Model Fitting¶

SpecViz utilizes Astropy Models and Fitting to fit models to its spectra. For example, you can fit one model to the continuum, another to an emission line of interest, and yet another to an absorption line.

Currently, the following models are available:

SpecViz Model Name	Astropy Model Class
BrokenPowerLaw	`BrokenPowerLaw1D`
Const	`Const1D`
ExponentialCutoffPowerLaw	`ExponentialCutoffPowerLaw1D`
Gaussian	`Gaussian1D`
GaussianAbsorption	`Gaussian1D` with negative amplitude
Linear	`Linear1D`
LogParabola	`LogParabola1D`
Lorentz	`Lorentz1D`
MexicanHat	`MexicanHat1D`
Trapezoid	`Trapezoid1D`
PowerLaw	`PowerLaw1D`
Scale	`Scale`
Shift	`Shift`
Sine	`Sine1D`
Spline	`UnivariateSpline`
Voigt	`Voigt1D`

The models can be fitted with the following fitters:

SpecViz Fitter Name	Astropy Fitter Class
Levenberg-Marquardt	`LevMarLSQFitter`
Simplex	`SimplexLSQFitter`
SLSQP	`SLSQPLSQFitter`

To use a model:

Select the layer you wish to operate on from the LAYERS window in the upper left.
Create and position a region of interest (ROI) as described in the Viewer section of

the documentation.”
Select the desired model from the Add Model drop-down box and click Select to add it to Current Models.
If desired, repeat the above step to add additional models.
A new model layer will be created under Layers (left panel) and it is attached to the selected data layer.

To edit model parameters or enter a better first estimate of the model parameters:

Select the model layer under Layers (left panel) that contains the desired model.
If desired, double-click on the model name to rename it. When you see a blinking cursor, enter its new name and press “Enter”.
Expand the model listing under Current Models on the right of the viewer.
Double-click on the desired model parameter value in the listing. When you see a blinking cursor, enter the new value and press Enter.

To fit a model:

Select the model layer under Layers that contains the model(s) you wish to fit to your data.
Click the lock icon next to any parameter to choose whether it should be kept fixed (closed lock) or allowed to vary (open lock) during fitting.
Select the desired fitter from Fitting using its drop-down menu.
Click Perform Fit. This may take up to a few seconds, depending on the complexity of the fit.
The associated model parameters will be adjusted accordingly.

The Arithmetic text box is used to define the relationship between different models for the same layer. If nothing is defined, the default is to add all the models together. To describe a non-default model relationship, adjust the math operators, as shown in the examples below and then press Enter to produce the compound model:

Linear1 + Gaussian1

Linear1 * Gaussian1

Gaussian1 - Gaussian2

The entity that results from lumping together all the models, and combining them either using the arithmetic behavior expression, or just adding them all together, is called a “compound model”.

Model names¶

When added to the Current Models list, a model will receive a default name that is generated from the model type (as listed in the drop down model selector) plus a running numerical suffix.

These names can be changed by clicking on the default name and entering a new name. Note that changing model names will require that any expression in the Arithmetic text box be edited accordingly.

For now, we are limited to only alphanumeric characters (and no white spaces) when re-naming models.

Spline model¶

Note that the Spline model is of an intrinsically different nature than the other models included in the drop down list of models. The Spline model, when added to a pre-existing list of models, or when added by itself to an empty list, will immediately be fit to the data within the currently defined Regions Of Interest (ROIs). That is, being a linear model, there is no need to iterate in search of a “best fit” spline. It is just computed once and for all, and kept as part of the compound model that is built from the models in the list and the arithmetic behavior expression.

This implies that, to change the regions of interest that define the spline, one must remove the spline from the list of models. Then, the user must redefine the ROIs and add a new spline to the list of models to be fit. To change a spline parameter, there is no need do discard the spline. Just do it in the same way as with other models: just type in the new value for the parameter.

Subsequently, when the fitter iterates the compound model in search of a best solution, the spline model will act as a constant. That is, it will be used to compute the global result of the compound model, but its parameters won’t be accessed, and varied, by the fitter. Thus, the spline parameters are not fitted, they are just a convenient mechanism that enables user access to the parameter’s values.

The documentation for the spline model can be seen here:

http://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.interpolate.UnivariateSpline.html

Note that SpecViz provides access, at this point, to just two of the parameters in the scipy implementation of th spline function. Pay special attention to the smooth parameter. SpecViz initializes it to a ‘best guess’ (len(wavelength)). Too small of a value may cause the spline to enter an infinite loop. Change the smooth value with care, trying to stay close to the default value.

Note

Model arithmetic is a work in progress.

Saving and Exporting Models to File¶

Selecting a model layer under “Layers” will enable the Save (the “floppy disk” icon) and Export (the “out the door” icon) buttons under “Current Models” on the right of the viewer. Saving a model to a file will enable SpecViz to read back that model into a new model layer. Exporting a model to a file wil create a Python script in a .py file. This file can be directly imported by Python in a command-line session.

Click on either button to get a file dialog window. Type in a file name. If this file name does not end with the correct suffix, the suffix will automatically be appended. Click “Save”, or just the Return/Enter key. The correct suffix for saved and exported files are .yaml and .py, respectively.

Save and Load¶

Saving the model to a file works in the same way as Export. The difference is that a saved model can be later read back into SpecViz via the “Load” button (the “folder” icon), also under “Current Models”.

For the “Load” button to be enabled, a data (spectrum) layer (not a model layer) must be selected under “Layers” listing. The selected .yaml model file will generate a model that will be attached to a new model layer associated under the selected data layer.

The file is writen using the YAML format. Being a plain text file with a self-explanatory structure, it can be edited at will by the user, e.g., to add bounds, fixed flags, and ties to the model parameters. Note that these extra, user-defined attributes, won’t be accessible from SpecViz’s user interface. They will however, be accessible by the fitter when a fit is run on the model. They will also be written ou correctly, either when saving or exporting the model.

Note

YAML format for saved models and usage of advanced features like bounds and fixed flags are work in progress.

Export¶

This will save the model in the currently selected model layer to a file that can be directly imported by Python. The file is just a plain text file with the model expressed recorded as a Python expression. The model is associated to a variable named 'model1'.

The following example uses the 'test3.py' file name, and a model comprised of a constant and a gaussian:

>>> import test3
>>> test3
<module 'test3' from '/my/saved/models/test3.py'>
>>> test3.model1
<CompoundModel0(amplitude_0=0.297160787184, amplitude_1=2.25396100263, mean_1=15117.1710847, stddev_1=948.493577186)>
>>> print(test3.model1)
Model: CompoundModel0
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
     amplitude_0    amplitude_1      mean_1       stddev_1
    -------------- ------------- ------------- -------------
    0.297160787184 2.25396100263 15117.1710847 948.493577186

The file can be edited at will by the user, e.g., to add bounds, fixed flags, and ties to the model parameters.

Note

Security issues importing model this way into Python and usage of advanced features like bounds and fixed flags are work in progress.