# Delta-Variance
from turbustat.statistics import DeltaVariance_Distance, DeltaVariance
delvar_distance = \
DeltaVariance_Distance(dataset1["moment0"],
dataset2["moment0"],
weights1=dataset1["moment0_error"][0],
weights2=dataset2["moment0_error"][0],
xhigh=11 * u.pix)
delvar_distance.distance_metric()
delvar = DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 *
u.pix)
delvar_val = delvar.delta_var
delvar_slope = delvar.slope
# Change boundary conditions
delvar_fill = \
DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 * u.pix,
boundary='fill')
delvar_fill_val = delvar_fill.delta_var
delvar_fill_slope = delvar_fill.slope
plt.rcParams['axes.unicode_minus'] = False
size = 256
markers = ['D', 'o']
# Make a single figure example to save space in the paper.
fig = plt.figure(figsize=figsize)
slope = 3.0
test_img = fits.PrimaryHDU(make_extended(size, powerlaw=slope))
# The power-law behaviour continues up to ~1/4 of the size
delvar = DeltaVariance(test_img).run(xlow=3 * u.pix,
xhigh=0.25 * size * u.pix,
boundary='wrap')
plt.xscale("log")
plt.yscale("log")
plt.errorbar(delvar.lags.value,
delvar.delta_var,
yerr=delvar.delta_var_error,
fmt=markers[0],
label='TurbuStat')
# Now plot the IDL output
tab = Table.read("deltavar_{}.txt".format(slope), format='ascii')
# First is pixel scale, second is delvar, then delvar error, and finally
# the fit values
plt.errorbar(tab['col1'],
img -= img.min()
plt.imshow(img, origin='lower')
plt.colorbar()
plt.tight_layout()
plt.savefig(osjoin(fig_path, 'missing_data_image.png'))
plt.close()
# Show image in the tutorial
pspec = PowerSpectrum(fits.PrimaryHDU(img))
pspec.run(verbose=True)
plt.savefig(osjoin(fig_path, 'missing_data_pspec.png'))
plt.close()
delvar = DeltaVariance(fits.PrimaryHDU(img))
delvar.run(verbose=True)
plt.savefig(osjoin(fig_path, 'missing_data_delvar.png'))
plt.close()
# Mask some of the data out
masked_img = img.copy()
masked_img[masked_img < np.percentile(img, 25)] = np.NaN
plt.imshow(masked_img, origin='lower')
plt.colorbar()
plt.tight_layout()
plt.savefig(osjoin(fig_path, 'missing_data_image_masked.png'))
plt.close()
genus_val = genus_distance.genus1.genus_stats
# Delta-Variance
from turbustat.statistics import DeltaVariance_Distance, DeltaVariance
delvar_distance = \
DeltaVariance_Distance(dataset1["moment0"],
dataset2["moment0"],
weights1=dataset1["moment0_error"][0],
weights2=dataset2["moment0_error"][0])
delvar_distance.distance_metric()
delvar = DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run()
delvar_val = delvar.delta_var
# VCA/VCS
from turbustat.statistics import VCA_Distance, VCS_Distance
vcs_distance = VCS_Distance(dataset1["cube"],
dataset2["cube"]).distance_metric()
vcs_val = vcs_distance.vcs1.ps1D
vca_distance = VCA_Distance(dataset1["cube"],
dataset2["cube"]).distance_metric()
plt.xlabel("Theta (rad)")
plt.ylabel("log Bispectrum")
plt.grid()
plt.tight_layout()
plt.savefig(osjoin(fig_path, "bispectrum_azim_slices.png"))
plt.close()
# Delta-Variance
if run_delvar:
from turbustat.statistics import DeltaVariance
moment0 = fits.open(osjoin(data_path, "Design4_flatrho_0021_00_radmc_moment0.fits"))[0]
moment0_err = fits.open(osjoin(data_path, "Design4_flatrho_0021_00_radmc_moment0.fits"))[1]
delvar = DeltaVariance(moment0, weights=moment0_err, distance=250 * u.pc)
delvar.run(verbose=True, xunit=u.pix,
save_name=osjoin(fig_path, "delvar_design4.png"))
# Now with fitting limits
delvar.run(verbose=True, xunit=u.pix, xlow=4 * u.pix, xhigh=30 * u.pix,
save_name=osjoin(fig_path, "delvar_design4_wlimits.png"))
# Now with fitting limits
delvar.run(verbose=True, xunit=u.pc, xlow=4 * u.pix, xhigh=30 * u.pix,
save_name=osjoin(fig_path, "delvar_design4_physunits.png"))
delvar.run(verbose=True, xunit=u.pc, xlow=4 * u.pix, xhigh=40 * u.pix,
brk=8 * u.pix,
save_name=osjoin(fig_path, "delvar_design4_break.png"))
def generate_unitvals():
import numpy as np
import astropy.units as u
# The machine producing these values should have emcee installed!
try:
import emcee
except ImportError:
raise ImportError("Install emcee to generate unit test data.")
