Mu Analysis and Synthesis Toolbox

Perform a singular value decomposition, spectral radius and Schur decomposition of a CONSTANT or VARYING matrix

Syntax

• s = vsvd(matin) 
  [u,s,v] = vsvd(matin) 
  out = vrho(matin) 
  t = vschur(matin) 
  [u,t] = vschur(matin)
  

Description
vsvd performs a singular value decomposition on a VARYING matrix. It is identical to MATLAB's svd routine, and will work on CONSTANT matrices as well. If there is one output argument, the output is a VARYING matrix with the singular values of matin at each point. If there are three output arguments, [u,s,v], then u is a VARYING matrix with the left singular vectors, s is a VARYING matrix with the singular values, and v is a VARYING matrix with the right singular vectors.

vrho finds the spectral radius, max(abs(eig(xtracti(matin,i)))), at each independent variable of a VARYING matrix.

vschur computes the Schur form of a VARYING matrix for each independent variable. It is identical to the MATLAB schur command, but also works on VARYING matrices. Given two output arguments, vschur returns two VARYING matrices u and t. t corresponds to the Schur form matrix and u is a VARYING unitary matrix such that

• matin = mmult(u,t,vcjt(u))
  

Examples
Construct a random VARYING matrix and find its singular values.

• see(matin)
  2 rows                   2 columns
  
  iv = 0.1
      0.93040.5269
      0.84620.0920
  iv = 0.4
      0.65390.7012
      0.41600.9103
  [u,s,v] = vsvd(matin);
  see(u)
  2 rows      2 columns
  iv = 0.1
  0.7884      0.6152
  0.6152     -0.7884
  
  iv = 0.4
  0.6909     -0.7229
  0.7229      0.6909
  see(s)
  
  iv = 0.1
  1.3400      0.2689
  
  iv = 0.4
  1.3681      0.2219
  see(v)
  2 rows      2 columns
  
  iv = 0.1
  0.9359     -0.3522
  0.3522      0.9359
  
  iv = 0.4
  0.5501     -0.8351
  0.8351      0.5501
  

Algorithm
vrho, vschur, and vsvd call the MATLAB commands svd, eig, and schur

See Also
eig, hess, pkvnorm, mu, qz, schur, svd, veig, vnorm

vpoly, vroots

vzoom