gftool.linearprediction.pcoeff_covar
- gftool.linearprediction.pcoeff_covar(x, order: int, rcond=None)[source]
Calculate linear prediction (LP) coefficients using covariance method.
The covariance method gives the equation
\[Ra = X^†X a = X^†x = -r\]where \(R\) is the covariance matrix and \(a\) are the LP coefficients. We solve \(Xa = x\) using linear least-squares.
- Parameters:
- x(…, N) complex np.ndarray
Data of the (time) series to be predicted.
- orderint
Prediction order, has to be smaller then N; for
order>N//2the system is under-determined.- rcondfloat, optional
Cut-off ratio for small singular values of a. For the purposes of rank determination, singular values are treated as zero if they are smaller than rcond times the largest singular value of a.
- Returns:
- a(…, order) complex np.ndarray
Prediction coefficients.
- rho(…) float np.ndarray
Error estimate \(‖x - Xa‖_2\).
- Raises:
- ValueError
If the prediction order is not smaller than the number of data points N.