt.figure(4)
full_ts.peek()
plt.savefig(savefig + '.full_ts_timeseries.%s' % (savefig_format))
plt.close('all')
"""
###############################################################
# Time series plots
# Plot all the analyzed time series
plt.figure(10)
for i in range(0, nx):
for j in range(0, ny):
plt.plot(t, dc_analysed[j, i, :])
plt.xlabel('time (seconds)')
plt.ylabel('analyzed emission ' + tsdetails)
plt.title(data_name)
plt.ylim(dc_analysed_minmax)
plt.xlim((t[0], t[-1]))
plt.savefig(savefig + '.all_analyzed_ts.%s' % (savefig_format))
# Plot a histogram of the studied data at each time
bins = 50
hist_dc_analysed = np.zeros((bins, nt))
for this_time in range(0, nt):
hist_dc_analysed[:, this_time], bin_edges = np.histogram(dc_analysed[:, :, this_time], bins=bins, range=dc_analysed_minmax)
hist_dc_analysed = hist_dc_analysed / (1.0 * nx * ny)
plt.figure(12)
plt.xlabel('time (seconds)')
plt.ylabel('analyzed emission ' + tsdetails)
plt.imshow(hist_dc_analysed, aspect='auto', origin='lower',
extent=(t[0], t[-1], dc_analysed_minmax[0], dc_analysed_minmax[1]))
plt.colorbar()
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_ts_histogram.%s' % (savefig_format))
###############################################################
# Fourier power plots
# Plot all the analyzed FFTs
plt.figure(11)
for i in range(0, nx):
for j in range(0, ny):
ts = TimeSeries(t, dc_analysed[j, i, :])
plt.loglog(freqs, ts.PowerSpectrum.ppower)
plt.loglog()
plt.axvline(five_min, color=s5min.color, linestyle=s5min.linestyle, label=s5min.label)
plt.axvline(three_min, color=s3min.color, linestyle=s3min.linestyle, label=s3min.label)
plt.xlabel('frequency (%s)' % (freqfactor[1]))
plt.ylabel('FFT power ' + tsdetails)
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_fft.%s' % (savefig_format))
# Plot a histogram of the studied FFTs at each time
bins = 50
minmax = [np.min(logpwr), np.max(logpwr)]
hist_dc_analysed_logpwr = np.zeros((bins, nposfreq))
for this_freq in range(0, nposfreq):
hist_dc_analysed_logpwr[:, this_freq], bin_edges = np.histogram(logpwr[:, :, this_freq], bins=bins, range=minmax)
hist_dc_analysed_logpwr = hist_dc_analysed_logpwr / (1.0 * nx * ny)
plt.figure(13)
plt.xlabel('frequency (%s)' % (freqfactor[1]))
plt.ylabel('FFT power ' + tsdetails)
plt.imshow(hist_dc_analysed_logpwr, aspect='auto', origin='lower',
extent=(freqs[0], freqs[-1], np.exp(minmax[0]), np.exp(minmax[1])))
plt.semilogy()
plt.colorbar()
plt.title(data_name)
plt.savefig(savefig + '.all_analyzed_fft_histogram.%s' % (savefig_format))
###############################################################
# Plot of the widths as a function of the frequency.
plt.figure(14)
plt.xlabel('frequency (%s)' % (freqfactor[1]))
plt.ylabel('decades of frequency')
plt.semilogx(freqs, (logiobs_distrib_width + error_logiobs_distrib_width) / np.log(10.0), label='+ error', linestyle='--')
plt.semilogx(freqs, (logiobs_distrib_width - error_logiobs_distrib_width) / np.log(10.0), label='- error', linestyle='--')
plt.semilogx(freqs, logiobs_distrib_width / np.log(10.0), label='estimated width')
plt.semilogx(freqs, logiobs_std / np.log(10.0), label='standard deviation')
plt.semilogx(freqs, (logiobs - logiobs_peak_location) / np.log(10.0), label='mean - fitted peak')
plt.title(data_name + ' - distribution widths')
plt.legend(loc=3, framealpha=0.3, fontsize=10)
plt.savefig(savefig + '.logiobs_distribution_width.%s' % (savefig_format))
###############################################################
# Save various data products
# Fourier Power of the analyzed data
ofilename = region_id
pkl_write(pkl_location,
'OUT.' + ofilename + '.fourier_power.pickle',
(freqs / freqfactor[0], pwr))
# Analyzed data
pkl_write(pkl_location,
'OUT.' + ofilename + '.dc_analysed.pickle',
(t, dc_analysed))
# Fourier transform
pkl_write(pkl_location,
'OUT.' + ofilename + '.fft_transform.pickle',
(freqs / freqfactor[0], fft_transform))
# Arithmetic mean of power spectra
pkl_write(pkl_location,
'OUT.' + ofilename + '.iobs.pickle',
(freqs / freqfactor[0], np.log(iobs)))
# Geometric mean of power spectra
#(freqs / freqfactor[0], logiobs, logiobs_distrib_width))
pkl_write(pkl_location,
'OUT.' + ofilename + '.logiobs.pickle',
(freqs / freqfactor[0], logiobs, iobs_peak, logiobs_peak_location, nx * ny, xccc, ccc, ccc_answer))
# Widths of the power distributions
pkl_write(pkl_location,
'OUT.' + ofilename + '.distribution_widths.pickle',
(freqs / freqfactor[0], logiobs_distrib_width, logiobs_std, np.abs(logiobs - logiobs_peak_location)))
