[Octave-bug-tracker] [bug #46123] diagonal matrix and diagonality preserving matrix operations

[jan]

URL:
  <http://savannah.gnu.org/bugs/?46123>

                 Summary: diagonal matrix and diagonality preserving matrix
operations
                 Project: GNU Octave
            Submitted by: pfa
            Submitted on: sön  4 okt 2015 18.53.44
                Category: Libraries
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Performance
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: dev
        Operating System: Any

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Details:


Diagonal matrix is essentially a sparse representation. However, functions
like permute produce full matrix, even if they are sparsity preserving.
[Permute is in fact identity function for diagonal matrix]. In comparision
e.g. inv() or expmI() preserve diagonality. 

As a goal I believe the basic matrix functions/operations (excluding the
elementwise functions) should preferably preserve the structure when the
operatin is closed in the class of diagonal matrices.

More generally, this relates to treating diagonal matrix sparse or not (i.e.
sparse(diag(1:2)) returns false, which is missleading for many uses.) The
memory usage is very different N vs. N^2, so this is somewhat supprising
result. 

As a side note, and somewhat supprisingly, elementwise function sqrt()
preserves the diagonal structure, whereas other elementswise functions like
sin() (for which sin(0)=0) do not. In general elementwise functions preserve
sparsity even if e.g. cos(0)=1.



>> permute(sparse(diag(1:2)),[1,2])
ans =

Compressed Column Sparse (rows = 2, cols = 2, nnz = 2 [50%])

  (1, 1) ->  1
  (2, 2) ->  2

>> permute((diag(1:2)),[1,2])
ans =

   1   0
   0   2







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