`CompressedColumnStorage<T>.Transpose` yields wrong result leading to sequential issues in `Solver`s about csparse.net HOT 9 CLOSED

I just looked up the documentation of the Multiply method and I agree it's a bit sparse:

Do you think changing the summary would be enough:

/// <summary>
/// Sparse matrix multiplication, C = A*B, where A is current instance.
/// </summary>

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I haven't tested any of the code you provided, but the first issue I see is

var aSparse = new CSparseMatrix(a.RowCount, a.ColumnCount)

That would only be ok for a square matrix. If a.RowCount != a.ColumnCount, you should write

var aSparse = new CSparseMatrix(a.ColumnCount, a.RowCount)

Can you please test this and report back. If the problems reside, I'll have a closer look.

from csparse.net.

Hi @wo80!

Thanks for the quick help, that was it!
But I do not understand at all why this is needed.
Also, it gives the transposed matrix, so I would need to transpose my minimization problem.
No biggy, but still would like to understand the thought process behind this limitation.

from csparse.net.

You need to understand how the matrix entries are stored (see for example https://www.smcm.iqfr.csic.es/docs/intel/mkl/mkl_manual/appendices/mkl_appA_SMSF.htm).

MathNet uses CSR storage (matrix entries are stored row-wise) while CSparse uses CSC storarge (entries are stored column-wise). So if you take the CSR storage and just interpret it as CSC, it will represent the transposed matrix. This means, if your original matrix stored as CSR is m x n, then it will represent a n x m matrix in CSC.

Also, it gives the transposed matrix, so I would need to transpose my minimization problem. No biggy, but still would like to understand the thought process behind this limitation.

Yes, if you want to solve a least-squares problem, make sure that the CSparse m x n matrix has m >= n, so the MathNet matrix should be built as n x m. You can also feed matrices with m < n to SparseQR, but it will then compute the transposed matrix internally:

from csparse.net.

Thanks a ton for clarifying, seems that I really misunderstood a few things.

I am actually thinking about rewriting most of my code to use CSparse directly, the performance is incredible!

Do you think changing the summary would be enough:

Absolutely, that makes it very explicit.
The issue that I have with

The sparse matrix multiplied to this instance.

is that one could interpret it as left multiplication, as right multiplication is quite uncommon.

from csparse.net.

I am actually thinking about rewriting most of my code to use CSparse directly, the performance is incredible!

I think you are right. The CSparse.NET is a port of CSparse by Tim. Davis. If i remember right, CSparse.NET had reasonably good performance compared to original CSparse although the original one is in native C or C++.

from csparse.net.

@ChristoWolf

I am actually thinking about rewriting most of my code to use CSparse directly, the performance is incredible!

In case you were using the dense QR from MathNet (or even native MKL), the difference will be considerable. You can set up your matrix using the CSparse.NET CoordinateStorage class, so in case you aren't using any other parts from MathNet, switching should be easy.

The issue that I have with [...] is that one could interpret it as left multiplication, as right multiplication is quite uncommon.

Alright, I will make sure to add a note that the matrix A is multiplied by the other matrix from the right.

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Please leave this issue open! I will close it with the next pull request.

from csparse.net.

Thanks a ton, @wo80!

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