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Problem in thin QR Solve

Feb 12, 2013 at 3:48 PM
I have found a problem when using the thin QR to solve a Least-Squares problem. Here's my test code:
Public Shared Function MathNetQRSolve(xArray(,) As Double, yColumn() As Double, useFull As Boolean) As Double()

        Dim QRType As LAGeneric.Factorization.QRMethod

        If useFull Then
            QRType = LAGeneric.Factorization.QRMethod.Full
            QRType = LAGeneric.Factorization.QRMethod.Thin
        End If

        Dim xMatrix As LAGeneric.Matrix(Of Double) = New DenseMatrix(xArray)
        Dim yVector As LAGeneric.Vector(Of Double) = New DenseVector(yColumn)

        Dim output As LAGeneric.Vector(Of Double)

            Dim tempQR As LAGeneric.Factorization.QR(Of Double) = xMatrix.QR(QRType)
            output = tempQR.Solve(yVector)

        Catch ex As Exception
            output = New SparseVector(yColumn.Count)
        End Try

        Return output.ToArray

    End Function
If I use the thin QR factorization then it throws an error, "All vectors must have the same dimensionality". The factorization itself is fine, it's just the solve method that doesn't work.

Feb 12, 2013 at 4:19 PM
Edited Feb 12, 2013 at 4:20 PM
Just having thought about it a little more, I think it's because for an M×N matrix:

Full QR Decomposition
Q is M×M
R is M×N

Thin QR Decomposition
Q is M×M
R is N×N (square matrix)

This means that when the solve method checks that the dimensions are the same then they won't be and that's where it throws the error.
Feb 13, 2013 at 6:53 AM
Edited Feb 14, 2013 at 6:42 AM
yep, in DenseQR we are checking
if (MatrixR.RowCount != input.RowCount)
but we we should be using the Q matrix not R.

Interesting that this passed the unit tests. I'll update the tests and check in a fix. [update: since we only tested square matrices when solving - doh!. Added tall matrix tests]
Marked as answer by cdrnet on 10/3/2013 at 5:49 PM
Feb 14, 2013 at 6:41 AM
Chris as merged the fix into the main branch. Thanks for reporting the error.
Feb 14, 2013 at 9:19 AM
No problem. Does this mean that the fix is available in the latest download or do I need to download the source code and compile it myself?

I assume that you caught this one in the same fix, but I think the Gram-Schmidt decomposition also had the same problem.
Feb 14, 2013 at 9:43 AM
For the moment you'll need to compile it yourself.

It didn't occur to me to check GS. It looks there is an issue with it - thanks!
Feb 14, 2013 at 10:01 AM
(There have been quite a few fixes lately, so I'm considering a patch release soon, i.e. v2.4.1)
Mar 14, 2015 at 10:16 PM
Hello there,

has this issue ever been solved? I am using the latest binaries but I get the same exception when trying to QR solve an MxN matrix (sparse or dense, full or thin method).
Mar 15, 2015 at 11:08 PM
Yes, this has been fixed roughly 2 years ago. Of course QR decompositions still require m >= n. Can you provide a repro?