def get_gal_pa(subject_id):
try:
p = Pipeline.load('lib/pipelines/{}.json'.format(subject_id))
except FileNotFoundError:
drawn_arms = gu.get_drawn_arms(subject_id, gu.classifications)
gal, angle = gu.get_galaxy_and_angle(subject_id)
pic_array, deprojected_image = gu.get_image(gal, subject_id, angle)
p = Pipeline(drawn_arms,
phi=angle,
ba=gal['PETRO_BA90'],
image_size=pic_array.shape[0])
arms = (Arm.load(os.path.join('lib/spiral_arms', f))
for f in os.listdir('lib/spiral_arms')
if re.match('^{}-[0-9]+.pickle$'.format(subject_id), f))
arms = [arm for arm in arms if not arm.FLAGGED_AS_BAD]
pa = np.zeros(len(arms))
sigma_pa = np.zeros(pa.shape)
length = np.zeros(pa.shape)
for i, arm in enumerate(arms):
pa[i] = arm.pa
length[i] = arm.length
sigma_pa[i] = arm.sigma_pa
if len(arms) == 0:
return (np.nan, np.nan,
np.stack((np.tile(subject_id, len(pa)), pa, sigma_pa, length),
axis=1))
combined_pa = (pa * length).sum() / length.sum()
combined_sigma_pa = np.sqrt((length**2 * sigma_pa**2).sum()) / length.sum()
return (
combined_pa,
combined_sigma_pa,
np.stack((np.tile(subject_id, len(pa)), pa, sigma_pa, length), axis=1),
)
def get_log_spirals(subject_id,
gal=None,
angle=None,
pic_array=None,
bar_length=0):
drawn_arms = gu.get_drawn_arms(subject_id, gu.classifications)
if gal is None or angle is None:
gal, angle = gu.get_galaxy_and_angle(subject_id)
if pic_array is None:
pic_array, deprojected_image = gu.get_image(gal, subject_id, angle)
path_to_subject = './lib/distances/subject-{}.npy'.format(subject_id)
distances = gu.get_distances(subject_id)
if distances is None or distances.shape[0] != len(
drawn_arms) or not os.path.exists(path_to_subject):
# print('\t- Calculating distances')
distances = metric.calculate_distance_matrix(drawn_arms)
np.save('./lib/distances/subject-{}.npy'.format(subject_id), distances)
p = Pipeline(drawn_arms,
phi=angle,
ba=gal['PETRO_BA90'],
image_size=pic_array.shape[0],
distances=distances)
arms = p.get_arms(clean_points=True, bar_length=bar_length)
# print('Identified {} spiral arms'.format(len(arms)))
return [arm.reprojected_log_spiral for arm in arms]
def make_arm_plots():
outfile = 'lib/duplicate_comb_spirals'
bar = Bar('Plotting arms',
max=len(dr8ids), suffix='%(percent).1f%% - %(eta)ds')
arm_loc = 'lib/duplicate_spiral_arms'
for i in range(len(dr8ids)):
original_id = ss_ids[i]
gal, angle = gu.get_galaxy_and_angle(original_id)
pic_array, _ = gu.get_image(gal, original_id, angle)
arms = [
Arm.load(os.path.join(arm_loc, f))
for f in os.listdir(arm_loc)
if re.match('^{}-[0-9]+.pickle$'.format(dr8ids[i]), f)
]
plt.figure(figsize=(8, 8))
plt.imshow(pic_array, cmap='gray')
for i, arm in enumerate(arms):
plt.plot(
*arm.reprojected_log_spiral.T,
c=('C2' if not arm.FLAGGED_AS_BAD else 'C1')
)
plt.savefig(os.path.join(outfile, '{}.png'.format(original_id)))
plt.close()
bar.next()
bar.finish()
def get_best_classification(subject_id, should_plot=False, should_save=False):
# grab all the required metadata for this galaxy
psf = gu.get_psf(subject_id)
diff_data = gu.get_image_data(subject_id)
pixel_mask = 1 - np.array(diff_data['mask'])[::-1]
galaxy_data = np.array(diff_data['imageData'])[::-1]
size_diff = diff_data['width'] / diff_data['imageWidth']
def _lf(rendered_model, y=galaxy_data):
Y = rg.convolve2d(rendered_model, psf, mode='same',
boundary='symm') * pixel_mask
return mean_squared_error(Y.flatten(),
0.8 * (y * pixel_mask).flatten())
classifications = gu.classifications.query(
'subject_ids == {}'.format(subject_id))
annotations = classifications['annotations'].apply(json.loads)
models = annotations.apply(pa.parse_annotation, size_diff=size_diff)
rendered_models = models.apply(rg.calculate_model,
args=(diff_data['width'], ))
scores = rendered_models.apply(_lf)
best_index = scores.idxmin()
best_cls = classifications.loc[best_index]
best_model = models.loc[best_index]
best_rendered_model = rendered_models.loc[best_index]
if should_plot:
gal, angle = gu.get_galaxy_and_angle(subject_id)
pic_array, deprojected_image = gu.get_image(gal, subject_id, angle)
# arcseconds per pixel for zooniverse image
pix_size = pic_array.shape[0] / (gal['PETRO_THETA'].iloc[0] * 4)
# arcseconds per pixel for galaxy data
pix_size2 = galaxy_data.shape[0] / (gal['PETRO_THETA'].iloc[0] * 4)
imshow_kwargs = {
'cmap':
'gray_r',
'origin':
'lower',
'extent': (
# left of image in arcseconds from centre
-pic_array.shape[0] / 2 / pix_size,
pic_array.shape[0] / 2 / pix_size, # right...
