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.. _swath:
Resampling of swath data
========================
Pyresample can be used to resample a swath dataset to a grid, a grid to a swath or a swath to another swath.
Resampling can be done using nearest neighbour method, Guassian weighting, weighting with an arbitrary radial function.
.. versionchanged:: 1.8.0
:class:`~pyresample.geometry.SwathDefinition` no longer checks the validity of the provided longitude
and latitude coordinates to improve performance. Longitude arrays are
expected to be between -180 and 180 degrees, latitude -90 to 90 degrees.
This also applies to all geometry definitions that are provided longitude
and latitude arrays on initialization. Use
:func:`~pyresample.utils.check_and_wrap` to preprocess your arrays.
pyresample.image
----------------
The ImageContainerNearest and ImageContanerBilinear classes can be used for resampling of swaths as well as grids. Below is an example using nearest neighbour resampling.
.. doctest::
>>> import numpy as np
>>> from pyresample import image, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> swath_con = image.ImageContainerNearest(data, swath_def, radius_of_influence=5000)
>>> area_con = swath_con.resample(area_def)
>>> result = area_con.image_data
For other resampling types or splitting the process in two steps use e.g. the functions in **pyresample.kd_tree** described below.
pyresample.kd_tree
------------------
This module contains several functions for resampling swath data.
Note distance calculation is approximated with cartesian distance.
Masked arrays can be used as data input. In order to have undefined pixels masked out instead of
assigned a fill value set **fill_value=None** when calling the **resample_*** function.
resample_nearest
****************
Function for resampling using nearest neighbour method.
Example showing how to resample a generated swath dataset to a grid using nearest neighbour method:
.. doctest::
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_nearest(swath_def, data,
... area_def, radius_of_influence=50000, epsilon=0.5)
If the arguments **swath_def** and **area_def** where switched (and **data** matched the dimensions of **area_def**) the grid of **area_def**
would be resampled to the swath defined by **swath_def**.
Note the keyword arguments:
* **radius_of_influence**: The radius around each grid pixel in meters to search for neighbours in the swath.
* **epsilon**: The distance to a found value is guaranteed to be no further than (1 + eps) times the distance to the correct neighbour. Allowing for uncertanty decreases execution time.
If **data** is a masked array the mask will follow the neighbour pixel assignment.
If there are multiple channels in the dataset the **data** argument should be of the shape of the lons and lat arrays
with the channels along the last axis e.g. (rows, cols, channels). Note: the convention of pyresample < 0.7.4 is to pass
**data** in the form of (number_of_data_points, channels) is still accepted.
.. doctest::
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> channel1 = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> channel2 = np.fromfunction(lambda y, x: y*x, (50, 10)) * 2
>>> channel3 = np.fromfunction(lambda y, x: y*x, (50, 10)) * 3
>>> data = np.dstack((channel1, channel2, channel3))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_nearest(swath_def, data,
... area_def, radius_of_influence=50000)
For nearest neighbour resampling the class **image.ImageContainerNearest** can be used as well as **kd_tree.resample_nearest**
resample_gauss
**************
Function for resampling using nearest Gussian weighting. The Gauss weigh function is defined as exp(-dist^2/sigma^2).
Note the pyresample sigma is **not** the standard deviation of the gaussian.
Example showing how to resample a generated swath dataset to a grid using Gaussian weighting:
.. doctest::
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_gauss(swath_def, data,
... area_def, radius_of_influence=50000, sigmas=25000)
If more channels are present in **data** the keyword argument **sigmas** must be a list containing a sigma for each channel.
If **data** is a masked array any pixel in the result data that has been "contaminated" by weighting of a masked pixel is masked.
Using the function **utils.fwhm2sigma** the sigma argument to the gauss resampling can be calculated from 3 dB FOV levels.
resample_custom
***************
Function for resampling using arbitrary radial weight functions.
Example showing how to resample a generated swath dataset to a grid using an arbitrary radial weight function:
.. doctest::
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> wf = lambda r: 1 - r/100000.0
>>> result = kd_tree.resample_custom(swath_def, data,
... area_def, radius_of_influence=50000, weight_funcs=wf)
If more channels are present in **data** the keyword argument **weight_funcs** must be a list containing a radial function for each channel.
If **data** is a masked array any pixel in the result data that has been "contaminated" by weighting of a masked pixel is masked.
Uncertainty estimates
*********************
Uncertainty estimates in the form of weighted standard deviation can be obtained from the **resample_custom** and **resample_gauss** functions.
