def get_circadian_movement(fus_df):
"""Calculates the circadian movement based on GPS location for participants
Basing implementation off of
https://github.com/sosata/CS120DataAnalysis/blob/master/features/estimate_circadian_movement.m
"""
# frequency range of 24 +- 0.5 hrs at a minute granularity
freq = np.linspace(86400 - 30 * 60, 86400 + 30 * 60, 60)
# scipy implementation requires angular frequency
freq = 2 * np.pi / freq
try:
# make sure to precenter each time series
energy_lat = sum(
lombscargle(fus_df['timestamp'],
fus_df['latitude'],
freq,
precenter=True,
normalize=True))
energy_long = sum(
lombscargle(fus_df['timestamp'],
fus_df['longitude'],
freq,
precenter=True,
normalize=True))
except ZeroDivisionError:
return np.nan
tot_energy = energy_lat + energy_long
if tot_energy > 0:
return np.log(energy_lat + energy_long)
else:
return np.nan
def test_normalize(self):
# Test normalize option of Lomb-Scarge.
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f)
pgram2 = lombscargle(t, x, f, normalize=True)
# check if normalization works as expected
assert_allclose(pgram * 2 / np.dot(x, x), pgram2)
assert_approx_equal(np.max(pgram2), 1.0, significant=2)
def test_precenter(self):
# Test if precenter gives the same result as manually precentering.
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
offset = 0.15 # Offset to be subtracted in pre-centering
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi) + offset
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f, precenter=True)
pgram2 = lombscargle(t, x - x.mean(), f, precenter=False)
# check if centering worked
assert_allclose(pgram, pgram2)
def test_normalize(self):
# Test normalize option of Lomb-Scarge.
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f)
pgram2 = lombscargle(t, x, f, normalize=True)
# check if normalization works as expected
assert_allclose(pgram * 2 / np.dot(x, x), pgram2)
assert_approx_equal(np.max(pgram2), 1.0, significant=2)
def test_precenter(self):
# Test if precenter gives the same result as manually precentering.
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
offset = 0.15 # Offset to be subtracted in pre-centering
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi) + offset
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f, precenter=True)
pgram2 = lombscargle(t, x - x.mean(), f, precenter=False)
# check if centering worked
assert_allclose(pgram, pgram2)
def __generate_ft__(self,
n=0,
s=500,
lock=False,
nymult=1,
num=1,
full=True,
se=0,
frange=[None]):
time, flux, meta = self.get_lc(n=n, full=full, se=se)
if not len(time) <= 1:
avg_sample_rate = (max(time) - min(time)) / len(time)
if avg_sample_rate != 0:
ny = 1 / (2 * avg_sample_rate)
res = 1 / (max(time) - min(time))
else:
ny = 1 / 24
res = 0.01
if lock:
us = s
else:
us = int(10 * ny / (res))
flux = self.normalize(flux)
start_freq = 0.1 * res
end_freq = nymult * ny
total_range = end_freq - start_freq
if frange[0] == None:
fts = np.zeros((num, 2, us))
for i in range(num):
sub_start = ((i / num) * total_range) + start_freq
sub_end = (((i + 1) / num) * total_range) + start_freq
f = np.linspace(sub_start, sub_end, us)
pgram = lombscargle(np.array(time),
np.array(flux),
f,
normalize=True)
fts[i][0] = f
fts[i][1] = pgram
else:
fts = np.zeros((1, 2, us))
f = np.linspace(frange[0], frange[1], us)
pgram = lombscargle(np.array(time),
np.array(flux),
f,
normalize=True)
fts[0][0] = f
fts[0][1] = pgram
return fts[:, 0, :], fts[:, 1, :], meta
else:
f = np.linspace(0, 1 / 24, s)
fts = np.zeros((num, 2, s))
for i in range(num):
fts[i][0] = f
fts[i][1] = np.zeros(s)
return fts[:, 0, :], fts[:, 1, :], meta
def findPeaks(times, rv, fap, oversample):
ntrials = 200
min_int = float("inf")
for i in range(len(times) - 1):
min_int = min(min_int, times[i + 1] - times[i])
# Identify frequencies at which to evaluate the periodogram
n0 = len(times)
T = max(times) - min(times)
k = np.linspace(1.0 / oversample, T / 1.5, T / 1.5 * oversample)
omegas = 2 * np.pi * k / T
# For each trial, randomly permute the data and generate a periodogram
maxes = []
for i in range(ntrials):
noise = np.random.permutation(rv)
psd = lombscargle(np.array(times), noise, omegas)
maxes.append(max(psd))
z = range(int(max(maxes) * 100 + 1))
# Calculate CDF for each z value
cdf = []
for i in z:
cdf.append(len([x for x in maxes if x > i / 100.0]) / float(ntrials))
#plot the CDF: P(max_peak > Z)
#plt.plot(np.array(z)/100.0, cdf)
#plt.show()
# Find the threshold frequency associated the given FAP
for i in range(len(cdf)):
if cdf[i] > fap:
idx = i
thres = z[idx + 1] / 100.0
psd = lombscargle(np.array(times), np.array(rv), omegas)
plt.plot(1 / omegas * 2 * np.pi, psd)
plt.axhline(thres, color='r')
plt.xlabel('Period (days)')
plt.ylabel('Power')
plt.show()
# find the periods for which the data has significant peaks
peaks = [
1 / omegas[x] * 2 * np.pi for x in range(len(psd)) if psd[x] > thres
]
print len(peaks)
return peaks
def findPeaks(times, rv, fap, oversample):
ntrials = 200
min_int = float("inf")
for i in range(len(times)-1):
min_int = min(min_int, times[i+1] - times[i])
# Identify frequencies at which to evaluate the periodogram
n0 = len(times)
