thztools.FitResult#

class thztools.FitResult(p_opt, _p_err, p_cov, mu_opt, _mu_err, mu_cov, psi_opt, psi_cov, frfun_opt, resnorm, dof, delta, delta_norm, delta_norm_cov, epsilon, epsilon_norm, epsilon_norm_cov, delta_norm_epsilon_norm_cov, r_tls, success, diagnostic)[source]#

Dataclass for the output of fit.

Parameters:

p_optndarray: Optimal fit parameters.
p_errndarray: Uncertainty estimate for p_opt, p_err = np.sqrt(np.diag(p_cov)).

Deprecated since version 0.6.0: This option is deprecated and will be removed in version 0.8.0.
p_covndarray: Covariance matrix estimate for p_opt, determined from the curvature of the cost function at (p_opt, mu_opt). To compute one standard deviation errors on the parameters, use p_err = np.sqrt(np.diag(p_cov)).
mu_optndarray: Optimal estimate of the input waveform.
mu_errndarray: Estimated uncertainty in mu_opt, determined from the curvature of the cost function at (p_opt, mu_opt).

Deprecated since version 0.6.0: This option is deprecated and will be removed in version 0.8.0.
mu_covndarray: Covariance matrix estimate for mu_opt, determined from the curvature of the cost function at (p_opt, mu_opt). To compute one standard deviation errors of the input waveform, use mu_err = np.sqrt(np.diag(mu_cov)).
psi_optndarray: Optimal estimate of the output waveform.
psi_covndarray: Covariance matrix estimate for psi_opt. To compute one standard deviation errors of the output waveform, use psi_err = np.sqrt(np.diag(psi_cov)).
frfun_optcomplex ndarray: Estimated values of the frequency response function at non-negative frequencies.
resnormfloat: Euclidean norm (i.e., sum of the squares) of the normalized total least-squares residuals.
dofint: Number of statistical degrees of freedom, dof = n - n_p - n_a - n_b, where n is the number of samples in each waveform, n_p is the number of fit parameters in the frequency response function, and n_a + n_b is the number of real parameters necessary to specify the frequency response function at the excluded frequencies.
deltandarray: Residuals of the input waveform x, defined as x - mu_opt.
delta_normndarray: Normalized residuals of the input waveform x, defined as delta/noise_model.noise_amp(xdata).
delta_norm_covndarray: Covariance matrix estimate for delta_norm.
epsilonndarray: Residuals of the output waveform y, defined as y - psi_opt, where psi_opt = thztools.apply_frf(frfun, mu, dt=dt, args=p_opt), frfun is the parameterized frequency response function, and p_opt is the array of optimized parameters.
epsilon_normndarray: Normalized residuals of the output waveform y, defined as epsilon/noise_model.noise_amp(ydata).
epsilon_norm_covndarray: Covariance matrix estimate for epsilon_norm.
delta_norm_epsilon_norm_covndarray: Cross-covariance matrix of the normalized residuals delta_norm and epsilon_norm.
r_tlsndarray: Normalized total least-squares residuals.
successbool: True if one of the convergence criteria is satisfied.
diagnosticscipy.optimize.OptimizeResult: Instance of scipy.optimize.OptimizeResult returned by scipy.optimize.least_squares.

Attributes

p_opt	(ndarray) Optimal fit parameters.
p_err	(ndarray) Uncertainty estimate for `p_opt`, `p_err = np.sqrt(np.diag(p_cov))`.
p_cov	(ndarray) Covariance matrix estimate for `p_opt`, determined from the curvature of the cost function at `(p_opt, mu_opt)`. To compute the standard errors for the parameters, use `p_err = np.sqrt(np.diag(p_cov))`.
mu_opt	(ndarray) Optimal estimate of the input waveform.
mu_err	(ndarray) Estimated uncertainty in `mu_opt`, determined from the curvature of the cost function at `(p_opt, mu_opt)`.
mu_cov	(ndarray) Covariance matrix estimate for `mu_opt`, determined from the curvature of the cost function at `(p_opt, mu_opt)`. To compute the standard errors for the input waveform, use `mu_err = np.sqrt(np.diag(mu_cov))`.
psi_opt	(ndarray) Optimal estimate of the output waveform.
psi_cov	(ndarray) Covariance matrix estimate for `psi_opt`. To compute the standard errors for the output waveform, use `psi_err = np.sqrt(np.diag(psi_cov))`.
frfun_opt	(complex ndarray) Estimated values of the frequency response function at non-negative frequencies.
resnorm	(float) Euclidean norm (i.e., sum of the squares) of the normalized total least-squares residuals.
dof	(int) Number of statistical degrees of freedom, `dof = n - n_p - n_a - n_b`, where `n` is the number of samples in each waveform, `n_p` is the number of fit parameters in the frequency response function, and `n_a + n_b` is the number of real parameters necessary to specify the frequency response function at the excluded frequencies.
delta	(ndarray) Residuals of the input waveform `x`, defined as `x - mu_opt`.
delta_norm	(ndarray) Normalized residuals of the input waveform `x`, defined as `delta/noise_model.noise_amp(xdata)`.
delta_norm_cov	(ndarray) Covariance matrix estimate for `delta_norm`.
epsilon	(ndarray) Residuals of the output waveform `y`, defined as `y - psi_opt`, where `psi_opt = thztools.apply_frf(frfun, mu, dt=dt, args=p_opt)`, `frfun` is the parameterized frequency response function, and `p_opt` is the array of optimized parameters.
epsilon_norm	(ndarray) Normalized residuals of the output waveform `y`, defined as `epsilon/noise_model.noise_amp(ydata)`.
epsilon_norm_cov	(ndarray) Covariance matrix estimate for `epsilon_norm`.
delta_norm_epsilon_norm_cov	(ndarray) Cross-covariance matrix of the normalized residuals `delta_norm` and `epsilon_norm`.
r_tls	(ndarray) Normalized total least-squares residuals.
success	(bool) True if one of the convergence criteria is satisfied.
diagnostic	(scipy.optimize.OptimizeResult) Instance of `scipy.optimize.OptimizeResult` returned by `scipy.optimize.least_squares`.