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[Octave-bug-tracker] [bug #60577] Detect (sparse) transposed lower trian
From: |
Marco Caliari |
Subject: |
[Octave-bug-tracker] [bug #60577] Detect (sparse) transposed lower triangular linear systems |
Date: |
Tue, 11 May 2021 02:55:56 -0400 (EDT) |
User-agent: |
Mozilla/5.0 (X11; Ubuntu; Linux x86_64; rv:88.0) Gecko/20100101 Firefox/88.0 |
URL:
<https://savannah.gnu.org/bugs/?60577>
Summary: Detect (sparse) transposed lower triangular linear
systems
Project: GNU Octave
Submitted by: caliari
Submitted on: Tue 11 May 2021 06:55:54 AM UTC
Category: Interpreter
Severity: 2 - Minor
Priority: 5 - Normal
Item Group: Performance
Status: None
Assigned to: None
Originator Name:
Originator Email:
Open/Closed: Open
Release: 6.1.0
Discussion Lock: Any
Operating System: GNU/Linux
_______________________________________________________
Details:
If I run the following code with M sparse or full
m = 500;
M = toeplitz(sparse([1,1],[1,2],[4,1],1,m));
R = chol(M); % try it with chol(full(M));
b = randn(m,1);
tic
for i = 1:10000
R\b;
end
toc
tic
for i = 1:10000
R'\b;
end
toc
I observe the transposed system 1.5x slower than the untransposed one in the
sparse case, while there is no difference in the full case. I have two
possible explanations:
1) in the full case the interpreter detects that R' is lower triangular and
avoids transposition
2) in the full case the computational cost hides the cost related to
transposition
Would it be possible to detect in any case that R' is lower triangular and
avoid transposition?
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