Optimization (Module)

This module stores classes and functions which are used for performing mathematical optimizations, a critical component of a Lomb-Scargle-based pre-whitening routine.

models

pywhiten.optimization.models stores all the functions used for optimizations. These are listed below.

  • chisq(data:numpy.array, model:numpy.array, err:numpy.array)->float | Returns the chi squared of the provided model.
  • sin_model(x:numpy.array, f:float, a:float, p:float) -> numpy.array | A sinusoidal model of the form f(x) = a*sin(2*pi*(fx+p))
  • cos_model(x:numpy.array, f:float, a:float, p:float) -> numpy.array | A (co-)sinusoidal model of the form f(x) = a*cos(2*pi*(fx+p))

  • n_sin_model(x:numpy.array, *params:float) -> numpy.array | A model consisting of n superimposed sinusoidal models from sin_model. *params must be of the form: *frequencies, *amplitudes, *phases, zero point, and therefore will be of length 3n+1.

  • n_cos_model(x:numpy.array, *params:float) -> numpy.array | A model consisting of n superimposed sinusoidal models from cos_model. *params must be of the form: *frequencies, *amplitudes, *phases, zero point, and therefore will be of length 3n+1.

  • n_model_poly(x:np.array, *params:float) -> np.array | A polynomial model of order n. *params must contain the polynomial coefficients and must of length n+1. The model is evaluated as f(x) = params[0] + x * params[1] + x^2 * params[2] ... x^n * params[n].

  • slf_noise(x:np.array, *params) -> np.array | The Bowman et al. (2019) SLF variability model. *params must be of the form [x0, alpha_0, gamma, Cw].

class Optimizer

A class which handles chi-squared minimization of single-frequency and multi-frequency sinusoidal models.

Attributes:

  • function sf_func | A sinusoidal function taking arguments of the format f(x:numpy.array, f:float, a:float, p:float) used for single-frequency optimizations and summed for multi-frequency optimizations (when using LMFit as the optimization engine, which is the only option at present).

  • function mf_func | A function taking arguments of the format x:ndarray, pars, where pars is an arbitrarily large set of floats arranged such that it contains a group of frequency guesses followed by a group of amplitude guesses followed by a group of phase guesses followed by a guess for the zero point. The frequency, amplitude, and phase guesses must be of equal size, meaning *pars should be of length 3n+1 where n is some positive integer. Not currently used for optimization, but left in case the scipy option for minimization is re-implemented.

  • dict cfg | A configuration dictionary.
  • c_zp | The zero point value of the last fit performed with this object.

Methods

__init__(cfg : dict)

Constructor for this object. Requires a configuration dictionary, and sets up the fitting functions.

Args:

  • dict cfg | A configuration dictionary.

single_frequency_optimization(x: numpy.array, data: numpy.array, err: numpy.array, f0: float, a0: float, p0: float)

Determines optimized parameters for a fit of a sinusoidal model to an x-y dataset.

Args:

  • numpy.array x | x-axis of data to be fit
  • numpy.array data | y-axis of data to be fit
  • numpy.array err | y-axis weights of data to be fit
  • float f0 | An initial guess for the model frequency
  • float a0 | An initial guess for the model amplitude
  • float p0 | An initial guess for the model phase

Returns:

  • float | The optimized model frequency
  • float | The optimized model amplitude
  • float | The optimized model phase
  • numpy.array | The optimized single-frequency model evaluated at all values of x

multi_frequency_optimization(x: numpy.array, data: numpy.array, err: numpy.array, freqs: list)

Determines the optimized parameters for a fit of a composite sinusoidal model to an x-y dataset, and updates parameters in place. Sets the c_zp attribute to the optimized value when the fit is complete as well.

Args:

  • numpy.array x | x-axis of data to be fit
  • numpy.array data | y-axis of data to be fit
  • numpy.array err | y-axis weights of data to be fit
  • list freqs | A list of pywhiten.data.Frequency objects. The values of f, a, and p for these objects are used as the initial guesses for the fit. When the optimization is complete, the Frequency object parameters are updated in-place.

Returns:

  • numpy.array | The optimized multi-frequency model evaluated at all values of x