Open in Colab: https://colab.research.google.com/github/casangi/cngi_prototype/blob/master/docs/imaging/imaging_weights_example.ipynb
Imaging Weights¶
This notebook will demonstrate how to create images with different imaging weighting schemes (natural, uniform, briggs) and how to make use of the storage_parms to append images.
For this demonstration data from the ALMA First Look at Imaging CASAguide (https://casaguides.nrao.edu/index.php/First_Look_at_Imaging) will be used. The measurement set has been converted to vis.zarr (using convert_ms in cngi.conversion)
This walkthrough is designed to be run in a Jupyter notebook on Google Colaboratory. To open the notebook in colab, go here.
Installation and Dataset Download¶
[1]:
import os
os.system("pip install cngi-prototype==0.0.91")
!gdown -q --id 1PNL0ANqnN7eyYOpQ_vMslQlorUhtrUmE
!unzip sis14_twhya_field_5_lsrk_pol_xx.vis.zarr.zip > /dev/null
%matplotlib widget
print('complete')
complete
Load Dataset¶
For an explanation of how the vis.zarr file was created and the chunking go to the continuum image example.
[2]:
import xarray as xr
from cngi.dio import read_vis
xr.set_options(display_style="html")
mxds = read_vis("sis14_twhya_field_5_lsrk_pol_xx.vis.zarr",chunks={'chan':192})
print(mxds.xds0)
overwrite_encoded_chunks True
<xarray.Dataset>
Dimensions: (baseline: 210, chan: 384, pol: 1, pol_id: 1, spw_id: 1, time: 270, uvw_index: 3)
Coordinates:
* baseline (baseline) int64 0 1 2 3 4 5 6 ... 204 205 206 207 208 209
* chan (chan) float64 3.725e+11 3.725e+11 ... 3.728e+11 3.728e+11
chan_width (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
effective_bw (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
* pol (pol) int32 9
* pol_id (pol_id) int32 0
resolution (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
* spw_id (spw_id) int32 0
* time (time) datetime64[ns] 2012-11-19T07:56:26.544000626 ... 2...
Dimensions without coordinates: uvw_index
Data variables: (12/17)
ANTENNA1 (baseline) int32 dask.array<chunksize=(210,), meta=np.ndarray>
ANTENNA2 (baseline) int32 dask.array<chunksize=(210,), meta=np.ndarray>
ARRAY_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
DATA (time, baseline, chan, pol) complex128 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
DATA_WEIGHT (time, baseline, chan, pol) float64 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
EXPOSURE (time, baseline) float64 dask.array<chunksize=(270, 210), meta=np.ndarray>
... ...
OBSERVATION_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
PROCESSOR_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
SCAN_NUMBER (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
STATE_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
TIME_CENTROID (time, baseline) float64 dask.array<chunksize=(270, 210), meta=np.ndarray>
UVW (time, baseline, uvw_index) float64 dask.array<chunksize=(270, 210, 3), meta=np.ndarray>
Attributes: (12/13)
bbc_no: 2
corr_product: [[0, 0]]
data_groups: [{'0': {'data': 'DATA', 'flag': 'FLAG', 'id': '0', 'uvw...
freq_group: 0
freq_group_name:
if_conv_chain: 0
... ...
