def main(args: Optional[list] = None,
opts: Optional[argparse.Namespace] = None):
"""Fit Combination Pal5 and GD1 to MW Potential Script Function.
Parameters
----------
args : list, optional
an optional single argument that holds the sys.argv list,
except for the script name (e.g., argv[1:])
"""
if opts is not None and args is None:
pass
else:
parser = make_parser()
opts = parser.parse_args(args)
fpath = opts.fpath + "/" if not opts.fpath.endswith("/") else opts.fpath
opath = opts.opath + "/" if not opts.opath.endswith("/") else opts.opath
# -----------------------
# Adding in the force measurements from Pal 5 *and* GD-1; also fitting
# $R_0$ and $V_c(R_0)$
plt.figure(figsize=(16, 5))
p_b15_pal5gd1_voro = mw_pot.fit(
fitc=True,
c=None,
addpal5=True,
addgd1=True,
fitvoro=True,
mc16=True,
plots=fpath + "fit.pdf",
)
# -----------------------
samples_savefilename = opath + "mwpot14varyc-fitvoro-pal5gd1-samples.pkl"
if os.path.exists(samples_savefilename):
with open(samples_savefilename, "rb") as savefile:
s = pickle.load(savefile)
else:
s = mw_pot.sample(
nsamples=100000,
params=p_b15_pal5gd1_voro[0],
fitc=True,
c=None,
plots=fpath + "mwpot14varyc-fitvoro-pal5gd1-samples.pdf",
mc16=True,
addpal5=True,
addgd1=True,
fitvoro=True,
)
save_pickles(samples_savefilename, s)
# -----------------------
plt.figure()
mw_pot.plot_samples(
s,
True,
True,
addpal5=True,
addgd1=True,
savefig=fpath + "mwpot14varyc-fitvoro-pal5gd1-samples-corner.pdf",
)
# -----------------------
bf_savefilename = opath + "mwpot14varyc-bf.pkl" # should already exist
if os.path.exists(bf_savefilename):
with open(bf_savefilename, "rb") as savefile:
cs = pickle.load(savefile)
bf_params = pickle.load(savefile)
else:
cs = np.arange(0.5, 4.1, 0.1)
bf_params = []
for c in tqdm(cs):
dum = mw_pot.fit(
fitc=False,
c=c,
plots=fpath + "mwpot14varyc-bf-fit.pdf",
)
bf_params.append(dum[0])
save_pickles(bf_savefilename, cs, bf_params)
# -----------------------
plt.figure()
bovy_plot.bovy_print(
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=15.0,
ytick_labelsize=15.0,
)
su.plot_mcmc_c(
s,
True,
cs,
bf_params,
savefig=fpath + "mwpot14varyc-bf-combo_pal5_gd1-dependence.pdf",
)
if save_figures:
plt.savefig(
os.path.join(
os.getenv("PAPERSDIR"),
"2016-mwhalo-shape",
"mwpot14-varyc-wp5g1.pdf",
),
bbox_inches="tight",
)
# -----------------------
plt.figure(figsize=(4, 4))
cindx = 9
dum = bovy_plot.bovy_hist(
s[cindx],
bins=36,
histtype="step",
lw=2.0,
xlabel=r"$c/a$",
xrange=[0.5, 1.5],
normed=True,
)
plt.savefig(fpath + "mwpot14varyc-bf-combo_pal5_gd1-shape_hist.pdf")
with open(opath + "fit_potential_combo-pal5-gd1.txt", "w") as file:
sortedc = np.array(sorted(s[cindx][-50000:]))
file.write("2.5%% and 0.5%% lower limits: %.3f, %.3f" % (
sortedc[int(np.floor(0.025 * len(sortedc)))],
sortedc[int(np.floor(0.005 * len(sortedc)))],
))
file.write("2.5%% and 0.5%% upper limits: %.3f, %.3f" % (
sortedc[int(np.floor(0.975 * len(sortedc)))],
sortedc[int(np.floor(0.995 * len(sortedc)))],
))
file.write("Median, 68%% confidence: %.3f, %.3f, %.3f" % (
np.median(sortedc),
sortedc[int(np.floor(0.16 * len(sortedc)))],
sortedc[int(np.floor(0.84 * len(sortedc)))],
))
file.write("Mean, std. dev.: %.2f,%.2f" % (
np.mean(sortedc),
np.std(sortedc),
))
# -----------------------
# What is the constraint on the mass of the halo?
tR = 20.0 / REFR0
skip = 1
hmass = []
for sa in tqdm(s.T[::skip]):
pot = mw_pot.setup_potential(
sa,
sa[-1],
True,
False,
REFR0 * sa[8],
REFV0 * sa[7],
fitvoro=True,
)
hmass.append(-integrate.quad(
lambda x: tR**2.0 * potential.evaluaterforces(
pot[2], tR * x, tR * np.sqrt(1.0 - x**2.0), phi=0.0),
0.0,
1.0,
)[0] * bovy_conversion.mass_in_1010msol(REFV0, REFR0) / 10.0)
hmass = np.array(hmass)
with open(opath + "fit_potential_combo-pal5-gd1.txt",
"a") as file: # append
file.write("\nMass Constraints:")
sortedhm = np.array(sorted(hmass))
file.write("2.5%% and 0.5%% lower limits: %.2f, %.2f" % (
sortedhm[int(np.floor(0.025 * len(sortedhm)))],
sortedhm[int(np.floor(0.005 * len(sortedhm)))],
))
file.write("2.5%% and 0.5%% upper limits: %.2f, %.2f" % (
sortedhm[int(np.floor(0.975 * len(sortedhm)))],
sortedhm[int(np.floor(0.995 * len(sortedhm)))],
))
file.write("Median, 68%% confidence: %.2f, %.2f, %.2f" % (
np.median(sortedhm),
sortedhm[int(np.floor(0.16 * len(sortedhm)))],
sortedhm[int(np.floor(0.84 * len(sortedhm)))],
))
# -----------------------
bovy_plot.scatterplot(
hmass,
s[-1, ::skip],
"k,",
onedhists=True,
bins=31,
xrange=[0.5, 1.5],
yrange=[0.5, 1.5],
xlabel=r"$M_{\mathrm{halo}} (r<20\,\mathrm{kpc})\,(M_\odot)$",
ylabel=r"$c/a$",
)
plt.savefig(fpath + "scatterplot.pdf")
def model_vary_d():