T = max(times)-min(times)
k = np.linspace(1.0/oversample, T / 1.5, T/1.5 *oversample)
omegas = 2 * np.pi * k / T
# For each trial, randomly permute the data and generate a periodogram
maxes = []
for i in range(ntrials):
noise = np.random.permutation(rv)
psd = lombscargle(np.array(times), noise, omegas)
maxes.append(max(psd))
z = range(int(max(maxes)*100 + 1))
# Calculate CDF for each z value
cdf = []
for i in z:
cdf.append(len([x for x in maxes if x > i/100.0])/float(ntrials))
#plot the CDF: P(max_peak > Z)
#plt.plot(np.array(z)/100.0, cdf)
#plt.show()
# Find the threshold frequency associated the given FAP
for i in range(len(cdf)):
if cdf[i] > fap:
idx = i
thres = z[idx+1]/100.0
psd = lombscargle(np.array(times), np.array(rv), omegas)
plt.plot(1/omegas * 2 * np.pi, psd)
plt.axhline(thres, color='r')
plt.xlabel('Period (days)')
plt.ylabel('Power')
plt.show()
# find the periods for which the data has significant peaks
peaks = [1/omegas[x] * 2 * np.pi for x in range(len(psd)) if psd[x] > thres]
print len(peaks)
return peaks
def periodogram(x, y, period_low=1, period_high=35, res=200):
""" calculate the periodogram at the specified frequencies, return
periods, pgram """
periods = np.linspace(period_low, period_high, res)
# periods = np.logspace(np.log10(period_low), np.log10(period_high),
# res)
freqs = 2*np.pi/periods
try: pgram = signal.lombscargle(x, y, freqs)
# Scipy bug, will be fixed in 1.5.0
except ZeroDivisionError: pgram = signal.lombscargle(x+1, y, freqs)
return periods, pgram
def funcPoint(iP, axes):
kA = 0
siteNo = siteNoLst[iP]
startDate = pd.datetime(1979, 1, 1)
endDate = pd.datetime(2019, 12, 31)
ctR = pd.date_range(startDate, endDate)
dfData = pd.DataFrame({'date': ctR}).set_index('date')
dfC = usgs.readSample(siteNo, codeLst=codeLst, startDate=startDate)
dfQ = usgs.readStreamflow(siteNo, startDate=startDate)
dfQ = dfQ.rename(columns={'00060_00003': '00060'})
dfData = dfData.join(dfQ)
dfData = dfData.join(dfC)
# plot normalized time series
ax = axes[kA]
kA = kA + 1
t = dfData.index.values
dfDataN = (dfData - dfData.mean()) / dfData.std()
varLst = dfData.columns.tolist()
data = [dfDataN[var].values for var in varLst]
legLst = ['streamflow'
] + [usgs.codePdf.loc[code]['shortName'] for code in codeLst]
axplot.plotTS(ax, t, data, styLst='-***', cLst='krgb', legLst=legLst)
# plot C-Q
nc = len(codeLst)
for k in range(nc):
code = codeLst[k]
q = dfData['00060']
c = dfData[code]
[q, c], ind = utils.rmNan([q, c])
ax = axes[kA]
kA = kA + 1
ax.plot(np.log(q), np.log(c), 'r*')
# plot fractual
for k in range(nc):
code = codeLst[k]
dfV = dfData[dfData[code].notna()]
nt = len(dfData)
x = dfV.index.values.astype('datetime64[D]')
y = dfV[code].values
freq = 2 * np.pi / np.linspace(2, nt, nt)
power = signal.lombscargle(x, y, freq)
ax = axes[kA]
kA = kA + 1
ax.plot(np.log(freq / 2 * np.pi), np.log(power), '-*')
fyr = 2 * np.pi / 365
pyr = signal.lombscargle(x, y, [fyr])
ax.plot(np.log(fyr / 2 * np.pi), np.log(pyr), 'r*')
def periodogram(sampler, resid, pmin=3):
logpost = sampler.lnprobfn.f
if logpost.nkep == 0 and logpost.Pfixed is None:
plt.figure()
plt.errorbar(logpost.t, resid, logpost.dy, fmt='.')
else:
pers = np.array([logpost.get_periods(p) for p in sampler.flatchain])
pers = np.mean(pers, axis=0)
for p in pers:
plt.figure()
plt.title('P = {}'.format(p))
plt.errorbar(logpost.t % p, resid, logpost.dy, fmt='.')
T = logpost.t[-1] - logpost.t[0]
dt = np.min(np.diff(logpost.t))
df = 1.0 / T
fmax = 1.0 / (2 * dt)
fs = np.arange(df, fmax, df)
rpsd = ss.lombscargle(logpost.t, resid, 2 * np.pi * fs)
psd = ss.lombscargle(logpost.t, logpost.y, 2 * np.pi * fs)
N = len(logpost.t)
plt.figure()
plt.title('Raw')
plt.plot(1.0 / fs, np.sqrt(4 * psd / N) * 1000, '-k')
plt.xscale('log')
plt.xlabel(r'$P$ (day)')
plt.ylabel(r'$A$ ($\mathrm{m}/\mathrm{s}$)')
plt.figure()
plt.title('Cleaned')
plt.plot(1.0 / fs, np.sqrt(4 * rpsd / N) * 1000, '-b')
plt.xscale('log')
plt.xlabel(r'$P$ (day)')
plt.ylabel(r'$A$ ($\mathrm{m}/\mathrm{s}$)')
pers = 1.0 / fs
sel = pers > pmin
ibest = np.argmax(rpsd[sel])
pbest = pers[sel][ibest]
print 'Maximum amplitude period is ', pbest, ' at ', 1000 * np.sqrt(
rpsd[sel][ibest] * 4 / len(resid))
return fs, rpsd
def lomb_scargle_ampspec(t, x):
tstep = np.mean(np.ediff1d(t))
freqs = np.fft.fftfreq(x.size, tstep)
idxx = np.argsort(freqs)
freqs2 = freqs[idxx]
freqs2 = freqs2[freqs2>0]
try:
pgram = sp.lombscargle(t, x, freqs2*2*np.pi)
except:
#slightly perturb frequencies to prevent crashes
#in case of perfectly evenly spaced data
#print("Warning: perturbed frequencies a bit to avoid bug in scipy")
#freqs2=freqs2*(1+0.00001*np.random.random(freqs2.size))
pgram = sp.lombscargle(t, x, freqs2*2*np.pi)
return freqs2, np.sqrt(pgram/(t.size/4))
def periodogram(sampler, resid, pmin=3):
logpost = sampler.lnprobfn.f
if logpost.nkep == 0 and logpost.Pfixed is None:
plt.figure()
plt.errorbar(logpost.t, resid, logpost.dy, fmt='.')
else:
pers = np.array([logpost.get_periods(p) for p in sampler.flatchain])
pers = np.mean(pers, axis=0)
for p in pers:
plt.figure()
plt.title('P = {}'.format(p))
plt.errorbar(logpost.t % p, resid, logpost.dy, fmt='.')