name: ALMA_RB_07#BB_2#SW-01#FULL_RES
net_sideband: 2
num_chan: 384
num_corr: 1
ref_frequency: 372520022603.63745
total_bandwidth: 234366781.0546875
Make Imaging Weights¶
make_imaging_weight documentation
[3]:
from ngcasa.imaging import make_imaging_weight
from cngi.vis import apply_flags
from ngcasa.imaging import make_psf
from ngcasa.imaging import make_image
grid_parms = {}
grid_parms['chan_mode'] = 'continuum'
grid_parms['image_size'] = [200,400]
grid_parms['cell_size'] = [0.08,0.08]
mxds_0 = apply_flags(mxds, 'xds0', flags='FLAG')
imaging_weights_parms = {}
imaging_weights_parms['weighting'] = 'natural'
sel_parms = {}
sel_parms['xds'] = 'xds0'
sel_parms['data_group_in_id'] = 0
sel_parms['data_group_out_id'] = 0
mxds_1 = make_imaging_weight(mxds_0, imaging_weights_parms, grid_parms, sel_parms)
##################
imaging_weights_parms['weighting'] = 'uniform'
sel_parms['xds'] = 'xds0'
sel_parms['data_group_in_id'] = 0
sel_parms['data_group_out_id'] = 1
sel_parms['imaging_weight'] = 'IMAGING_WEIGHT_UNI'
mxds_2 = make_imaging_weight(mxds_1, imaging_weights_parms, grid_parms, sel_parms)
##################
imaging_weights_parms['weighting'] = 'briggs'
imaging_weights_parms['robust'] = 0.6 #number, default:0.5, acceptable values [-2,2]
sel_parms = {}
sel_parms['xds'] = 'xds0'
sel_parms['data_group_in_id'] = 0
sel_parms['data_group_out_id'] = 2
sel_parms['imaging_weight'] = 'IMAGING_WEIGHT_BRG'
mxds_3 = make_imaging_weight(mxds_2, imaging_weights_parms, grid_parms, sel_parms)
print(mxds_3.xds0)
######################### Start make_imaging_weights #########################
Setting data_group_in to {'data': 'DATA', 'flag': 'FLAG', 'id': '0', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_out [' data '] to DATA
Setting default data_group_out [' flag '] to FLAG
Setting default data_group_out [' uvw '] to UVW
Setting default data_group_out [' weight '] to DATA_WEIGHT
Setting default data_group_out [' imaging_weight '] to IMAGING_WEIGHT
Since weighting is natural input weight will be reused as imaging weight.
######################### Created graph for make_imaging_weight #########################
######################### Start make_imaging_weights #########################
Setting data_group_in to {'id': '0', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_out [' data '] to DATA
Setting default data_group_out [' flag '] to FLAG
Setting default data_group_out [' uvw '] to UVW
Setting default data_group_out [' weight '] to DATA_WEIGHT
Setting default image_center to [100 200]
Setting default fft_padding to 1.2
######################### Created graph for make_imaging_weight #########################
######################### Start make_imaging_weights #########################
Setting data_group_in to {'id': '0', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_out [' data '] to DATA
Setting default data_group_out [' flag '] to FLAG
Setting default data_group_out [' uvw '] to UVW
Setting default data_group_out [' weight '] to DATA_WEIGHT
Setting default image_center to [100 200]
Setting default fft_padding to 1.2
######################### Created graph for make_imaging_weight #########################
<xarray.Dataset>
Dimensions: (baseline: 210, chan: 384, pol: 1, pol_id: 1, spw_id: 1, time: 270, uvw_index: 3)
Coordinates:
* baseline (baseline) int64 0 1 2 3 4 5 ... 204 205 206 207 208 209
* chan (chan) float64 3.725e+11 3.725e+11 ... 3.728e+11
* pol (pol) int32 9
* time (time) datetime64[ns] 2012-11-19T07:56:26.544000626 ....
chan_width (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
effective_bw (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
* pol_id (pol_id) int32 0
resolution (chan) float64 dask.array<chunksize=(192,), meta=np.ndarray>
* spw_id (spw_id) int32 0
Dimensions without coordinates: uvw_index
Data variables: (12/19)
ANTENNA1 (baseline) int32 dask.array<chunksize=(210,), meta=np.ndarray>
ANTENNA2 (baseline) int32 dask.array<chunksize=(210,), meta=np.ndarray>
ARRAY_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
DATA (time, baseline, chan, pol) complex128 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
DATA_WEIGHT (time, baseline, chan, pol) float64 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
EXPOSURE (time, baseline) float64 dask.array<chunksize=(270, 210), meta=np.ndarray>
... ...