# ----------------------------------------------------------
# The Pal 5 stream is not very sensitive to changes in $b$.
# Vary the distance:
p_b15 = [
0.60122692,
0.36273147,
-0.97591502,
-3.34169377,
0.71877924,
-0.01519337,
-0.01928001,
]
progs = []
progfs = []
times = np.linspace(0.0, 3.0, 101)
ds = np.linspace(22.5, 24.5, 101)
for d in ds:
pot = mw_pot.setup_potential(p_b15, 1.0, False, False, REFR0, REFV0)
prog = Orbit(
[229.018, -0.124, d, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
)
prog.integrate(times, pot)
progs.append(prog)
prog = Orbit(
[229.018, -0.124, d, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
).flip()
prog.integrate(times, pot)
prog.flip(inplace=True)
progfs.append(prog)
# -------------------------------------------
plt.figure(figsize=(12, 4))
for d, orb, orbf in zip(ds, progs, progfs):
tc = cmap((d - np.amin(ds)) / (np.amax(ds) - np.amin(ds)))
plt.subplot(1, 2, 1)
orb.plot(d1="ra", d2="dec", color=tc, overplot=True)
orbf.plot(d1="ra", d2="dec", color=tc, overplot=True)
plt.subplot(1, 2, 2)
orb.plot(d1="ra", d2="vlos", color=tc, overplot=True)
orbf.plot(d1="ra", d2="vlos", color=tc, overplot=True)
plot_data_add_labels(color="k")
add_colorbar(
np.amin(ds),
np.amax(ds),
r"$\mathrm{distance}\,(\mathrm{kpc})$",
save_figures=False,
)
plt.savefig("figures/varyd.pdf")
def model_vary_pm_perp():
# ----------------------------------------------------------
# Vary the proper motion perpendicular to the stream:
p_b15 = [
0.60122692,
0.36273147,
-0.97591502,
-3.34169377,
0.71877924,
-0.01519337,
-0.01928001,
]
progs = []
progfs = []
times = np.linspace(0.0, 2.5, 101)
pms = np.linspace(-0.3, 0.3, 101)
for pm in pms:
pot = mw_pot.setup_potential(p_b15, 1.0, False, False, REFR0, REFV0)
prog = Orbit(
[
229.018,
-0.124,
23.2,
-2.296 + pm,
-2.257 - 2.296 / 2.257 * pm,
-58.7,
],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
)
prog.integrate(times, pot)
progs.append(prog)
prog = Orbit(
[
229.018,
-0.124,
23.2,
-2.296 + pm,
-2.257 - 2.296 / 2.257 * pm,
-58.7,
],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
).flip()
prog.integrate(times, pot)
prog.flip(inplace=True)
progfs.append(prog)
plt.figure(figsize=(12, 4))
for pm, orb, orbf in zip(pms, progs, progfs):
tc = cmap((pm - np.amin(pms)) / (np.amax(pms) - np.amin(pms)))
plt.subplot(1, 2, 1)
orb.plot(d1="ra", d2="dec", color=tc, overplot=True)
orbf.plot(d1="ra", d2="dec", color=tc, overplot=True)
plt.subplot(1, 2, 2)
orb.plot(d1="ra", d2="vlos", color=tc, overplot=True)
orbf.plot(d1="ra", d2="vlos", color=tc, overplot=True)
plot_data_add_labels(color="k")
add_colorbar(
np.amin(pms),
np.amax(pms),
r"$\mathrm{proper\ motion\ offset}\,(\mathrm{mas\,yr}^{-1})$",
save_figures=False,
)
plt.savefig("figures/varypm-perp.pdf")
def model_vary_b_for_c_1_pa_45():
# ----------------------------------------------------------
# Vary $b$ for $c=1$ (pa=45 degree):
p_b15 = [
0.60122692,
0.36273147,
-0.97591502,
-3.34169377,
0.71877924,
-0.01519337,
-0.01928001,
]
progs = []
progfs = []
times = np.linspace(0.0, 3.0, 101)
bs = np.arange(0.5, 2.1, 0.1)
for b in bs:
pot = mw_pot.setup_potential(p_b15,
1.0,
False,
False,
REFR0,
REFV0,
b=b,
pa=np.pi / 4.0)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
)
prog.integrate(times, pot)
progs.append(prog)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
).flip()
prog.integrate(times, pot)
prog.flip(inplace=True)
progfs.append(prog)
# -------------------------------------------
plt.figure(figsize=(12, 4))
for b, orb, orbf in zip(bs, progs, progfs):
tc = cmap((b - 0.5) / 1.5)
plt.subplot(1, 2, 1)
orb.plot(d1="ra", d2="dec", color=tc, overplot=True)
orbf.plot(d1="ra", d2="dec", color=tc, overplot=True)
plt.subplot(1, 2, 2)
orb.plot(d1="ra", d2="vlos", color=tc, overplot=True)
orbf.plot(d1="ra", d2="vlos", color=tc, overplot=True)
plot_data_add_labels(color="k")
add_colorbar(0.5, 2.0, r"$b$", save_figures=False)
plt.savefig("figures/varyb_c-1_pa-45.pdf")
return
def model_vary_c_along_the_best_fit_line():
bf_savefilename = _MW_POT_SCRIPT_FOLDER + "/output/mwpot14varyc-bf.pkl"
if os.path.exists(bf_savefilename):
with open(bf_savefilename, "rb") as savefile:
cs = pickle.load(savefile)
bf_params = pickle.load(savefile)
else:
IOError(("Need to calculate best-fit potentials for different c "
"in MWPotential2014-varyc.ipynb first"))
bf_params = np.array(bf_params)
bf_params = bf_params[cs <= 3.0]
cs = cs[cs <= 3.0]
# ----------------------------------------------------------
progs = []
progfs = []
times = np.linspace(0.0, 3.0, 101)
for bp, c in zip(bf_params, cs):
pot = mw_pot.setup_potential(bp, c, False, False, REFR0, REFV0)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
)
prog.integrate(times, pot)
progs.append(prog)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=REFR0,
vo=REFV0,
solarmotion=[-11.1, 24.0, 7.25],
).flip()
prog.integrate(times, pot)
prog.flip(inplace=True)
progfs.append(prog)
# ----------------------------------------------------------
# Vary $c$ along the best-fit line
plt.figure(figsize=(12, 4))
for c, orb, orbf in zip(cs, progs, progfs):
tc = cmap((c - 0.5) / 2.5)
plt.subplot(1, 2, 1)
orb.plot(d1="ra", d2="dec", color=tc, overplot=True)
orbf.plot(d1="ra", d2="dec", color=tc, overplot=True)
plt.subplot(1, 2, 2)
orb.plot(d1="ra", d2="vlos", color=tc, overplot=True)
orbf.plot(d1="ra", d2="vlos", color=tc, overplot=True)
plot_data_add_labels(color="k")
add_colorbar(0.5, 3.0, r"$c$", save_figures=False)
plt.savefig("figures/varyc_bestfitline.pdf")
return
def fiducial_model(
sdf_trailing="output/sdf_trailing.pkl",
sdf_leading="output/sdf_leading.pkl",
threshold=0.3,
ro=REFR0,
vo=REFV0,
):
"""Fiducial Model.
