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:

  1. Select the layer you wish to operate on from the “Layer List” window in the bottom left. For example, you can choose the layer containing your emission or absorption line.
  2. Create and position a region of interest (ROI) as described in the Viewer section of the documentation.
  3. Select the desired model from the Add Model drop-down box and click Select to add it to Current Models.
  4. If desired, repeat the above step to add additional models.
  5. A new model layer will be created under your data layer in the “Layer List” window.

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

  1. Select the model layer in the “Layer List” window that contains the desired model.
  2. If desired, double-click on the model name to rename it. When you see a blinking cursor, enter its new name and press “Enter”.
  3. Expand the model listing under Current Models on the right of the viewer.
  4. 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:

  1. Select the model layer under Layers that contains the model(s) you wish to fit to your data.
  2. 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.
  3. Select the desired fitter from Fitting using its drop-down menu.
  4. Click Perform Fit. This may take up to a few seconds, depending on the complexity of the fit.
  5. 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 found 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 a 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. When a model is saved as a file on disk, it can later be read into SpecViz as described below. 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. Provide a name for the model file, if this file name does not end with the correct suffix, the suffix will automatically be appended. Click “Save”, or just press 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”, whereas the exported model cannot.

For the “Load” button to be enabled, a data (spectrum) layer (not a model layer) must be selected in the “Layer List” window. The selected .yaml model file will generate a model that will be attached to a new model layer associated with the selected data layer.

The file is writen in 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 used by the fitter when a fit is run on the model. They will also be written out 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 given as a Python expression. The model is associated 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 by the user, e.g., to add bounds, fixed flags, and ties to the model parameters.

Warning

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