def plot_cluster_centroids(centroids, x_vec, legend_mode=1, x_label=None, y_label=None, title=None, axis=None,
overlayed=True, amp_units=None, **kwargs):
"""
Parameters
----------
centroids : numpy.ndarray
2D array. Centroids of clusters
x_vec : numpy.ndarray
1D array. Vector against which the curves are plotted
legend_mode : int, optional. default = 1
Appearance of legend:
0 - inside the plot
1 - outside the plot on the right
else - colorbar instead of legend
x_label : str, optional, default = None
Label for x axis
y_label : str, optional, default = None
Label for y axis
title : str, optional, default = None
Title for the plot
axis : matplotlib.axes.Axes object, optional.
Axis to plot this image onto. Will create a new figure by default or will use this axis object to plot into
overlayed : bool, optional
If True - all curves will be plotted overlayed on a single plot. Else, curves will be plotted separately
amp_units : str, optional
Units for amplitude
kwargs : dict
will be passed on to plot_line_family(), plot_complex_spectra, plot_curves
Returns
-------
fig, axes
"""
if isinstance(centroids, (list, tuple)):
centroids = np.array(centroids)
if not isinstance(centroids, np.ndarray):
raise TypeError('centroids should be a numpy array')
if centroids.ndim != 2:
raise ValueError('centroids should be a 2D numpy array - i.e. - 1D spectra')
if not isinstance(x_vec, (list, tuple)):
x_vec = np.array(x_vec)
if not isinstance(x_vec, np.ndarray):
raise TypeError('x_vec should be a array-like')
if x_vec.ndim != 1:
raise ValueError('x_vec should be a 1D array')
if not isinstance(legend_mode, int):
raise TypeError('legend_mode should be an integer')
if axis is not None:
if not isinstance(axis, mpl.axes.Axes):
raise TypeError('axis must be a matplotlib.axes.Axes object')
if not isinstance(overlayed, bool):
raise TypeError('overlayed should be a boolean value')
if amp_units is not None:
if not (isinstance(amp_units, (str, unicode)) or
(isinstance(amp_units, np.ndarray) and amp_units.dtype.type == np.str_)):
raise TypeError('amp_units should be a str')
else:
amp_units = 'a.u.'
cmap = kwargs.get('cmap', default_cmap)
num_clusters = centroids.shape[0]
def __overlay_curves(axis, curve_stack):
plot_line_family(axis, x_vec, curve_stack, label_prefix='Cluster', cmap=cmap)
if legend_mode == 0:
axis.legend(loc='best', fontsize=14)
elif legend_mode == 1:
axis.legend(loc='upper left', bbox_to_anchor=(1, 1), fontsize=14)
else:
sm = make_scalar_mappable(0, num_clusters - 1, cmap=discrete_cmap(num_clusters, cmap))
plt.colorbar(sm)
if overlayed:
if centroids.dtype in [np.complex64, np.complex128, np.complex]:
fig, axes = plt.subplots(nrows=2, figsize=kwargs.pop('figsize', (5.5, 2 * 5)))
for axis, func in zip(axes.flat, [np.abs, np.angle]):
__overlay_curves(axis, func(centroids))
for var, var_name, func in zip([y_label, y_label, x_label], ['y_label', 'y_label', 'x_label'],
[axes[1].set_ylabel, axes[1].set_xlabel]):
if var is not None:
if not isinstance(var, (str, unicode)):
raise TypeError(var_name + ' should be a string')
func(var)
if title is not None:
if not isinstance(title, (str, unicode)):
raise TypeError('title should be a string')
for axis, comp_name, units in zip(axes.flat, ['Amplitude', 'Phase'], [amp_units, 'rad']):
axis.set_title('{} - {} ({})'.format(title, comp_name, units))
else:
if axis is None:
fig, axis = plt.subplots(figsize=kwargs.pop('figsize', (5.5, 5)))
else:
fig = None
__overlay_curves(axis, centroids)
for var, var_name, func in zip([title, x_label, y_label], ['title', 'x_label', 'y_label'],
[axis.set_title, axis.set_xlabel, axis.set_ylabel]):
if var is not None:
if not isinstance(var, (str, unicode)):
raise TypeError(var_name + ' should be a string')
func(var)
if fig is not None:
fig.tight_layout()
return fig, axis
else:
if centroids.dtype in [np.complex64, np.complex128, np.complex]:
return plot_complex_spectra(centroids, x_vec=x_vec, title=title, x_label=x_label, y_label=y_label,
subtitle_prefix='Cluster', amp_units=amp_units, **kwargs)
else:
return plot_curves(x_vec, centroids, x_label=x_label, y_label=y_label, title=title,
subtitle_prefix='Cluster ', **kwargs)
def plot_cluster_centroids(centroids,
x_vec,
legend_mode=1,
x_label=None,
y_label=None,
title=None,
axis=None,
overlayed=True,
amp_units=None,
**kwargs):
"""
Parameters
----------
centroids : numpy.ndarray
2D array. Centroids of clusters
x_vec : numpy.ndarray
1D array. Vector against which the curves are plotted
legend_mode : int, optional. default = 1
Appearance of legend:
0 - inside the plot
1 - outside the plot on the right
else - colorbar instead of legend
x_label : str, optional, default = None
Label for x axis
y_label : str, optional, default = None
Label for y axis
title : str, optional, default = None
Title for the plot
axis : matplotlib.axes.Axes object, optional.
