# Support for units and quantities¶

Note

The functionality presented here was recently added. If you run into any issues, please don’t hesitate to open an issue in the issue tracker.

The `astropy.modeling`

package includes partial support for the use of units and
quantities in model parameters, models, and during fitting. At this time, only
some of the built-in models (such as
`Gaussian1D`

) support units, but this
will be extended in future to all models where this is appropriate.

## Setting parameters to quantities¶

Models can take `Quantity`

objects as parameters:

```
>>> from astropy import units as u
>>> from astropy.modeling.models import Gaussian1D
>>> g1 = Gaussian1D(mean=3 * u.m, stddev=2 * u.cm, amplitude=3 * u.Jy)
```

Accessing the parameter then returns a Parameter object that contains the value and the unit:

```
>>> g1.mean
Parameter('mean', value=3.0, unit=m)
```

It is then possible to access the individual properties of the parameter:

```
>>> g1.mean.name
'mean'
>>> g1.mean.value
3.0
>>> g1.mean.unit
Unit("m")
```

If a parameter has been initialized as a Quantity, it should always be set to a quantity, but the units don’t have to be compatible with the initial ones:

```
>>> g1.mean = 3 * u.s
>>> g1
<Gaussian1D(amplitude=3. Jy, mean=3. s, stddev=2. cm)>
```

To change the value of a parameter and not the unit, simply set the value property:

```
>>> g1.mean.value = 2
>>> g1
<Gaussian1D(amplitude=3. Jy, mean=2. s, stddev=2. cm)>
```

Setting a parameter which was originally set to a quantity to a scalar doesn’t work because it’s ambiguous whether the user means to change just the value and preserve the unit, or get rid of the unit:

```
>>> g1.mean = 2
Traceback (most recent call last):
...
UnitsError : The 'mean' parameter should be given as a Quantity because it
was originally initialized as a Quantity
```

On the other hand, if a parameter previously defined without units is given a Quantity with a unit, this works because it is unambiguous:

```
>>> g2 = Gaussian1D(mean=3)
>>> g2.mean = 3 * u.m
```

In other words, once units are attached to a parameter, they can’t be removed due to ambiguous meaning.

## Evaluating models with quantities¶

Quantities can be passed to model during evaluation:

```
>>> g3 = Gaussian1D(mean=3 * u.m, stddev=5 * u.cm)
>>> g3(2.9 * u.m)
<Quantity 0.1353352832366122>
>>> g3(2.9 * u.s)
Traceback (most recent call last):
...
UnitsError : Units of input 'x', s (time), could not be converted to
required input units of m (length)
```

In this case, since the mean and standard deviation have units, the value passed during evaluation also needs units:

```
>>> g3(3)
Traceback (most recent call last):
...
UnitsError : Units of input 'x', (dimensionless), could not be converted to
required input units of m (length)
```

## Equivalencies¶

Equivalencies require special care - a Gaussian defined in frequency space is not a Gaussian in wavelength space for example. For this reason, we don’t allow equivalencies to be attached to the parameters themselves. Instead, we take the approach of converting the input data to the parameter space, and any equivalencies should be applied at evaluation time to the data (not the parameters).

Let’s consider a model that is Gaussian in wavelength space:

```
>>> g4 = Gaussian1D(mean=3 * u.micron, stddev=1 * u.micron, amplitude=3 * u.Jy)
```

By default, passing a frequency will not work:

```
>>> g4(1e2 * u.THz)
Traceback (most recent call last):
...
UnitsError : Units of input 'x', THz (frequency), could not be converted to
required input units of micron (length)
```

But you can pass a dictionary of equivalencies to the equivalencies argument (this needs to be a dictionary since some models can contain multiple inputs):

```
>>> g4(110 * u.THz, equivalencies={'x': u.spectral()})
<Quantity 2.888986819525229 Jy>
```

The key of the dictionary should be the name of the inputs according to:

```
>>> g4.inputs
('x',)
```

It is also possible to set default equivalencies for the input parameters using the input_units_equivalencies property:

```
>>> g4.input_units_equivalencies = {'x': u.spectral()}
>>> g4(110 * u.THz)
<Quantity 2.888986819525229 Jy>
```

## Fitting models with units to data¶

Fitting models with units to data with units should be seamless provided that the model supports fitting with units. To demonstrate this, we start off by generating synthetic data:

```
import numpy as np
from astropy import units as u
import matplotlib.pyplot as plt
x = np.linspace(1, 5, 30) * u.micron
y = np.exp(-0.5 * (x - 2.5 * u.micron)**2 / (200 * u.nm)**2) * u.mJy
plt.plot(x, y, 'ko')
plt.xlabel('Wavelength (microns)')
plt.ylabel('Flux density (mJy)')
```

and we then define the initial guess for the fitting and we carry out the fit as we would without any units:

```
from astropy.modeling import models, fitting
g5 = models.Gaussian1D(mean=3 * u.micron, stddev=1 * u.micron, amplitude=1 * u.Jy)
fitter = fitting.LevMarLSQFitter()
g5_fit = fitter(g5, x, y)
plt.plot(x, y, 'ko')
plt.plot(x, g5_fit(x), 'r-')
plt.xlabel('Wavelength (microns)')
plt.ylabel('Flux density (mJy)')
```