The fiducial model assumes a spherical halo, with the best-fit
parameters from fitting to the MWPotential2014 data
"""
p_b15 = [
0.60122692,
0.36273147,
-0.97591502,
-3.34169377,
0.71877924,
-0.01519337,
-0.01928001,
]
pot = mw_pot.setup_potential(p_b15, 1.0, False, False, ro, vo)
prog = Orbit(
[229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
)
aAI = actionAngleIsochroneApprox(pot=pot, b=0.8)
sigv = 0.2
# ----------------------------------------------------------
try:
with open(sdf_trailing, "rb") as file:
sdf_trailing = pickle.load(file)
except Exception:
sdf_trailing = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
leading=False,
nTrackChunks=11,
tdisrupt=10.0 / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=pal5_util._TPAL5,
)
with open(sdf_trailing, "wb") as file:
pickle.dump(sdf_trailing, file)
try:
with open(sdf_leading, "rb") as file:
sdf_leading = pickle.load(file)
except Exception:
sdf_leading = streamdf(
sigv / vo,
progenitor=prog,
pot=pot,
aA=aAI,
leading=True,
nTrackChunks=11,
tdisrupt=10.0 / bovy_conversion.time_in_Gyr(vo, ro),
ro=ro,
vo=vo,
R0=ro,
vsun=[-11.1, vo + 24.0, 7.25],
custom_transform=pal5_util._TPAL5,
)
with open(sdf_leading, "wb") as file:
pickle.dump(sdf_leading, file)
# ----------------------------------------------------------
print("Angular length: %f deg (leading,trailing)=(%f,%f) deg" % (
sdf_leading.length(ang=True, coord="customra", threshold=threshold) +
sdf_trailing.length(ang=True, coord="customra", threshold=threshold),
sdf_leading.length(ang=True, coord="customra", threshold=threshold),
sdf_trailing.length(ang=True, coord="customra", threshold=threshold),
))
print("Angular width (FWHM): %f arcmin" %
(pal5_util.width_trailing(sdf_trailing)))
print("Velocity dispersion: %f km/s" %
(pal5_util.vdisp_trailing(sdf_trailing)))
# ----------------------------------------------------------
trackRADec_trailing = bovy_coords.lb_to_radec(
sdf_trailing._interpolatedObsTrackLB[:, 0],
sdf_trailing._interpolatedObsTrackLB[:, 1],
degree=True,
)
trackRADec_leading = bovy_coords.lb_to_radec(
sdf_leading._interpolatedObsTrackLB[:, 0],
sdf_leading._interpolatedObsTrackLB[:, 1],
degree=True,
)
lb_sample_trailing = sdf_trailing.sample(n=10000, lb=True)
lb_sample_leading = sdf_leading.sample(n=10000, lb=True)
radec_sample_trailing = bovy_coords.lb_to_radec(lb_sample_trailing[0],
lb_sample_trailing[1],
degree=True)
radec_sample_leading = bovy_coords.lb_to_radec(lb_sample_leading[0],
lb_sample_leading[1],
degree=True)
# ----------------------------------------------------------
# plotting
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
bovy_plot.bovy_plot(
trackRADec_trailing[:, 0],
trackRADec_trailing[:, 1],
color=sns.color_palette()[0],
xrange=[250.0, 210.0],
yrange=[-15.0, 9.0],
xlabel=r"$\mathrm{RA}\,(\mathrm{degree})$",
ylabel=r"$\mathrm{Dec}\,(\mathrm{degree})$",
gcf=True,
)
bovy_plot.bovy_plot(
trackRADec_leading[:, 0],
trackRADec_leading[:, 1],
color=sns.color_palette()[0],
overplot=True,
)
plt.plot(
radec_sample_trailing[:, 0],
radec_sample_trailing[:, 1],
"k.",
alpha=0.01,
zorder=0,
)
plt.plot(
radec_sample_leading[:, 0],
radec_sample_leading[:, 1],
"k.",
alpha=0.01,
zorder=0,
)
plt.errorbar(
pos_radec[:, 0],
pos_radec[:, 1],
yerr=pos_radec[:, 2],
ls="none",
marker="o",
color=sns.color_palette()[2],
)
plt.subplot(1, 2, 2)
bovy_plot.bovy_plot(
trackRADec_trailing[:, 0],
sdf_trailing._interpolatedObsTrackLB[:, 3],
color=sns.color_palette()[0],
xrange=[250.0, 210.0],
yrange=[-80.0, 0.0],
xlabel=r"$\mathrm{RA}\,(\mathrm{degree})$",
ylabel=r"$V_{\mathrm{los}}\,(\mathrm{km\,s}^{-1})$",
gcf=True,
)
bovy_plot.bovy_plot(
trackRADec_leading[:, 0],
sdf_leading._interpolatedObsTrackLB[:, 3],
color=sns.color_palette()[0],
overplot=True,
)
plt.plot(
radec_sample_trailing[:, 0],
lb_sample_trailing[3],
"k.",
alpha=0.01,
zorder=0,
)
plt.plot(
radec_sample_leading[:, 0],
lb_sample_leading[3],
"k.",
alpha=0.01,
zorder=0,
)
plt.errorbar(
rvel_ra[:, 0],
rvel_ra[:, 1],
yerr=rvel_ra[:, 2],
ls="none",
marker="o",
color=sns.color_palette()[2],
)
plt.savefig("figures/fiducial_model.pdf")
return
def main(args: Optional[list] = None, opts: Optional[Namespace] = None):
"""Fit MWPotential2014 Script Function.