By default the functions return the result of the resampling as a single numpy array. If the functions are given the keyword argument **with_uncert=True**
then the following list of numpy arrays will be returned instead: **(result, stddev, count)**. **result** is the usual result. **stddev** is the weighted standard deviation for each element in the result. **count** is the number of data values used in the weighting for each element in the result.
The principle is to view the calculated value for each element in the result as a weighted average of values sampled from a statistical variable.
An estimate of the standard deviation of the distribution is calculated using the unbiased weighted estimator given as
**stddev = sqrt((V1 / (V1 ** 2 + V2)) * sum(wi * (xi - result) ** 2))** where **result** is the result of the resampling. **xi** is the value of a contributing neighbour
and **wi** is the corresponding weight. The coefficients are given as **V1 = sum(wi)** and **V2 = sum(wi ** 2)**. The standard deviation is only calculated for elements in
the result where more than one neighbour has contributed to the weighting. The **count** numpy array can be used for filtering at a higher number of contributing neigbours.
Usage only differs in the number of return values from **resample_gauss** and **resample_custom**. E.g.:
>>> result, stddev, count = pr.kd_tree.resample_gauss(swath_def, ice_conc, area_def,
... radius_of_influence=20000,
... sigmas=pr.utils.fwhm2sigma(35000),
... fill_value=None, with_uncert=True)
Below is shown a plot of the result of the resampling using a real data set:
.. image:: /_static/images/uncert_conc_nh.png
The corresponding standard deviations:
.. image:: /_static/images/uncert_stddev_nh.png
And the number of contributing neighbours for each element:
.. image:: /_static/images/uncert_count_nh.png
Notice the standard deviation is only calculated where there are more than one contributing neighbour.
Resampling from neighbour info
******************************
The resampling can be split in two steps:
First get arrays containing information about the nearest neighbours to each grid point.
Then use these arrays to retrive the resampling result.
This approch can be useful if several datasets based on the same swath are to be resampled. The computational
heavy task of calculating the neighbour information can be done once and the result can be used to
retrieve the resampled data from each of the datasets fast.
.. doctest::
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> valid_input_index, valid_output_index, index_array, distance_array = \
... kd_tree.get_neighbour_info(swath_def,
... area_def, 50000,
... neighbours=1)
>>> res = kd_tree.get_sample_from_neighbour_info('nn', area_def.shape, data,
... valid_input_index, valid_output_index,
... index_array)
Note the keyword argument **neighbours=1**. This specifies only to consider one neighbour for each
grid point (the nearest neighbour). Also note **distance_array** is not a required argument for
**get_sample_from_neighbour_info** when using nearest neighbour resampling
Segmented resampling
********************
Whenever a resampling function takes the keyword argument **segments** the number of segments to split the resampling process in can be specified. This affects the memory footprint of pyresample. If the value of **segments** is left to default pyresample will estimate the number of segments to use.
pyresample.bilinear
-------------------
Compared to nearest neighbour resampling, bilinear interpolation
produces smoother results near swath edges of polar satellite data and
edges of geostationary satellites.
The algorithm is implemented from http://www.ahinson.com/algorithms_general/Sections/InterpolationRegression/InterpolationIrregularBilinear.pdf
Below is shown a comparison between image generated with nearest
neighbour resampling (top) and with bilinear interpolation
(bottom):
.. image:: /_static/images/nearest_overview.png
:width: 50%
.. image:: /_static/images/bilinear_overview.png
:width: 50%
Click images to see the full resolution versions.
The *perceived* sharpness of the bottom image is lower, but there is more detail present.
XArrayBilinearResampler
***********************
**bilinear.XArrayBilinearResampler** is a class that handles bilinear interpolation for data in
`xarray.DataArray` arrays. The parallelization is done automatically using `dask`.
>>> import numpy as np
>>> import dask.array as da
>>> from xarray import DataArray
>>> from pyresample.bilinear import XArrayBilinearResampler
>>> from pyresample import geometry
>>> target_def = geometry.AreaDefinition('areaD',
... 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = DataArray(da.from_array(np.fromfunction(lambda y, x: y*x, (500, 100))), dims=('y', 'x'))
>>> lons = da.from_array(np.fromfunction(lambda y, x: 3 + x * 0.1, (500, 100)))
>>> lats = da.from_array(np.fromfunction(lambda y, x: 75 - y * 0.1, (500, 100)))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> resampler = XArrayBilinearResampler(source_def, target_def, 30e3)
>>> result = resampler.resample(data)
The resampling info can be saved for later reuse and much faster processing for a matching area. The
data are saved to a Zarr archive, so `zarr` Python package needs to be installed.
