def test_oadev_ci(self):
s32rows = testutils.read_stable32(resultfile='oadev_decade.txt',
datarate=1.0)
for row in s32rows:
data = testutils.read_datafile(data_file)
(taus, devs, errs, ns) = allan.oadev(data,
rate=rate,
taus=[row['tau']])
edf = allan.edf_greenhall(alpha=row['alpha'],
d=2,
m=row['m'],
N=len(data),
overlapping=True,
modified=False,
verbose=True)
(lo, hi) = allan.confidence_intervals(devs[0],
ci=0.68268949213708585,
edf=edf)
print("n check: ", testutils.check_equal(ns[0], row['n']))
print("dev check: ",
testutils.check_approx_equal(devs[0], row['dev']))
print(
"min dev check: ", lo, row['dev_min'],
testutils.check_approx_equal(lo,
row['dev_min'],
tolerance=1e-3))
print(
"max dev check: ", hi, row['dev_max'],
testutils.check_approx_equal(hi,
row['dev_max'],
tolerance=1e-3))
def test_phasedat_adev(self):
#(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns) = read_stable32( 'phase_dat_adev_octave.txt' , 1.0 )
s32_rows = testutils.read_stable32( 'phase_dat_adev_octave.txt' , 1.0 )
phase = testutils.read_datafile('PHASE.DAT')
(taus,devs,errs,ns) = allan.adev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
los=[]
his=[]
for (d,t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall( alpha=0, d=2, m=t, N=len(phase), overlapping = False, modified=False )
(lo,hi) = allan.confidence_intervals( dev=d, ci=0.68268949213708585, edf=edf2 ) # 0.68268949213708585
#(lo2,hi2) = allan.confidence_intervals( dev=d, ci=0.68268949213708585, edf=edf2, use_scipy_chi2_ppf=False )
#testutils.check_approx_equal(lo, lo2, tolerance=1e-4)
#testutils.check_approx_equal(hi, hi2, tolerance=1e-4)
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (s32['n'], s32['tau'], s32['dev_min'], s32['dev'], s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" % (n2, t2, round(lo2,5), round(d2,5), round(hi2,5) ))
testutils.check_approx_equal(s32['dev_min'], lo2,tolerance=1e-3)
testutils.check_approx_equal(s32['dev'], d2,tolerance=1e-4)
testutils.check_approx_equal(s32['dev_max'], hi2,tolerance=1e-3)
print("----")
def test_phasedat_totdev(self):
(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi,
s32_ns) = read_stable32('phase_dat_totdev_octave.txt', 1.0)
phase = read_datafile('PHASE.DAT')
(taus, devs, errs, ns) = allan.totdev(phase, taus=s32_taus)
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=3, m=t, S=1, F=t, N=len(phase) )
#edf2 = greenhall_edf( alpha=0, d=3, m=int(t), N=len(phase), overlapping = True, modified=False )
#print(edf,edf2,edf2/edf)
edf = allan.edf_totdev(len(phase), t, alpha=0)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (t1, d1, lo1, hi1, n1, t2, d2, lo2, hi2,
n2) in zip(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns,
taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (n1, t1, lo1, d1, hi1))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 7), round(d2, 7), round(hi2, 7)))
approx_equal(lo1, lo2, tolerance=1e-3)
approx_equal(hi1, hi2, tolerance=1e-3)
print("----")
def test_phasedat_mdev(self):
s32_rows = testutils.read_stable32( 'phase_dat_mdev_octave.txt' , 1.0 )
phase = testutils.read_datafile('PHASE.DAT')
(taus,devs,errs,ns) = allan.mdev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
# alhpa= +2,...,-4 noise power
# d= 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m = tau/tau0 averaging factor
# F filter factor, 1 modified variance, m unmodified variance
# S stride factor, 1 nonoverlapped estimator, m overlapped estimator (estimator stride = tau/S )
# N number of phase obs
los=[]
his=[]
for (d,t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall( alpha=0, d=2, m=int(t), N=len(phase), overlapping = True, modified=True )
#print(edf,edf2,edf2/edf)
(lo,hi) = allan.confidence_intervals( dev=d, ci=0.68268949213708585, edf=edf2 ) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (s32['n'], s32['tau'], s32['dev_min'], s32['dev'], s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" % (n2, t2, round(lo2,5), round(d2,5), round(hi2,5) ))
testutils.check_approx_equal(s32['dev_min'], lo2,tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2,tolerance=1e-3)
print("----")
def test_phasedat_totdev(self):
s32_rows = testutils.read_stable32('phase_dat_totdev_octave.txt', 1.0)
phase = testutils.read_datafile('PHASE.DAT')
