Implement solve methods for QR and SVD decompositions about eigen-js HOT 5 CLOSED

Thanks a lot Betrand, this is super helpful!
I see I have to go through some more linear algebra lectures to get back on track 😅

Also glad that you like the Observable platform! I'm a huge fan as well 😊

With respect to the original question, I still think it would be helpful (from a user perspective) to expose Eigen's own solve methods for the decompositions though. What do you think?
Again, I'm sorry for my lack in C++ skills, because I'd just propose a PR then. But I'd need a pointer on where to start...

from eigen-js.

Hi Chris,

Thanks for the encouraging feedback!
Did you check the decomposition class?
https://bertrandbev.github.io/eigen-js/#/decompositions
It currently features LU, QR, SVD & Cholesky decompositions.

from eigen-js.

Thanks for you reply 😊

Sorry for being unclear: My goal is to solve a system of linear equations (Ax = b). I checked the decompositions classes (https://bertrandbev.github.io/eigen-js/#/decompositions), but unfortunately I do not understand how I would use them for solving for x:

const A = new eig.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]);
const b = new eig.Matrix([5,6,7]);
// solve Ax=b
const qr = eig.Decompositions.qr(A);
// the following fails due to the length of rows in R not being equal to the columns
// furthermore, solving for x should ideally avoid taking the inverse of anything..
// http://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html
const x = qr.R.inverse()
  .matMul(qr.Q.transpose())
  .matMul(b)
// for this exact purpose, Eigen decompositions export a solve method:
// x = A.colPivHouseholderQr().solve(b)
// or using SVD
// x = A.bdcSvd(ComputeThinU | ComputeThinV).solve(b)

I also made a small Observable notebook to illustrate my confusion:

https://observablehq.com/d/3c9a3e40b6804dff

I'm assuming Eigen uses (back-)substitution for solving the equation system, but I'm not sure. Therefore I'd really appreciate if you could provide a brief example of how this could be done using this library!

Sorry for my lack of knowledge, really appreciate your help!

from eigen-js.

Ok, thanks for sharing that notebook! (I didn't know Observable, it's a really nice platform!)
So solving linear systems with QR decomposition still involves an upper linear triangular system resolution, it's more straightforward to go with SVD.
When performing the SVD, eigen prunes away the zeros form the singular value vector. So you need to instantiate a singular value matrix of the correct dimension first before computing VSigma^tU^t

sigmaCross = {
  const sigmaCross = new eigen.Matrix(SVD.U.cols(), SVD.V.rows());
  sigmaCross.setBlock(0, 0, eigen.Matrix.diagonal(SVD.sv).inverse());
  return sigmaCross.transpose();
}

I took the liberty of forking your notebook to implement that fix
https://observablehq.com/@bbev/hello-eigen-js

Let me know if it makes sense!

from eigen-js.

Yes for sure, it would be a nice addition! I'll take a look at it when I find the time

from eigen-js.