Axis to plot this image onto. Will create a new figure by default or will use this axis object to plot into
overlayed : bool, optional
If True - all curves will be plotted overlayed on a single plot. Else, curves will be plotted separately
amp_units : str, optional
Units for amplitude
kwargs : dict
will be passed on to plot_line_family(), plot_complex_spectra, plot_curves
Returns
-------
fig, axes
"""
if isinstance(centroids, (list, tuple)):
centroids = np.array(centroids)
if not isinstance(centroids, np.ndarray):
raise TypeError('centroids should be a numpy array')
if centroids.ndim != 2:
raise ValueError(
'centroids should be a 2D numpy array - i.e. - 1D spectra')
if not isinstance(x_vec, (list, tuple)):
x_vec = np.array(x_vec)
if not isinstance(x_vec, np.ndarray):
raise TypeError('x_vec should be a array-like')
if x_vec.ndim != 1:
raise ValueError('x_vec should be a 1D array')
if not isinstance(legend_mode, int):
raise TypeError('legend_mode should be an integer')
if axis is not None:
if not isinstance(axis, mpl.axes.Axes):
raise TypeError('axis must be a matplotlib.axes.Axes object')
if not isinstance(overlayed, bool):
raise TypeError('overlayed should be a boolean value')
if amp_units is not None:
if not (isinstance(amp_units, (str, unicode)) or
(isinstance(amp_units, np.ndarray)
and amp_units.dtype.type == np.str_)):
raise TypeError('amp_units should be a str')
else:
amp_units = 'a.u.'
cmap = kwargs.get('cmap', default_cmap)
num_clusters = centroids.shape[0]
def __overlay_curves(axis, curve_stack):
plot_line_family(axis,
x_vec,
curve_stack,
label_prefix='Cluster',
cmap=cmap)
if legend_mode == 0:
axis.legend(loc='best', fontsize=14)
elif legend_mode == 1:
axis.legend(loc='upper left', bbox_to_anchor=(1, 1), fontsize=14)
else:
sm = make_scalar_mappable(0,
num_clusters - 1,
cmap=discrete_cmap(num_clusters, cmap))
plt.colorbar(sm)
if overlayed:
if centroids.dtype in [np.complex64, np.complex128, np.complex]:
fig, axes = plt.subplots(nrows=2,
figsize=kwargs.pop(
'figsize', (5.5, 2 * 5)))
for axis, func in zip(axes.flat, [np.abs, np.angle]):
__overlay_curves(axis, func(centroids))
for var, var_name, func in zip(
[y_label, y_label, x_label], ['y_label', 'y_label', 'x_label'],
[axes[1].set_ylabel, axes[1].set_xlabel]):
if var is not None:
if not isinstance(var, (str, unicode)):
raise TypeError(var_name + ' should be a string')
func(var)
if title is not None:
if not isinstance(title, (str, unicode)):
raise TypeError('title should be a string')
for axis, comp_name, units in zip(axes.flat,
['Amplitude', 'Phase'],
[amp_units, 'rad']):
axis.set_title('{} - {} ({})'.format(
title, comp_name, units))
else:
if axis is None:
fig, axis = plt.subplots(
figsize=kwargs.pop('figsize', (5.5, 5)))
else:
fig = None
__overlay_curves(axis, centroids)
for var, var_name, func in zip(
[title, x_label, y_label], ['title', 'x_label', 'y_label'],
[axis.set_title, axis.set_xlabel, axis.set_ylabel]):
if var is not None:
if not isinstance(var, (str, unicode)):
raise TypeError(var_name + ' should be a string')
func(var)
if fig is not None:
fig.tight_layout()
return fig, axis
else:
if centroids.dtype in [np.complex64, np.complex128, np.complex]:
return plot_complex_spectra(centroids,
x_vec=x_vec,
title=title,
x_label=x_label,
y_label=y_label,
subtitle_prefix='Cluster',
amp_units=amp_units,
**kwargs)
else:
return plot_curves(x_vec,
centroids,
x_label=x_label,
y_label=y_label,
title=title,
subtitle_prefix='Cluster ',
**kwargs)
def plot_svd(h5_main, savefig=False, num_plots=16, **kwargs):
'''
Replots the SVD showing the skree, abundance maps, and eigenvectors.