(taus, devs, errs,
ns) = allan.totdev(phase, taus=[s32['tau'] for s32 in s32_rows])
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=3, m=t, S=1, F=t, N=len(phase) )
#edf2 = greenhall_edf( alpha=0, d=3, m=int(t), N=len(phase), overlapping = True, modified=False )
#print(edf,edf2,edf2/edf)
edf = allan.edf_totdev(len(phase), t, alpha=0)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his,
ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" %
(s32['n'], s32['tau'], s32['dev_min'], s32['dev'],
s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
testutils.check_approx_equal(s32['dev_min'], lo2, tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2, tolerance=1e-3)
print("----")
def slow_failing_phasedat_mtotdev(self):
s32_rows = testutils.read_stable32( 'phase_dat_mtotdev_octave_alpha0.txt' , 1.0 )
phase = testutils.read_datafile('PHASE.DAT')
(taus,devs,errs,ns) = allan.mtotdev(phase, taus=[s32['tau'] for s32 in s32_rows])
los=[]
his=[]
for (d,t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=3, m=t, S=1, F=t, N=len(phase) )
if int(t)<10:
edf = allan.edf_greenhall( alpha=0, d=2, m=int(t), N=len(phase), overlapping = True, modified=True )
else:
edf = allan.edf_mtotdev(len(phase), t, alpha=0)
#print edf, edf2
#print(edf,edf2,edf2/edf)
print(edf)
(lo,hi) = allan.confidence_intervals( dev=d, ci=0.68268949213708585, edf=edf ) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (s32['n'], s32['tau'], s32['dev_min'], s32['dev'], s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" % (n2, t2, round(lo2,5), round(d2,5), round(hi2,5) ))
testutils.check_approx_equal(s32['dev_min'], lo2,tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2,tolerance=1e-3)
print("----")
def test_mdev_ci(self):
s32rows = testutils.read_stable32(resultfile='mdev_decade.txt', datarate=1.0)
for row in s32rows:
data = testutils.read_datafile(data_file)
(taus, devs, errs, ns) = allan.mdev(data, rate=rate,
taus=[ row['tau'] ])
edf = allan.edf_greenhall(alpha=row['alpha'],d=2,m=row['m'],N=len(data),overlapping=True, modified = True, verbose=True)
(lo,hi) =allan.confidence_intervals(devs[0],ci=0.68268949213708585, edf=edf)
print("n check: ", testutils.check_equal( ns[0], row['n'] ) )
print("dev check: ", testutils.check_approx_equal( devs[0], row['dev'] ) )
print("min dev check: ", lo, row['dev_min'], testutils.check_approx_equal( lo, row['dev_min'], tolerance=1e-3 ) )
print("max dev check: ", hi, row['dev_max'], testutils.check_approx_equal( hi, row['dev_max'], tolerance=1e-3 ) )
def test_phasedat_tdev(self):
s32_rows = testutils.read_stable32('phase_dat_tdev_octave.txt', 1.0)
phase = testutils.read_datafile('PHASE.DAT')
(taus, devs, errs,
ns) = allan.tdev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
# alhpa= +2,...,-4 noise power
# d= 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m = tau/tau0 averaging factor
# N number of phase obs
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=2,
m=int(t),
N=len(phase),
overlapping=True,
modified=True)
# covert to mdev
# taus * md / np.sqrt(3.0)
mdev = d / t * np.sqrt(3.0)
(lo,
hi) = allan.confidence_intervals(dev=mdev,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
# convert back to tdev
lo = t * lo / np.sqrt(3.0)
hi = t * hi / np.sqrt(3.0)
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his,
ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" %
(s32['n'], s32['tau'], s32['dev_min'], s32['dev'],
s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
testutils.check_approx_equal(s32['dev_min'], lo2, tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2, tolerance=1e-3)
print("----")
def test_phasedat_mdev(self):
(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi,
s32_ns) = read_stable32('phase_dat_mdev_octave.txt', 1.0)
phase = read_datafile('PHASE.DAT')
(taus, devs, errs, ns) = allan.mdev(phase, taus=s32_taus)
# CI computation
# alhpa= +2,...,-4 noise power
# d= 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m = tau/tau0 averaging factor
# F filter factor, 1 modified variance, m unmodified variance
# S stride factor, 1 nonoverlapped estimator, m overlapped estimator (estimator stride = tau/S )
# N number of phase obs
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=2,
m=int(t),
N=len(phase),
overlapping=True,
