l2normΒΆ
Computes the L-2 norm of a complex valued function.
\[\mathcal{L}_2 = \left(\int_{-\infty}^\infty ||\mathbf{F}(i\omega)||^2_{F2}\,d\omega\right)^{0.5}\]
where \(||\mathbf{F}(i\omega)||_{F2}\) refers to teh Frobenius norm calculated by
sharpy.utils.frequencyutils.frobenius_norm().
- param y_freq
Complex valued function.
- type y_freq
np.ndarray
- param wv
Frequency array.
- type wv
np.ndarray
- param **kwargs
Key word arguments for max and min frequencies. See below.
- Keyword Args
vmin (float): Lower bound value to find index in
wv. vmax (float): Upper bound value to find index inwv.
- returns
L-2 norm of
y_freq.- rtype
float
References
Antoulas, A. Approximation to Large Scale Dynamical Systems. SIAM 2005. Ch 5, Eq 5.10, pg 126