>>> import os
>>> from tempfile import gettempdir
>>> cache_file = os.path.join(gettempdir(), "bilinear_resampling_luts.zarr")
>>> resampler.save_resampling_info(cache_file)
>>> new_resampler = XArrayBilinearResampler(source_def, target_def, 30e3)
>>> new_resampler.load_resampling_info(cache_file)
>>> result = new_resampler.resample(data)
NumpyBilinearResampler
**********************
**bilinear.NumpyBilinearResampler** is a plain Numpy version of **XArrayBilinearResampler**. If
`fill_value` isn't given to `get_sample_from_bil_info()`, a masked array will be returned.
>>> import numpy as np
>>> from pyresample.bilinear import NumpyBilinearResampler
>>> from pyresample import geometry
>>> target_def = geometry.AreaDefinition('areaD',
... 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (500, 100))
>>> lons = np.fromfunction(lambda y, x: 3 + x * 0.1, (500, 100))
>>> lats = np.fromfunction(lambda y, x: 75 - y * 0.1, (500, 100))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> resampler = NumpyBilinearResampler(source_def, target_def, 30e3)
>>> result = resampler.resample(data)
resample_bilinear
*****************
Convenience function for resampling using bilinear interpolation for irregular source grids.
.. note::
The use of this function is deprecated. Depending on the input data format, please use directly
the **bilinear.NumpyBilinearResampler** or **bilinear.XArrayBilinearResampler** classes and their
**.resample()** method shown above.
.. doctest::
>>> import numpy as np
>>> from pyresample import bilinear, geometry
>>> target_def = geometry.AreaDefinition('areaD',
... 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (500, 100))
>>> lons = np.fromfunction(lambda y, x: 3 + x * 0.1, (500, 100))
>>> lats = np.fromfunction(lambda y, x: 75 - y * 0.1, (500, 100))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = bilinear.resample_bilinear(data, source_def, target_def,
... radius=50e3, neighbours=32,
... nprocs=1, fill_value=0,
... reduce_data=True, segments=None,
... epsilon=0)
The **target_area** needs to be an area definition with **proj_str**
attribute.
..
The **source_def** can be either an area definition as above,
or a 2-tuple of (lons, lats).
Keyword arguments which are passed to **kd_tree**:
* **radius**: radius around each target pixel in meters to search for
neighbours in the source data
* **neighbours**: number of closest locations to consider when
selecting the four data points around the target location. Note that this
value needs to be large enough to ensure "surrounding" the target!
* **nprocs**: number of processors to use for finding the closest pixels
* **fill_value**: fill invalid pixel with this value. If
**fill_value=None** is used, masked arrays will be returned
* **reduce_data**: do/don't do preliminary data reduction before calculating
the neigbour info
* **epsilon**: maximum uncertainty allowed in neighbour search
The example above shows the default value for each keyword argument.
Resampling from bilinear coefficients
*************************************
.. note::
This usage is deprecated, please use the **bilinear.NumpyBilinearResampler** or
**bilinear.XArrayBilinearResampler** classes directly depending on the input data format.
As for nearest neighbour resampling, also bilinear interpolation can
be split in two steps.
* Calculate interpolation coefficients, input data reduction matrix
and mapping matrix
* Use this information to resample several datasets between these two
areas/swaths
Only the first step is computationally expensive operation, so by
re-using this information the overall processing time is reduced
significantly. This is also done internally by the
**resample_bilinear** function, but separating these steps makes it
possible to cache the coefficients if the same transformation is done
over and over again. This is very typical in operational
geostationary satellite image processing. Note that the output shape is now
defined so that the result is reshaped to correct shape. This reshaping
is done internally in **resample_bilinear**.
.. doctest::
>>> import numpy as np
>>> from pyresample import bilinear, geometry
>>> target_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> t_params, s_params, input_idxs, idx_ref = \
... bilinear.get_bil_info(source_def, target_def, radius=50e3, nprocs=1)
>>> res = bilinear.get_sample_from_bil_info(data.ravel(), t_params, s_params,
... input_idxs, idx_ref,
... output_shape=target_def.shape)
pyresample.ewa
--------------
Pyresample makes it possible to resample swath data to a uniform grid
using an Elliptical Weighted Averaging algorithm or EWA for short.
This algorithm behaves differently than the KDTree based resampling
algorithms that pyresample provides. The KDTree-based algorithms
process each output grid pixel by searching for all "nearby" input
pixels and applying a certain interpolation (nearest neighbor, gaussian, etc).