-pic_array.shape[1] / 2 / pix_size, # bottom...
pic_array.shape[1] / 2 / pix_size # top...
),
}
tc, tp = make_transforms(galaxy_data, pix_size2)
plot_model(best_rendered_model, galaxy_data, psf, best_model,
pixel_mask, imshow_kwargs, tc, tp, best_cls)
plt.savefig('best_residual/{}.pdf'.format(subject_id))
plt.close()
if should_save:
with open('best_annotation/{}.json'.format(subject_id), 'w') as f:
f.write(json.dumps(pa.make_json(best_model)))
return best_cls
def get_optimized_model(subject_id, mode='best'):
gal, angle = gu.get_galaxy_and_angle(subject_id)
sep = coords.separation(
SkyCoord(ra=gal['RA'] * u.degree, dec=gal['DEC'] * u.degree))
idxmin_sep = np.argmin(sep)
if not sep[idxmin_sep] < 1 * u.arcsec:
return None
pic_array, deprojected_image = gu.get_image(gal, subject_id, angle)
psf = gu.get_psf(subject_id)
diff_data = gu.get_image_data(subject_id)
pixel_mask = 1 - np.array(diff_data['mask'])[::-1]
galaxy_data = np.array(diff_data['imageData'])[::-1]
size_diff = diff_data['width'] / diff_data['imageWidth']
# arcseconds per pixel for zooniverse image
pix_size = pic_array.shape[0] / (gal['PETRO_THETA'].iloc[0] * 4)
# arcseconds per pixel for galaxy data
pix_size2 = galaxy_data.shape[0] / (gal['PETRO_THETA'].iloc[0] * 4)
try:
if mode == 'agg':
agg_fname = os.path.join('..', 'component-clustering',
'cluster-output',
'{}.json'.format(subject_id))
with open(agg_fname) as f:
model = pa.parse_aggregate_model(json.load(f),
size_diff=size_diff)
elif mode == 'best':
c = gu.classifications.query('classification_id == {}'.format(
best_cls[str(subject_id)])).iloc[0]
a = json.loads(c['annotations'])
model = pa.parse_annotation(a, size_diff=size_diff)
else:
raise ValueError('Invalid value for "mode"')
except KeyError:
print('\nFailed: {}'.format(subject_id))
return None
no_spiral_model = deepcopy(model)
no_spiral_model['spiral'] = []
mf_nosp = ModelFitter(no_spiral_model, galaxy_data, psf, pixel_mask)
md_nosp = mf_nosp.model
try:
new_nosp_model, res = mf_nosp.fit(options={'maxiter': 100})
except ValueError:
print('\nCould not fit: {}'.format(subject_id))
return None
m0_nosp = Model(no_spiral_model, galaxy_data, psf, pixel_mask)
m1_nosp = Model(new_nosp_model, galaxy_data, psf, pixel_mask)
return (subject_id, m0_nosp, m1_nosp, sd.iloc[idxmin_sep], pix_size2)
s = clf.score(
X_test[:, :-1],
t_test,
sample_weight=point_weights[test]
)
params.append(clf.coef_)
score += s / n_splits
return score, params
if __name__ == '__main__':
chosenId = 21097008
# chosenId = 21686558
gal, angle = gu.get_galaxy_and_angle(chosenId)
pic_array, deprojected_image = gu.get_image(
gal, chosenId, angle
)
drawn_arms = gu.get_drawn_arms(chosenId, gu.classifications)
galaxy_object = GalaxySpirals(
drawn_arms,
ba=gal['SERSIC_BA'].iloc[0],
phi=-angle
)
try:
distances
except NameError:
distances = galaxy_object.calculate_distances()
db = galaxy_object.cluster_lines(distances)
plt.title('Combined galaxy')
plt.imshow(pic_array, origin='lower', cmap='gray_r')
ax = plt.gca()
for p in patches:
ax.add_patch(p)
plt.axis('off')
