-
Notifications
You must be signed in to change notification settings - Fork 24
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
Direct Linear Solvers for Symmetric Positive Definite Toeplitz Matrices #64
Direct Linear Solvers for Symmetric Positive Definite Toeplitz Matrices #64
Conversation
eab7c10
to
1aca52e
Compare
Codecov ReportBase: 91.45% // Head: 91.66% // Increases project coverage by
Additional details and impacted files@@ Coverage Diff @@
## master #64 +/- ##
==========================================
+ Coverage 91.45% 91.66% +0.21%
==========================================
Files 2 3 +1
Lines 468 600 +132
==========================================
+ Hits 428 550 +122
- Misses 40 50 +10
Help us with your feedback. Take ten seconds to tell us how you rate us. Have a feature suggestion? Share it here. ☔ View full report at Codecov. |
Further notes:
|
Not a good idea: there’s no equivalent in LinearAlgebra. The analogue there is explicitly calling |
This is not central to this PR, just adding my thoughts:
|
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
I found a few minor style issues.
Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
I just committed your suggestions. |
Is anything holding this up? @dkarrasch @SebastianAment |
There was a problem hiding this comment.
Choose a reason for hiding this comment
The reason will be displayed to describe this comment to others. Learn more.
A few more style suggestions.
Out of curiosity, why not make the overloaded functions available in |
@dkarrasch if the only thing missing is a couple style changes, perhaps we should just apply the changes and merge, to avoid holding this up too long? |
I still wonder... There will be |
Presumably they will be, but that would require a PR in StatsBase.jl. |
@dlfivefifty could you merge this? |
Overview
This PR adds implementations of the Durbin and Levinson algorithms that improve on the performance of StatsBase's implementations by a factor of two for larger matrices. The performance advantage starts to appear before
n = 32
and grow withn
. Experiments were run on a 2021 MacBook Pro with an M1 Pro.Since this package specializes on Toeplitz matrices, I think the implementations are better incorporated here than at StatsBase. Further, this PR also adds Trench's algorithm for the efficient inversion of symmetric positive definite Toeplitz matrices. See below for performance benchmarks.
For a reference, see Golub and Van Loan, page 208.
Benchmarks
Durbin
n = 4096
n = 32
Levinson
n = 4096
n = 32
Trench
n = 4096
n = 32