bug #54142: The sort() and issorted() routines for diagonal matrices isn't as fast as it should be

 Submitter: Dan Sebald Submitted: Mon 18 Jun 2018 07:40:14 PM UTC Category: Performance Severity: 1 - Wish Priority: 5 - Normal Item Group: Feature Request Status: Confirmed Assigned to: None Originator Name: Open/Closed:  * Open Release:  * dev Operating System:  * Any Fixed Release: None Planned Release: None
* Mandatory Fields

Add a New Comment Rich Markup

Discussion

Wed 25 Jul 2018 06:30:08 PM UTC, comment #1:

The place for this is in liboctave/array/DiagArray2.[h|cc].  The template for the header file can be borrowed from Array.h.  Dan's code can then be placed in DiagArray2.cc.

Rik <rik5>
Mon 18 Jun 2018 07:40:14 PM UTC, original submission:

In the bug report

https://savannah.gnu.org/bugs/?53198

is an analysis of nnz for diagonal matrices, with greatly improved speed when taking into consideration how sparse the diagonal matrix is.

A similar thing can be said for sort() applied to diagonal matrices.  E.g.,

octave:1> N = 1e2;
octave:2>
octave:2> f = zeros(N,1);
octave:3> for i=1:N
>   r = rand(5000,1);
>   s = diag(r);
>   tic;
>   z = sort(s);
>   f(i)=toc;
> endfor
octave:4>
octave:4> sum(f)
ans =  23.499

It should be possible to speed up this operation by noting that we can:

1) Construct an all-zeros matrix of the same size.
2) Take the diagonal vector and distribute it either to the starting or ending position of the colum (or row) of the zeros matrix. E.g.,

x_out = zeros(N_i,N_j);
for (ivec=0; ivec<N_vec; ivec++)
{
if (xsparse(ivec) < 0)
{
if (col)
x_out(0, ivec) = x_diag(ivec);
else
x_out(ivec, 0) = x_diag(ivec);
}
else
{
if (col)
x_out(N_i-1, ivec) = x_diag(ivec);
else
x_out(ivec, N_j-1) = x_diag(ivec);
}
}

and the issorted() routine boils down to a series of logical statements:

1) If the matrix size is 2 or less along the direction of sort, use the full matrix sort.  Not much penalty is incurred by that.
2) If the diagonal vector is all zeros, the matrix is sorted.
3) Otherwise, the matrix is not sorted.

Dan Sebald <sebald>

Attached Files

(Note: upload size limit is set to 16384 kB, after insertion of the required escape characters.)

Attach Files:

Comment:

No files currently attached

Dependencies

Depends on the following items: None found

Items that depend on this one: None found

Mail Notification Carbon-Copy List

Carbon-Copy List
• -email is unavailable- added by rik5 (Updated the item)
• -email is unavailable- added by sebald (Submitted the item)
•

There are 0 votes so far. Votes easily highlight which items people would like to see resolved in priority, independently of the priority of the item set by tracker managers.

Only group members can vote.

History

Follow 3 latest changes.

Date Changed by Updated Field Previous Value => Replaced by
2018-06-19 rik5 Severity3 - Normal 1 - Wish
Item GroupNone Feature Request
StatusNone Confirmed