Add six Krylov processes #618

amontoison · 2022-08-30T18:01:50Z

https://juliasmoothoptimizers.github.io/Krylov.jl/previews/PR618/processes/

docs/src/processes.md

codecov · 2022-08-30T18:11:14Z

Codecov Report

Base: 97.97% // Head: 98.06% // Increases project coverage by +0.08% 🎉

Coverage data is based on head (8752a04) compared to base (0604212).
Patch coverage: 100.00% of modified lines in pull request are covered.

❗ Current head 8752a04 differs from pull request most recent head 56e4c48. Consider uploading reports for the commit 56e4c48 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #618      +/-   ##
==========================================
+ Coverage   97.97%   98.06%   +0.08%     
==========================================
  Files          36       37       +1     
  Lines        6072     6349     +277     
==========================================
+ Hits         5949     6226     +277     
  Misses        123      123

Impacted Files	Coverage Δ
src/krylov_processes.jl	`100.00% <100.00%> (ø)`

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github-actions · 2022-08-30T18:38:23Z

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
FletcherPenaltySolver.jl
JSOSolvers.jl
LLSModels.jl
Percival.jl
RipQP.jl

tmigot

It looks good to me, thanks!

tmigot · 2022-08-31T12:47:57Z

docs/src/processes.md

@@ -0,0 +1,282 @@
+### Notations


Similar to the other pages in the doc, I think it misses Krylov processes as a title followed by one sentence explaining what is here.

dpo

This will be of great help. I have the impression that the code is for the complex case, the algorithms are for the real case, and the description is a mixture :-).

docs/src/processes.md

dpo · 2022-09-03T15:52:51Z

docs/src/processes.md

+```math
+\begin{align*}
+  A V_k &= V_k T_k +        \beta_{k+1} v_{k+1} e_k^T = V_{k+1} T_{k+1,k}, \\
+  B U_k &= U_k S_k + \bar{\gamma}_{k+1} u_{k+1} e_k^T = U_{k+1} S_{k+1,k}, \\


A bit confused here. $S_k$ should be $T_k^T$.

Do you mean that $S_k$ arises from the formulation for complex numbers? If so, you shouldn't be using transposed matrices everywhere, but transposed conjugates.

dpo · 2022-09-03T15:58:22Z

docs/src/processes.md

+  \bar{\gamma}_2 & \bar{\alpha}_2 & \ddots          &                \\
+                 & \ddots         & \ddots          & \bar{\beta}_k  \\
+                 &                & \bar{\gamma}_k  & \bar{\alpha}_k
+\end{bmatrix},


Looks like $S_k = T_k^*$ ?!

dpo · 2022-09-03T15:59:30Z

docs/src/processes.md

+```
+
+!!! note
+    We also have the relations $T_k = S_k^T$, $\enspace T_{k,k+1} = \begin{bmatrix} T_{k} & \gamma_{k+1} e_k \end{bmatrix} = S_{k+1,k}^T \enspace$ and $\enspace S_{k,k+1} = \begin{bmatrix} S_{k} & \bar{\beta}_{k+1} e_k \end{bmatrix} = T_{k+1,k}^T$.


$T_k = S_k^T$ only in the real case.

github-actions · 2022-09-07T02:24:53Z

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
FletcherPenaltySolver.jl
JSOSolvers.jl
LLSModels.jl
Percival.jl
RipQP.jl

amontoison · 2022-09-07T04:25:53Z

@tmigot @dpo
It's ready for a second round of review.

github-actions · 2022-09-07T04:48:58Z

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
FletcherPenaltySolver.jl
JSOSolvers.jl
LLSModels.jl
Percival.jl
RipQP.jl

github-actions · 2022-09-07T04:57:48Z

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
FletcherPenaltySolver.jl
JSOSolvers.jl
LLSModels.jl
Percival.jl
RipQP.jl

github-actions · 2022-09-07T18:57:44Z

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
FletcherPenaltySolver.jl
JSOSolvers.jl
LLSModels.jl
Percival.jl
RipQP.jl

src/krylov_processes.jl

docs/src/processes.md

dpo · 2022-09-10T15:34:10Z

docs/src/processes.md

+
+## Symmetric Lanczos
+
+![symmetric_lanczos](./graphics/symmetric_lanczos.png)


Out of curiosity, does MathJax allow us to typeset algorithms?

Also, specify that $A = A^H$.

Out of curiosity, does MathJax allow us to typeset algorithms?

I will try pseudocode.js.

docs/src/processes.md

src/krylov_processes.jl

docs/src/processes.md

amontoison · 2022-09-23T14:19:11Z

With #637, we should be able to run the processes on GPUs.

Co-authored-by: Dominique <[email protected]>

…i processes

Co-authored-by: Dominique <[email protected]>

amontoison requested review from dpo and tmigot August 30, 2022 18:01

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amontoison force-pushed the krylov_processes branch from eb07f92 to c8d522d Compare September 7, 2022 18:23

amontoison force-pushed the krylov_processes branch from c8d522d to f48cd66 Compare September 10, 2022 04:41

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amontoison commented Sep 15, 2022

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amontoison force-pushed the krylov_processes branch from 60bdbd3 to 5f965b4 Compare September 23, 2022 04:57

amontoison force-pushed the krylov_processes branch from 5f965b4 to 53897f0 Compare September 23, 2022 16:23

amontoison and others added 9 commits September 27, 2022 20:55

Add six Krylov processes

32c7f02

Update docs/src/processes.md

a587805

Move the docstring of golub_kahan

ab29c1a

Apply suggestions from @dpo

8ac09c8

Co-authored-by: Dominique <[email protected]>

Add a new test for the SSY process

32e7494

Use the letter G for the projection of block-Lanczos and block-Arnols…

81c38ea

…i processes

Update krylov_processes.jl

65b6e91

Update algorithms

ee89233

Improve the documentation of Krylov processes

b4ad5b3

amontoison and others added 7 commits September 27, 2022 20:55

Use H instead of T to denote the Hermitian transpose

5f74963

Apply suggestions from code review

bed415d

Co-authored-by: Dominique <[email protected]>

[documentation] Update the section about Krylov processes

a7b6a72

Test Krylov processes on GPUs

7ba6b41

Fix a typo

5d3830a

Test processes only on Nvidia GPUs

e239515

Final modifications before we add the Krylov processes

5d9a9a0

amontoison force-pushed the krylov_processes branch from e24b5b4 to 5d9a9a0 Compare September 28, 2022 00:55

Update processes.md

876b34c

amontoison merged commit 426557d into main Sep 28, 2022

amontoison deleted the krylov_processes branch September 28, 2022 04:15

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Add six Krylov processes #618

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amontoison commented Sep 23, 2022


		## Symmetric Lanczos

		![symmetric_lanczos](./graphics/symmetric_lanczos.png)

Add six Krylov processes #618

Add six Krylov processes #618

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