[R] package:Matrix handling of data with identical indices

[Thaden, John J]

Thanks. I see in the UMFPACK manual that the convention for csc matrices
for monotonic-increasing row indices is as you say.  

I notice UMFPACK flags errors liberally. What if Matrix or some other
package were made to interface with UMFPACK directly, to tap these and
other features?

-John Thaden

dmbates at gmail.com wrote:

...
...
DB> It is not permissible to have repeated indices in the compressed
form.  In the compressed form there is a well-defined ordering of the
indices, first by columns then by row within column and the row
indices must be increasing within columns.

DB> Your matrix Mc should be flagged as invalid.  Martin and I should
discuss whether we want to add such a test to the validity method.  It
is not difficult to add the test but there will be a penalty in that
it will slow down all operations on such matrices and I'm not sure if
we want to pay that price to catch a rather infrequently occuring
problem.

DB> There is some documentation of the internal representations of these
formats in the directory $R_LIB/Matrix/doc/UFSparse/.  The User Guides
in that directory are taken directly from the various sparse matrix
packages that Tim Davis at the University of Florida has written.  He
has a book that is scheduled for publication this  September

DB> Tim Davis (2006), Direct Methods for Sparse Linear Systems, SIAM,
Philadelphia, PA

DB> I hope we will be able to refer to that book for details of the
representation and algorithms.

On 7/8/06, Thaden, John J <ThadenJohnJ at uams.edu> wrote:
> In the Matrix package v. 0.995-11 I see that the dgTMatrix
> Class for compressed, sparse, triplet-form matrices handles
> Identically indexed data instances by summing their values,
> e.g.,
>
> library(Matrix)
> (Mt <- new("dgTMatrix",
>    i = as.integer(c(0,0,1,1,4)),
>    j = as.integer(c(0,1,2,2,4)),
>    x = as.double(1:5),
>    Dim = as.integer(c(5,5))))
> ## 5 x 5 sparse Matrix of class "dgTMatrix"
> ## [1,] 1 2 . . .
> ## [2,] . . 7 . .    <--- 7 = 3 + 4.
> ## [3,] . . . . .
> ## [4,] . . . . .
> ## [5,] . . . . 5
>
> # If instead I make a dgCMatrix-class matrix, the first
> # instance is overwritten by the second, e.g.,
>
> library(Matrix)
> (Mc <- new("dgCMatrix",
>    i = as.integer(c(0,0,1,1,4)),
>    p = as.integer(c(0,1,2,4,5)),
>    x = as.double(1:5),
>    Dim = as.integer(c(5,5))))
> ## 5 x 5 sparse Matrix of class "dgCMatrix"
> ##
> ## [1,] 1 2 . .
> ## [2,] . . 4 .   <-- the datum '3' has been lost.
> ## [3,] . . . .
> ## [4,] . . . .
> ## [5,] . . . 5
>
> # If one arrives at the dgCMatrix via the dgTMatrix class,
> # the summed value is of course preserved, e.g.,
>
> (Mtc <- as(Mt, "dgCMatrix"))
> ## 5 x 5 sparse Matrix of class "dgCMatrix"
> ##
> ## [1,] 1 2 . . .
> ## [2,] . . 7 . .
> ## [3,] . . . . .
> ## [4,] . . . . .
> ## [5,] . . . . 5
>
> As there is nothing inherent in either compressed, sparse,
> format that would prevent recognition and handling of
> duplicated index pairs, I'm curious why the dgCMatrix
> class doesn't also add x values in those instances?
> I wonder also if others might benefit also by being able
> to choose how these instances are handled, i.e.,
> whether they are summed, averaged or overwritten?
>
> -John Thaden, Ph.D.
> Research Assistant Professor of Geriatrics
> University of Arkansas for Medical Sciences
> Little Rock AR, USA
>
>
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