astra.contrib.thecannon.fitting

Fitting functions for use in The Cannon.

Module Contents

Functions

fit_spectrum(flux, ivar, initial_labels, vectorizer, theta, s2, fiducials, scales, dispersion=None, use_derivatives=True, op_kwds=None) Fit a single spectrum by least-squared fitting.
fit_theta_by_linalg(flux, ivar, s2, design_matrix) Fit theta coefficients to a set of normalized fluxes for a single pixel.
chi_sq(theta, design_matrix, flux, ivar, axis=None, gradient=True) Calculate the chi-squared difference between the spectral model and flux.
L1Norm_variation(theta) Return the L1 norm of theta (except the first entry) and its derivative.
fit_pixel_fixed_scatter(flux, ivar, initial_thetas, design_matrix, regularization, censoring_mask, **kwargs) Fit theta coefficients and noise residual for a single pixel, using
astra.contrib.thecannon.fitting.fit_spectrum(flux, ivar, initial_labels, vectorizer, theta, s2, fiducials, scales, dispersion=None, use_derivatives=True, op_kwds=None)

Fit a single spectrum by least-squared fitting.

Parameters:
  • flux – The normalized flux values.
  • ivar – The inverse variance array for the normalized fluxes.
  • initial_labels – The point(s) to initialize optimization from.
  • vectorizer – The vectorizer to use when fitting the data.
  • theta – The theta coefficients (spectral derivatives) of the trained model.
  • s2 – The pixel scatter (s^2) array for each pixel.
  • dispersion – [optional] The dispersion (e.g., wavelength) points for the normalized fluxes.
  • use_derivatives – [optional] Boolean True indicating to use analytic derivatives provided by the vectorizer, None to calculate on the fly, or a callable function to calculate your own derivatives.
  • op_kwds – [optional] Optimization keywords that get passed to scipy.optimize.leastsq.
Returns:

A three-length tuple containing: the optimized labels, the covariance matrix, and metadata associated with the optimization.
astra.contrib.thecannon.fitting.fit_theta_by_linalg(flux, ivar, s2, design_matrix)

Fit theta coefficients to a set of normalized fluxes for a single pixel.

Parameters:
  • flux – The normalized fluxes for a single pixel (across many stars).
  • ivar – The inverse variance of the normalized flux values for a single pixel across many stars.
  • s2 – The noise residual (squared scatter term) to adopt in the pixel.
  • design_matrix – The model design matrix.
Returns:

The label vector coefficients for the pixel, and the inverse variance matrix.
astra.contrib.thecannon.fitting.chi_sq(theta, design_matrix, flux, ivar, axis=None, gradient=True)

Calculate the chi-squared difference between the spectral model and flux.

Parameters:
  • theta – The theta coefficients.
  • design_matrix – The model design matrix.
  • flux – The normalized flux values.
  • ivar – The inverse variances of the normalized flux values.
  • axis – [optional] The axis to sum the chi-squared values across.
  • gradient – [optional] Return the chi-squared value and its derivatives (Jacobian).
Returns:

The chi-squared difference between the spectral model and flux, and optionally, the Jacobian.
astra.contrib.thecannon.fitting.L1Norm_variation(theta)

Return the L1 norm of theta (except the first entry) and its derivative.

Parameters:theta – An array of finite values.
Returns:A two-length tuple containing: the L1 norm of theta (except the first entry), and the derivative of the L1 norm of theta.
astra.contrib.thecannon.fitting.fit_pixel_fixed_scatter(flux, ivar, initial_thetas, design_matrix, regularization, censoring_mask, **kwargs)

Fit theta coefficients and noise residual for a single pixel, using an initially fixed scatter value.

Parameters:
  • flux – The normalized flux values.
  • ivar – The inverse variance array for the normalized fluxes.
  • initial_thetas – A list of initial theta values to start from, and their source. For example: `[(theta_0, “guess”), (theta_1, “old_theta”)]
  • design_matrix – The model design matrix.
  • regularization – The regularization strength to apply during optimization (Lambda).
  • censoring_mask – A per-label censoring mask for each pixel.
Keyword Arguments:
 
  • op_method – The optimization method to use. Valid options are: l_bfgs_b, powell.
  • op_kwds – A dictionary of arguments that will be provided to the optimizer.
Returns:

The optimized theta coefficients, the noise residual s2, and metadata related to the optimization process.