SCAN_NUMBER (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
STATE_ID (time, baseline) int32 dask.array<chunksize=(270, 210), meta=np.ndarray>
TIME_CENTROID (time, baseline) float64 dask.array<chunksize=(270, 210), meta=np.ndarray>
UVW (time, baseline, uvw_index) float64 dask.array<chunksize=(270, 210, 3), meta=np.ndarray>
IMAGING_WEIGHT_UNI (time, baseline, chan, pol) float64 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
IMAGING_WEIGHT_BRG (time, baseline, chan, pol) float64 dask.array<chunksize=(270, 210, 192, 1), meta=np.ndarray>
Attributes: (12/13)
bbc_no: 2
corr_product: [[0, 0]]
data_groups: [{'0': {'id': '0', 'data': 'DATA', 'flag': 'FLAG', 'uvw...
freq_group: 0
freq_group_name:
if_conv_chain: 0
... ...
name: ALMA_RB_07#BB_2#SW-01#FULL_RES
net_sideband: 2
num_chan: 384
num_corr: 1
ref_frequency: 372520022603.63745
total_bandwidth: 234366781.0546875
Make Image and PSF¶
[4]:
from ngcasa.imaging import make_image
from ngcasa.imaging import make_pb
from cngi.dio import write_image
import dask
import xarray as xr
grid_parms = {}
grid_parms['chan_mode'] = 'continuum'
grid_parms['image_size'] = [200,200]
grid_parms['cell_size'] = [0.04,0.04]
grid_parms['phase_center'] = mxds.FIELD.PHASE_DIR[0,0,:].data.compute()
############################### Natural
vis_sel_parms = {}
vis_sel_parms['xds'] = 'xds0'
vis_sel_parms['data_group_in_id'] = 0
img_sel_parms = {}
img_sel_parms['data_group_out_id'] = 0
img_sel_parms['psf'] = 'PSF_NAT'
img_sel_parms['psf_sum_weight'] = 'PSF_SUM_WEIGHT_NAT'
img_sel_parms['image'] = 'IMAGE_NAT'
img_sel_parms['sum_weight'] = 'SUM_WEIGHT_NAT'
img_sel_parms['psf_fit'] = 'PSF_FIT_NAT'
img_xds = xr.Dataset() #empty dataset
img_xds = make_psf(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
img_xds = make_image(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
############################### Uniform
vis_sel_parms = {}
vis_sel_parms['xds'] = 'xds0'
vis_sel_parms['data_group_in_id'] = 1
img_sel_parms = {}
img_sel_parms['data_group_out_id'] = 1
img_sel_parms['psf'] = 'PSF_UNI'
img_sel_parms['psf_sum_weight'] = 'PSF_SUM_WEIGHT_UNI'
img_sel_parms['image'] = 'IMAGE_UNI'
img_sel_parms['sum_weight'] = 'SUM_WEIGHT_UNI'
img_sel_parms['psf_fit'] = 'PSF_FIT_UNI'
img_xds = make_psf(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
img_xds = make_image(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
############################### Briggs
vis_sel_parms = {}
vis_sel_parms['xds'] = 'xds0'
vis_sel_parms['data_group_in_id'] = 2
img_sel_parms = {}
img_sel_parms['data_group_out_id'] = 2
img_sel_parms['psf'] = 'PSF_BRG'
img_sel_parms['psf_sum_weight'] = 'PSF_SUM_WEIGHT_BRG'
img_sel_parms['image'] = 'IMAGE_BRG'
img_sel_parms['sum_weight'] = 'SUM_WEIGHT_BRG'
img_sel_parms['psf_fit'] = 'PSF_FIT_BRG'
img_xds = make_psf(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
img_xds = make_image(mxds_3, img_xds, grid_parms, vis_sel_parms, img_sel_parms)
print(img_xds)
######################### Start make_psf #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '0', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0'}
######################### Created graph for make_psf #########################
######################### Start make_image #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '0', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT', 'imaging_weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', 'psf': 'PSF_NAT', 'psf_fit': 'PSF_FIT_NAT'}
Setting default data_group_out [' psf '] to PSF_NAT
Setting default data_group_out [' psf_fit '] to PSF_FIT_NAT
######################### Created graph for make_image #########################
