Support for SparseMatrix

[epsi1on]

Hi, It would be great to have support for sparse matrices in your library. As you know, large structures have a big stiffness matrix and not possible to have their stiffness matrix in dense format. A good implementation is the CSparse.NET, which does handles several features such as ordering, factorization etc.

Thanks

[EduardBargues]

Definitely something to consider. I'll look into it!!

Btw, do you have any other feedback?

[epsi1on]

Thanks for sharing library to opensource, and i think it would be good to have a separated project for unit tests (e.g. NonLinearEquationsSolver.Tests) also a brief example documentation on usage would be very good. I was working on a finite element project named BriefFiniteElemement for some years, which is only a brief linear finite element analysis implementation for solids and structures. Now I'm looking for some opportunities to switch to nonlinear and do make a nonlinear framework.

[EduardBargues]

good for you !! I created this project after my master thesis and did not continue inmproving it because my professional path took me somewhere else. I created another issue to create unit tests. Have a good day!

[epsi1on]

Thanks, Let me know if i can do any help.

[EduardBargues]

Let me first update the repo. It-s quite old. Then, maybe I can split the work so that you can also contribute.

[EduardBargues]

Hello @epsi1on, I invited you to be a collaborator in this repo so you can review the newly created pull-request. Let me know in your comments if you think the issue might be solved with the pull-request 👍

[epsi1on]

OK, Thanks... I think we should do few changes, First is to replace MathNet Matrix<double> with CSparse Matrix which is base class for both dense and sparse matrices in CSparse, it also implements ILinearOperator. What do you think @wo80 ? i can make the pull-request. Thanks

[wo80]

Well, I'm not sure if Eduard wants to move away from MathNet, but here are some points to consider.

• CSparse.NET has no Vector<T> class (this will either be part of the CSparse.Extensions project, or could be added to the original library, let me know what you think).
• CSparse.NET does not implement direct solvers for dense matrices (and never will, they will be part of the extensions package)

Regarding the first point: there are a couple of places where NonLinearEquationsSolver uses the MathNet vectors with operator notation, for example https://github.com/EduardBargues/NonLinearEquationsSolver/blob/69f44cb4f6ad01e0e2b4cfbbdf9b0f62efe3e15e/NLES/Correction/Corrector.cs#L60 Those would have to be replaced with something like

equilibrium = info.InitialLoad.Clone();
equilibrium.Add(newState.Lambda, info.ReferenceLoad, equilibrium); // axpy
equilibrium.Add(-1.0, reaction, equilibrium); // axpy

It's more verbose, but reducing pressure on the GC, since it involves allocation of only one array, while operator notation involves 3 allocations.

[EduardBargues]

@epsi1on the pull request i did removes any usage of a Matrix and uses an ILinearSolver interface. That, I think, is enough to use any implementation you want to optimize allocation (CSparse) or computation (anything different from Math-Net).

hello @wo80, i was thinking to do the same for the Vector. That way I'll be able to move away from Math.Net and allow you to use any implementation.

What do you think guys?

[epsi1on]

@epsi1on the pull request i did removes any usage of a Matrix and uses an ILinearSolver interface. That, I think, is enough to use any implementation you want to optimize allocation (CSparse) or computation (anything different from Math-Net).

I've forked this repo (available here) and am working on for supporting CSparse and using double array instead of Vector, once done will make it as pull request to main repo. I put several hours today to convert all Vector<double> to double[] and Matrix<double> to CSparse.Double.SparseMatrix. I have a suggestion, to improve performance it is good to use an ArrayPool for allocating new arrays in memory, As this is iterative based procedure and large arrays are allocated and destructed several times.

[wo80]

@EduardBargues Removing the Math.NET dependency would be great. You could either use arrays like CSparse.NET (see Vector helper class) or implement a simple vector type which wraps a double array.

@epsi1on The ILinearSolver allows to choose whichever matrix implementation you like and the goal is to be completely independend of any third party library.

EDIT: introducing an array pool is a good idea, but might not be necessary. To eliminate the cloning of the array in the example code above, the Corrector would need to have a working array of the appropriate size (which could be initialized when the NonLinearSolver is built):

// equilibrium array/vector is a class member
info.InitialLoad.CopyTo(equilibrium);
equilibrium.Add(newState.Lambda, info.ReferenceLoad, equilibrium);
equilibrium.Add(-1.0, reaction, equilibrium);

[EduardBargues]

Hello @epsi1on and @wo80 . I'm going to close this issue because we already achieved the goal through the ILinearSolver interface. I'll open a new one to remove the Math.Net dependency.

Thank you!!