if outfile is not None:
plt.savefig(outfile)
if __name__ == "__main__":
sid_list = sorted(np.loadtxt('lib/subject-id-list.csv', dtype='u8'))
to_iter = sid_list
for subject_id in tqdm(to_iter):
gal, angle = gu.get_galaxy_and_angle(subject_id)
pic_array, deprojected_image = gu.get_image(gal, subject_id, angle)
pix_size = pic_array.shape[0] / (gal['PETRO_THETA'].iloc[0] * 4
) # pixels per arcsecond
disk_res, bulge_res, bar_res = cluster_components(subject_id)
spirals = get_log_spirals(subject_id,
gal=gal,
angle=angle,
pic_array=pic_array,
bar_length=10)
xtick_labels = np.linspace(-100, 100, 11).astype(int)
xtick_positions = xtick_labels * pix_size + pic_array.shape[0] / 2
xtick_mask = (xtick_positions > 0) & (xtick_positions <
pic_array.shape[0])
import numpy as np
import gzbuilder_analysis.parsing as parsing
import gzbuilder_analysis.spirals as spirals
from scipy.integrate import odeint
from scipy.optimize import minimize
import lib.galaxy_utilities as gu
subject_id = 20902040
galaxy_classifcations = gu.classifications.query(
'subject_ids == {}'.format(subject_id))
drawn_arms = spirals.get_drawn_arms(galaxy_classifcations)
gal, angle = gu.get_galaxy_and_angle(subject_id)
ba = gal['PETRO_BA90']
im = gu.get_image(subject_id)
psf = gu.get_psf(subject_id)
diff_data = gu.get_diff_data(subject_id)
pixel_mask = 1 - np.array(diff_data['mask'])[::-1]
galaxy_data = np.array(diff_data['imageData'])[::-1]
size_diff = diff_data['width'] / diff_data['imageWidth']
# functions for plotting
# tv = lambda v: parsing.transform_val(v, np.array(im).shape[0], gal['PETRO_THETA'])
# ts = lambda v: parsing.transform_shape(v, galaxy_data.shape[0], gal['PETRO_THETA'])
# ts_a = lambda v: parsing.transform_shape(v, galaxy_data.shape[0], gal['PETRO_THETA'])
# imshow_kwargs = dict(cmap='gray', origin='lower', extent=[tv(0), tv(np.array(im).shape[0])]*2)
# Swing amplification model (not using sklearn pipelines)
def _swing_amplification_dydt(r, theta, b):
def plot_aggregation(subject_id, model=None, cluster_masks=None, arms=None):
if model is None or cluster_masks is None or arms is None:
print(model)
model_path = os.path.join(
'cluster-output', '{}.json'.format(subject_id)
)
masks_path = os.path.join('cluster_masks', '{}.npy'.format(subject_id))
if not (os.path.exists(model_path) and os.path.exists(masks_path)):
return
with open(model_path) as f:
model = json.load(f)
with open(masks_path) as f:
cluster_masks = np.load(f)
arms = get_spiral_arms(subject_id, should_recreate=False)
annotations = gu.classifications[
gu.classifications['subject_ids'] == subject_id
]['annotations'].apply(json.loads)
models = annotations\
.apply(ash.remove_scaling)\
.apply(pa.parse_annotation)\
.apply(sanitize_model)
spirals = models.apply(lambda d: d.get('spiral', None))
geoms = pd.DataFrame(
models.apply(get_geoms).values.tolist(),
columns=('disk', 'bulge', 'bar')
)
logsps = [arm.reprojected_log_spiral for arm in arms]
disk_cluster_geoms = geoms['disk'][cluster_masks[0]]
bulge_cluster_geoms = geoms['bulge'][cluster_masks[1]]
bar_cluster_geoms = geoms['bar'][cluster_masks[2]]