T = logpost.t[-1] - logpost.t[0]
dt = np.min(np.diff(logpost.t))
df = 1.0/T
fmax = 1.0/(2*dt)
fs = np.arange(df, fmax, df)
rpsd = ss.lombscargle(logpost.t, resid, 2*np.pi*fs)
psd = ss.lombscargle(logpost.t, logpost.y, 2*np.pi*fs)
N = len(logpost.t)
plt.figure()
plt.title('Raw')
plt.plot(1.0/fs, np.sqrt(4*psd/N)*1000, '-k')
plt.xscale('log')
plt.xlabel(r'$P$ (day)')
plt.ylabel(r'$A$ ($\mathrm{m}/\mathrm{s}$)')
plt.figure()
plt.title('Cleaned')
plt.plot(1.0/fs, np.sqrt(4*rpsd/N)*1000, '-b')
plt.xscale('log')
plt.xlabel(r'$P$ (day)')
plt.ylabel(r'$A$ ($\mathrm{m}/\mathrm{s}$)')
pers = 1.0/fs
sel = pers > pmin
ibest = np.argmax(rpsd[sel])
pbest = pers[sel][ibest]
print 'Maximum amplitude period is ', pbest, ' at ', 1000*np.sqrt(rpsd[sel][ibest]*4/len(resid))
return fs, rpsd
def find_period(times, mags, minperiod=2., maxperiod=35., nbins=1000):
"""
Find the period of a lightcurve. The parameters used here imply magnitudes
but there is no reason this would not work if fluxes are passed.
:param times: A list of times for the given observations
:param mags: A list of magnitudes for the object at the given times
:param minperiod: Minimum period to search
:param maxperiod: Maximum period to search
:param nbins: Number of frequency bins to use in the search
:returns: Period in the same units as used in times. This is simply
the max value in the Lomb-Scargle periodogram
"""
# Recenter the magnitude measurements about zero
dmags = mags - np.median(mags)
# Create frequency bins
f = np.linspace(1./maxperiod, 1./minperiod, nbins)
# Calculate periodogram
pgram = lombscargle(times, dmags, f)
idx = np.argmax(pgram)
# Return period of the bin with the max value in the periodogram
return 1./f[idx]
def lomb(time, counts, frequencies):
"""Compute the lombscargle periodigram
Necessary wrapper around the set lomscargle algorithm
https://github.com/scipy/scipy/issues/2643
Parameters
----------
time : np.ndarray
array of data times
counts : np.ndarray
array of counts
frequencies : np.ndarray
What frequencies
Returns
-------
freqs : np.ndarray
calculated freqencies
"""
time = time.byteswap().newbyteorder().astype('float64')
counts = counts.byteswap().newbyteorder().astype('float64')
freqs = lombscargle(time, counts, frequencies)
return freqs
def test_lombscargle(
self,
lombscargle_gen,
num_in_samps,
num_out_samps,
precenter,
normalize,
use_numba,
):
cpu_x, cpu_y, cpu_f, gpu_x, gpu_y, gpu_f = lombscargle_gen(
num_in_samps, num_out_samps)
cpu_lombscargle = signal.lombscargle(cpu_x, cpu_y, cpu_f, precenter,
normalize)
gpu_lombscargle = cp.asnumpy(
cusignal.lombscargle(
gpu_x,
gpu_y,
gpu_f,
precenter,
normalize,
use_numba=use_numba,
))
assert array_equal(cpu_lombscargle, gpu_lombscargle)
def freq_hrv_ls(self, t, y):
"""Returns HRV (heart rate variability) in frequency domain using Lomb-Scargle periodogram.
Note - it may contain noise.
:param t: (array) input time stamps of phase values
:param y: (array) input phase values
:return: periodogram value amplitudes with corresponding frequencies
"""
indexes_peaks = indexes(y, min_dist=self.samp_rate / 2)
if len(indexes_peaks) < 2:
return np.array([0]), np.array([0])
peaklist = indexes_peaks
RR_list = np.diff(t[indexes_peaks]) * 1000
RR_x = peaklist[1:]
RR_y = RR_list
f = np.linspace(0.01, 0.5, 100)
try:
pgram = signal.lombscargle(RR_x, RR_y, f, normalize=True)
except ValueError:
return np.array([0]), np.array([0])
return pgram, f
def lomb(time, counts, frequencies):
"""Compute the lombscargle periodigram
Necessary wrapper around the set lomscargle algorithm
https://github.com/scipy/scipy/issues/2643
Parameters
----------
time : np.ndarray
array of data times
counts : np.ndarray
array of counts
frequencies : np.ndarray
What frequencies
Returns
-------
freqs : np.ndarray
calculated freqencies
"""
time = time.byteswap().newbyteorder().astype('float64')
counts = counts.byteswap().newbyteorder().astype('float64')
freqs = lombscargle(time, counts, frequencies)
return freqs
def periodogram_rvs(self,freqs=np.linspace(0.01,10,100)):
from scipy.signal import lombscargle
self.pgram = lombscargle(self.time_data,self.rvs_data,freqs,normalize=True)
plt.ylabel('Power')
plt.xlabel('Period')
plt.plot(1/freqs,self.pgram)
plt.show()
def parameter_initialiser(x, y, p):
t_min = np.amin(x)
t_range = np.amax(x) - t_min
if t_range == 0.0:
t_range = 1.0
# Estimate frequency. Starting with a Lomb-Scargle periodogram (which
# supports irregularly-spaced samples), we pick the strongest frequency
# component which leads to a pi time larger than t_min.
#
# TODO: Could use better heuristics for frequency range based on minimum
# distance between points -> aliasing.
freq = np.pi / t_range
freqs = np.linspace(0.1 * freq, 10 * freq, 2 * len(x))
pgram = lombscargle(x, y, freqs, precenter=True)
freq_order = np.argsort(-pgram)
for f in freqs[freq_order]:
t = 2 * np.pi / f
if t / 2 > t_min:
p["t_period"] = t
break
p["t_dead"] = 0.0
p["y_lower"] = np.clip(2 * np.mean(y) - 1, 0, 1)
# TODO: Estimate decay time constant using RMS amplitude from global mean
# in first and last chunk.
p["tau_decay"] = 1
def Lomb_Scargle(data, precision, min_period, max_period, period_jobs=1):
"""
Returns the period of *data* according to the
`Lomb-Scargle periodogram <https://en.wikipedia.org/wiki/Least-squares_spectral_analysis#The_Lomb.E2.80.93Scargle_periodogram>`_.