If h5_main is a Dataset, it will default to the most recent SVD group from that
Dataset.
If h5_main is the results group, then it will plot the values for that group.
Parameters
----------
h5_main : USIDataset or h5py Dataset or h5py Group
savefig : bool, optional
Saves the figures to disk with some default names
num_plots : int
Default number of eigenvectors and abundance plots to show
kwargs : dict, optional
keyword arguments for svd filtering
Returns
-------
None
'''
if isinstance(h5_main, h5py.Group):
_U = find_dataset(h5_main, 'U')[-1]
_V = find_dataset(h5_main, 'V')[-1]
units = 'arbitrary (a.u.)'
h5_spec_vals = np.arange(_V.shape[1])
h5_svd_group = _U.parent
else:
h5_svd_group = find_results_groups(h5_main, 'SVD')[-1]
units = h5_main.attrs['quantity']
h5_spec_vals = h5_main.get_spec_values('Time')
h5_U = h5_svd_group['U']
h5_V = h5_svd_group['V']
h5_S = h5_svd_group['S']
_U = USIDataset(h5_U)
[num_rows, num_cols] = _U.pos_dim_sizes
abun_maps = np.reshape(h5_U[:, :16], (num_rows, num_cols, -1))
eigen_vecs = h5_V[:16, :]
skree_sum = np.zeros(h5_S.shape)
for i in range(h5_S.shape[0]):
skree_sum[i] = np.sum(h5_S[:i]) / np.sum(h5_S)
plt.figure()
plt.plot(skree_sum, 'bo')
plt.title('Cumulative Variance')
plt.xlabel('Total Components')
plt.ylabel('Total variance ratio (a.u.)')
if savefig:
plt.savefig('Cumulative_variance_plot.png')
fig_skree, axes = plot_utils.plot_scree(h5_S, title='Scree plot')
fig_skree.tight_layout()
if savefig:
plt.savefig('Scree_plot.png')
fig_abun, axes = plot_utils.plot_map_stack(abun_maps,
num_comps=num_plots,
title='SVD Abundance Maps',
color_bar_mode='single',
cmap='inferno',
reverse_dims=True,
fig_mult=(3.5, 3.5),
facecolor='white',
**kwargs)
fig_abun.tight_layout()
if savefig:
plt.savefig('Abundance_maps.png')
fig_eigvec, axes = plot_utils.plot_curves(h5_spec_vals * 1e3,
eigen_vecs,
use_rainbow_plots=False,
x_label='Time (ms)',
y_label=units,
num_plots=num_plots,
subtitle_prefix='Component',
title='SVD Eigenvectors',
evenly_spaced=False,
**kwargs)
fig_eigvec.tight_layout()
if savefig:
plt.savefig('Eigenvectors.png')
return
def test_filter(resp_wfm,
frequency_filters=None,
noise_threshold=None,
excit_wfm=None,
show_plots=True,
plot_title=None,
verbose=False):
"""
Filters the provided response with the provided filters.