Parameters
----------
args : list, optional
an optional single argument that holds the sys.argv list,
except for the script name (e.g., argv[1:])
opts : Namespace, optional
pre-constructed results of parsed args
if not None, used ONLY if args is None
"""
if opts is not None and args is None:
pass
else:
if opts is not None:
warnings.warn("Not using `opts` because `args` are given")
parser = make_parser()
opts = parser.parse_args(args)
fpath = opts.fpath + "/" if not opts.fpath.endswith("/") else opts.fpath
opath = opts.opath + "/" if not opts.opath.endswith("/") else opts.opath
# plot chains
print("Plotting Chains")
fig = mcmc_util.plot_chains(opath)
fig.savefig(fpath + "chains.pdf")
plt.close(fig)
print("Need to continue chains:", end=" ")
for i in range(32):
ngood = mcmc_util.determine_nburn(
filename=opath + f"mwpot14-fitsigma-{i:02}.dat", return_nsamples=True,
)
if ngood < 4000:
print(f"{i:02} (N={ngood})", end=", ")
###############################################################
# RESULTING PDFS
data, _, weights, _ = read_mcmc(nburn=None, skip=1, evi_func=lambda x: 1.0)
plot_corner(data, weights=weights)
plt.savefig("figures/PDFs/corner.pdf")
plt.close()
# --------------
savefilename = "output/pal5_forces_mcmc.pkl"
if not os.path.exists(savefilename):
data_wf, index_wf, weights_wf, evi_wf = read_mcmc(
nburn=None, addforces=True, skip=1, evi_func=lambda x: 1.0
)
save_pickles(savefilename, data_wf, index_wf, weights_wf, evi_wf)
else:
with open(savefilename, "rb") as savefile:
data_wf = pickle.load(savefile)
index_wf = pickle.load(savefile)
weights_wf = pickle.load(savefile)
evi_wf = pickle.load(savefile)
# --------------
plot_corner(data_wf, weights=weights_wf, addvcprior=False)
plt.savefig("figures/PDFs/corner_wf.pdf")
plt.close()
# --------------
# Which potential is preferred?
data_noforce, potindx, weights, evidences = read_mcmc(evi_func=evi_harmonic)
fig = plt.figure(figsize=(6, 4))
bovy_plot.bovy_plot(
potindx,
np.log(evidences),
"o",
xrange=[-1, 34],
yrange=[-35, -22],
xlabel=r"$\mathrm{Potential\ index}$",
ylabel=r"$\ln\ \mathrm{evidence}$",
)
data_noforce, potindx, weights, evidences = read_mcmc(evi_func=evi_laplace)
bovy_plot.bovy_plot(potindx, np.log(evidences) - 30.0, "d", overplot=True)
data_noforce, potindx, weights, evidences = read_mcmc(
evi_func=lambda x: np.exp(np.amax(x[:, -1]))
)
bovy_plot.bovy_plot(potindx, np.log(evidences) - 8.0, "s", overplot=True)
data_noforce, potindx, weights, evidences = read_mcmc(
evi_func=lambda x: np.exp(-25.0)
if (np.log(evi_harmonic(x)) > -25.0)
else np.exp(-50.0)
)
bovy_plot.bovy_plot(potindx, np.log(evidences), "o", overplot=True)
plt.savefig("figures/PDFs/preferred_pot.pdf")
plt.close()
###############################################################
# Look at the results for individual potentials
# --------------
# The flattening $c$
npot = 32
nwalkers = 12
plt.figure(figsize=(16, 6))
cmap = cm.plasma
maxl = np.zeros((npot, 2))
for en, ii in enumerate(range(npot)):
data_ip, _, weights_ip, evi_ip = read_mcmc(singlepot=ii, evi_func=evi_harmonic)
try:
maxl[en, 0] = np.amax(data_ip[:, -1])
maxl[en, 1] = np.log(evi_ip[0])
except ValueError:
maxl[en] = -10000000.0
plt.subplot(2, 4, en // 4 + 1)
bovy_plot.bovy_hist(
data_ip[:, 0],
range=[0.5, 2.0],
bins=26,
histtype="step",
color=cmap((en % 4) / 3.0),
normed=True,
xlabel=r"$c$",
lw=1.5,
overplot=True,
)
if en % 4 == 0:
bovy_plot.bovy_text(
r"$\mathrm{Potential\ %i\ to\ % i}$" % (en, en + 3),
size=17.0,
top_left=True,
)
plt.tight_layout()
plt.savefig("figures/flattening_c.pdf")
plt.close()
###############################################################
# What is the effective prior in $(F_R,F_Z)$?
frfzprior_savefilename = "frfzprior.pkl"
if not os.path.exists(frfzprior_savefilename):
# Compute for each potential separately
nvoc = 10000
ro = 8.0
npot = 32
fs = np.zeros((2, nvoc, npot))
for en, ii in tqdm(enumerate(range(npot))):
fn = f"output/fitsigma/mwpot14-fitsigma-{i:02}.dat"
# Read the potential parameters
with open(fn, "r") as savefile:
line1 = savefile.readline()
potparams = [float(s) for s in (line1.split(":")[1].split(","))]
for jj in range(nvoc):
c = np.random.uniform() * 1.5 + 0.5
tvo = np.random.uniform() * 50.0 + 200.0
pot = mw_pot.setup_potential(potparams, c, False, False, REFR0, tvo)
fs[:, jj, ii] = np.array(pal5_util.force_pal5(pot, 23.46, REFR0, tvo))[
:2
]
save_pickles(frfzprior_savefilename, fs)
else:
with open(frfzprior_savefilename, "rb") as savefile:
fs = pickle.load(savefile)
# --------------
plt.figure(figsize=(6, 6))
bovy_plot.scatterplot(
fs[0].flatten(),
fs[1].flatten(),
"k,",
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.2],
xlabel=r"$F_R(\mathrm{Pal\ 5})$",
ylabel=r"$F_Z(\mathrm{Pal\ 5})$",
onedhists=True,
)
bovy_plot.scatterplot(
data_wf[:, 7],
data_wf[:, 8],
weights=weights_wf,
bins=26,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.2],
justcontours=True,
cntrcolors="w",
overplot=True,
onedhists=True,
)
plt.axvline(-0.81, color=sns.color_palette()[0])
plt.axhline(-1.85, color=sns.color_palette()[0])
