Rectangular QR decomposition with MathNet.Numerics

[kenryot]

Hi,

Thank you very much for publishing this library. Really great to have an open source sparse solver in .NET. I've got just one question. I encountered an error with feeding a rectangular matrix defined in MathNet.Numerics to CSparse for QR decomposition. I followed the tutorial from this page (https://github.com/wo80/CSparse.NET/wiki/Math.NET-Numerics-and-CSparse) but didn't manage to figure out the cause. It seems to work fine for square matrices.

Have anyone made it work? If it is supported, could you elaborate the procedure?

Best, Kenryo

[wo80]

Maybe you forgot to switch the roles of rows and columns (CSC vs CSR storage). Here's the SparseQR.Create(...) method. If this doesn't help, I'll post the full code as a gist.

public static SparseQR Create(SparseMatrix matrix, CSparse.ColumnOrdering ordering)
{
    int rows = matrix.RowCount;
    int cols = matrix.ColumnCount;

    // Get CSR storage.
    var storage = (SparseCompressedRowMatrixStorage<double>)matrix.Storage;

    // Create CSparse matrix.
    var A = new CSparseMatrix(cols, rows);

    // Assign storage arrays.
    A.ColumnPointers = storage.RowPointers;
    A.RowIndices = storage.ColumnIndices;
    A.Values = storage.Values;

    return new SparseQR(CSparseQR.Create(A, ordering), cols, rows);
}

[kenryot]

It seems I'm getting an error for not being a square matrix in AMD class.. Is it possible ?

private static SymbolicColumnStorage ConstructMatrix(SymbolicColumnStorage A, ColumnOrdering order) { SymbolicColumnStorage result = null;

        // Compute A'
        var AT = A.Transpose();

        int m = A.RowCount;
        int n = A.ColumnCount;

        if (order == ColumnOrdering.MinimumDegreeAtPlusA)
        {
            if (n != m)
            {
                throw new ArgumentException(Resources.MatrixSquare, "A");
            }

            // Return A+A'
            result = A.Add(AT);
        }

[wo80]

If the matrix isn't square, you cannot compute A^t + A. Use ColumnOrdering.MinimumDegreeAtA instead.

[kenryot]

Right! Now the code runs. Thanks a lot.

Kenryo,