# l2norm¶

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 in wv.

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