I'm confused because this function is only called for isinstance(norm, str).

So this function exists because the norm keyword accepts Normalize objects in addition to strings.
This is fundamentally the same error you get if you give an invalid norm to a Colorizer object.

In main, the @norm.setter on colorizer.Colorizer reads:

    @norm.setter
    def norm(self, norm):
        _api.check_isinstance((colors.Normalize, str, None), norm=norm)
        if norm is None:
            norm = colors.Normalize()
        elif isinstance(norm, str):
            try:
                scale_cls = scale._scale_mapping[norm]
            except KeyError:
                raise ValueError(
                    "Invalid norm str name; the following values are "
                    f"supported: {', '.join(scale._scale_mapping)}"
                ) from None
            norm = _auto_norm_from_scale(scale_cls)()
    ...

The _get_scale_cls_from_str() exists in this PR because this functionality is now needed by both colorizer.Colorizer.norm() and colors.MultiNorm.
Note this PR does not include changes to colorizer.Colorizer.norm() so that it makes use of _get_scale_cls_from_str(). These changes follow in the next PR: #29877 .

Is broadcasting reasonable here? I would assume that most MultiNorms have different scales and thus need per-element entries anyway. It could also be an oversight to pass a single value instead of multiple values.

I'm therefore tempted to not allow scalars here but require exactly n_variables values. A more narrow and explicit interface may be the better start. We can always later expand the API to broadcast scalars if we see that's a typical case and reasonable in terms of usability.

@timhoffm Perhaps this is also a topic for the weekly meeting :)

I'm perfectly fine with removing this here, and perhaps that is a good starting point.

My entry into this topic was a use case (dark-field X-ray microscopy, DFXRM) where we typically want vmax0 = vmax1 = -vmin0 =-vmin1, i.e. equal normalizations, and centered on zero, and given that entry point it felt natural to me to include broadcasting.

We still need a decision here. I slightly favor the more restrictive version of always requiring a tuple, but could be convinced otherwise.

Just for clarification, any iterable, or strictly tuple?
I'm thinking any iterable. In any case, I can remove the broadcasting.

Yes, any iterable, but internally coerced to tuple - as with norms in __init__.

why do we accept None here? I don't see an advantage of [None, None] over ["linear", "linear"]. Quite the opposite, the first one is less readable.

Maybe in case folks want to update the list later?

That doesn't make sense to me. (1) None is resolved to Normalize immediately. (2) Not sure why one wanted to lated update but that's possible either way.

I rather suspect that it's because it along the lines of: In 1D some other places - e.g. ScalarMappable.set_norm - accept None. But likely the othe places only accept it intentionally or unintentionally because norm=None is somewhere a default kwarg and that is passed through.

I rather suspect that it's because it along the lines of: In 1D some other places - e.g. ScalarMappable.set_norm - accept None. But likely the othe places only accept it intentionally or unintentionally because norm=None is somewhere a default kwarg and that is passed through.

Exactly this.
My thinking was that a common use case is not to supply a norm:

ax.imshow((A, B), cmap='BiOrangeBlue')

In this case the norm keyword (default: None) is singular, but to be compatible with the data/cmap it needs to have a length of 2, so in this case the norm keyword is repeated and becomes [None, None], and this then gets passed to the MultiNorm constructor.

In any case, it is better if, as you say we only accept strings.
I will make the change later.

see colorizer.py → _ensure_norm(norm, n_variates=n_variates) here for the proposed implementation. (This can also be simplified if we no longer accept None)

That doesn't make sense to me. (1) None is resolved to Normalize immediately. (2) Not sure why one wanted to lated update but that's possible either way.

What happens with ['linear', None]?

It would be parsed to ['linear', 'linear'], but will now (with the update) produce an error.
If we find we need this functionality, we can always bring it back in a later PR.

So how do you denote ['linear', mpl.NoNorm()]? is that ['linear', 'none']?

Minor nit. As with inverse we don't need separation of the commands by empty lines.

Generally, we should describe the inputs and outputs in more detail. Holds also for inverse, autoscale and autoscale_None. I'm a bit torn whether we should do this in every functions or once in the class docstring.

We still need a decision here. I slightly favor the more restrictive version of always requiring a tuple, but could be convinced otherwise.