Re: [Matplotlib-users] problem with design of matplotlib.pyplot.scatter?

Phillip M. Feldman wrote:
> Hello Eric-
> 
> I've looked at the code in colors.py.  I think that I'm starting to 
> understand what's going on, but I'm unclear about a few things.  In 
> particular:
> 
> - Why do we need to define both forward and reverse transformations?  
> Shouldn't the forward transformation be sufficient?

The inverse is used by colorbar to auto-generate the boundaries and 
values arrays when they are not specified.  The norms that do not have 
inverses have special-case code in colorbar to handle this.

> 
> - I don't follow what the snippet of code below is doing:
> 
>        if cbook.iterable(value):
>            vtype = 'array'
>            val = ma.asarray(value).astype(np.float)
>        else:
>            vtype = 'scalar'
>            val = ma.array([value]).astype(np.float)
> 
> - In some cases I'd like to map the data values to discrete output 
> values, e.g., values below x_0 map to 0 (which the colormap in turn maps 
> to red), values between x_0 and x_1 map to 0.5 (which maps to yellow), 
> and values greater than x_1 map to 1 (which maps to green).  Such a 
> function does not have a mathematical inverse because it is a many to 
> one mapping.  How does one handle this situation?

BoundaryNorm does exactly this--when working with a suitable 
colormap---and its lack of an inverse is handled inside colorbar.

from matplotlib import colors
x_0 = 0
x_1 = 0.5
cmap = colors.ListedColormap(['y'])
cmap.set_under('r')
cmap.set_over('g')
norm = colors.BoundaryNorm([x_0, x_1], cmap.N)
z = (np.arange(100) / 50.0) - 1.0
z.shape = (10,10)
imshow(z, cmap=cmap, norm=norm, interpolation='nearest')

> 
> The ability to pass in an ordinary function (or a pair of functions if 
> the inverse is really necessary) would be a great benefit.

I will try to get to this ASAP.

Eric

> 
> Thanks!
> 
> Phillip
> 
> Eric Firing wrote:
>> Dr. Phillip M. Feldman wrote:
>>> I'd like to generate a scatter plot in which symbols are colored using a
>>> specified colormap, with a specified mapping from the range of the 
>>> data to
>>> the [0,1] colormap interval. I thought at first that one could use 
>>> the norm
>>> argument to specify a function that would perform this mapping, but from
>>> closer reading of the documentation (and experimentation) it seems as 
>>> though
>>> one cannot do this. Is there another mechanism for doing this? (I could
>>> remap the data itself before plotting it, but this is unacceptable 
>>> because
>>> the colorbar tic lables would then take values in [0,1] rather than 
>>> values
>>> from the range of the data).
>>>
>>
>> I don't understand--what you say you want to do is exactly what the 
>> norm is designed for.  Maybe the problem is that you can't pass in a 
>> simple function--you need to subclass colors.Normalize.  An example is 
>> colors.LogNorm.
>>
>> It looks like what we need is a FuncNorm, which would be initialized 
>> with two functions, the forward and inverse transformation functions, 
>> each taking vmin, vmax, and a val.
>>
>> Eric
>>
>