**Parameters**
data : array-like, shape = [n_samples, 2] or [n_samples, 3]
Array containing columns *time*, *mag*, and (optional) *error*.
precision : number
Distance between contiguous frequencies in search-space.
min_period : number
Minimum period in search-space.
max_period : number
Maximum period in search-space.
period_jobs : int, optional
Number of simultaneous processes to use while searching. Only one
process will ever be used, but argument is included to conform to
*periodogram* standards of :func:`find_period` (default 1).
**Returns**
period : number
The period of *data*.
"""
time, mags, *err = data.T
scaled_mags = (mags - mags.mean()) / mags.std()
minf, maxf = 2 * np.pi / max_period, 2 * np.pi / min_period
freqs = np.arange(minf, maxf, precision)
pgram = lombscargle(time, scaled_mags, freqs)
return 2 * np.pi / freqs[np.argmax(pgram)]
def test_lombscargle(num_in_samps, num_out_samps, precenter, normalize,
use_numba):
A = 2.0
w = 1.0
phi = 0.5 * np.pi
frac_points = 0.9 # Fraction of points to select
r = np.random.rand(num_in_samps)
x = np.linspace(0.01, 10 * np.pi, num_in_samps)
x = x[r >= frac_points]
y = A * np.cos(w * x + phi)
f = np.linspace(0.01, 10, num_out_samps)
cpu_lombscargle = signal.lombscargle(x, y, f, precenter, normalize)
d_x = cp.asarray(x)
d_y = cp.asarray(y)
d_f = cp.asarray(f)
gpu_lombscargle = cp.asnumpy(
cusignal.lombscargle(
d_x,
d_y,
d_f,
precenter,
normalize,
use_numba=use_numba,
))
assert array_equal(cpu_lombscargle, gpu_lombscargle)
def test_lombscargle_atan_vs_atan2(self):
# https://github.com/scipy/scipy/issues/3787
# This raised a ZeroDivisionError.
t = np.linspace(0, 10, 1000, endpoint=False)
x = np.sin(4 * t)
f = np.linspace(0, 50, 500, endpoint=False) + 0.1
q = lombscargle(t, x, f * 2 * np.pi)
def find_period_LS(times, mags, minperiod=2., maxperiod=35., nbinmax=10**5, verbose=False):
"""
Find the period of a lightcurve using scipy's lombscargle method.
The parameters used here imply magnitudes but there is no reason this would not work if fluxes are passed.
:param times: A list of times for the given observations
:param mags: A list of magnitudes for the object at the given times
:param minperiod: Minimum period to search
:param maxperiod: Maximum period to search
:param nbinmax: Maximum number of frequency bins to use in the search
:returns: Period in the same units as used in times. This is simply
the max value in the Lomb-Scargle periodogram
"""
if minperiod < 0:
minperiod = 0.01
nbins = int((times.max() - times.min())/minperiod * 1000)
if nbins > nbinmax:
if verbose:
print 'lowered nbins'
nbins = nbinmax
# Recenter the magnitude measurements about zero
dmags = mags - np.median(mags)
# Create frequency bins
f = np.linspace(1./maxperiod, 1./minperiod, nbins)
# Calculate periodogram
pgram = lombscargle(times, dmags, f)
idx = np.argmax(pgram)
# Return period of the bin with the max value in the periodogram
return 1./f[idx]
def test_frequency(self):
"""Test if frequency location of peak corresponds to frequency of
generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01 * np.pi, 10. * np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w * t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
P = lombscargle(t, x, f)
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
delta = f[1] - f[0]
assert_(w - f[np.argmax(P)] < (delta / 2.))
def test_amplitude(self):
"""Test if height of peak in normalized Lomb-Scargle periodogram
corresponds to amplitude of the generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01 * np.pi, 10. * np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w * t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f)
# Normalize
pgram = np.sqrt(4 * pgram / t.shape[0])
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
assert_approx_equal(np.max(pgram), ampl, significant=2)
def periodogram(time, flux, f):
# computed periodogram is unnormalized
# takes the value (A**2) * N/4
# for a harmonic signal with amplitude A for sufficiently large N
pgram = lombscargle(time, flux, f)
plt.subplot(2, 1, 1)
plt.plot(time, flux, '.')
plt.xlabel('Time (MJD)')
plt.ylabel('Flux')
normval = t.shape[0]
plt.subplot(2, 1, 2)
power = np.sqrt(4*(pgram/normval))
# plot normalized periodogram
plt.plot(f, power)
plt.xlabel('Ang. Frequency (MJD)')
plt.ylabel('Power')
plt.show()
big_frequency = f[np.argmax(pgram)] # dominant ang. frequency
big_power = power[np.argmax(pgram)] # dominant power
print "dominant ang. frequency =", big_frequency
print "domninant power =", big_power
def get_pgram(times, mags, periods):
freqs = 2*np.pi / periods
scaled_mags = (mags - np.mean(mags)) / np.std(mags)
pgram = lombscargle(times, scaled_mags, freqs)
return pgram
def plotlb(outputfile,index,columnfile,name='',plot=True,getarg=False,periods=np.linspace(0.2, 1.4, 4000)):
datagoodmjd= createdatadicclean(outputfile,index,columnfile,name=name,timeformat='mjd')
t, mag, dmag = datagoodmjd['time'], datagoodmjd['VEGAMAG'],datagoodmjd['errorsmag']
# Choose a period grid
periods = periods
#periods = np.linspace(0.2, 1.4, 4000)
ang_freqs = 2 * np.pi / periods
# compute the (unnormalized) periodogram
# note pre-centering of y values!
power = lombscargle(t.flatten(), mag - mag.mean(), ang_freqs,normalize=False,precenter=True)
# normalize the power
N = len(t.flatten())
#power *= 2 / (N * mag.std() ** 2)
if plot == True:
# plot the results
fig, ax = plt.subplots()
ax.plot(periods, power)
ax.set(ylim=(0, 0.8), xlabel='period (days)',
ylabel='Lomb-Scargle Power');
if getarg == True:
return periods, power,t,mag,dmag
def test_frequency(self):
"""Test if frequency location of peak corresponds to frequency of
generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
P = lombscargle(t, x, f)
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
delta = f[1] - f[0]
assert_(w - f[np.argmax(P)] < (delta/2.))