The EWA algorithm processes each input pixel mapping it to one or more output
pixels. Once each input pixel has been analyzed, the intermediate results are
averaged to produce the final gridded result.
The EWA algorithm also has limitations on how the input data are structured
compared to the generic KDTree algorithms. EWA assumes that data in the array
is organized geographically; adjacent data in the array is adjacent data
geographically. The algorithm uses this to configure parameters based on the
size and location of the swath pixels. It also assumes that data are
scan-based, recorded by a orbiting satellite scan by scan, and the user must
provide scan size with the ``rows_per_scan`` option.
The EWA algorithm consists of two
steps: ll2cr and fornav. The algorithm was originally part of the
MODIS Swath to Grid Toolbox (ms2gt) created by the
NASA National Snow & Ice Data Center (NSIDC). Its default parameters
work best with MODIS L1B data, but it has been proven to produce high
quality images from VIIRS and AVHRR data with the right parameters.
.. note::
This code was originally part of the CSPP Polar2Grid project. This
documentation and the API documentation for this algorithm may still
use references or concepts from Polar2Grid until everything can
be updated.
Resampler
*********
The :class:`~pyresample.ewa.DaskEWAResampler` is the easiest way to use the
EWA resampling algorithm. Internally this resampler uses the ``dask`` library
to perform all of its operations in parallel. This will typically provide
better performance than any of the below methods, but does require the
``dask`` library to be installed. The below code assumes you have a
``swath_def`` object (:class:`~pyresample.geometry.SwathDefinition`), an
``area_def`` object (:class:`~pyresample.geometry.AreaDefinition`), and
some array data in ``data``. Data can be a numpy array, a dask array, or
an xarray DataArray object.
.. testsetup::
import numpy as np
from pyresample import geometry
import dask.array as da
import xarray as xr
area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
{'a': '6378144.0', 'b': '6356759.0',
'lat_0': '50.00', 'lat_ts': '50.00',
'lon_0': '8.00', 'proj': 'stere'},
800, 800,
[-1370912.72, -909968.64,
1029087.28, 1490031.36])
data = np.fromfunction(lambda y, x: y*x, (50, 10))
dask_data = da.from_array(data, chunks='auto')
xr_data = xr.DataArray(dask_data)
lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
dask_lons = da.from_array(lons, chunks='auto')
dask_lats = da.from_array(lats, chunks='auto')
xr_lons = xr.DataArray(dask_lons)
xr_lats = xr.DataArray(dask_lats)
xr_swath_def = geometry.SwathDefinition(lons=xr_lons, lats=xr_lats)
.. testcode::
from pyresample.ewa import DaskEWAResampler
resampler = DaskEWAResampler(swath_def, area_def)
# if the data are scan based, specify how many data rows make up one scan
rows_per_scan = 5
result = resampler.resample(data, rows_per_scan=rows_per_scan)
.. note::
As a convenience, you can set rows_per_scan to 0 to have it set to the
number of rows in the input data. This can be helpful when testing EWA
on data that is not necessarily scan based, but still has nice results
with EWA.
Legacy Dask Resampler
*********************
This resampler is similar to the above, but only works on xarray DataArray
objects backed by dask arrays. Although it uses dask underneath, it doesn't
use it optimally and in most cases will use a lot of memory.
.. testcode::
from pyresample.ewa import LegacyDaskEWAResampler
resampler = LegacyDaskEWAResampler(xr_swath_def, area_def)
# if the data are scan based, specify how many data rows make up one scan
rows_per_scan = 5
result = resampler.resample(xr_data, rows_per_scan=rows_per_scan)
Legacy Function Interface
*************************
It is recommended to use the Resampler interfaces described above whenever
possible. However, the low-level ``ll2cr`` and ``fornav`` functions can be
used if desired. These functions will only work on basic numpy arrays and
although fast, they will use a lot of memory for large input arrays or large
target areas.
.. testcode::
from pyresample.ewa import ll2cr, fornav
# ll2cr converts swath longitudes and latitudes to grid columns and rows
swath_points_in_grid, cols, rows = ll2cr(swath_def, area_def)
# if the data are scan based, specify how many data rows make up one scan
rows_per_scan = 5
# fornav resamples the swath data to the gridded area
num_valid_points, gridded_data = fornav(cols, rows, area_def, data, rows_per_scan=rows_per_scan)
pyresample.bucket
-----------------
.. autoclass:: pyresample.bucket.BucketResampler
:noindex:
See :class:`~pyresample.bucket.BucketResampler` API documentation for
the details of method parameters.
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