# normws

Computes the weighted Schatten p-norm (WS,P).

## Contents

- Syntax
- Description
- Input Arguments
- More About
- See Also
- Code

## 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

- innerhs.html

## 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