From db3520fca3583dc0ab877490fdd220381766bd05 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Thu, 15 Sep 2022 14:38:24 -0400
Subject: [PATCH] Add more examples with the preconditioners

---
 docs/src/preconditioners.md | 35 +++++++++++++++++++++++++++++++++++
 1 file changed, 35 insertions(+)

diff --git a/docs/src/preconditioners.md b/docs/src/preconditioners.md
index 133020dc0..e37ab378a 100644
--- a/docs/src/preconditioners.md
+++ b/docs/src/preconditioners.md
@@ -172,3 +172,38 @@ using ILUZero, Krylov
 Pᵣ = ilu0(A)
 x, stats = bicgstab(A, b, N=Pᵣ, ldiv=true)  # right preconditioning
 ```
+
+```julia
+using LDLFactorizations, Krylov
+
+M = ldl(E)
+N = ldl(F)
+
+# [E  A] [x] = [b]
+# [Aᴴ F] [y]   [c]
+x, y, stats = tricg(A, b, c, M=M, N=N, ldiv=true)
+```
+
+```julia
+using SuiteSparse, Krylov
+import LinearAlgebra.ldiv!
+
+M = cholesky(E)
+
+# ldiv! is not implemented for the sparse Cholesky factorization (SuiteSparse.CHOLMOD)
+ldiv!(y::Vector{T}, F::SuiteSparse.CHOLMOD.Factor{T}, x::Vector{T}) where T = (y .= F \ x)
+
+# [E  A] [x] = [b]
+# [Aᴴ 0] [y]   [c]
+x, y, stats = trimr(A, b, c, M=M, sp=true, ldiv=true)
+```
+
+```julia
+using Krylov
+
+C = lu(M)
+
+# [M  A] [x] = [b]
+# [B  0] [y]   [c]
+x, y, stats = gpmr(A, B, b, c, C=C, gsp=true, ldiv=true)
+```