[R] Question regarding lu in package Matrix

[Douglas Bates]

On Wed, Jul 9, 2008 at 12:01 PM, Ulrike Grömping <groemp at tfh-berlin.de> wrote:

> Dear R-helpers,

> I have a question regarding LU-decomposition with function lu in package
> Matrix. The following simple example confuses me: Why is as.matrix(elu$U)
> not an upper triangular matrix?

> u3 <-
> matrix(c(1,1,1,1,1,1,-1,1,0,0,0,0,0,-1,1,0,0,0,-1,0,1,0,0,0,0,0,-1,1,0,0),5,6,byrow=T)
> elu <- expand(lu(Matrix(u3,sparse=F)))
> as.matrix(elu$U)

I get

> elu$U
5 x 6 Matrix of class "dtrMatrix"
     [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
[1,]  1.0000000  0.0000000  0.0000000  0.0000000  1.0000000  1.0000000
[2,]          .  2.0000000  0.0000000  0.0000000  1.0000000  1.0000000
[3,]          .          .  1.5000000  0.0000000  0.0000000  0.5000000
[4,]          .          .          .  1.3333333  0.0000000  0.3333333
[5,]          .          .          .          .  0.0000000  0.0000000

which is about as upper-triangular as it can be, considering that the
original matrix is not square.

The help page for 'lu' does say that it gives the triangular
decomposition of a square matrix, although the decomposition is
defined for non-square.  It's just not as useful as it would be for
square matrices.

Are you suggesting that we should check the argument to lu and report
an error if it is not square?


> I only have very limited experience with the package and its different types
> of matrices, and I am lost where to start looking for a reason.
>
> Regards,
> Ulrike Grömping
>
>
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