# Error in the Widths of the power distributions
pkl_write(pkl_location,
'OUT.' + ofilename + '.distribution_widths_error.pickle',
(freqs / freqfactor[0], error_logiobs_distrib_width))
# Bump fit
#pkl_write(pkl_location,
# 'OUT.' + ofilename + '.bump_fit_all.pickle',
# (bump_ans_all, bump_err_all))
# Simple fit
#pkl_write(pkl_location,
# 'OUT.' + ofilename + '.simple_fit_all.pickle',
# (simple_ans_all, simple_err_all))
# Save the full time series to a CSV file
csv_timeseries_write(os.path.join(os.path.expanduser(scsv), window, manip),
'.'.join((data_name, 'average_analyzed_ts.csv')),
(t, full_data))
# Original data
csv_timeseries_write(os.path.join(os.path.expanduser(scsv)),
'.'.join((ident, 'average_original_ts.csv')),
(t, doriginal))
# plot some histograms of the log power at a small number of equally spaced
# frequencies
findex = np.arange(0, nposfreq, nposfreq / 5)
plt.figure(3)
plt.xlabel('$\log_{10}(power)$')
plt.ylabel('proportion found at given frequency')
plt.title(data_name + ' - power distributions')
for f in findex:
plt.plot(h[1][1:] / np.log(10.0), hpwr[f, :], label='%7.5f Hz' % (freqs[f]))
plt.legend(loc=3, fontsize=10)
plt.savefig(savefig + '.power_spectra_distributions.png')
# plot out the time series
plt.figure(4)
full_ts.peek()
plt.savefig(savefig + '.full_ts_timeseries.png')
#
# Make maps of the Fourier power
#
fmap = []
franges = [[1.0/360.0, 1.0/240.0], [1.0/240.0, 1.0/120.0]]
for fr in franges:
ind = []
for i, testf in enumerate(freqs):
if testf >= fr[0] and testf <= fr[1]:
ind.append(i)
fmap.append(np.sum(pwr[:,:,ind[:]], axis=2))
alpha = 0.0001
data[0] = 1.0
for i in range(0, nt - 1):
data[i+1] = data[i] + alpha*np.random.normal()
ts = TimeSeries(dt * np.arange(0, nt), data)
plt.figure(1)
ts.peek_ps()
plt.loglog()
plt.figure(2)
ts.peek()
this = ([ts.pfreq, ts.ppower],)
norm_estimate = np.zeros((3,))
norm_estimate[0] = ts.ppower[0]
norm_estimate[1] = norm_estimate[0] / 1000.0
norm_estimate[2] = norm_estimate[0] * 1000.0
background_estimate = np.zeros_like(norm_estimate)
background_estimate[0] = np.mean(ts.ppower[-10:-1])
background_estimate[1] = background_estimate[0] / 1000.0
background_estimate[2] = background_estimate[0] * 1000.0
estimate = {"norm_estimate": norm_estimate,
"background_estimate": background_estimate}
raise ValueError, "Input vector needs to be bigger than window size."
if window_len < 3:
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
s = np.r_[2 * x[0] - x[window_len - 1::-1], x, 2 * x[-1] - x[-1:-window_len:-1]]
if window == 'flat': #moving average
w = np.ones(window_len, 'd')
else:
w = eval('np.' + window + '(window_len)')
y = np.convolve(w / w.sum(), s, mode='same')
return y[window_len:-window_len + 1]
tsoriginal = TimeSeries(t, data)
plt.figure(10)
tsoriginal.peek()
meandata = np.mean(data)
# relative
data = (data - meandata) / meandata
#data = data - smooth(data, window_len=84)
# Create a time series object
ts = TimeSeries(t, data)
ts.label = 'emission'
ts.units = 'arb. units'
ts.name = 'simulated data [n=%4.2f]' % (model_param[1])
# frequencies
findex = np.arange(0, nposfreq, nposfreq / 5)
plt.figure(3)
plt.xlabel('$\log_{10}(power)$')
plt.ylabel('proportion found at given frequency')
plt.title(data_name + ' - power distributions')
for f in findex:
plt.plot(h[1][1:] / np.log(10.0),
hpwr[f, :],
label='%7.5f Hz' % (freqs[f]))
plt.legend(loc=3, fontsize=10)
plt.savefig(savefig + '.power_spectra_distributions.png')
# plot out the time series
plt.figure(4)
full_ts.peek()
plt.savefig(savefig + '.full_ts_timeseries.png')
#
# Make maps of the Fourier power
#
fmap = []
franges = [[1.0 / 360.0, 1.0 / 240.0], [1.0 / 240.0, 1.0 / 120.0]]
for fr in franges:
ind = []
for i, testf in enumerate(freqs):
if testf >= fr[0] and testf <= fr[1]:
ind.append(i)
fmap.append(np.sum(pwr[:, :, ind[:]], axis=2))
#
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
s = np.r_[2 * x[0] - x[window_len - 1::-1], x,
2 * x[-1] - x[-1:-window_len:-1]]
if window == 'flat': #moving average
w = np.ones(window_len, 'd')
else:
w = eval('np.' + window + '(window_len)')
y = np.convolve(w / w.sum(), s, mode='same')
return y[window_len:-window_len + 1]
tsoriginal = TimeSeries(t, data)
plt.figure(10)
tsoriginal.peek()
meandata = np.mean(data)
# relative
data = (data - meandata) / meandata
#data = data - smooth(data, window_len=84)
# Create a time series object
ts = TimeSeries(t, data)
ts.label = 'emission'
ts.units = 'arb. units'
ts.name = 'simulated data [n=%4.2f]' % (model_param[1])
# Get the normalized power and the positive frequencies