from turbustat.tests._testing_data import dataset1, dataset2
# Wavelet Transform
from turbustat.statistics import Wavelet_Distance, Wavelet
wavelet_distance = \
Wavelet_Distance(dataset1["moment0"],
dataset2["moment0"]).distance_metric()
wavelet_val = wavelet_distance.wt1.values
wavelet_slope = wavelet_distance.wt1.slope
# Wavelet with a break
wave_break = Wavelet(dataset1['moment0']).run(xhigh=7 * u.pix,
brk=5.5 * u.pix)
wavelet_slope_wbrk = wave_break.slope
wavelet_brk_wbrk = wave_break.brk.value
# MVC
from turbustat.statistics import MVC_Distance, MVC
mvc_distance = MVC_Distance(dataset1, dataset2).distance_metric()
mvc = MVC(dataset1["centroid"], dataset1["moment0"], dataset1["linewidth"])
mvc.run()
mvc_val = mvc.ps1D
mvc_slope = mvc.slope
mvc_slope2D = mvc.slope2D
# Spatial Power Spectrum/ Bispectrum
from turbustat.statistics import (PSpec_Distance, Bispectrum_Distance,
Bispectrum, PowerSpectrum)
pspec_distance = \
PSpec_Distance(dataset1["moment0"],
dataset2["moment0"]).distance_metric()
pspec = PowerSpectrum(dataset1['moment0'])
pspec.run()
pspec_val = pspec.ps1D
pspec_slope = pspec.slope
pspec_slope2D = pspec.slope2D
bispec_distance = \
Bispectrum_Distance(dataset1["moment0"],
dataset2["moment0"]).distance_metric()
bispec_val = bispec_distance.bispec1.bicoherence
azimuthal_slice = bispec_distance.bispec1.azimuthal_slice(
16, 10, value='bispectrum_logamp', bin_width=5 * u.deg)
bispec_azim_bins = azimuthal_slice[16][0]
bispec_azim_vals = azimuthal_slice[16][1]
bispec_azim_stds = azimuthal_slice[16][2]
bispec_meansub = Bispectrum(dataset1['moment0'])
bispec_meansub.run(mean_subtract=True)
bispec_val_meansub = bispec_meansub.bicoherence
# Genus
from turbustat.statistics import GenusDistance, Genus
smooth_scales = np.linspace(1.0, 0.1 * min(dataset1["moment0"][0].shape),
5)
genus_distance = \
GenusDistance(dataset1["moment0"],
dataset2["moment0"],
lowdens_percent=20,
genus_kwargs=dict(match_kernel=True)).distance_metric()
# The distance method requires standardizing the data. Make a
# separate version that isn't
genus = Genus(dataset1['moment0'], smoothing_radii=smooth_scales)
genus.run(match_kernel=True)
genus_val = genus.genus_stats
# Delta-Variance
from turbustat.statistics import DeltaVariance_Distance, DeltaVariance
delvar_distance = \
DeltaVariance_Distance(dataset1["moment0"],
dataset2["moment0"],
weights1=dataset1["moment0_error"][0],
weights2=dataset2["moment0_error"][0],
delvar_kwargs=dict(xhigh=11 * u.pix))
delvar_distance.distance_metric()
delvar = DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 *
u.pix)
delvar_val = delvar.delta_var
delvar_slope = delvar.slope
# Test with a break point
delvar_wbrk = \
DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 * u.pix,
brk=6 * u.pix)
delvar_slope_wbrk = delvar_wbrk.slope
delvar_brk = delvar_wbrk.brk.value
# Change boundary conditions
delvar_fill = \
DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 * u.pix,
boundary='fill',
nan_treatment='interpolate')
delvar_fill_val = delvar_fill.delta_var
delvar_fill_slope = delvar_fill.slope
# VCA/VCS
from turbustat.statistics import VCA_Distance, VCS_Distance, VCA
vcs_distance = VCS_Distance(dataset1["cube"],
dataset2["cube"],
fit_kwargs=dict(high_cut=0.3 / u.pix,
low_cut=3e-2 / u.pix))
vcs_distance.distance_metric()