modified=True)
#print(edf,edf2,edf2/edf)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
#print greenhall_simple_edf( alpha=0, d=2, m=1, S=1, F=1, N=len(phase) )
#print confidence_intervals( dev
# tau N edf chi2 chi2 dev_lo dev dev_hi
# 1 999 782.030 821.358 742.689 2.8515e-01 2.9223e-01 2.9987e-01
# 2 997 540.681 573.374 507.975 1.9520e-01 2.0102e-01 2.0738e-01
for (t1, d1, lo1, hi1, n1, t2, d2, lo2, hi2,
n2) in zip(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns,
taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (n1, t1, lo1, d1, hi1))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
approx_equal(lo1, lo2, tolerance=1e-3)
approx_equal(hi1, hi2, tolerance=1e-3)
print("----")
def test_mdev_ci(self):
s32rows = testutils.read_stable32(resultfile="mdev_octave.txt", datarate=1.0)
for row in s32rows:
data = testutils.read_datafile(data_file)
data = allan.frequency2fractional(data, mean_frequency=1.0e7)
(taus, devs, errs, ns) = allan.mdev(data, rate=rate, data_type="freq", taus=[row["tau"]])
edf = allan.edf_greenhall(
alpha=row["alpha"], d=2, m=row["m"], N=len(data), overlapping=True, modified=True, verbose=True
)
(lo, hi) = allan.confidence_intervals(devs[0], ci=0.68268949213708585, edf=edf)
print("n check: ", testutils.check_equal(ns[0], row["n"]))
print("dev check: ", devs[0], row["dev"], testutils.check_approx_equal(devs[0], row["dev"], tolerance=2e-3))
print(
"min dev check: ", lo, row["dev_min"], testutils.check_approx_equal(lo, row["dev_min"], tolerance=2e-3)
)
print(
"max dev check: ", hi, row["dev_max"], testutils.check_approx_equal(hi, row["dev_max"], tolerance=2e-3)
)
def test_phasedat_oadev(self):
s32_rows = testutils.read_stable32('phase_dat_oadev_octave.txt', 1.0)
phase = testutils.read_datafile('PHASE.DAT')
(taus, devs, errs,
ns) = allan.oadev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
# alhpa +2,...,-4 noise power
# d 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m tau/tau0 averaging factor
# F filter factor, 1 modified variance, m unmodified variance
# S stride factor, 1 nonoverlapped estimator, m overlapped estimator (estimator stride = tau/S )
# N number of phase observations
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=2,
m=int(t),
N=len(phase),
overlapping=True,
modified=False)
#print(edf,edf2,edf2/edf)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his,
ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" %
(s32['n'], s32['tau'], s32['dev_min'], s32['dev'],
s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
testutils.check_approx_equal(s32['dev_min'], lo2, tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2, tolerance=1e-3)
print("----")
def test_phasedat_adev(self):
(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi,
s32_ns) = read_stable32('phase_dat_adev_octave.txt', 1.0)
phase = read_datafile('PHASE.DAT')
(taus, devs, errs, ns) = allan.adev(phase, taus=s32_taus)
# CI computation
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=2,
m=t,
N=len(phase),
overlapping=False,
modified=False)
#print(edf,edf2,edf2/edf)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
#print greenhall_simple_edf( alpha=0, d=2, m=1, S=1, F=1, N=len(phase) )
#print confidence_intervals( dev
# tau N edf chi2_l
# 1 999 782.030 821.358 , 742.689
# 2.851498, 2.922319 2.998720
for (t1, d1, lo1, hi1, n1, t2, d2, lo2, hi2,
n2) in zip(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns,
taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (n1, t1, lo1, d1, hi1))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
approx_equal(lo1, lo2, tolerance=1e-3)
approx_equal(hi1, hi2, tolerance=1e-3)
print("----")
def test_phasedat_hdev(self):
(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi,
s32_ns) = read_stable32('phase_dat_hdev_octave.txt', 1.0)
phase = read_datafile('PHASE.DAT')
(taus, devs, errs, ns) = allan.hdev(phase, taus=s32_taus)
# CI computation
# alhpa= +2,...,-4 noise power
# d= 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m = tau/tau0 averaging factor
# N number of phase obs
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=3, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=3,
m=int(t),
N=len(phase),
overlapping=False,
modified=False)