aggregate_disk_geom = ash.make_ellipse(model['disk'])
aggregate_bulge_geom = ash.make_ellipse(model['bulge'])
aggregate_bar_geom = ash.make_box(model['bar'])
gal, angle = gu.get_galaxy_and_angle(subject_id)
pic_array, _ = gu.get_image(gal, subject_id, angle)
def ts(s):
return ash.transform_shape(s, pic_array.shape[0],
gal['PETRO_THETA'].iloc[0])
def tv(v):
return ash.transform_val(v, pic_array.shape[0],
gal['PETRO_THETA'].iloc[0])
imshow_kwargs = {
'cmap': 'gray',
'origin': 'lower',
'extent': [tv(0), tv(pic_array.shape[0])]*2,
}
fig, ((ax0, ax1), (ax2, ax3)) = plt.subplots(
ncols=2, nrows=2,
figsize=(10, 10),
sharex=True, sharey=True
)
ax0.imshow(pic_array, **imshow_kwargs)
for comp in geoms['disk'].values:
if comp:
ax0.add_patch(
PolygonPatch(ts(comp), fc='C0', ec='k',
alpha=0.2, zorder=3)
)
ax1.imshow(pic_array, **imshow_kwargs)
for comp in geoms['bulge'].values:
if comp:
ax1.add_patch(
PolygonPatch(ts(comp), fc='C1', ec='k',
alpha=0.5, zorder=3)
)
ax2.imshow(pic_array, **imshow_kwargs)
for comp in geoms['bar'].values:
if comp:
ax2.add_patch(
PolygonPatch(ts(comp), fc='C2', ec='k',
alpha=0.2, zorder=3)
)
ax3.imshow(pic_array, **imshow_kwargs)
for arm in arms:
for a in arm.arms:
ax3.plot(*tv(a).T)
for i, ax in enumerate((ax0, ax1, ax2, ax3)):
ax.set_xlim(imshow_kwargs['extent'][:2])
ax.set_ylim(imshow_kwargs['extent'][2:])
if i % 2 == 0:
ax.set_ylabel('Arcseconds from center')
if i > 1:
ax.set_xlabel('Arcseconds from center')
fig.subplots_adjust(wspace=0.05, hspace=0.05)
plt.savefig('drawn_shapes/{}.pdf'.format(subject_id), bbox_inches='tight')
plt.close()
fig, ((ax0, ax1), (ax2, ax3)) = plt.subplots(
ncols=2, nrows=2,
figsize=(10, 10),
sharex=True, sharey=True
)
ax0.imshow(pic_array, **imshow_kwargs)
for comp in disk_cluster_geoms.values:
ax0.add_patch(
PolygonPatch(ts(comp), fc='C0', ec='k', alpha=0.1, zorder=3)
)
if model['disk'] is not None:
aggregate_disk_geom = ash.make_ellipse(model['disk'])
ax0.add_patch(
PolygonPatch(ts(aggregate_disk_geom), fc='C1', ec='k', alpha=0.5,
zorder=3)
)
ax1.imshow(pic_array, **imshow_kwargs)
for comp in bulge_cluster_geoms.values:
ax1.add_patch(
PolygonPatch(ts(comp), fc='C1', ec='k', alpha=0.1, zorder=3)
)
if aggregate_bulge_geom is not None:
ax1.add_patch(
PolygonPatch(ts(aggregate_bulge_geom), fc='C2', ec='k', alpha=0.5,
zorder=3)
)
ax2.imshow(pic_array, **imshow_kwargs)
for comp in bar_cluster_geoms.values:
ax2.add_patch(
PolygonPatch(ts(comp), fc='C2', ec='k', alpha=0.1, zorder=3)
)
if aggregate_bar_geom is not None:
ax2.add_patch(
PolygonPatch(ts(aggregate_bar_geom), fc='C3', ec='k', alpha=0.5,
zorder=3)
)
ax3.imshow(pic_array, **imshow_kwargs)
for arm in arms:
plt.plot(*tv(arm.coords).T, '.', alpha=0.5, markersize=0.5)
for arm in logsps:
plt.plot(*tv(arm).T)
for i, ax in enumerate((ax0, ax1, ax2, ax3)):
ax.set_xlim(imshow_kwargs['extent'][:2])
ax.set_ylim(imshow_kwargs['extent'][2:])
if i % 2 == 0:
ax.set_ylabel('Arcseconds from center')
if i > 1:
ax.set_xlabel('Arcseconds from center')
fig.subplots_adjust(wspace=0.05, hspace=0.05)
