Hello everyone,
for the past months we have been working on making recursive matrices
work in eigen. Here is an example:
SparseMatrix<Matrix<double,4,3>> A;
Matrix<Matrix<double,4,1>,-1,1> x,b;
x = A * b;
The obvious advantage is that we get support for block matrices on all
eigen types for "free" ( DiagonalMatrix,TriangularView,LDLT,...). After
some testing, the performance appeared to be "better than expected" and
we have decided to write a paper on how to apply recursive matrices on
non-linear least squares problems. The paper is accepted and will be
published at HPG in July. Here is the current version:
https://cloud9.cs.fau.de/index.php/s/UINyrgAUtaAiWvR
Unfortunately there are two limitations which I was not able to fix.
1. All inner matrix types require an additional wrapper class, which I
have called "MatrixScalar". The matrix A from above is then:
SparseMatrix<MatrixScalar<Matrix<double,4,3>>> A;
2. Some eigen kernels do not work directly. For example, some operations
use the function scaleAndAddTo(..., Scalar(1)), which does not work if
"Scalar" is a recursive matrix type. To fix this I had to specialize a
lot of eigen kernels, which creates redundancy with only minor changes.
So here are my questions to you:
What do you think about this idea?
Do you think a deep integration into eigen would be possible? (Without
recursive specializations and without "MatrixScalar" class)
The code can be found here:
https://github.com/darglein/EigenRecursive
Example for sparse block-matrices:
https://github.com/darglein/EigenRecursive/blob/master/samples/sparseOperators/sparseOperators_main.cpp
With best regards,
Darius
--
Darius Rueckert
Informatik 9 (Graphische Datenverarbeitung) http://lgdv.tf.fau.de
Universitaet Erlangen-Nuernberg, Cauerstraße 11, 91058 Erlangen