plt.savefig("figures/effective_force_prior.pdf")
plt.close()
# --------------
# The ratio of the posterior and the prior
bovy_plot.bovy_print(
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=14.0,
ytick_labelsize=14.0,
)
plt.figure(figsize=(12.5, 4))
def axes_white():
for k, spine in plt.gca().spines.items(): # ax.spines is a dictionary
spine.set_color("w")
plt.gca().tick_params(axis="x", which="both", colors="w")
plt.gca().tick_params(axis="y", which="both", colors="w")
[t.set_color("k") for t in plt.gca().xaxis.get_ticklabels()]
[t.set_color("k") for t in plt.gca().yaxis.get_ticklabels()]
return None
bins = 32
trange = [[-1.75, -0.25], [-2.5, -1.2]]
tw = copy.deepcopy(weights_wf)
tw[index_wf == 14] = 0.0 # Didn't converge properly
H_prior, xedges, yedges = np.histogram2d(
fs[0].flatten(), fs[1].flatten(), bins=bins, range=trange, normed=True
)
H_post, xedges, yedges = np.histogram2d(
data_wf[:, 7], data_wf[:, 8], weights=tw, bins=bins, range=trange, normed=True,
)
H_like = H_post / H_prior
H_like[H_prior == 0.0] = 0.0
plt.subplot(1, 3, 1)
bovy_plot.bovy_dens2d(
H_prior.T,
origin="lower",
cmap="viridis",
interpolation="nearest",
xrange=[xedges[0], xedges[-1]],
yrange=[yedges[0], yedges[-1]],
xlabel=r"$F_R(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$",
ylabel=r"$F_Z(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$",
gcf=True,
)
bovy_plot.bovy_text(r"$\mathbf{Prior}$", top_left=True, size=19.0, color="w")
axes_white()
plt.subplot(1, 3, 2)
bovy_plot.bovy_dens2d(
H_post.T,
origin="lower",
cmap="viridis",
interpolation="nearest",
xrange=[xedges[0], xedges[-1]],
yrange=[yedges[0], yedges[-1]],
xlabel=r"$F_R(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$",
gcf=True,
)
bovy_plot.bovy_text(r"$\mathbf{Posterior}$", top_left=True, size=19.0, color="w")
axes_white()
plt.subplot(1, 3, 3)
bovy_plot.bovy_dens2d(
H_like.T,
origin="lower",
cmap="viridis",
interpolation="nearest",
vmin=0.1,
vmax=4.0,
xrange=[xedges[0], xedges[-1]],
yrange=[yedges[0], yedges[-1]],
xlabel=r"$F_R(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$",
gcf=True,
)
bovy_plot.bovy_text(r"$\mathbf{Likelihood}$", top_left=True, size=19.0, color="w")
axes_white()
def qline(FR, q=0.95):
return 2.0 * FR / q ** 2.0
q = 0.94
plt.plot([-1.25, -0.2], [qline(-1.25, q=q), qline(-0.2, q=q)], "w--")
bovy_plot.bovy_text(-1.7, -2.2, r"$q_\Phi = 0.94$", size=16.0, color="w")
plt.plot((-1.25, -1.02), (-2.19, qline(-1.02, q=q)), "w-", lw=0.8)
plt.tight_layout()
plt.savefig(
"figures/pal5post.pdf", bbox_inches="tight",
)
plt.close()
# --------------
# Projection onto the direction perpendicular to constant $q = 0.94$:
frs = np.tile(0.5 * (xedges[:-1] + xedges[1:]), (len(yedges) - 1, 1)).T
fzs = np.tile(0.5 * (yedges[:-1] + yedges[1:]), (len(xedges) - 1, 1))
plt.figure(figsize=(6, 4))
txlabel = r"$F_\perp$"
dum = bovy_plot.bovy_hist(
(-2.0 * (frs + 0.8) + 0.94 ** 2.0 * (fzs + 1.82)).flatten(),
weights=H_prior.flatten(),
bins=21,
histtype="step",
lw=2.0,
xrange=[-1.5, 1.5],
xlabel=txlabel,
normed=True,
)
dum = bovy_plot.bovy_hist(
(-2.0 * (frs + 0.8) + 0.94 ** 2.0 * (fzs + 1.82)).flatten(),
weights=H_post.flatten(),
bins=21,
histtype="step",
lw=2.0,
overplot=True,
xrange=[-1.5, 1.5],
normed=True,
)
dum = bovy_plot.bovy_hist(
(-2.0 * (frs + 0.8) + 0.94 ** 2.0 * (fzs + 1.82)).flatten(),
weights=H_like.flatten(),
bins=21,
histtype="step",
lw=2.0,
overplot=True,
xrange=[-1.5, 1.5],
normed=True,
)
plt.savefig("figures/PDFs/projection_perp_to_q0p94.pdf")
plt.close()
mq = (
np.sum(
(-2.0 * (frs + 0.8) + 0.94 ** 2.0 * (fzs + 1.82)).flatten()
* H_like.flatten()
)
) / np.sum(H_like.flatten())
print(
mq,
np.sqrt(
(
np.sum(
((-2.0 * (frs + 0.8) + 0.94 ** 2.0 * (fzs + 1.82)).flatten() - mq)
** 2.0
* H_like.flatten()
)
)
/ np.sum(H_like.flatten())
),
)
# --------------
# Projection onto the direction parallel to constant $q = 0.94$:
frs = np.tile(0.5 * (xedges[:-1] + xedges[1:]), (len(yedges) - 1, 1)).T
fzs = np.tile(0.5 * (yedges[:-1] + yedges[1:]), (len(xedges) - 1, 1))
plt.figure(figsize=(6, 4))
txlabel = r"$F_\parallel$"
dum = bovy_plot.bovy_hist(
(0.94 ** 2.0 * (frs + 0.8) + 2.0 * (fzs + 1.82)).flatten(),
weights=H_prior.flatten(),
bins=21,
histtype="step",
lw=2.0,
xrange=[-2.5, 2.5],
xlabel=txlabel,
normed=True,
)
dum = bovy_plot.bovy_hist(
(0.94 ** 2.0 * (frs + 0.8) + 2.0 * (fzs + 1.82)).flatten(),
weights=H_post.flatten(),
bins=21,
histtype="step",
lw=2.0,
overplot=True,
xrange=[-2.5, 2.5],
normed=True,
)
dum = bovy_plot.bovy_hist(
(0.94 ** 2.0 * (frs + 0.8) + 2.0 * (fzs + 1.82)).flatten(),
weights=H_like.flatten(),
bins=21,
histtype="step",
lw=2.0,
overplot=True,
xrange=[-2.5, 2.5],
normed=True,
)
plt.savefig("figures/PDFs/projection_prll_to_q0p94.pdf")
plt.close()
mq = (
np.sum(
(0.94 ** 2.0 * (frs + 0.8) + 2.0 * (fzs + 1.82)).flatten()
* H_like.flatten()
)
) / np.sum(H_like.flatten())
print(
mq,
np.sqrt(
(
np.sum(
((0.94 ** 2.0 * (frs + 0.8) + 2.0 * (fzs + 1.82)).flatten() - mq)
** 2.0
* H_like.flatten()
)
)
/ np.sum(H_like.flatten())
),
)
