A (coarse) feature matrix of LAWA
In principle LAWAcan be divided in two main building blocks. General Wavelet Basis Constructions for different domains and adaptive wavelet algorithms.
Wavelets / Basis Constructions
LAWA is organized with respect to several rather orthogonal criteria. These are mostly reflected by different template parameters. We show a summary of all currently available realizations of wavelet bases and some outlook.
First we take a look at the realizations of biorthogonal wavelet constructions available. The whole library is centered around biorthogonal wavelets; this is indeed the main focus.
|
domain |
construction |
status |
|
R |
CDF |
final |
|
Periodic |
CDF |
final |
|
Interval |
DKU, Primbs, Dijkema |
some minor polishing necessary |
|
|
based on interval bases |
working |
|
more general domain |
based on interval bases |
to be done yet (middle p.) |
For all these biorthogonal wavelet constructions we realized both the primal and the corresponding duals for the B-splines and the wavelets.
LAWA provides different kinds of wavelets:
|
kind of wavelets |
domain |
construction |
status |
|
orthogonal |
R |
Daubechies |
just coefficients, final |
|
orthogonal |
|
Multiwavelets |
polishing to be done |
|
biorthogonal |
see table above |
see table above |
see table above |
|
semiorthogonal |
Interval |
BU |
to be done yet (high p.) |
For the n-dimensional cube, and therefor especially also for the interval, homogeneous Dirichlet boundary conditions or no/free boundary conditions have been realized. Other boundary conditions could be easily added. Just a matter of implementation time.
Adaptive realizations
not documented yet ...