######################### Start make_psf #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '1', 'imaging_weight': 'IMAGING_WEIGHT_UNI', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'imaging_weight': 'IMAGING_WEIGHT_UNI', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', 'image': 'IMAGE_NAT', 'psf': 'PSF_NAT', 'psf_fit': 'PSF_FIT_NAT'}
Setting default data_group_out [' image '] to IMAGE_NAT
######################### Created graph for make_psf #########################
######################### Start make_image #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '1', 'imaging_weight': 'IMAGING_WEIGHT_UNI', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'imaging_weight': 'IMAGING_WEIGHT_UNI', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', 'image': 'IMAGE_NAT', 'psf': 'PSF_NAT', 'psf_fit': 'PSF_FIT_NAT'}
Setting default data_group_out [' psf '] to PSF_NAT
Setting default data_group_out [' psf_fit '] to PSF_FIT_NAT
######################### Created graph for make_image #########################
######################### Start make_psf #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '2', 'imaging_weight': 'IMAGING_WEIGHT_BRG', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'imaging_weight': 'IMAGING_WEIGHT_BRG', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', 'image': 'IMAGE_NAT', 'psf': 'PSF_NAT', 'psf_fit': 'PSF_FIT_NAT'}
Setting default data_group_out [' image '] to IMAGE_NAT
######################### Created graph for make_psf #########################
######################### Start make_image #########################
Setting default image_center to [100 100]
Setting default fft_padding to 1.2
Setting data_group_in to {'id': '2', 'imaging_weight': 'IMAGING_WEIGHT_BRG', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_out to {'id': '3', 'imaging_weight': 'IMAGING_WEIGHT_BRG', 'data': 'DATA', 'flag': 'FLAG', 'uvw': 'UVW', 'weight': 'DATA_WEIGHT'}
Setting default data_group_in to {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', 'image': 'IMAGE_NAT', 'psf': 'PSF_NAT', 'psf_fit': 'PSF_FIT_NAT'}
Setting default data_group_out [' psf '] to PSF_NAT
Setting default data_group_out [' psf_fit '] to PSF_FIT_NAT
######################### Created graph for make_image #########################
<xarray.Dataset>
Dimensions: (chan: 1, elps_index: 3, l: 200, m: 200, pol: 1, time: 1)
Coordinates:
* chan (chan) float64 3.726e+11
* l (l) float64 1.939e-05 1.92e-05 ... -1.9e-05 -1.92e-05
* m (m) float64 -1.939e-05 -1.92e-05 ... 1.9e-05 1.92e-05
* pol (pol) int32 9
* time (time) datetime64[ns] 2012-11-19T08:26:09.618666673
chan_width (chan) float64 dask.array<chunksize=(1,), meta=np.ndarray>
right_ascension (l, m) float64 2.888 2.888 2.888 ... 2.888 2.888 2.888
declination (l, m) float64 -0.6057 -0.6057 -0.6057 ... -0.6057 -0.6057
Dimensions without coordinates: elps_index
Data variables:
SUM_WEIGHT_NAT (time, chan, pol) float64 dask.array<chunksize=(1, 1, 1), meta=np.ndarray>
PSF_NAT (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
PSF_FIT_NAT (time, chan, pol, elps_index) float64 dask.array<chunksize=(1, 1, 1, 3), meta=np.ndarray>
IMAGE_NAT (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
SUM_WEIGHT_UNI (time, chan, pol) float64 dask.array<chunksize=(1, 1, 1), meta=np.ndarray>
PSF_UNI (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
PSF_FIT_UNI (time, chan, pol, elps_index) float64 dask.array<chunksize=(1, 1, 1, 3), meta=np.ndarray>
IMAGE_UNI (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
SUM_WEIGHT_BRG (time, chan, pol) float64 dask.array<chunksize=(1, 1, 1), meta=np.ndarray>
PSF_BRG (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
PSF_FIT_BRG (time, chan, pol, elps_index) float64 dask.array<chunksize=(1, 1, 1, 3), meta=np.ndarray>
IMAGE_BRG (l, m, time, chan, pol) float64 dask.array<chunksize=(200, 200, 1, 1, 1), meta=np.ndarray>
Attributes:
data_groups: [{'0': {'id': '0', 'sum_weight': 'SUM_WEIGHT_NAT', ...