# --------------
# Thus, there is only a weak constraint on $F_\parallel$.
nrow = int(np.ceil(npot / 4.0))
plt.figure(figsize=(16, nrow * 4))
for en, ii in enumerate(range(npot)):
plt.subplot(nrow, 4, en + 1)
if ii % 4 == 0:
tylabel = r"$F_Z(\mathrm{Pal\ 5})$"
else:
tylabel = None
if ii // 4 == nrow - 1:
txlabel = r"$F_R(\mathrm{Pal\ 5})$"
else:
txlabel = None
bovy_plot.scatterplot(
fs[0][:, en],
fs[1][:, en],
"k,",
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
xlabel=txlabel,
ylabel=tylabel,
gcf=True,
)
bovy_plot.scatterplot(
data_wf[:, 7],
data_wf[:, 8],
weights=weights_wf,
bins=26,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
justcontours=True,
cntrcolors="w",
overplot=True,
)
bovy_plot.scatterplot(
data_wf[index_wf == ii, 7],
data_wf[index_wf == ii, 8],
weights=weights_wf[index_wf == ii],
bins=26,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
justcontours=True,
# cntrcolors=sns.color_palette()[2],
overplot=True,
)
plt.axvline(-0.80, color=sns.color_palette()[0])
plt.axhline(-1.83, color=sns.color_palette()[0])
bovy_plot.bovy_text(r"$\mathrm{Potential}\ %i$" % ii, size=17.0, top_left=True)
plt.savefig("figures/PDFs/constain_F_prll.pdf")
plt.close()
# --------------
# Let's plot four representative ones for the paper:
bovy_plot.bovy_print(
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=14.0,
ytick_labelsize=14.0,
)
nullfmt = NullFormatter()
nrow = 1
plt.figure(figsize=(15, nrow * 4))
for en, ii in enumerate([0, 15, 24, 25]):
plt.subplot(nrow, 4, en + 1)
if en % 4 == 0:
tylabel = (
r"$F_Z(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$"
)
else:
tylabel = None
if en // 4 == nrow - 1:
txlabel = (
r"$F_R(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$"
)
else:
txlabel = None
bovy_plot.scatterplot(
fs[0][:, ii],
fs[1][:, ii],
"k,",
bins=31,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
xlabel=txlabel,
ylabel=tylabel,
gcf=True,
)
bovy_plot.scatterplot(
data_wf[:, 7],
data_wf[:, 8],
weights=weights_wf,
bins=21,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
justcontours=True,
cntrcolors=sns.color_palette("colorblind")[2],
cntrls="--",
cntrlw=2.0,
overplot=True,
)
bovy_plot.scatterplot(
data_wf[index_wf == ii, 7],
data_wf[index_wf == ii, 8],
weights=weights_wf[index_wf == ii],
bins=21,
xrange=[-1.75, -0.25],
yrange=[-2.5, -1.0],
justcontours=True,
cntrcolors=sns.color_palette("colorblind")[0],
cntrlw=2.5,
overplot=True,
)
if en > 0:
plt.gca().yaxis.set_major_formatter(nullfmt)
plt.tight_layout()
plt.savefig(
"figures/pal5post_examples.pdf", bbox_inches="tight",
)
plt.close()
###############################################################
# What about $q_\Phi$?
bins = 47
plt.figure(figsize=(6, 4))
dum = bovy_plot.bovy_hist(
np.sqrt(2.0 * fs[0].flatten() / fs[1].flatten()),
histtype="step",
lw=2.0,
bins=bins,
xlabel=r"$q_\mathrm{\Phi}$",
xrange=[0.7, 1.25],
normed=True,
)
dum = bovy_plot.bovy_hist(
np.sqrt(16.8 / 8.4 * data_wf[:, -2] / data_wf[:, -1]),
weights=weights_wf,
histtype="step",
lw=2.0,
bins=bins,
overplot=True,
xrange=[0.7, 1.25],
normed=True,
)
mq = np.sum(
np.sqrt(16.8 / 8.4 * data_wf[:, -2] / data_wf[:, -1]) * weights_wf
) / np.sum(weights_wf)
sq = np.sqrt(
np.sum(
(np.sqrt(16.8 / 8.4 * data_wf[:, -2] / data_wf[:, -1]) - mq) ** 2.0
* weights_wf
)
/ np.sum(weights_wf)
)
print("From posterior samples: q = %.3f +/- %.3f" % (mq, sq))
Hq_post, xedges = np.histogram(
np.sqrt(16.8 / 8.4 * data_wf[:, -2] / data_wf[:, -1]),
weights=weights_wf,
bins=bins,
range=[0.7, 1.25],
normed=True,
)
Hq_prior, xedges = np.histogram(
np.sqrt(2.0 * fs[0].flatten() / fs[1].flatten()),
bins=bins,
range=[0.7, 1.25],
normed=True,
)
qs = 0.5 * (xedges[:-1] + xedges[1:])
Hq_like = Hq_post / Hq_prior
Hq_like[Hq_post == 0.0] = 0.0
mq = np.sum(qs * Hq_like) / np.sum(Hq_like)
sq = np.sqrt(np.sum((qs - mq) ** 2.0 * Hq_like) / np.sum(Hq_like))
print("From likelihood of samples: q = %.3f +/- %.3f" % (mq, sq))
plt.savefig("figures/q_phi.pdf")
plt.close()