plt.savefig('clustered_shapes/{}.pdf'.format(subject_id),
bbox_inches='tight')
plt.close()
fig = plt.figure(figsize=(10, 10))
ax = plt.gca()
ax.imshow(pic_array, **imshow_kwargs)
if aggregate_disk_geom is not None:
ax.add_patch(
PolygonPatch(ts(aggregate_disk_geom), fc='C0', ec='k', alpha=0.25,
zorder=3)
)
if aggregate_bulge_geom is not None:
ax.add_patch(
PolygonPatch(ts(aggregate_bulge_geom), fc='C1', ec='k', alpha=0.25,
zorder=3)
)
if aggregate_bar_geom is not None:
ax.add_patch(
PolygonPatch(ts(aggregate_bar_geom), fc='C2', ec='k', alpha=0.25,
zorder=3)
)
for arm in logsps:
plt.plot(*tv(arm).T, c='C3')
ax.set_xlim(imshow_kwargs['extent'][:2])
ax.set_ylim(imshow_kwargs['extent'][2:])
ax.set_ylabel('Arcseconds from center')
ax.set_xlabel('Arcseconds from center')
plt.savefig('aggregate_model/{}.pdf'.format(subject_id),
bbox_inches='tight')
plt.close()
def main(mangaid, subject_id):
gal, angle = gu.get_galaxy_and_angle(subject_id)
unit_converter = convert_arcsec_to_km(gal)
df = read_file(mangaid)
invalid_mask = df.values == -9999.0
mask = np.any(invalid_mask, axis=1)
df.iloc[mask] = np.nan
df = df.dropna()
df['R-arcsec'] = df['R']
df['R'] = unit_converter(df['R'])
scale = 4 * float(gal['PETRO_THETA'])
zoo_coords_r = df['R-arcsec'].values / scale
keys = (
'GAS_IC-V',
'GAS___-V',
'BTH_IC-V',
'BTH___-V',
)
labels = (
r'$H_\alpha$ velocity, fixed center & inclination',
r'$H_\alpha$ velocity, varying center & inclination',
r'$H_\alpha$ and stellar velocity, fixed center & inclination',
r'$H_\alpha$ and stellar velocity, varying centre and inclination',
)
drawn_arms = gu.get_drawn_arms(subject_id, gu.classifications)
arm_pipeline = Pipeline(drawn_arms,
phi=angle,
ba=gal['PETRO_BA90'],
image_size=512,
parallel=True)
arms = arm_pipeline.get_arms()
gzb_pa, gzb_sigma_pa = arm_pipeline.get_pitch_angle(arms)
arm_details = [{
'pa':
arm.pa,
'sigma_pa':
arm.sigma_pa,
'min_r':
unit_converter(
np.linalg.norm(arm.log_spiral - (256, 256), axis=1).min() *
float(gal['PETRO_THETA']) * 4 / 512),
'max_r':
unit_converter(
np.linalg.norm(arm.log_spiral - (256, 256), axis=1).max() *
float(gal['PETRO_THETA']) * 4 / 512)
} for arm in arms]
min_r = min(a['min_r'] for a in arm_details)
max_r = max(a['max_r'] for a in arm_details)
fitted = {}
fig, ax = plt.subplots(figsize=(8, 6))
sa_pas = []
sa_pa_datas = []
for i, (key, label) in enumerate(zip(keys, labels)):
f = tanh_model(df['R'].values, df[key].values)
p = least_squares(f, (160, 1E-17), x_scale=(10, 1E-17))['x']
fitted[key] = f(p) + df[key].values
# Calculate shear from analytic solve of dln(Ω)/dln(R)
shear = shear_from_tanh(p[1], df['R'].values)
omega = df[key] / (2 * np.pi * df['R'])
shear_data = get_shear(omega[:-1], df['R'].values[:-1])
plt.plot(df['R'], shear, c='C{}'.format(i % 10), label=label)
plt.plot(np.stack((df['R'][:-1], df['R'][1:])).mean(axis=0),
shear_data,
'--',
c='C{}'.format(i % 10))
sa_pa = np.rad2deg(get_predicted_pa(shear))
sa_pa_data = np.rad2deg(get_predicted_pa(shear_data))
sa_pas.append(sa_pa)
sa_pa_datas.append(sa_pa_data)