def get_best_n(self):
periods = 10**np.linspace(-3,4,1000)
omega = 2*np.pi/periods
res=sig.lombscargle(self.t-self.t[0],self.vr,omega)
max_pers = np.argsort(res)
return omega[max_pers[-1]]
def lomb(data_df: pd.DataFrame, min_period: float, max_period: float):
"""
Lomb–Scargle periodogram implementation
:param data: list
:param high_frequency: float
:param low_frequency: float
:return lomb-scargle pgram and frequency values
"""
time_stamps = data_df.Dt.values
samples = data_df.altdiff_dem.values
window = signal.tukey(len(samples))
samples *= window
# nout = 10000 # number of frequency-space points at which to calculate the signal strength (output)
periods = np.linspace(min_period, max_period, len(data_df) * 100)
freqs = 1.0 / periods
frequency_range = 2 * np.pi * freqs
# frequency_range = np.linspace(low_frequency, high_frequency, len(data_df))
result = signal.lombscargle(time_stamps,
samples,
frequency_range,
precenter=True,
normalize=True)
return result, frequency_range
def get_best_n(self):
periods = 10**np.linspace(-3, 4, 1000)
omega = 2 * np.pi / periods
res = sig.lombscargle(self.t - self.t[0], self.vr, omega)
max_pers = np.argsort(res)
return omega[max_pers[-1]]
def calculate_frequency_features(data_RR, frequency_options):
"""
Calculate frequency-based features for given chunk of pulse.
Args
data_RR (np.array of np.int64): data in format (time [ms], interval [ms])
frequency_options (dict): see get_default_pulse_features_params()
Returns
features (dict): namesa and calculated features for given pulse chunk
"""
times = data_RR[:, 0].copy().astype(float)
intervals = data_RR[:, 1].copy().astype(float)
features = []
f = np.linspace(0.001, 0.4, 100)
pgram = sg.lombscargle(times/1000, intervals/1000, f)
bounds_names = ['ULF', 'VLF', 'LF', 'HF']
frequency_bounds = frequency_options['frequency bounds']
power = np.mean(pgram) * (frequency_bounds[-1] - frequency_bounds[0])
for i in xrange(len(frequency_bounds) - 1):
idx = (f > frequency_bounds[i]) * (f <= frequency_bounds[i+1])
features.append([bounds_names[i], np.mean(pgram[idx]) * (frequency_bounds[i+1] - frequency_bounds[i])])
features.append([bounds_names[i] + 'rel', np.sum(pgram[idx]) / power])
features.append([bounds_names[i] + 'peak', f[idx][np.argmax(pgram[idx])]])
if i > 1:
features.append([bounds_names[i] + 'normalized', np.sum(pgram[idx]) / (power - features[3][1])]) #features[3][1] is VLF and is already calculated
features.append(['LF/HF', pgram[2] / pgram[3]])
return features
def find_period_LS(times, mags, minperiod=2., maxperiod=35., nbinmax=10**5, verbose=False):
"""Find the period of a lightcurve using scipy's lombscargle method.
The parameters used here imply magnitudes but there is no reason this would not work if fluxes are passed.
:param times: A list of times for the given observations
:param mags: A list of magnitudes for the object at the given times
:param minperiod: Minimum period to search
:param maxperiod: Maximum period to search
:param nbinmax: Maximum number of frequency bins to use in the search
:returns: Period in the same units as used in times. This is simply
the max value in the Lomb-Scargle periodogram
"""
if minperiod < 0:
minperiod = 0.01
nbins = int((times.max() - times.min())/minperiod * 1000)
if nbins > nbinmax:
if verbose:
print('lowered nbins')
nbins = nbinmax
# Recenter the magnitude measurements about zero
dmags = mags - np.median(mags)
# Create frequency bins
f = np.linspace(1./maxperiod, 1./minperiod, nbins)
# Calculate periodogram
pgram = lombscargle(times, dmags, f)
idx = np.argmax(pgram)
# Return period of the bin with the max value in the periodogram
return 1./f[idx]
def test_amplitude(self):
"""Test if height of peak in normalized Lomb-Scargle periodogram
corresponds to amplitude of the generated input signal.
"""
# Input parameters
ampl = 2.
w = 1.
phi = 0.5 * np.pi
nin = 100
nout = 1000
p = 0.7 # Fraction of points to select
# Randomly select a fraction of an array with timesteps
np.random.seed(2353425)
r = np.random.rand(nin)
t = np.linspace(0.01*np.pi, 10.*np.pi, nin)[r >= p]
# Plot a sine wave for the selected times
x = ampl * np.sin(w*t + phi)
# Define the array of frequencies for which to compute the periodogram
f = np.linspace(0.01, 10., nout)
# Calculate Lomb-Scargle periodogram
pgram = lombscargle(t, x, f)
# Normalize
pgram = np.sqrt(4 * pgram / t.shape[0])
# Check if difference between found frequency maximum and input
# frequency is less than accuracy
assert_approx_equal(np.max(pgram), ampl, significant=2)
def Lomb_Scargle(data, precision, min_period, max_period, period_jobs=1):
"""
Returns the period of *data* according to the
`Lomb-Scargle periodogram <https://en.wikipedia.org/wiki/Least-squares_spectral_analysis#The_Lomb.E2.80.93Scargle_periodogram>`_.
**Parameters**
data : array-like, shape = [n_samples, 2] or [n_samples, 3]
Array containing columns *time*, *mag*, and (optional) *error*.
precision : number
Distance between contiguous frequencies in search-space.
min_period : number
Minimum period in search-space.
max_period : number
Maximum period in search-space.
period_jobs : int, optional
Number of simultaneous processes to use while searching. Only one
process will ever be used, but argument is included to conform to
*periodogram* standards of :func:`find_period` (default 1).
**Returns**
period : number
The period of *data*.
"""
time, mags, *err = data.T
scaled_mags = (mags-mags.mean())/mags.std()
minf, maxf = 2*np.pi/max_period, 2*np.pi/min_period
freqs = np.arange(minf, maxf, precision)
pgram = lombscargle(time, scaled_mags, freqs)
return 2*np.pi/freqs[np.argmax(pgram)]
def narrow_periodgram(time, amplitude, center_frequency, frequency_width,
num=1000):
f_min = center_frequency - frequency_width / 2
f_max = center_frequency + frequency_width / 2
frequencies = np.linspace(f_min, f_max, num=num)
pgram = signal.lombscargle(time, amplitude, 2 * np.pi * frequencies)
return (frequencies, pgram)
def RRI_2_LFHF_ls(dataset):
time = dataset["elapsed_time"]
t = np.array(time)
rri = dataset["rri"]
ibi = np.array(rri)
phi = 4.0 * np.pi
f = np.linspace(0.001, phi, 1000)
Pgram = lombscargle(t, ibi, f, normalize=True)
vlf = 0.04
lf = 0.15
hf = 0.4
Fs = 250
lf_freq_band = (f >= vlf) & (f <= lf)
hf_freq_band = (f >= lf) & (f <= hf)
dy = 1.0 / Fs
LF = np.trapz(y=abs(Pgram[lf_freq_band]), x=None, dx=dy)
HF = np.trapz(y=abs(Pgram[hf_freq_band]), x=None, dx=dy)
LF_HF = float(LF) / HF
return LF_HF
def test_lombscargle_atan_vs_atan2(self):