vcs_val = vcs_distance.vcs1.ps1D
vcs_slopes = vcs_distance.vcs1.slope
vca_distance = VCA_Distance(dataset1["cube"],
dataset2["cube"]).distance_metric()
vca = VCA(dataset1['cube'])
vca.run()
vca_val = vca.ps1D
vca_slope = vca.slope
vca_slope2D = vca.slope2D
# Tsallis
from turbustat.statistics import Tsallis
tsallis_kwargs = {"sigma_clip": 5, "num_bins": 100}
tsallis = Tsallis(dataset1['moment0'], lags=[1, 2, 4, 8, 16] * u.pix)
tsallis.run(periodic=True, **tsallis_kwargs)
tsallis_val = tsallis.tsallis_params
tsallis_stderrs = tsallis.tsallis_stderrs
tsallis_noper = Tsallis(dataset1['moment0'], lags=[1, 2, 4, 8, 16] * u.pix)
tsallis_noper.run(periodic=False, num_bins=100)
tsallis_val_noper = tsallis_noper.tsallis_params
# High-order stats
from turbustat.statistics import StatMoments_Distance, StatMoments
moment_distance = \
StatMoments_Distance(dataset1["moment0"],
dataset2["moment0"]).distance_metric()
kurtosis_val = moment_distance.moments1.kurtosis_hist[1]
skewness_val = moment_distance.moments1.skewness_hist[1]
# Save a few from the non-distance version
tester = StatMoments(dataset1["moment0"])
tester.run()
kurtosis_nondist_val = tester.kurtosis_hist[1]
skewness_nondist_val = tester.skewness_hist[1]
# Non-periodic
tester = StatMoments(dataset1["moment0"])
tester.run(periodic=False)
kurtosis_nonper_val = tester.kurtosis_hist[1]
skewness_nonper_val = tester.skewness_hist[1]
# PCA
from turbustat.statistics import PCA_Distance, PCA
pca_distance = PCA_Distance(dataset1["cube"],
dataset2["cube"]).distance_metric()
pca = PCA(dataset1["cube"], distance=250 * u.pc)
pca.run(mean_sub=True,
eigen_cut_method='proportion',
min_eigval=0.75,
spatial_method='contour',
spectral_method='walk-down',
fit_method='odr',
brunt_beamcorrect=False,
spectral_output_unit=u.m / u.s)
pca_val = pca.eigvals
pca_spectral_widths = pca.spectral_width().value
pca_spatial_widths = pca.spatial_width().value
pca_fit_vals = {
"index": pca.index,
"gamma": pca.gamma,
"intercept": pca.intercept().value,
"sonic_length": pca.sonic_length()[0].value
}
# Now get those values using mcmc
pca.run(mean_sub=True,
eigen_cut_method='proportion',
min_eigval=0.75,
spatial_method='contour',
spectral_method='walk-down',
fit_method='bayes',
brunt_beamcorrect=False,
spectral_output_unit=u.m / u.s)
pca_fit_vals["index_bayes"] = pca.index
pca_fit_vals["gamma_bayes"] = pca.gamma
pca_fit_vals["intercept_bayes"] = pca.intercept().value
pca_fit_vals["sonic_length_bayes"] = pca.sonic_length()[0].value
# Record the number of eigenvalues kept by the auto method
pca.run(mean_sub=True,
n_eigs='auto',
min_eigval=0.001,
eigen_cut_method='value',
decomp_only=True)
pca_fit_vals["n_eigs_value"] = pca.n_eigs
# Now w/ the proportion of variance cut
pca.run(mean_sub=True,
n_eigs='auto',
min_eigval=0.99,
eigen_cut_method='proportion',
decomp_only=True)
pca_fit_vals["n_eigs_proportion"] = pca.n_eigs
# SCF
from turbustat.statistics import SCF_Distance, SCF
scf_distance = SCF_Distance(dataset1["cube"], dataset2["cube"],
size=11).distance_metric()
scf = SCF(dataset1['cube'], size=11).run()
scf_val = scf.scf_surface
scf_spectrum = scf.scf_spectrum
scf_slope = scf.slope
scf_slope2D = scf.slope2D
# Now run the SCF when the boundaries aren't continuous
scf_distance_cut_bound = SCF_Distance(dataset1["cube"],