# It appears that $q_\Phi$ is the quantity that is the most strongly constrained by the Pal 5 data.
###############################################################
# A sampling of tracks from the MCMC
savefilename = "mwpot14-pal5-mcmcTracks.pkl"
pmdecpar = 2.257 / 2.296
pmdecperp = -2.296 / 2.257
if os.path.exists(savefilename):
with open(savefilename, "rb") as savefile:
pal5_track_samples = pickle.load(savefile)
forces = pickle.load(savefile)
all_potparams = pickle.load(savefile)
all_params = pickle.load(savefile)
else:
np.random.seed(1)
ntracks = 21
multi = 8
pal5_track_samples = np.zeros((ntracks, 2, 6, pal5varyc[0].shape[1]))
forces = np.zeros((ntracks, 2))
all_potparams = np.zeros((ntracks, 5))
all_params = np.zeros((ntracks, 7))
for ii in range(ntracks):
# Pick a random potential from among the set, but leave 14 out
pindx = 14
while pindx == 14:
pindx = np.random.permutation(32)[0]
# Load this potential
fn = f"output/fitsigma/mwpot14-fitsigma-{pindx:02}.dat"
with open(fn, "r") as savefile:
line1 = savefile.readline()
potparams = [float(s) for s in (line1.split(":")[1].split(","))]
all_potparams[ii] = potparams
# Now pick a random sample from this MCMC chain
tnburn = mcmc_util.determine_nburn(fn)
tdata = np.loadtxt(fn, comments="#", delimiter=",")
tdata = tdata[tnburn::]
tdata = tdata[np.random.permutation(len(tdata))[0]]
all_params[ii] = tdata
tvo = tdata[1] * REFV0
pot = mw_pot.setup_potential(potparams, tdata[0], False, False, REFR0, tvo)
forces[ii, :] = pal5_util.force_pal5(pot, 23.46, REFR0, tvo)[:2]
# Now compute the stream model for this setup
dist = tdata[2] * 22.0
pmra = -2.296 + tdata[3] + tdata[4]
pmdecpar = 2.257 / 2.296
pmdecperp = -2.296 / 2.257
pmdec = -2.257 + tdata[3] * pmdecpar + tdata[4] * pmdecperp
vlos = -58.7
sigv = 0.4 * np.exp(tdata[5])
prog = Orbit(
[229.018, -0.124, dist, pmra, pmdec, vlos],
radec=True,
ro=REFR0,
vo=tvo,
solarmotion=[-11.1, 24.0, 7.25],
)
tsdf_trailing, tsdf_leading = pal5_util.setup_sdf(
pot,
prog,
sigv,
10.0,
REFR0,
tvo,
multi=multi,
nTrackChunks=8,
trailing_only=False,
verbose=True,
useTM=False,
)
# Compute the track
for jj, sdf in enumerate([tsdf_trailing, tsdf_leading]):
trackRADec = bovy_coords.lb_to_radec(
sdf._interpolatedObsTrackLB[:, 0],
sdf._interpolatedObsTrackLB[:, 1],
degree=True,
)
trackpmRADec = bovy_coords.pmllpmbb_to_pmrapmdec(
sdf._interpolatedObsTrackLB[:, 4],
sdf._interpolatedObsTrackLB[:, 5],
sdf._interpolatedObsTrackLB[:, 0],
sdf._interpolatedObsTrackLB[:, 1],
degree=True,
)
# Store the track
pal5_track_samples[ii, jj, 0] = trackRADec[:, 0]
pal5_track_samples[ii, jj, 1] = trackRADec[:, 1]
pal5_track_samples[ii, jj, 2] = sdf._interpolatedObsTrackLB[:, 2]
pal5_track_samples[ii, jj, 3] = sdf._interpolatedObsTrackLB[:, 3]
pal5_track_samples[ii, jj, 4] = trackpmRADec[:, 0]
pal5_track_samples[ii, jj, 5] = trackpmRADec[:, 1]
save_pickles(
savefilename, pal5_track_samples, forces, all_potparams, all_params
)
# --------------
bovy_plot.bovy_print(
axes_labelsize=17.0,
text_fontsize=12.0,
xtick_labelsize=14.0,
ytick_labelsize=14.0,
)
plt.figure(figsize=(12, 8))
gs = gridspec.GridSpec(2, 2, wspace=0.225, hspace=0.1, right=0.94)
ntracks = pal5_track_samples.shape[0]
cmap = cm.plasma
alpha = 0.7
for ii in range(ntracks):
tc = cmap((forces[ii, 1] + 2.5) / 1.0)
for jj in range(2):
# RA, Dec
plt.subplot(gs[0])
plt.plot(
pal5_track_samples[ii, jj, 0],
pal5_track_samples[ii, jj, 1],
"-",
color=tc,
alpha=alpha,
)
# RA, Vlos
plt.subplot(gs[1])
plt.plot(
pal5_track_samples[ii, jj, 0],
pal5_track_samples[ii, jj, 3],
"-",
color=tc,
alpha=alpha,
)
# RA, Dist
plt.subplot(gs[2])
plt.plot(
pal5_track_samples[ii, jj, 0],
pal5_track_samples[ii, jj, 2] - all_params[ii, 2] * 22.0,
"-",
color=tc,
alpha=alpha,
)
# RA, pm_parallel
plt.subplot(gs[3])
plt.plot(
pal5_track_samples[ii, jj, 0, : 500 + 500 * (1 - jj)],
np.sqrt(1.0 + (2.257 / 2.296) ** 2.0)
* (
(pal5_track_samples[ii, jj, 4, : 500 + 500 * (1 - jj)] + 2.296)
* pmdecperp
- (pal5_track_samples[ii, jj, 5, : 500 + 500 * (1 - jj)] + 2.257)
)
/ (pmdecpar - pmdecperp),
"-",
color=tc,
alpha=alpha,
)
plot_data_add_labels(
p1=(gs[0],), p2=(gs[1],), noxlabel_dec=True, noxlabel_vlos=True
)
plt.subplot(gs[2])
plt.xlim(250.0, 221.0)
plt.ylim(-3.0, 1.5)
bovy_plot._add_ticks()
plt.xlabel(r"$\mathrm{RA}\,(\mathrm{degree})$")
plt.ylabel(r"$\Delta\mathrm{Distance}\,(\mathrm{kpc})$")
plt.subplot(gs[3])
plt.xlim(250.0, 221.0)
plt.ylim(-0.5, 0.5)
bovy_plot._add_ticks()
plt.xlabel(r"$\mathrm{RA}\,(\mathrm{degree})$")
plt.ylabel(r"$\Delta\mu_\parallel\,(\mathrm{mas\,yr}^{-1})$")
# Colorbar
gs2 = gridspec.GridSpec(2, 1, wspace=0.0, left=0.95, right=0.975)
plt.subplot(gs2[:, -1])
sm = plt.cm.ScalarMappable(cmap=cmap, norm=plt.Normalize(vmin=-2.5, vmax=-1.5))
sm._A = []
CB1 = plt.colorbar(sm, orientation="vertical", cax=plt.gca())
CB1.set_label(
r"$F_Z(\mathrm{Pal\ 5})\,(\mathrm{km\,s}^{-1}\,\mathrm{Myr}^{-1})$",
fontsize=18.0,
)
plt.savefig(
"figures/pal5tracksamples.pdf", bbox_inches="tight",
)
plt.close()