# https://github.com/scipy/scipy/issues/3787
# This raised a ZeroDivisionError.
t = np.linspace(0, 10, 1000, endpoint=False)
x = np.sin(4*t)
f = np.linspace(0, 50, 500, endpoint=False) + 0.1
q = lombscargle(t, x, f*2*np.pi)
def parameter_initialiser(x, y, p):
# Sort data by time (x-axis)
mask = np.argsort(x)
x = x[mask]
y = y[mask]
min_step = np.min(x[1:] - x[:-1])
duration = x[-1] - x[0]
# Nyquist limit does not apply to irregularly spaced data
# We'll use it as a starting point anyway...
f_max = 0.5 / min_step
# relaxed Fourier limit
f_min = 0.25 / duration
omega_list = 2 * np.pi * np.linspace(f_min, f_max, int(f_max / f_min))
# the periodogram should give the correct width up-to a factor of 2
pgram = lombscargle(x, y, omega_list, precenter=True)
p["width"] = omega_list[np.argmax(pgram)] / np.pi
p['y0'] = np.mean(y)
y_diff = y - p['y0']
peak_ind = np.argmax(np.abs(y_diff))
p['x0'] = x[peak_ind]
p['a'] = y[peak_ind] - p['y0']
return p
def getPeriodograms_SLOW(self, rejectSet, times, window, normalize,
ang_freqs):
pgrams = []
t = np.array(times) # times
hammingWindow = np.array(window)
n = len(t)
print "n: " + str(n)
for ch in rejectSet:
y = np.array(ch) # samples
y = y * hammingWindow # apply hamming window
y = y - np.mean(
y
) # demeaned samples ******** IS THIS NECESSARY?? Answer: yes to avoid low frequency noise
pgram = signal.lombscargle(t, y, ang_freqs)
if normalize:
pgram = np.sqrt(4 * (pgram / n))
print "len(pgram): " + str(len(pgram))
pgrams.append(pgram)
return pgrams
def lombscarglescipy(self, period):
f = np.linspace(0.1, 1000, 10000)
pgram = signal.lombscargle(self.d, self.m, f)
periods = 2 * np.pi / f
normval = self.d.shape[0]
power = np.sqrt(4 * (pgram / normval))
x = periods
y = power
fig, axes = plt.subplots(1, 2, figsize=(8, 8))
ax1, ax2 = axes.flatten()
ax1.plot(x, y, color="red", linewidth=2)
ax1.set_xlabel("period (days)")
ax1.set_ylabel("Lomb-Scargle.scipy Power")
ax1.set_xlim(0, 10)
ax1.legend()
phase = 1.0 * self.d / (period)
phase = phase % 1 * 1
ax2.plot(phase, self.m, 'ro')
ax2.set_xlabel("phase")
ax2.set_ylabel("Mag")
#ax2.set_ylim(0,1)
ax2.set_xlim(0, 1)
ax2.legend()
# plt.savefig('/home/yf/ptftry/pic/Lomb-Scargle.png')
plt.show()
def Gen_FT(time, flux, NyFreq, s, power_spec=False, periodigram=False):
"""
Description:
Generate a Fourier Transform (Lomb Scargle Periodigram techniacally) given a time
and value set. Can also generate a power spectrum.
Args:
time - Time string to pass in (numeric 1D iteratable)
flux - value string to pass in (numeric 1D iteratable)
NyFreq - Nyquist frequency of the time string (float)
s - number of samples in frequency array (int)
power_spec - generate a power spectrum of not (bool)
returns:
dicionay:
'Freq' - Frequency array in Hz (float)
'Amp' - Amplitude array for FT (float)
Raises:
HARD FAIL - Raised on exessive NaN values in Time Array
"""
# return Gen_flsp(time, flux, NyFreq, s)
# return Gen_fft(time, flux, NyFreq)
timeSansNAN = []
for checksum in time:
if math.isnan(checksum) is False:
timeSansNAN.append(checksum)
# Power Spectrum
if len(timeSansNAN) > 0:
res = 1 / (max(timeSansNAN) - min(timeSansNAN))
else:
warn('NON FATAL ERROR (time Not Build Correctly) |'
'ATTEMPTING RECOVERING WITH DEFAULT SETTINGS')
try:
res = 1.0 / 30.0
warn('RECOVERY [OKAY]')
except:
warn('RECOVERY [FAILED] | HARD FAIL')
return -1
# samples = int(NyFreq/res) * 10
samples = s
f = np.linspace(res / 10, NyFreq, samples)
xuse = np.asarray(time)
yuse = np.asarray(flux)
if not periodigram:
try:
pgram = lombscargle(xuse, yuse, f * 2 * np.pi)
except ZeroDivisionError:
warn('Zero division encountered in GEN_FT')
pgram = np.linspace(0, 1, samples)
normval = xuse.shape[0]
if power_spec is False:
pgramgraph = np.sqrt(4 * (pgram / normval))
else:
pgramgraph = pgram
fgo = f
return {'Freq': fgo.tolist(), 'Amp': pgramgraph.tolist()}
else:
frequency, chi2 = periodigram()
def lombscargle_scipy(t,
y,
frequency,
normalization='normalized',
center_data=True):
"""Lomb-Scargle Periodogram
This is a wrapper of ``scipy.signal.lombscargle`` for computation of the
Lomb-Scargle periodogram. This is a relatively fast version of the naive
O[N^2] algorithm, but cannot handle heteroskedastic errors.
Parameters
----------
t, y: array_like
times, values, and errors of the data points. These should be
broadcastable to the same shape.
frequency : array_like
frequencies (not angular frequencies) at which to calculate periodogram
normalization : string (optional, default='normalized')
Normalization to use for the periodogram
TODO: figure out what options to use
center_data : bool (optional, default=True)
if True, pre-center the data by subtracting the weighted mean
of the input data.
Returns
-------
power : array_like
Lomb-Scargle power associated with each frequency.