dataset2["cube"],
size=11,
boundary='cut').distance_metric()
scf_val_noncon_bound = scf_distance_cut_bound.scf1.scf_surface
scf_fitlims = SCF(dataset1['cube'], size=11)
scf_fitlims.run(boundary='continuous', xlow=1.5 * u.pix, xhigh=4.5 * u.pix)
scf_slope_wlimits = scf_fitlims.slope
scf_slope_wlimits_2D = scf_fitlims.slope2D
# Cramer Statistic
from turbustat.statistics import Cramer_Distance
cramer_distance = Cramer_Distance(
dataset1["cube"], dataset2["cube"], noise_value1=0.1,
noise_value2=0.1).distance_metric(normalize=False)
cramer_val = cramer_distance.data_matrix1
# Dendrograms
from turbustat.statistics import Dendrogram_Distance, Dendrogram_Stats
min_deltas = np.logspace(-1.5, 0.5, 40)
dendro_distance = Dendrogram_Distance(
dataset1["cube"], dataset2["cube"],
min_deltas=min_deltas).distance_metric()
dendrogram_val = dendro_distance.dendro1.numfeatures
# With periodic boundaries
dendro = Dendrogram_Stats(dataset1['cube'], min_deltas=min_deltas)
dendro.run(periodic_bounds=True)
dendrogram_periodic_val = dendro.numfeatures
# PDF
from turbustat.statistics import PDF_Distance
pdf_distance = \
PDF_Distance(dataset1["moment0"],
dataset2["moment0"],
min_val1=0.05,
min_val2=0.05,
weights1=dataset1["moment0_error"][0]**-2.,
weights2=dataset2["moment0_error"][0]**-2.,
do_fit=False,
normalization_type='standardize')
pdf_distance.distance_metric()
pdf_val = pdf_distance.PDF1.pdf
pdf_ecdf = pdf_distance.PDF1.ecdf
pdf_bins = pdf_distance.bins
# Do a fitted version of the PDF pca
pdf_fit_distance = \
PDF_Distance(dataset1["moment0"],
dataset2["moment0"],
min_val1=0.05,
min_val2=0.05,
do_fit=True,
normalization_type=None)
pdf_fit_distance.distance_metric()
np.savez_compressed('checkVals',
wavelet_val=wavelet_val,
wavelet_slope=wavelet_slope,
wavelet_slope_wbrk=wavelet_slope_wbrk,
wavelet_brk_wbrk=wavelet_brk_wbrk,
mvc_val=mvc_val,
mvc_slope=mvc_slope,
mvc_slope2D=mvc_slope2D,
pspec_val=pspec_val,
pspec_slope=pspec_slope,
pspec_slope2D=pspec_slope2D,
bispec_val=bispec_val,
bispec_azim_bins=bispec_azim_bins,
bispec_azim_vals=bispec_azim_vals,
bispec_azim_stds=bispec_azim_stds,
bispec_val_meansub=bispec_val_meansub,
genus_val=genus_val,
delvar_val=delvar_val,
delvar_slope=delvar_slope,
delvar_slope_wbrk=delvar_slope_wbrk,
delvar_brk=delvar_brk,
delvar_fill_val=delvar_fill_val,
delvar_fill_slope=delvar_fill_slope,
vcs_val=vcs_val,
vcs_slopes=vcs_slopes,
vca_val=vca_val,
vca_slope=vca_slope,
vca_slope2D=vca_slope2D,
tsallis_val=tsallis_val,
tsallis_stderrs=tsallis_stderrs,
tsallis_val_noper=tsallis_val_noper,
kurtosis_val=kurtosis_val,
skewness_val=skewness_val,
kurtosis_nondist_val=kurtosis_nondist_val,
skewness_nondist_val=skewness_nondist_val,
kurtosis_nonper_val=kurtosis_nonper_val,
skewness_nonper_val=skewness_nonper_val,
pca_val=pca_val,
pca_fit_vals=pca_fit_vals,
pca_spectral_widths=pca_spectral_widths,
pca_spatial_widths=pca_spatial_widths,
scf_val=scf_val,
scf_slope_wlimits=scf_slope_wlimits,
scf_slope_wlimits_2D=scf_slope_wlimits_2D,
scf_val_noncon_bound=scf_val_noncon_bound,
scf_spectrum=scf_spectrum,
scf_slope=scf_slope,
scf_slope2D=scf_slope2D,
cramer_val=cramer_val,
dendrogram_val=dendrogram_val,
dendrogram_periodic_val=dendrogram_periodic_val,
pdf_val=pdf_val,
pdf_bins=pdf_bins,
pdf_ecdf=pdf_ecdf)
np.savez_compressed(
'computed_distances',