###############################################################
# What about Kuepper et al. (2015)?
# Can we recover the Kuepper et al. (2015) result as prior + $q_\Phi =
# 0.94 \pm 0.05$ + $V_c(R_0)$ between 200 and 280 km/s? For simplicity
# we will not vary $R_0$, which should not have a big impact.
s = sample_kuepper_flattening_post(50000, 0.94, 0.05)
plot_kuepper_samples(s)
plt.savefig("figures/kuepper_samples.pdf")
plt.close()
# The constraint on the potential flattening gets you far, but there
# is more going on (the constraint on the halo mass and scale
# parameter appear to come completely from the $V_c(R_0)$ constraint).
# Let's add the weak constraint on the sum of the forces, scaled to
# Kuepper et al.'s best-fit acceleration (which is higher than ours):
s = sample_kuepper_flatteningforce_post(50000, 0.94, 0.05, -0.83, 0.36)
plot_kuepper_samples(s)
plt.savefig("figures/kuepper_samples_flatF.pdf")
plt.close()
# This gets a tight relation between $M_\mathrm{halo}$ and the scale
# parameter of the halo, but does not lead to a constraint on either
# independently; the halo potential flattening constraint is that of
# Kuepper et al. Based on this, it appears that the information that
# ties down $M_\mathrm{halo}$ comes from the overdensities, which may
# be spurious (Thomas et al. 2016) and whose use in dynamical modeling
# is dubious anyway.
# What is Kuepper et al.'s prior on $a_{\mathrm{Pal\ 5}}$?
apal5s = []
ns = 100000
for ii in range(ns):
Mh = np.random.uniform() * (10.0 - 0.001) + 0.001
a = np.random.uniform() * (100.0 - 0.1) + 0.1
q = np.random.uniform() * (1.8 - 0.2) + 0.2
pot = setup_potential_kuepper(Mh, a)
FR, FZ = force_pal5_kuepper(pot, q)
apal5s.append(np.sqrt(FR ** 2.0 + FZ ** 2.0))
apal5s = np.array(apal5s)
plt.figure(figsize=(6, 4))
dum = bovy_plot.bovy_hist(
apal5s, range=[0.0, 10.0], lw=2.0, bins=51, histtype="step", normed=True,
)
plt.savefig("figures/kuepper_samples_prior.pdf")
plt.close()
def read_mcmc(
filename: str = "output/fitsigma/mwpot14-fitsigma-*.dat",
nburn: Optional[int] = None,
evi_func: FunctionType = evi_laplace,
evi_cut: float = -10.0,
addforces: bool = False,
addmwpot14weights: bool = False,
singlepot: Optional[int] = None,
skip: int = 1,
):
"""Read MCMC.
Parameters
----------
filename : str
nburn : int, optional
evi_func : FunctionType, optional
evidence function
evi_cut : float, optional
addforces : bool, optional
addmwpot14weights : bool, optional
singlepot : int, optional
whether to use a single potential, specified by number
default (None) is to use all
skip : int, optional
Returns
-------
alldata
indx : ndarray
shape (N, )
weights : ndarray
shape (N, )
evis: ndarray
shape (N, )
"""
fn = glob.glob(filename) # filename
alldata = np.zeros((0, 7 + 2 * addforces))
indx = np.zeros((0, 1))
weights = np.zeros((0, 1))
evis = np.zeros((0, 1))
for f in tqdm(fn):
pindx = int(f.split("-")[2].split(".dat")[0])
# if pindx == 14 or pindx > 27:
# print("Remember: skipping 14 and > 27 for now ...")
# continue
if singlepot is not None and not pindx == singlepot:
continue
continue_flag = False
try:
if nburn is None:
tnburn = mcmc_util.determine_nburn(f)
else:
tnburn = nburn
tdata = np.loadtxt(f, comments="#", delimiter=",")
tdata = tdata[tnburn::skip]
tdata = tdata[tdata[:, -1] > np.nanmax(tdata[:, -1]) + evi_cut]
if len(tdata) < 100:
continue_flag = True
except:
continue_flag = True # not enough samples yet
if continue_flag:
continue
# Needs to be before addforces, because evi uses -1 as the lnlike index
tweights = np.ones((len(tdata), 1)) / float(len(tdata)) * evi_func(tdata)
evis = np.vstack((evis, np.ones((len(tdata), 1)) * evi_func(tdata)))
if addforces:
# Read the potential from the file
with open(f, "r") as savefile: # not byte b/c split with str
line1 = savefile.readline()
potparams = [float(s) for s in (line1.split(":")[1].split(","))]
forces = np.empty((len(tdata), 2))
for ee, c in enumerate(tdata[:, 0]):
tvo = tdata[ee, 1] * REFV0
pot = mw_pot.setup_potential(potparams, c, False, False, REFR0, tvo)
forces[ee, :] = pal5_util.force_pal5(pot, 23.46, REFR0, tvo)[:2]
tdata = np.hstack((tdata, forces))
if addmwpot14weights:
# Not terribly useful right now
# Add the relative importance weights of this (c,vc) compared to the one
# that this potential was sampled from
# Read the potential from the file
with open(f, "rb") as savefile:
line1 = savefile.readline()
potparams = [float(s) for s in (line1.split(":")[1].split(","))]
# Also load the samples to find the c that this set was sampled with
with open("mwpot14varyc-samples.pkl", "rb") as savefile:
s = pickle.load(savefile)
rndindx = np.argmin(np.fabs(s[0] - potparams[0]))
pot_params = s[:, rndindx]
print(pot_params[7])
base_like = mw_pot.like_func(
pot_params,
pot_params[7],
surfrs,
kzs,
kzerrs,
termdata,
700.0,
False,
False,
False,
False,
REFR0,
220.0,
)
for ee, c in enumerate(tdata[:, 0]):
tvo = tdata[ee, 1] * REFV0
tweights[ee] *= np.exp(
-mw_pot.like_func(
pot_params,
c,
surfrs,
kzs,
kzerrs,
termdata,
700.0,
False,
False,
False,
False,
REFR0,
tvo,
) # last one is no vo prior
+ base_like
)
# Only keep
alldata = np.vstack((alldata, tdata))
indx = np.vstack((indx, np.zeros((len(tdata), 1), dtype="int") + pindx))
weights = np.vstack((weights, tweights))
return alldata, indx[:, 0], weights[:, 0], evis[:, 0]
