Re: [ublas] Fwd: [GSOC2015] uBLAS Matrix Solver Project

Subject: Re: [ublas] Fwd: [GSOC2015] uBLAS Matrix Solver Project
From: Rajaditya Mukherjee (rajaditya.mukherjee_at_[hidden])
Date: 2015-03-09 14:56:53

HI Nasos,

Thanks for your inputs and your valuable suggestions regarding the style. I
have a few comments :

1) As a library which chooses to emulate BLAS and LAPACK fortran style libs
with a header only format, I plan to emulate the API functionality of the
existing implementations of lu solver.

2) I am not so sure about the parallel implementations. I think as per a
previous suggestion, it will be more useful to apply bindings to
High-Performance BLAS implementations like Intel-MKL which has platform
specific parallelism optimized for the architecture. They will be faster
than generic C++ std::threads implementations.

3) I plan to focus for now on the dense implementations for a matured
eigensolver class. Sparse EigenSolvers are almost completely monopolized by
ARPACK and it can be added as a optional time-available module.(Though I
agree that it will be extremely useful specially for subspace FEA)

*Rajaditya Mukherjee *
*3rd Year Graduate Student*
Dept. of Computer Science and Engineering
The Ohio State University
Columbus, Ohio
Tel :- [phone]
email :- rajaditya.mukherjee_at_[hidden] <mukherjee.62_at_[hidden]>,
raj_at_[hidden] <mukherjr_at_[hidden]>

On Mon, Mar 9, 2015 at 11:34 AM, Nasos Iliopoulos <nasos_i_at_[hidden]>
wrote:

>  This is a good list of potential matrix operations. I would add a sparse
> LU decomposition also. For performance optimization on  sparse containers I
> would suggest to focus on the a couple  types in uBlas and not all of them
> (at least compressed_matrix). FYI most applications (like FEA for example)
> are using sparse matrices with dense vectors and combinations like sparse
> matrix/sparse vector are less important.
>
> Two more items you may want to consider:
> 1. It would really add value to your proposal to include examples or
> architectural considerations of how those would integrate with uBlas. Since
> uBlas promotes a functional style, the same would be appropriate for the
> solvers interface. The simpler the interface the better.
>
> 2. Consider implementing parallel implementations using std::thread (or
> whatever from C++11 is appropriate).
>
> 3. Callback control for larger systems so that the solver can signal its
> caller about it's progress, or for other control reasons (i.e. stopping the
> solver). This should not interfere with performance and should probably
> implemented using some sort of static dispatch so that the user can choose
> which version to use ( with or without callback functions). Please note
> that those callbacks should probably be implemented using std::function.
>
> Please take a look at the last years proposals on how to draft yours
> because laying down your ideas is as crucial as your intention and
> capabilities to implement them.
>
> Regards,
> Nasos
>
>
>
> On 03/06/2015 10:30 AM, Rajaditya Mukherjee wrote:
>
>  Hi,
>
>  My name is Raj and I am Phd student in Computer Graphics. I am
> interested in tackling the problem of uBLAS Matrix Solver and in order to
> write my proposal, I am looking for inputs for which of the following
> algorithms will be most useful for prospective users in boost-numeric
> library. Here is a categorical list of all the prospective ones which will
> bring uBLAS updated to other commercial libraries like Eigen/Armadillo.
> Please let me know your preferences....
>
>  *David Bellot* : As a potential mentor, do you have any specific
> additions or deletions for this list? This could also be useful for other
> candidates pursuing this project.
>
>  *DENSE SOLVERS AND DECOMPOSITION* :
> 1) *QR Decomposition* - *(Must have)* For orthogonalization of column
> spaces and solutions to linear systems. (Bonus : Also rank revealing..)
> 2) *Cholesky Decomposition* - *(Must have)* For symmetric Positive
> Definite systems often encountered in PDE for FEM Systems...
> 3) *Householder Method* - Conversion to tridiagonal form for eigen
> solvers.
>
>  *SPARSE SOLVERS AND PRECONDITIONERS* :
> 1) *Conjugate Gradient* - *(Must have)* For symmetric Positive Definite
> systems, this is the kryvlov space method of choice. Both general and
> preconditioned variants need to be implemented for convergence issues.  2)
> *BiCGSTAB* *(Needs introspection)* - For non symmetric systems..
> 3) *Incomplete Cholesky Decomposition* *(Good to have)* - For symmetric
> Positive definite sparse matrices, to be used as preconditioner as
> extension to (1) for preconditioned CG Methods ...
> 4) *Jacobi Preconditioner* *(Must have)* - As prerequisite for step(1).
>
>  *EIGEN DECOMPOSITION MODULES (ONLY FOR DENSE MODULES)**:*
> 1) *Symmetric Eigen Values* - *(Must have)* Like SSYEV Module in Lapack -
> That is first reduction to a tridiagonal form using Householder then using
> QR Algorithm for Eigen Value computation.
> 2) *NonSymmetric Eigen Values* - *(Good to have)* Like SGEEV module in
> Lapack - using Schur decompositions as an intermediate step in the above
> algorithm.
> 3) *Generalized Eigen Values* - *(needs introspection)* I use this in my
> research a lot and its a good thing to have..
>
>  ** Computing Eigen Decomposition of sparse modules needs special robust
> numerical treatment using implicitly restarted arnoldi iterations and may
> be treated as optional extensions.
>
>
>
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