Description

These are all related issues:

• Model.standard_broadcasting is not documented.
• _validate_input_shapes does not use argument validate_broadcasting which I believe is the Model.standard_broadcasting flag and should turn off validation if True.
• _validate_input_shapes claims it checks if inputs are broadcastable. In reality it checks that the shapes of the inputs are the same. This prevents some valid use cases from running, e.g. multiply when input shapes are (10, 1) and (24,)

Expected behavior

• When Model.standard_broadcasting=False inputs with non-broadcastable shapes should be accepted (and handled by the model.

• This example should work

from astropy.modeling.models import math as astmath
t=np.array([np.linspace(0,1,10)]).T 
astmath.MultiplyUfunc()(t, np.arange(4))

Actual behavior

astmath.MultiplyUfunc()(t, np.arange(4))
...
~/dev/astropy/astropy/modeling/core.py in _validate_input_shapes(inputs, argnames, n_models, model_set_axis, validate_broadcasting)
   3708     if input_shape is None:
   3709         raise ValueError(
-> 3710             "All inputs must have identical shapes or must be scalars.")
   3711