ConjugateSpectrum

class screens.conjspec.ConjugateSpectrum(conjspec, tau, fd, noise=None, d_eff=None, mu_eff=None, theta=None, magnification=None)

Bases: object

Conjugate spectrum and methods to fit it.

The code is meant to be agnostic to which axes are which, but some may assume a shape of (..., doppler_axis, delay_axis).

Parameters:

conjspecndarray

Fourier transform of a dynamic spectrum.

fdQuantity

Doppler factors of the conjugate spectrum. Normally time conjugate but can be arbitrary (e.g., conjugate of f*t). Should have the the proper shape to broadcast with conjspec.

tauQuantity

Delays of the conjugate spectrum. Should have the proper shape to broadcast with dynspec.

noisefloat

The uncertainty in the real and imaginary components of the conjugate spectrum.

d_effQuantity

Assumed effective distance. This is used throughout and not fit, but can be treated as a scaling parameters.

mu_effQuantity, optional

Initial guess for the effective proper motion, v_eff/d_eff.

thetaQuantity, optional

Grid of theta angles to use for modelling the dynamic spectrum. Probably more usefully calculated later using theta_grid.

magnificationQuantity, optional

Magnifications at each theta. More typically inferred by fitting the secondary spectrum.

Attributes Summary

secspec

Secondary spectrum, i.e., the power of the conjugate spectrum.

Methods Summary

from_dynamic_spectrum(dynspec[, normalization])	Create a conjugate spectrum from a dynamic one.
locate_mu_eff([mu_eff_trials, power, verbose])	Try reproducing the secondary spectrum for a range of proper motion.
model([magnification, mu_eff, conserve])	Calculate the expected conjugate spectrum for given parameters.
theta_grid([oversample_tau, oversample_fd])	Calculate a grid of theta for modelling the secondary spectrum.
theta_theta([mu_eff, conserve, theta_grid])	Project the secondary spectrum into theta-theta space.

Attributes Documentation

secspec

Secondary spectrum, i.e., the power of the conjugate spectrum.

Methods Documentation

classmethod from_dynamic_spectrum(dynspec, normalization='mean', **kwargs)

Create a conjugate spectrum from a dynamic one.

Easiest if the input is a DynamicSpectrum instance.

By passing in an explicit time axis using t, one can get a different delay factor conjugate. Particularly useful with t=f*t, which takes into account the frequency dependence of the time variation of scintles.

Note that the dynamic spectrum is assumed to have shape (..., time_axis, frequency_axis).

Parameters:

dynspecarray_like or DynamicSpectrum

Input dynamic spectrum for which the fourier transform will be calculated. If it has attributes f, t, d_eff, theta, magnification, and noise, those will be used as default inputs. TODO: noise is likely wrong!

normalization‘mean’ or None

Normalize such that the 0, 0 element equals the mean of the dynamic spectrum.

**kwargs

Other arguments to initialize the conjugate spectrum.

locate_mu_eff(mu_eff_trials=None, power=True, verbose=False)

Try reproducing the secondary spectrum for a range of proper motion.

For each proper motion, construct a theta-theta array, calculte the largest eigenvalue and use the corresponding eigenvector as the model one-dimensional screen.

Parameters:

mu_eff_trialsQuantity

Proper motions to try.

powerbool

Whether to just decompose the powers or the full complex secondary spectrum. The former is faster and varies less quickly with proper motion, so can be used to find the global minimum before re-running on the full complex values.

verbosebool

Whether or not to give summary statistics for each trial.

Returns:

curvatureQTable

Table with the following columns: - mu_eff : Input proper motions. - theta : grid in theta used. - w : Largest eigenvalue. - recovered : corresponding eigenvector, i.e., magnifications. - th_ms : Mean-square residual in theta-theta space. - ndof : degrees of freedom n_dynspec - n_theta - 2. - redchi2 : reduced chi2 ((dynspec - model)/noise)**2/ndof.

Notes

The resulting table is also stored on the instance, as curvature.

Note that the noise in the secondary spectrum is currently ignored.

model(magnification=None, mu_eff=None, conserve=False)

Calculate the expected conjugate spectrum for given parameters.

theta_grid(oversample_tau=2, oversample_fd=4, **kwargs)

Calculate a grid of theta for modelling the secondary spectrum.

Wraps screens.fields.theta_grid with defaults from the class. See that function for details. Oversampling is set relatively high here, since covariances between the theta are not as important as for fitting a dynamic spectrum.

Note that this does not set the angles on the class, so typical usage is ds.theta = ds.theta_grid().

theta_theta(mu_eff=None, conserve=False, theta_grid=True, **kwargs)

Project the secondary spectrum into theta-theta space.

For a given grid in theta (possibly calculated) and a set of pairs found using screens.fields.theta_theta_indices, interpolate in the secondary spectrum to find the theta-theta arrays.

Parameters:

mu_effQuantity, optional

Effective proper motion to use. Defaults to that stored on the instance. Will update the instance if given.

conservebool

Whether to conserve flux per surface area. Doing so reduces sensitivity to points near the axes, but means one cannot directly use any eigenvectors directly in constructing dynamic spectra.

theta_gridbool, optional

Whether to calculate a new theta grid, or use the one stored on the instance. By default, calculate it only if mu_eff is passed in. If True, this will update the grid stored on the instance.

**kwargs

Any further arguments are passed on to theta_grid