Parameters
----------
resp_wfm : array-like, 1D
Raw response waveform in the time domain
frequency_filters : (Optional) FrequencyFilter object or list of
Frequency filters to apply to signal
noise_threshold : (Optional) float
Noise threshold to apply to signal
excit_wfm : (Optional) 1D array-like
Excitation waveform in the time domain. This waveform is necessary for plotting loops. If the length of
resp_wfm matches excit_wfm, a single plot will be returned with the raw and filtered signals plotted against the
excit_wfm. Else, resp_wfm and the filtered (filt_data) signal will be broken into chunks matching the length of
excit_wfm and a figure with multiple plots (one for each chunk) with the raw and filtered signal chunks plotted
against excit_wfm will be returned for fig_loops
show_plots : (Optional) Boolean
Whether or not to plot FFTs before and after filtering
plot_title : str / unicode (Optional)
Title for the raw vs filtered plots if requested. For example - 'Row 15'
verbose : (Optional) Boolean
Prints extra debugging information if True. Default False
Returns
-------
filt_data : 1D numpy float array
Filtered signal in the time domain
fig_fft : matplotlib.pyplot.figure object
handle to the plotted figure if requested, else None
fig_loops : matplotlib.pyplot.figure object
handle to figure with the filtered signal and raw signal plotted against the excitation waveform
"""
if not isinstance(resp_wfm, (np.ndarray, list)):
raise TypeError('resp_wfm should be array-like')
resp_wfm = np.array(resp_wfm)
show_loops = False
if excit_wfm is not None and show_plots:
if len(resp_wfm) % len(excit_wfm) == 0:
show_loops = True
else:
raise ValueError(
'Length of resp_wfm should be divisibe by length of excit_wfm')
if show_loops:
if plot_title is None:
plot_title = 'FFT Filtering'
else:
assert isinstance(plot_title, (str, unicode))
if frequency_filters is None and noise_threshold is None:
raise ValueError(
'Need to specify at least some noise thresholding / frequency filter'
)
if noise_threshold is not None:
if noise_threshold >= 1 or noise_threshold <= 0:
raise ValueError('Noise threshold must be within (0 1)')
samp_rate = 1
composite_filter = 1
if frequency_filters is not None:
if not isinstance(frequency_filters, Iterable):
frequency_filters = [frequency_filters]
if not are_compatible_filters(frequency_filters):
raise ValueError(
'frequency filters must be a single or list of FrequencyFilter objects'
)
composite_filter = build_composite_freq_filter(frequency_filters)
samp_rate = frequency_filters[0].samp_rate
resp_wfm = np.array(resp_wfm)
num_pts = resp_wfm.size
fft_pix_data = np.fft.fftshift(np.fft.fft(resp_wfm))
if noise_threshold is not None:
noise_floor = get_noise_floor(fft_pix_data, noise_threshold)[0]
if verbose:
print('The noise_floor is', noise_floor)
fig_fft = None
if show_plots:
w_vec = np.linspace(-0.5 * samp_rate, 0.5 * samp_rate, num_pts) * 1E-3
fig_fft, [ax_raw, ax_filt] = plt.subplots(figsize=(12, 8), nrows=2)
axes_fft = [ax_raw, ax_filt]
set_tick_font_size(axes_fft, 14)
r_ind = num_pts
if isinstance(composite_filter, np.ndarray):
r_ind = np.max(np.where(composite_filter > 0)[0])
x_lims = slice(len(w_vec) // 2, r_ind)
amp = np.abs(fft_pix_data)
ax_raw.semilogy(w_vec[x_lims], amp[x_lims], label='Raw')
if frequency_filters is not None:
ax_raw.semilogy(w_vec[x_lims],
(composite_filter[x_lims] + np.min(amp)) *
(np.max(amp) - np.min(amp)),
linewidth=3,
color='orange',
label='Composite Filter')
if noise_threshold is not None:
ax_raw.axhline(
noise_floor,
# ax_raw.semilogy(w_vec, np.ones(r_ind - l_ind) * noise_floor,
linewidth=2,
color='r',
label='Noise Threshold')
ax_raw.legend(loc='best', fontsize=14)