Units of the result depend on the normalization.
References
----------
.. [1] M. Zechmeister and M. Kurster, A&A 496, 577-584 (2009)
.. [2] W. Press et al, Numerical Recipies in C (2002)
.. [3] Scargle, J.D. 1982, ApJ 263:835-853
"""
if not HAS_SCIPY:
raise ValueError("scipy must be installed to use lombscargle_scipy")
t, y = np.broadcast_arrays(t, y)
frequency = np.asarray(frequency)
assert t.ndim == 1
assert frequency.ndim == 1
if center_data:
y = y - y.mean()
# Note: scipy input accepts angular frequencies
p = signal.lombscargle(t, y, 2 * np.pi * frequency)
if normalization == 'unnormalized':
pass
elif normalization == 'normalized':
p *= 2 / (t.size * np.mean(y**2))
else:
raise ValueError("normalization='{0}' "
"not recognized".format(normalization))
return p
def get_ls(times, dat):
'''Given time and data arrays, return a Lomb-Scargle periodogram:
a tuple (freq, Fdat) of a frequency array and an intensity array.'''
freqs = np.fft.fftfreq(int(times[-1] - times[0])) # interval, not size
Fdat = spsignal.lombscargle(times, dat, 2*np.pi*freqs) # 1/s -> rad/s
return (freqs, Fdat)
def get_outputs(self, output_refs: List[int]):
try:
pgram = si.lombscargle(np.roll(self.buffer[0], self.index),
np.roll(self.buffer[1], self.index), self.w)
except ZeroDivisionError:
return [0 for _ in output_refs]
outputs = np.sqrt(4 * (pgram / self.normval))
return [outputs[output_ref] for output_ref in output_refs]
def window(b):
time, depth = np.genfromtxt("data/l45b{0}_cadence.txt".format(b)).T
ps = np.linspace(0.1, 100, 1000)
fs = 1.0 / ps
ys = np.ones_like(time)
normval = time.shape[0]
pgram = sps.lombscargle(time, ys, 2 * np.pi * fs)
return ps, pgram, normval, time, depth
def lombscargle_scipy(t, y, frequency, normalization='normalized',
center_data=True):
"""Lomb-Scargle Periodogram
This is a wrapper of ``scipy.signal.lombscargle`` for computation of the
Lomb-Scargle periodogram. This is a relatively fast version of the naive
O[N^2] algorithm, but cannot handle heteroskedastic errors.
Parameters
----------
t, y: array_like
times, values, and errors of the data points. These should be
broadcastable to the same shape.
frequency : array_like
frequencies (not angular frequencies) at which to calculate periodogram
normalization : string (optional, default='normalized')
Normalization to use for the periodogram
TODO: figure out what options to use
center_data : bool (optional, default=True)
if True, pre-center the data by subtracting the weighted mean
of the input data.
Returns
-------
power : array_like
Lomb-Scargle power associated with each frequency.
Units of the result depend on the normalization.
References
----------
.. [1] M. Zechmeister and M. Kurster, A&A 496, 577-584 (2009)
.. [2] W. Press et al, Numerical Recipies in C (2002)
.. [3] Scargle, J.D. 1982, ApJ 263:835-853
"""
if not HAS_SCIPY:
raise ValueError("scipy must be installed to use lombscargle_scipy")
t, y = np.broadcast_arrays(t, y)
frequency = np.asarray(frequency)
assert t.ndim == 1
assert frequency.ndim == 1
if center_data:
y = y - y.mean()
# Note: scipy input accepts angular frequencies
p = signal.lombscargle(t, y, 2 * np.pi * frequency)
if normalization == 'unnormalized':
pass
elif normalization == 'normalized':
p *= 2 / (t.size * np.mean(y ** 2))
else:
raise ValueError("normalization='{0}' "
"not recognized".format(normalization))
return p
def compute_power_series(data, min_period, max_period, n=250):
periods = np.linspace(min_period, max_period, n)
assert (periods > 0).all(), "Periods must be greater than 0"
freqs = 2. * np.pi / periods
med_flux = np.median(data.flux)
power = signal.lombscargle(data.mjd.astype(float),
(data.flux - med_flux).astype(float),
freqs)
return PowerSeries(periods, power)
def periodogram(x, rv, f, max_period):
'''
Computes a Lomb-Scargle Periodogram of the input RV data.
This was adapted from Jake Vanderplas' article "Fast Lomb-Scargle Periodograms in Python."
Parameters
----------
x : list
The times at which the data points were gathered.
rv : list
The values of the measurand at the corresponding time, x.
f : float
The number of samples to take over the interval.
max_period : float
The maximum of the interval of periods to check.
Returns
-------
periods : array_like[len(f)]
Equally spaced array of possible period values.
powers : array_like[len(f)]
The calculated Power values over the range of periods,
these form the normalized Lomb-Scargle Periodogram.
delta_x : float
The smallest separation between two values in x.
'''