print('For key: {}'.format(key))
msk = (df['R'] > min_r) & (df['R'] < max_r)
print('\tRotation-predicted: {:.4f}°'.format(sa_pa[msk].mean()))
print('\tGZB measured PA: {:.4f} ± {:.4f}°'.format(
gzb_pa, gzb_sigma_pa))
plt.plot([], [], 'k-', label=r'Analytic differentiation')
plt.plot([], [], 'k--', label='Numerical differentiation')
plt.xlabel('Distance from galaxy centre [km]')
plt.ylabel(r'Shear rate, $\Gamma$')
plt.legend()
plt.savefig('{}_shear.pdf'.format(mangaid), bbox_inches='tight')
plt.close()
np.save('pavr', np.stack((zoo_coords_r, sa_pas[0]), axis=1))
imshow_kwargs = {
'cmap': 'gray',
'origin': 'lower',
'extent': [-0.5 * scale, 0.5 * scale] * 2,
}
pic_array, _ = gu.get_image(gal, subject_id, angle)
fig, ax = plt.subplots(ncols=1, figsize=(5, 5))
plt.imshow(pic_array, **imshow_kwargs)
for i, arm in enumerate(arms):
varying_arm_t = fit_varying_pa(arm, zoo_coords_r,
np.stack(sa_pas).mean(axis=0))
t_predict = np.linspace(varying_arm_t.min(), varying_arm_t.max(), 100)
f = interp1d(varying_arm_t, zoo_coords_r)
varying_arm = xy_from_r_theta(f(t_predict), t_predict)
log_spiral = xy_from_r_theta(*np.flipud(arm.polar_logsp))
plt.plot(*arm.deprojected_coords.T * scale, '.', markersize=1, alpha=1)
plt.plot(*log_spiral * scale, c='r', linewidth=3, alpha=0.8)
plt.plot(*varying_arm * scale, c='g', linewidth=3, alpha=0.8)
# plots for legend
plt.plot([], [],
c='g',
linewidth=3,
alpha=0.8,
label='Swing-amplified spiral')
plt.plot([], [], c='r', linewidth=3, alpha=0.8, label='Logarithmic spiral')
plt.axis('equal')
plt.xlabel('Arcseconds from galaxy centre')
plt.ylabel('Arcseconds from galaxy centre')
plt.xlim(-25, 25)
plt.ylim(-25, 25)
plt.legend()
plt.savefig('{}_varying-pa.pdf'.format(mangaid), bbox_inches='tight')
plt.close()
return
fig, ax = plt.subplots(figsize=(8, 6))
for sa_pa, label in zip(sa_pas, labels):
plt.plot(df['R'], sa_pa, label=label)
for row in arm_details:
plt.hlines(row['pa'], row['min_r'], row['max_r'])
plt.fill_between(
np.linspace(row['min_r'], row['max_r'], 2),
row['pa'] - row['sigma_pa'],
row['pa'] + row['sigma_pa'],
color='k',
alpha=0.2,
)
plt.legend()
plt.xlabel('Distance from galaxy centre [km]')
plt.ylabel('Pitch angle [degrees]')
plt.savefig('{}_pa.pdf'.format(mangaid), bbox_inches='tight')
plt.close()
fig, ax = plt.subplots(figsize=(8, 6))
# df.plot('R', keys, label=labels, ax=ax)
for i, key in enumerate(keys):
plt.fill_between(
df['R'].values,
df[key].values - df[key + 'e'].values,
df[key].values + df[key + 'e'].values,
color='C{}'.format(i % 10),
alpha=0.1,
)
plt.plot(df['R'].values, df[key].values, '--', c='C{}'.format(i % 10))
plt.plot(df['R'].values, fitted[key], c='C{}'.format(i % 10))
for i, label in enumerate(labels):
plt.plot([], [], c='C{}'.format(i % 10), label=label)
plt.plot([], [], 'k-', label=r'$A\tanh(bR)$ model')
plt.plot([], [], 'k--', label='Data')
plt.legend()
plt.xlabel('Distance from galaxy centre [km]')
plt.ylabel(r'Rotational velocity [$\mathrm{km}\mathrm{s}^{-1}$]')
plt.savefig('{}_rotational-velocity_2.pdf'.format(mangaid),
bbox_inches='tight')
plt.close()