#print(edf,edf2,edf2/edf)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (t1, d1, lo1, hi1, n1, t2, d2, lo2, hi2,
n2) in zip(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns,
taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (n1, t1, lo1, d1, hi1))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
approx_equal(lo1, lo2, tolerance=1e-3)
approx_equal(hi1, hi2, tolerance=1e-3)
print("----")
def test_phasedat_adev(self):
#(s32_taus, s32_devs, s32_devs_lo, s32_devs_hi, s32_ns) = read_stable32( 'phase_dat_adev_octave.txt' , 1.0 )
s32_rows = testutils.read_stable32('phase_dat_adev_octave.txt', 1.0)
phase = testutils.read_datafile('PHASE.DAT')
(taus, devs, errs,
ns) = allan.adev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
los = []
his = []
for (d, t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall(alpha=0,
d=2,
m=t,
N=len(phase),
overlapping=False,
modified=False)
(lo,
hi) = allan.confidence_intervals(dev=d,
ci=0.68268949213708585,
edf=edf2) # 0.68268949213708585
#(lo2,hi2) = allan.confidence_intervals( dev=d, ci=0.68268949213708585, edf=edf2, use_scipy_chi2_ppf=False )
#testutils.check_approx_equal(lo, lo2, tolerance=1e-4)
#testutils.check_approx_equal(hi, hi2, tolerance=1e-4)
#allan.uncertainty_estimate(len(phase), t, d,ci=0.683,noisetype='wf')
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his,
ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" %
(s32['n'], s32['tau'], s32['dev_min'], s32['dev'],
s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" %
(n2, t2, round(lo2, 5), round(d2, 5), round(hi2, 5)))
testutils.check_approx_equal(s32['dev_min'], lo2, tolerance=1e-3)
testutils.check_approx_equal(s32['dev'], d2, tolerance=1e-4)
testutils.check_approx_equal(s32['dev_max'], hi2, tolerance=1e-3)
print("----")
def test_phasedat_tdev(self):
s32_rows = testutils.read_stable32( 'phase_dat_tdev_octave.txt' , 1.0 )
phase = testutils.read_datafile('PHASE.DAT')
(taus,devs,errs,ns) = allan.tdev(phase, taus=[s32['tau'] for s32 in s32_rows])
# CI computation
# alhpa= +2,...,-4 noise power
# d= 1 first-difference variance, 2 allan variance, 3 hadamard variance
# alpha+2*d >1
# m = tau/tau0 averaging factor
# N number of phase obs
los=[]
his=[]
for (d,t, n) in zip(devs, taus, ns):
#edf = greenhall_simple_edf( alpha=0, d=2, m=t, S=1, F=t, N=len(phase) )
edf2 = allan.edf_greenhall( alpha=0, d=2, m=int(t), N=len(phase), overlapping = True, modified=True )
# covert to mdev
# taus * md / np.sqrt(3.0)
mdev = d/t*np.sqrt(3.0)
(lo,hi) = allan.confidence_intervals( dev=mdev, ci=0.68268949213708585, edf=edf2 ) # 0.68268949213708585
# convert back to tdev
lo = t*lo/np.sqrt(3.0)
hi = t*hi/np.sqrt(3.0)
los.append(lo)
his.append(hi)
for (s32, t2, d2, lo2, hi2, n2) in zip(s32_rows, taus, devs, los, his, ns):
print("s32 %03d %03f %1.6f %1.6f %1.6f" % (s32['n'], s32['tau'], s32['dev_min'], s32['dev'], s32['dev_max']))
print("at %03d %03f %1.6f %1.6f %1.6f" % (n2, t2, round(lo2,5), round(d2,5), round(hi2,5) ))
testutils.check_approx_equal(s32['dev_min'], lo2,tolerance=1e-3)
testutils.check_approx_equal(s32['dev_max'], hi2,tolerance=1e-3)
print("----")
(taus,devs,errs,ns) = at.adev(phase, taus='octave')
# Confidence-intervals for each (tau,adev) pair separately.
cis=[]
for (t,dev) in zip(taus,devs):
# Greenhalls EDF (Equivalent Degrees of Freedom)
# alpha +2,...,-4 noise type, either estimated or known
# d 1 first-difference variance, 2 allan variance, 3 hadamard variance
# we require: alpha+2*d >1 (is this ever false?)
# m tau/tau0 averaging factor
# N number of phase observations
edf = at.edf_greenhall( alpha=0, d=2, m=t, N=len(phase), overlapping = False, modified=False )
# with the known EDF we get CIs
# for 1-sigma confidence we set
# ci = scipy.special.erf(1/math.sqrt(2)) = 0.68268949213708585
(lo,hi) = at.confidence_intervals( dev=dev, ci=0.68268949213708585, edf=edf )
cis.append( (lo,hi) )
# now we are ready to print and plot the results
print "Tau\tmin Dev\t\tDev\t\tMax Dev"
for (tau,dev,ci) in zip(taus,devs,cis):
print "%d\t%f\t%f\t%f" % (tau, ci[0], dev, ci[1] )
""" output is
Tau min Dev Dev Max Dev
1 0.285114 0.292232 0.299910
2 0.197831 0.205102 0.213237
4 0.141970 0.149427 0.158198
8 0.102541 0.110135 0.119711
16 0.056510 0.062381 0.070569
32 0.049153 0.056233 0.067632
64 0.027109 0.032550 0.043536