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