normws
Computes the weighted Schatten p-norm (WS,P).
Contents
Syntax
normA = normws(A,seti)
Description
normA = normws(A,seti) computes the weighted Schatten p-Norm. The weight is seti.dSMeas and p is seti.pNorm.
Input Arguments
- A : Complex matrix of size seti.measNb x seti.incNb.
- seti.pNorm : Schatten p-Norm with p = seti.pNorm.
- seti.dSMeas : Approximation of the infinitesimal element of a closed contour with control points. See also expSetup.html, pntsGeometry.html, and dS2D.html.
More About
Notation
- WS: weighted Schatten norm (case pNorm ~= 2)
- HS: WS,2 (case pNorm == 2): weighted Schatten 2-norm is weighted Hilbert-Schmidt norm (WHS)
- Keep in mind: dSMeas is in HS-Norm:
See Also
Code
function normA = normws(A,seti) if seti.pNorm == 2 normA = sqrt(abs(innerhs(A,A,seti))); % Norm which is induced by innerhs ($\langle A,B \rangle_\mathrm{dis}$). else S = svd(diag(seti.dSMeas^(1/seti.pNorm))*A); normA = norm(S,seti.pNorm); end end