plot_projection_error()#
- PODBasis.plot_projection_error(threshold=None, right: int = None, ax: Axes = None, **options)[source]#
Plot the relative projection error of the training snapshots as a function of the basis size.
The relative projection error for the rank-\(r\) POD basis corresponding to the training snapshot matrix \(\Q\in\RR^{n\times k}\) is defined by
\[\rho_r = \frac{\|\Q - \Vr\Vr\trp\Q\|_{F}}{\|\Q\|_{F}},\]where \(\Vr\in\RR^{n \times r}\) are the basis entries. This method plots \(\rho_r\) as a function of \(r\); \(\rho_r\) is calculated via the singular values:
\[\rho_r = \sqrt{\frac{\sum_{j = r + 1}^{\ell}\sigma_{j}^{2}}{ \sum_{j=1}^{\ell}\sigma_{j}^{2}}}\]- Parameters:
- thresholdfloat or list[float] or None
Cutoff value(s) to mark on the plot.
- rightint or None
Maximum singular value index to plot (
plt.xlim(right=right)).- axmatplotlib.Axes or None
Axes to plot on. If
None(default), a new single-axes figure is created.- optionsdict
Options to pass to
matplotlib.pyplot.semilogy().
- Returns:
- axmatplotlib.Axes
Axes for the plot.
Notes
This method shows the projection error of the training snapshots. See
projection_error()to calculate the projection error for an arbitrary snapshot or collection of snapshots.