## Fitting with equivalencies¶

Let’s now consider the case where the data is not equivalent to those of the parameters, but they are convertible via equivalencies. In this case, the equivalencies can either be passed via a dictionary as shown higher up for the evaluation examples:

```
g6 = models.Gaussian1D(mean=110 * u.THz, stddev=10 * u.THz, amplitude=1 * u.Jy)
g6_fit = fitter(g6, x, y, equivalencies={'x': u.spectral()})
plt.plot(x, g6_fit(x, equivalencies={'x': u.spectral()}), 'b-')
plt.xlabel('Wavelength (microns)')
plt.ylabel('Flux density (mJy)')
```

In this case, the fit (in blue) is slightly worse, because a Gaussian in frequency space (blue) is not a Gaussian in wavelength space (red). As mentioned previously, you can also set input_units_equivalencies on the model itself to avoid having to pass extra arguments to the fitter:

```
g6.input_units_equivalencies = {'x': u.spectral()}
g6_fit = fitter(g6, x, y)
```

## Adding support for units in a model (Advanced)¶

### Evaluation¶

To make it so that your models can accept parameters with units and be evaluated
using inputs with units, you need to make sure that the
`evaluate()`

method works correctly with
input values and parameters with units. For simple arithmetic, this may work
out of the box since `Quantity`

objects are understood by
a number of Numpy functions.

If users of your models provide input during evaluation that is not compatible with the parameter units, they may get cryptic errors such as:

```
UnitsError : Can only apply 'subtract' function to dimensionless quantities
when other argument is not a quantity (unless the latter is all
zero/infinity/nan)
```

There are several attributes or properties that can be set on models that adjust the behavior of models with units. These attributes can be changed from the defaults in the class definition, e.g.:

```
class MyModel(Model):
input_units = {'x': u.deg}
...
```

Note that these are all optional.

`input_units`

¶

You can easily add checking of the input units by adding an `input_units`

property or attribute on your model class. This should return either `None`

(to
indicate no constraints) or a dictionary where the keys are the input names
(e.g. `x`

for many 1D models) and the values are the units expected, which can
be a function of the parameter units:

```
@property
def input_units(self):
if self.mean.unit is None:
return None
else:
return {'x': self.mean.unit}
```

If the user then gives values with incorrect input units, a clear error will be displayed:

```
UnitsError: Units of input 'x', (dimensionless), could not be converted to
required input units of m (length)
```

Note that the input units don’t have to match exactly those returned by
`input_units`

, but be convertible to them. In addition, `input_units`

can
also be specified as an attribute rather than a property in simple cases:

```
input_units = {'x': u.deg}
```

`return_units`

¶

Similarly to `return_units`

, this should be dictionary that maps the return
values of a model to units. If `evaluate()`

was called
with quantities but returns unitless values, the units are added to the output.
If the return values are quantities in different units, they are converted to
`return_units`

.

`input_units_strict`

¶

If set to `True`

, values that are passed in compatible units will be converted
to the exact units specified in `input_units`

.

This attribute can also be a dictionary that maps input names to a Boolean to enable converting of that input to the specified unit.

`input_units_equivalencies`

¶

This can be set to a dictionary that maps the input names to a list of equivalencies, for example:

```
input_units_equivalencies = {'nu': u.spectral()}
```

`input_units_allow_dimensionless`

¶

If set to `True`

, values that are plain scalars or Numpy arrays can be passed to
evaluate even if `input_units`

specifies that the input should have units. It
is up to the `evaluate()`

to then decide how to
handle these dimensionless values. This attribute can also be a dictionary that
maps input names to a Boolean to enable passing dimensionless values to
`evaluate()`

for that input.

### Fitting¶

To allow models with parameters that have units to be fit to data with units,
you will need to add a method called `_parameter_units_for_data_units`

to your
model class. This should take two arguments `input_units`

and
`output_units`

- `input_units`

will be set to a dictionary with
the units of the independent variables in the data, while `output_units`

will
be set to a dictionary with the units the dependent variables in the data (for
example, for a simple 1D model, `input_units`

will have one key, `x`

, and
`output_units`

will have one key, `y`

). This method should then return
a dictionary giving for each parameter the units the parameter should be
converted to so that the model could be used on the data if units were removed
from both the models and the data. The following example shows the
implementation for the 1D Gaussian:

```
def _parameter_units_for_data_units(self, inputs_unit, outputs_unit):
return OrderedDict([('mean', inputs_unit['x']),
('stddev', inputs_unit['x']),
('amplitude', outputs_unit['y'])])
```

With this method in place, the model can then be fit to data that has units.