Inputs to modeling not always broadcasted as expected

Description

This might not actually be a bug and nobody but me expects it to work this way, but this worked when I ran the same code through astropy.wcs.WCS and it fails with gwcs.WCS because of the input behaviour in modeling.

Expected behavior

When calling a 2D model with sparse, broadcastable inputs I expect the inputs to be broadcasted together.

Actual behavior

Traceback saying ValueError: All inputs must have identical shapes or must be scalars.

Steps to Reproduce

import numpy as np
from astropy.modeling import models
import astropy.units as u

shape = (3, 3)
data = np.arange(np.product(shape)).reshape(shape) * u.m / u.s

points_unit = u.pix
points = [np.arange(size) * points_unit for size in shape]

kwargs = {
    'bounds_error': False,
    'fill_value': np.nan,
    'method': 'nearest',
}

transform = models.Tabular2D(points, data, **kwargs)
print(transform)

Model: Tabular2D
N_inputs: 2
N_outputs: 1
Parameters: 
  points: [<Quantity [0., 1., 2.] pix>, <Quantity [0., 1., 2.] pix>]
  lookup_table: [[0. 1. 2.]
 [3. 4. 5.]
 [6. 7. 8.]] m / s
  method: nearest
  fill_value: nan
  bounds_error: False

points = np.meshgrid(np.arange(3), np.arange(3), indexing='ij', sparse=True)
print(points)

[array([[0],
       [1],
       [2]]), array([[0, 1, 2]])]

transform(*points)

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-14-e007ddf28445> in <module>
----> 1 import codecs, os;__pyfile = codecs.open('''/tmp/pypuTmFL''', encoding='''utf-8''');__code = __pyfile.read().encode('''utf-8''');__pyfile.close();os.remove('''/tmp/pypuTmFL''');exec(compile(__code, '''/tmp/pypuTmFL''', 'exec'));

/tmp/pypuTmFL in <module>

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in __call__(self, model_set_axis, with_bounding_box, fill_value, equivalencies, inputs_map, *inputs, **new_inputs)
    398                            ('inputs_map', None)])
    399 
--> 400             new_call = make_function_with_signature(
    401                 __call__, args, kwargs, varargs='inputs', varkwargs='new_inputs')
    402 

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in __call__(self, *inputs, **kwargs)
    377             def __call__(self, *inputs, **kwargs):
    378                 """Evaluate this model on the supplied inputs."""
--> 379                 return super(cls, self).__call__(*inputs, **kwargs)
    380 
    381             # When called, models can take two optional keyword arguments:

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in __call__(self, *args, **kwargs)
    911         new_args, kwargs = self._get_renamed_inputs_as_positional(*args, **kwargs)
    912 
--> 913         return generic_call(self, *new_args, **kwargs)
    914 
    915     def _get_renamed_inputs_as_positional(self, *args, **kwargs):

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in generic_call(self, *inputs, **kwargs)
   3945 def generic_call(self, *inputs, **kwargs):
   3946     """ The base ``Model. __call__`` method."""
-> 3947     inputs, format_info = self.prepare_inputs(*inputs, **kwargs)
   3948     if isinstance(self, CompoundModel):
   3949         # CompoundModels do not normally hold parameters at that level

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in prepare_inputs(self, model_set_axis, equivalencies, *inputs, **kwargs)
   1608         inputs = [np.asanyarray(_input, dtype=float) for _input in inputs]
   1609 
-> 1610         _validate_input_shapes(inputs, self.inputs, n_models,
   1611                                model_set_axis, self.standard_broadcasting)
   1612 

~/.virtualenvs/ndcube-dev/lib/python3.8/site-packages/astropy/modeling/core.py in _validate_input_shapes(inputs, argnames, n_models, model_set_axis, validate_broadcasting)
   3885     input_shape = check_consistent_shapes(*all_shapes)
   3886     if input_shape is None:
-> 3887         raise ValueError(
   3888             "All inputs must have identical shapes or must be scalars.")
   3889 

ValueError: All inputs must have identical shapes or must be scalars.

What I expect the output to be is what happens if you set sparse=False:

points = np.meshgrid(np.arange(3), np.arange(3), indexing='ij', sparse=False) * u.pix
print(transform(*points))

[[[0. 0. 0.]
  [1. 1. 1.]
  [2. 2. 2.]]

 [[0. 1. 2.]
  [0. 1. 2.]
  [0. 1. 2.]]] pix

System Details

Astropy 4.1

[nden]

This is a known issue. I attempted a solution in #10362 but it’s incomplete - handling of the bounding box needs to be fixed. Similar issues: #9953 , #10170

[nden]

@WilliamJamieson 👍 The above numbers match the answer without units.