fcond=framebounds(F); [A,B]=framebounds(F); [...]=framebounds(F,Ls);
framebounds(F) calculates the ratio \(B/A\) of the frame bounds of the frame given by F. The length of the system the frame bounds are calculated for is given by L=framelength(F,1).
framebounds(F,Ls) additionally specifies a signal length for which the frame should work. The actual length used is L=framelength(F,Ls).
[A,B]=framebounds(F) returns the frame bounds A and B instead of just their ratio.
'framebounds` accepts the following optional parameters:
| 'fac' | Use a factorization algorithm. The function will throw an error if no algorithm is available. |
| 'iter' | Call eigs to use an iterative algorithm. |
| 'full' | Call eig to solve the full problem. |
| 'auto' | Choose the fac method if possible, otherwise use the full method for small problems and the iter method for larger problems. This is the default. |
| 'crossover',c | Set the problem size for which the 'auto' method switches between full and iter. Default is 200. |
The following parameters specifically related to the iter method:
| 'tol',t | Stop if relative residual error of eigs is less than the specified tolerance. Default is 1e-9 |
| 'maxit',n | Do at most n iterations in eigs. Default is 100. |
| 'pcgtol',t | Stop if relative residual error of pcg is less than the specified tolerance. Default is 1e-6 |
'pcgmaxit=n Do at most n iterations in pcg. Default is 150.'
| 'p',p | The number of Lanzcos basis vectors to use. More vectors will result in faster convergence, but a larger amount of memory. The optimal value of p is problem dependent and should be less than L. The default value chosen automatically by eigs. |
| 'print' | Display the progress. |
| 'quiet' | Don't print anything, this is the default. |