axis_units: ['rad', 'rad', 'time', 'Hz', 'pol']
direction_reference: FK5
spectral_reference: lsrk
velocity_type: radio
unit: Jy/beam
[5]:
dask.visualize(img_xds,'weighting_image_graph.png')
[5]:
Save To Disk¶
[6]:
from cngi.dio import write_image
img_xds = write_image(img_xds, outfile='twhya_standard_gridder_lsrk_mfs.img.zarr')
Time to store and execute graph write_zarr 35.28575277328491
Plot¶
[7]:
import xarray as xr
import matplotlib.pylab as plt
img_xds = xr.open_zarr('twhya_standard_gridder_lsrk_mfs.img.zarr').isel(time=0,chan=0,pol=0)
import numpy as np
plt.close('all')
## Plot PSF images
plt.figure()
plt.plot(img_xds.PSF_NAT[100,75:125].m,img_xds.PSF_NAT[100,75:125],label='natural')
plt.plot(img_xds.PSF_NAT[100,75:125].m,img_xds.PSF_UNI[100,75:125],label='uniform')
plt.plot(img_xds.PSF_NAT[100,75:125].m,img_xds.PSF_BRG[100,75:125],label='briggs, robust='+str(imaging_weights_parms['robust']))
plt.legend()
plt.title('PSF')
plt.xlabel('m')
plt.ylabel('Amplitude')
plt.show()
extent = extent=(np.min(img_xds.m),np.max(img_xds.m),np.min(img_xds.l),np.max(img_xds.l))
fig0, ax0 = plt.subplots(1, 3, sharey=True,figsize=(12, 5))
im0 = ax0[0].imshow(img_xds.PSF_NAT,extent=extent)
im1 = ax0[1].imshow(img_xds.PSF_UNI,extent=extent)
im2 = ax0[2].imshow(img_xds.PSF_BRG,extent=extent)
ax0[0].title.set_text('PSF Natural Weighting')
ax0[1].title.set_text('PSF Uniform Weighting')
ax0[2].title.set_text('PSF Briggs, robust='+str(imaging_weights_parms['robust']))
ax0[0].set_xlabel('m'),ax0[1].set_xlabel('m'),ax0[0].set_ylabel('l'),ax0[1].set_ylabel('l'),ax0[2].set_xlabel('m'),ax0[2].set_ylabel('l')
fig0.colorbar(im0, ax=ax0[0], fraction=0.046, pad=0.04)
fig0.colorbar(im1, ax=ax0[1], fraction=0.046, pad=0.04)
fig0.colorbar(im2, ax=ax0[2], fraction=0.046, pad=0.04)
plt.show()
fig0, ax0 = plt.subplots(1, 3, sharey=True,figsize=(12, 5))
im0 = ax0[0].imshow(img_xds.IMAGE_NAT,extent=extent)
im1 = ax0[1].imshow(img_xds.IMAGE_UNI,extent=extent)
im2 = ax0[2].imshow(img_xds.IMAGE_BRG,extent=extent)
ax0[0].title.set_text('Dirty Image Natural Weighting')
ax0[1].title.set_text('Dirty Image Uniform Weighting')
ax0[2].title.set_text('Dirty Image Briggs, robust='+str(imaging_weights_parms['robust']))
ax0[0].set_xlabel('m'),ax0[1].set_xlabel('m'),ax0[0].set_ylabel('l'),ax0[1].set_ylabel('l'),ax0[2].set_xlabel('m'),ax0[2].set_ylabel('l')
fig0.colorbar(im0, ax=ax0[0], fraction=0.046, pad=0.04)
fig0.colorbar(im1, ax=ax0[1], fraction=0.046, pad=0.04)
fig0.colorbar(im2, ax=ax0[2], fraction=0.046, pad=0.04)
plt.show()
