[Numpy-discussion] is __array_ufunc__ ready for prime-time?

[Ryan May]

On Thu, Nov 2, 2017 at 6:56 AM, <josef.pktd at gmail.com> wrote:

> On Thu, Nov 2, 2017 at 8:46 AM, <josef.pktd at gmail.com> wrote:
>
>> On Wed, Nov 1, 2017 at 6:55 PM, Nathan Goldbaum <nathan12343 at gmail.com>
>> wrote:
>>
>>> I think the biggest issues could be resolved if __array_concatenate__
>>> were finished. Unfortunately I don't feel like I can take that on right now.
>>>
>>> See Ryan May's talk at scipy about using an ndarray subclass for units
>>> and the issues he's run into:
>>>
>>> https://www.youtube.com/watch?v=qCo9bkT9sow
>>>
>>
>>
>> Interesting talk, but I don't see how general library code should know
>> what units the output has.
>> for example if units are some flows per unit of time and we average, sum
>> or integrate over time, then what are the new units? (e.g. pandas time
>> aggregation)
>> What are units of covariance or correlation between two variables with
>> the same units, and what are they between variables with different units?
>>
>> How do you concatenate and operate arrays with different units?
>>
>> interpolation or prediction would work with using the existing units.
>>
>> partially related:
>> statsmodels uses a wrapper for pandas Series and DataFrames and tries to
>> preserve the index when possible and make up a new DataFrame or Series if
>> the existing index doesn't apply.
>> E.g. predicted values and residuals are in terms of the original provided
>> index, and could also get original units assigned. That would also be
>> possible with prediction confidence intervals. But for the rest, see above.
>>
>
> using pint
>
> >>> x
> <Quantity([0 1 2 3 4], 'meter')>
> >>> x / x
> <Quantity([ nan   1.   1.   1.   1.], 'dimensionless')>
>
> >>> x / (1 + x)
> Traceback (most recent call last):
>   File "<stdin>", line 1, in <module>
>   File "C:\...\python-3.4.4.amd64\lib\site-packages\pint\quantity.py",
> line 669, in __add__
>     raise DimensionalityError(self._units, 'dimensionless')
>     return self._add_sub(other, operator.add)
>   File "C:\...\python-3.4.4.amd64\lib\site-packages\pint\quantity.py",
> line 580, in _add_sub
> pint.errors.DimensionalityError: Cannot convert from 'meter' to
> 'dimensionless'
>

I'm not sure why you have a problem with that results. You tried to take a
number in meters and add a dimensionless value to that--that's not a
defined operation. That's like saying: "I have a distance of 12 meters and
added 1 to it." 1 what? 1 meter? Great. 1 centimeter? I need to convert,
but I can do that operation. 1 second? That makes no sense.

If you add units to the 1 then it's a defined operation:

>>> reg = pint.UnitRegistry()
>>> x / (1 * ureg.meters + x)
<Quantity([ 0.          0.5         0.66666667  0.75        0.8       ],
'dimensionless')>


> np.exp(x)
> raises
> pint.errors.DimensionalityError: Cannot convert from 'meter' ([length])
> to 'dimensionless' (dimensionless)
>

Well, the Taylor series for exp (around a=0) is:

exp(x) = 1 + x + x**2 / 2 + x**3 / 6 + ...

so for that to properly add up, x needs to be dimensionless. It should be
noted, though, that I've *never* seen a formula, theoretically derived or
empirically fit, require directly taking exp(x) where x is a physical
quantity with units. Instead, you have:

f = a * exp(kx)

Properly calculated values for a, k will have appropriate units attached to
them that allows the calculation to proceed without error

Ryan

-- 
Ryan May
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