mvc_distance=mvc_distance.distance,
pca_distance=pca_distance.distance,
vca_distance=vca_distance.distance,
pspec_distance=pspec_distance.distance,
scf_distance=scf_distance.distance,
wavelet_distance=wavelet_distance.distance,
delvar_curve_distance=delvar_distance.curve_distance,
delvar_slope_distance=delvar_distance.slope_distance,
# tsallis_distance=tsallis_distance.distance,
kurtosis_distance=moment_distance.kurtosis_distance,
skewness_distance=moment_distance.skewness_distance,
cramer_distance=cramer_distance.distance,
genus_distance=genus_distance.distance,
vcs_distance=vcs_distance.distance,
bispec_mean_distance=bispec_distance.mean_distance,
bispec_surface_distance=bispec_distance.surface_distance,
dendrohist_distance=dendro_distance.histogram_distance,
dendronum_distance=dendro_distance.num_distance,
pdf_hellinger_distance=pdf_distance.hellinger_distance,
pdf_ks_distance=pdf_distance.ks_distance,
pdf_lognorm_distance=pdf_fit_distance.lognormal_distance)
plt.subplot(122)
plt.imshow(bispec2.bicoherence, vmin=0, vmax=1, origin='lower')
plt.title("With mean subtraction")
plt.savefig(osjoin(fig_path, "bispectrum_w_and_wo_meansub_coherence"))
plt.close()
# Delta-Variance
if run_delvar:
from turbustat.statistics import DeltaVariance
moment0 = fits.open(
osjoin(data_path, "Design4_flatrho_0021_00_radmc_moment0.fits"))[0]
moment0_err = fits.open(
osjoin(data_path, "Design4_flatrho_0021_00_radmc_moment0.fits"))[1]
delvar = DeltaVariance(moment0, weights=moment0_err, distance=250 * u.pc)
delvar.run(verbose=True,
xunit=u.pix,
save_name=osjoin(fig_path, "delvar_design4.png"))
# Now with fitting limits
delvar.run(verbose=True,
xunit=u.pix,
xlow=4 * u.pix,
xhigh=30 * u.pix,
save_name=osjoin(fig_path, "delvar_design4_wlimits.png"))
# Now with fitting limits
delvar.run(verbose=True,
xunit=u.pc,
xlow=4 * u.pix,
img -= img.min()
plt.imshow(img, origin='lower')
plt.colorbar()
plt.tight_layout()
plt.savefig(osjoin(fig_path, 'missing_data_image.png'))
plt.close()
# Show image in the tutorial
pspec = PowerSpectrum(fits.PrimaryHDU(img))
pspec.run(verbose=True)
plt.savefig(osjoin(fig_path, 'missing_data_pspec.png'))
plt.close()
delvar = DeltaVariance(fits.PrimaryHDU(img))
delvar.run(verbose=True)
plt.savefig(osjoin(fig_path, 'missing_data_delvar.png'))
plt.close()
# Mask some of the data out
masked_img = img.copy()
masked_img[masked_img < np.percentile(img, 25)] = np.NaN
plt.imshow(masked_img, origin='lower')
plt.colorbar()
plt.tight_layout()
plt.savefig(osjoin(fig_path, 'missing_data_image_masked.png'))
plt.close()
genus_val = genus.genus_stats
# Delta-Variance
from turbustat.statistics import DeltaVariance_Distance, DeltaVariance
delvar_distance = \
DeltaVariance_Distance(dataset1["moment0"],
dataset2["moment0"],
weights1=dataset1["moment0_error"][0],
weights2=dataset2["moment0_error"][0],
delvar_kwargs=dict(xhigh=11 * u.pix))
delvar_distance.distance_metric()
delvar = DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 * u.pix)
delvar_val = delvar.delta_var
delvar_slope = delvar.slope
# Test with a break point
delvar_wbrk = \
DeltaVariance(dataset1["moment0"],
weights=dataset1['moment0_error'][0]).run(xhigh=11 * u.pix,
brk=6 * u.pix)
delvar_slope_wbrk = delvar_wbrk.slope
delvar_brk = delvar_wbrk.brk.value
# Change boundary conditions