from scipy.signal import lombscargle
# Sort the time data chronologically.
x = np.sort(np.array(x))
rv = np.array(rv)
# Start delta_x very large
delta_x = np.inf
# Iteratively lower delta_x
for i in range(0, len(x)-2):
if x[i+1]-x[i] < delta_x and x[i+1]-x[i] != 0:
delta_x = x[i+1]-x[i]
# Compute the periodogram
periods = np.linspace(delta_x, max_period, num = f)
ang_freqs = 2 * pi / periods
powers = lombscargle(x, rv - rv.mean(), ang_freqs)
powers *= 2 / (len(x) * rv.std() ** 2)
return periods, powers, delta_x
def pgram_peaks(freq, flux, f, num):
from scipy.signal import lombscargle
normval = freq.shape[0]
pgram = lombscargle(freq, flux, f)/normval
pgram = np.sqrt(4*(pgram/normval))
# find local maxima not at the edge of the periodogram
maxmask = np.r_[False, pgram[1:] > pgram[:-1]] &\
np.r_[pgram[:-1] > pgram[1:], False]
sortarg = np.argsort(pgram[maxmask])
peak_freqs = f[maxmask][sortarg[-num:]]
peak_flux = pgram[maxmask][sortarg[-num:]]
return pgram, peak_freqs, peak_flux
def psd(data,timestamp,winLen=2000,graph=False,overlap=1,nout=20,maxFreq=20):
psd=[]
data=np.array(data)
timestamp=np.array(timestamp)
norm=[]
f=0
for i in data:
norm.append(np.sqrt(i[0]**2+i[1]**2+i[2]**2))
norm=np.array(norm)
#Create windows of 2seconds of data
previous=0
for i in range(len(timestamp)-overlap):
if i>0:
if timestamp[i]-timestamp[previous]>winLen and len(norm[previous:i])>10:
dataWindow=norm[previous:i]
timeWindow=timestamp[previous:i]
timeWindow=(timeWindow-timeWindow[0])/1000
f = np.linspace(0.01, maxFreq, nout)
tempOut=sp2.lombscargle(timeWindow,dataWindow,f)
tempOut=np.sqrt(4*tempOut/len(dataWindow))
previous=previous+overlap
psd.append(tempOut)
if graph:
plt.subplot(2, 1, 1)
plt.plot(timeWindow,dataWindow, 'b')
plt.subplot(2, 1, 2)
plt.plot(f, tempOut)
plt.show()
return psd,f,norm
#First calculate the power spectrum density on the norm
#then calculate statistics over the resulting
#have in mind that I should use different frequencies
#for the power spectrum density estimation
#Also, remember that the PSD is calculated over a window
#of data ideally here I also produce the labels
#for the data points as well
#Once all this is done I guess the remaining part is just the Crossvalidation
print(norm)
pass
def apply_filter(self, array):
if len(array.shape)!=1:
return False
# make frequency axis
df = 1/abs(array.coords[0][-1] - array.coords[0][0]) # time is stored in ps -> 1/ps = THz
my = max(abs(array.data))
data_f = np.linspace(df/array.shape[0], df*(array.shape[0]-1)*np.pi, array.shape[0]) # Lomb-Scargle doesn't allow f=0
#data_f = data_f[:len(data_f)/2-1] # return frequencies up to 1/dt/2 to be consistent with FFT (not compulsory)
# calculate spectrum
data_s = abs(lombscargle(array.coords[0], array.data/my, data_f))*my**2
array.coords[0] = data_f/(2*np.pi)
array.data = data_s
return True
def _fk_ls_filter_eliminate_phase_sp(ArrayData, y_dist=False, radius=None, maxk=False):
"""
Only use with the function fk_filter!
Function to test the fk workflow with synthetic data
param data: data of the array
type data: numpy.ndarray
param snes: slownessvalue of the desired extracted phase
type snes: int
"""
# Define freq Array
freq = np.zeros((len(ArrayData), len(ArrayData[0]) / 2 + 1)) + 1j
for i in range(len(ArrayData)):
freq_new = np.fft.rfftn(ArrayData[i])
freq[i] = freq_new
# Define k Array
freqT = freq.conj().transpose()
knum = np.zeros( ( len(freqT), len(freqT[0]) /2 +1 ))
#calc best range
N = len(freqT[0])
dN = ( max(freqT[0]) - min(freqT[0]) / N )
f_temp = np.fft.rfftfreq(len(freqT[0]), dN) * 2.* np.pi
#1. try:
#period_range = np.linspace(min_wavelength, max_bound, len(freqT[0]))
#2. try:
#period_range = np.linspace(f_temp[1], max(f_temp), N)
#3. try:
period_range = f_temp
#period_range = period_range.astype('float')
period_range[0] = 1.
#after this change the first outputparameter of the periodogram to a
#correlation between the signal and a e^0 function ;)
period_range = period_range.astype('float')
for j in range(len(freqT)):
k_new = signal.lombscargle(y_dist, abs(freqT[j]), period_range)
k_new = ls2ifft_prep(k_new, abs(freqT[j]))
knum[j] = k_new
#change dtype to integer, for further processing
period_range = period_range.astype('int')
fkspectra = knum
dsfft = line_set_zero(fkspectra, 0, radius)
return fkspectra.conj().transpose(), period_range
def periodicity(df, col):
x = df[col]
t = (df.position_update_timestamp - df.position_update_timestamp.min())/pd.Timedelta('1s')
# We sample at 1 hz best, so we can't measure any components above 0.5 hz
# We can in principle see very low frequency all the way down to dc
# but we can't tell the difference between dc and an 8h frequency
# If we chunk down to 30m or 1h, 1e-4 is a better lower bound
f = np.logspace(-4, np.log10(0.5), 10000)# in hertz
try:
return f, signal.lombscargle(t.values, x.values.astype(float), f)
except ZeroDivisionError:
return [], []
def get_period(curva):
from scipy.signal import lombscargle
x = np.array(curva.index) - min(curva.index)
mag_mean, mag_std = np.mean(curva['mag']), np.std(curva['mag'])
y = (np.array(curva['mag']) - mag_mean)/mag_std
T_tot = np.amax(x) - np.amin(x)
f_N = 0.5*(1/get_avg_timestep(curva))
f = np.arange(4/T_tot, 10, 0.1/T_tot)
f = f*2*np.pi
P = lombscargle(x, y, f)
f_max = f[P.argmax()]/(2*np.pi)
return 1/f_max
def period(mag, index):
from scipy.signal import lombscargle
x = np.array(index) - min(index)
mag_mean, mag_std = np.mean(mag), np.std(mag)
y = (np.array(mag) - mag_mean)/mag_std
T_tot = np.amax(x) - np.amin(x)
f_N = 0.5*(1/get_avg_timestep(index))
f = np.arange(4/T_tot, 10, 0.1/T_tot)
f = f*2*np.pi
P = lombscargle(np.ravel(x), np.ravel(y), np.ravel(f))
f_max = f[P.argmax()]/(2*np.pi)
return 1/f_max
def periodogram(self,pmin=0.5,pmax=60,npts=2000,
recalc=False):
pers = np.logspace(np.log10(pmin),np.log10(pmax),npts)
if np.array_equal(pers,self._pers) and not recalc:
pgram = self._pgram
else:
freqs = (2*np.pi)/(pers)
t = self.t[~self.mask]
f = self.f[~self.mask]
pgram = lombscargle(t.astype('float64'),
f.astype('float64'),
freqs.astype('float64'))
self._pgram = pgram
self._pers = pers
return pers,pgram
def get_period(time, flux):
scaled_flux = (flux - flux.mean()) / flux.std()
freqs = np.linspace(0, 100, len(time))[1:]
power = lombscargle(time, scaled_flux, freqs)
# Normalize
# power = np.sqrt(4.0 * power / time.shape[0])
# Calculate false alarm probability
# fap = get_fap(freqs, time, power)
# Get period
period = 1. / (freqs / 2.0 / np.pi)
print(period, power)
return period, power#, fap