ax_raw.set_title('Raw Signal', fontsize=16)
ax_raw.set_ylabel('Magnitude (a. u.)', fontsize=14)
fft_pix_data *= composite_filter
if noise_threshold is not None:
fft_pix_data[
np.abs(fft_pix_data) <
noise_floor] = 1E-16 # DON'T use 0 here. ipython kernel dies
if show_plots:
ax_filt.semilogy(w_vec[x_lims], np.abs(fft_pix_data)[x_lims])
ax_filt.set_title('Filtered Signal', fontsize=16)
ax_filt.set_xlabel('Frequency(kHz)', fontsize=14)
ax_filt.set_ylabel('Magnitude (a. u.)', fontsize=14)
if noise_threshold is not None:
ax_filt.set_ylim(
bottom=noise_floor
) # prevents the noise threshold from messing up plots
fig_fft.tight_layout()
filt_data = np.real(np.fft.ifft(np.fft.ifftshift(fft_pix_data)))
if verbose:
print('The shape of the filtered data is {}'.format(filt_data.shape))
print('The shape of the excitation waveform is {}'.format(
excit_wfm.shape))
fig_loops = None
if show_loops:
if len(resp_wfm) == len(excit_wfm):
# single plot:
fig_loops, axis = plt.subplots(figsize=(5.5, 5))
axis.plot(excit_wfm, resp_wfm, 'r', label='Raw')
axis.plot(excit_wfm, filt_data, 'k', label='Filtered')
axis.legend(fontsize=14)
set_tick_font_size(axis, 14)
axis.set_xlabel('Excitation', fontsize=16)
axis.set_ylabel('Signal', fontsize=16)
axis.set_title(plot_title, fontsize=16)
fig_loops.tight_layout()
else:
# N loops:
raw_pixels = np.reshape(resp_wfm, (-1, len(excit_wfm)))
filt_pixels = np.reshape(filt_data, (-1, len(excit_wfm)))
print(raw_pixels.shape, filt_pixels.shape)
fig_loops, axes_loops = plot_curves(
excit_wfm, [raw_pixels, filt_pixels],
line_colors=['r', 'k'],
dataset_names=['Raw', 'Filtered'],
x_label='Excitation',
y_label='Signal',
subtitle_prefix='Col ',
num_plots=16,
title=plot_title)
return filt_data, fig_fft, fig_loops
def test_filter(resp_wfm, frequency_filters=None, noise_threshold=None, excit_wfm=None, show_plots=True,
plot_title=None, verbose=False):
"""
Filters the provided response with the provided filters.
Parameters
----------
resp_wfm : array-like, 1D
Raw response waveform in the time domain
frequency_filters : (Optional) FrequencyFilter object or list of
Frequency filters to apply to signal
noise_threshold : (Optional) float
Noise threshold to apply to signal
excit_wfm : (Optional) 1D array-like
Excitation waveform in the time domain. This waveform is necessary for plotting loops. If the length of
resp_wfm matches excit_wfm, a single plot will be returned with the raw and filtered signals plotted against the
excit_wfm. Else, resp_wfm and the filtered (filt_data) signal will be broken into chunks matching the length of
excit_wfm and a figure with multiple plots (one for each chunk) with the raw and filtered signal chunks plotted
against excit_wfm will be returned for fig_loops
show_plots : (Optional) Boolean
Whether or not to plot FFTs before and after filtering
plot_title : str / unicode (Optional)
Title for the raw vs filtered plots if requested. For example - 'Row 15'
verbose : (Optional) Boolean
Prints extra debugging information if True. Default False
Returns
-------
filt_data : 1D numpy float array
Filtered signal in the time domain
fig_fft : matplotlib.pyplot.figure object
handle to the plotted figure if requested, else None
fig_loops : matplotlib.pyplot.figure object
handle to figure with the filtered signal and raw signal plotted against the excitation waveform
"""
if not isinstance(resp_wfm, (np.ndarray, list)):
raise TypeError('resp_wfm should be array-like')
resp_wfm = np.array(resp_wfm)
show_loops = False
if excit_wfm is not None and show_plots:
if len(resp_wfm) % len(excit_wfm) == 0:
show_loops = True
else:
raise ValueError('Length of resp_wfm should be divisibe by length of excit_wfm')
