<div dir="ltr"><div class="gmail_default" style="font-family:courier new,monospace">HI Nasos, </div><div class="gmail_default" style="font-family:courier new,monospace"><br></div><div class="gmail_default" style="font-family:courier new,monospace">Thanks for your inputs and your valuable suggestions regarding the style. I have a few comments : </div><div class="gmail_default" style="font-family:courier new,monospace"><br></div><div class="gmail_default" style="font-family:courier new,monospace">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. </div><div class="gmail_default" style="font-family:courier new,monospace"><br></div><div class="gmail_default" style="font-family:courier new,monospace">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. </div><div class="gmail_default" style="font-family:courier new,monospace"><br></div><div class="gmail_default" style="font-family:courier new,monospace">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) </div></div><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature"><div dir="ltr"><font face="courier new, monospace"><b>Rajaditya Mukherjee
</b></font><div><font face="courier new, monospace"><i>3rd Year Graduate Student</i> <br>Dept. of Computer Science and Engineering <br>The Ohio State University<br>Columbus, Ohio <br></font></div>
<div><font face="courier new, monospace">Tel :- +1-(614)-271-4439</font></div>
<div><font face="courier new, monospace">email :- <a href="mailto:mukherjee.62@osu.edu" target="_blank">rajaditya.mukherjee@gmail.com</a>,<a href="mailto:mukherjr@cse.ohio-state.edu" target="_blank">raj@rajaditya.com</a></font></div><div><br></div></div></div></div>
<br><div class="gmail_quote">On Mon, Mar 9, 2015 at 11:34 AM, Nasos Iliopoulos <span dir="ltr"><<a href="mailto:nasos_i@hotmail.com" target="_blank">nasos_i@hotmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000">
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.<br>
<br>
Two more items you may want to consider:<br>
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.<br>
<br>
2. Consider implementing parallel implementations using std::thread
(or whatever from C++11 is appropriate).<br>
<br>
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.<br>
<br>
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.<br>
<br>
Regards,<br>
Nasos<div><div class="h5"><br>
<br>
<br>
<div>On 03/06/2015 10:30 AM, Rajaditya
Mukherjee wrote:<br>
</div>
</div></div><blockquote type="cite"><div><div class="h5">
<div dir="ltr">
<div class="gmail_default" style="font-family:courier new,monospace">Hi, <br>
</div>
<div class="gmail_quote">
<div dir="ltr">
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace">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.... </div>
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace"><b>David
Bellot</b> : 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. </div>
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace"><u>DENSE
SOLVERS AND DECOMPOSITION</u> : </div>
<div style="font-family:courier new,monospace">1) <b>QR
Decomposition</b> - <i>(Must have)</i> For
orthogonalization of column spaces and solutions to linear
systems. (Bonus : Also rank revealing..) </div>
<div style="font-family:courier new,monospace">2) <b>Cholesky
Decomposition</b> - <i>(Must have)</i> For symmetric
Positive Definite systems often encountered in PDE for FEM
Systems... </div>
<div style="font-family:courier new,monospace">3) <b>Householder
Method</b> - Conversion to tridiagonal form for eigen
solvers. </div>
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace"><u>SPARSE
SOLVERS AND PRECONDITIONERS</u> : </div>
<div style="font-family:courier new,monospace">1) <b>Conjugate
Gradient</b> - <i>(Must have)</i> 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) <b>BiCGSTAB</b> <i>(Needs
introspection)</i> - For non symmetric systems.. </div>
<div style="font-family:courier new,monospace">3) <b>Incomplete
Cholesky Decomposition</b> <i>(Good to have)</i> - For
symmetric Positive definite sparse matrices, to be used as
preconditioner as extension to (1) for preconditioned CG
Methods ... </div>
<div style="font-family:courier new,monospace">4) <b>Jacobi
Preconditioner</b> <i>(Must have)</i> - As prerequisite
for step(1).</div>
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace"><u>EIGEN
DECOMPOSITION MODULES (ONLY FOR DENSE MODULES)**:</u> </div>
<div style="font-family:courier new,monospace">1) <b>Symmetric
Eigen Values</b> - <i>(Must have)</i> Like SSYEV Module
in Lapack - That is first reduction to a tridiagonal form
using Householder then using QR Algorithm for Eigen Value
computation. </div>
<div style="font-family:courier new,monospace">2) <b>NonSymmetric
Eigen Values</b> - <i>(Good to have)</i> Like SGEEV
module in Lapack - using Schur decompositions as an
intermediate step in the above algorithm. </div>
<div style="font-family:courier new,monospace">3) <b>Generalized
Eigen Values</b> - <i>(needs introspection)</i> I use
this in my research a lot and its a good thing to have.. </div>
<div style="font-family:courier new,monospace"><br>
</div>
<div style="font-family:courier new,monospace">** Computing
Eigen Decomposition of sparse modules needs special robust
numerical treatment using implicitly restarted arnoldi
iterations and may be treated as optional extensions.<br>
</div>
</div>
</div>
<br>
</div>
<br>
<fieldset></fieldset>
<br>
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