heatherw3521/structmats

Computing with Vandermonde, Toeplitz, Hankel and other matrices that have special displacement structures

structmats's Issues

[rework] Error reporting

I'm not happy with how I've been handling error-reporting so far. I'd like to redesign the way that errors are caught in the overridden operators.

(currently, the implementation is very hackish and doesn't make use of matlab's inbuilt errors)

Fix error reporting in toep_apply

This seems like a small issue, but I can't get it to report errors how I want...

FIX LATER

Toeplitz Structure

Implement the basics for the Toeplitz data structure. This includes:

1. Main class with good documentation

• [DONE ] 2. Constructor
• [DONE ] 3. Elementwise operations (+, -, .*, ./)
• [ DONE ] 4. Toeplitz-vector product
• [ DONE ] 5. Toeplitz-matrix product

6. Fast Toeplitz solve

*Note: These initial implementations should be optimized, but there will be another ticket raised later to verify optimality.

FIX interaction of subsref with subscripts like "3:end" and "3:" etc.

Note ":" works, I just have to parse things that include "end". This can be done by getting the relevant dimension and substituting it in for "end".

TO DO initial implementation

1) test hm-toolbox functionality in code
2) Make Toeplitz solver work for any dimension size (currently works on powers of 2 only).
3) Make Toeplitz solver work for least squares problems
4) Normal equations for NUDFT problems (use MATLAB nuffts instead of calling finufft)
5) Add in fast matvec pack
6) Hankel matrices
7) automatically deal with multiple RHS in nudft solver
8) Arbitrary fast direct least squares solver

Figure out where @hss is

Toeps (Toeplitz Solve) is a wrapper for a function in @hss. I'm not sure where this is... Figure it out!

Future Goals

Here are some goals we set at the 4/15 meeting:

• "Nearby" function to get a close Toeplitz, Hankel, Cauchy, etc. approximation to a given matrix
• "Norms" fast norm computations for our structured matrices
• "Rank" fast eps-rank computations using theoretical results
• "IsLowRank" convenient check of whether a structured matrix is 'low' rank.
• "Toep2Cauchy" and "Hankel2Cauchy" to transform to cauchy-like matrices. The 'Toeps' code should have the Toeplitz -> Cauchylike transformation.
• Expand testing suite
• Gallery
• Rand functions for our structures
• Block compatibility

Big goal: write our own hierarchical code and build FMM

Not storing tc for circulant matrices

Figure out how to not store tr for circulant matrices without matlab getting fussy