if show_loops:
if plot_title is None:
plot_title = 'FFT Filtering'
else:
assert isinstance(plot_title, (str, unicode))
if frequency_filters is None and noise_threshold is None:
raise ValueError('Need to specify at least some noise thresholding / frequency filter')
if noise_threshold is not None:
if noise_threshold >= 1 or noise_threshold <= 0:
raise ValueError('Noise threshold must be within (0 1)')
samp_rate = 1
composite_filter = 1
if frequency_filters is not None:
if not isinstance(frequency_filters, Iterable):
frequency_filters = [frequency_filters]
if not are_compatible_filters(frequency_filters):
raise ValueError('frequency filters must be a single or list of FrequencyFilter objects')
composite_filter = build_composite_freq_filter(frequency_filters)
samp_rate = frequency_filters[0].samp_rate
resp_wfm = np.array(resp_wfm)
num_pts = resp_wfm.size
fft_pix_data = np.fft.fftshift(np.fft.fft(resp_wfm))
if noise_threshold is not None:
noise_floor = get_noise_floor(fft_pix_data, noise_threshold)[0]
if verbose:
print('The noise_floor is', noise_floor)
fig_fft = None
if show_plots:
w_vec = np.linspace(-0.5 * samp_rate, 0.5 * samp_rate, num_pts) * 1E-3
fig_fft, [ax_raw, ax_filt] = plt.subplots(figsize=(12, 8), nrows=2)
axes_fft = [ax_raw, ax_filt]
set_tick_font_size(axes_fft, 14)
r_ind = num_pts
if isinstance(composite_filter, np.ndarray):
r_ind = np.max(np.where(composite_filter > 0)[0])
x_lims = slice(len(w_vec) // 2, r_ind)
amp = np.abs(fft_pix_data)
ax_raw.semilogy(w_vec[x_lims], amp[x_lims], label='Raw')
if frequency_filters is not None:
ax_raw.semilogy(w_vec[x_lims], (composite_filter[x_lims] + np.min(amp)) * (np.max(amp) - np.min(amp)),
linewidth=3, color='orange', label='Composite Filter')
if noise_threshold is not None:
ax_raw.axhline(noise_floor,
# ax_raw.semilogy(w_vec, np.ones(r_ind - l_ind) * noise_floor,
linewidth=2, color='r', label='Noise Threshold')
ax_raw.legend(loc='best', fontsize=14)
ax_raw.set_title('Raw Signal', fontsize=16)
ax_raw.set_ylabel('Magnitude (a. u.)', fontsize=14)
fft_pix_data *= composite_filter
if noise_threshold is not None:
fft_pix_data[np.abs(fft_pix_data) < noise_floor] = 1E-16 # DON'T use 0 here. ipython kernel dies
if show_plots:
ax_filt.semilogy(w_vec[x_lims], np.abs(fft_pix_data)[x_lims])
ax_filt.set_title('Filtered Signal', fontsize=16)
ax_filt.set_xlabel('Frequency(kHz)', fontsize=14)
ax_filt.set_ylabel('Magnitude (a. u.)', fontsize=14)
if noise_threshold is not None:
ax_filt.set_ylim(bottom=noise_floor) # prevents the noise threshold from messing up plots
fig_fft.tight_layout()
filt_data = np.real(np.fft.ifft(np.fft.ifftshift(fft_pix_data)))
if verbose:
print('The shape of the filtered data is {}'.format(filt_data.shape))
print('The shape of the excitation waveform is {}'.format(excit_wfm.shape))
fig_loops = None
if show_loops:
if len(resp_wfm) == len(excit_wfm):
# single plot:
fig_loops, axis = plt.subplots(figsize=(5.5, 5))
axis.plot(excit_wfm, resp_wfm, 'r', label='Raw')
axis.plot(excit_wfm, filt_data, 'k', label='Filtered')
axis.legend(fontsize=14)
set_tick_font_size(axis, 14)
axis.set_xlabel('Excitation', fontsize=16)
axis.set_ylabel('Signal', fontsize=16)
axis.set_title(plot_title, fontsize=16)
fig_loops.tight_layout()
else:
# N loops:
raw_pixels = np.reshape(resp_wfm, (-1, len(excit_wfm)))
filt_pixels = np.reshape(filt_data, (-1, len(excit_wfm)))
print(raw_pixels.shape, filt_pixels.shape)
fig_loops, axes_loops = plot_curves(excit_wfm, [raw_pixels, filt_pixels], line_colors=['r', 'k'],
dataset_names=['Raw', 'Filtered'], x_label='Excitation',
y_label='Signal', subtitle_prefix='Col ', num_plots=16,
title=plot_title)
return filt_data, fig_fft, fig_loops