From 88965d8b2b3dbbd07150bb64486117690a013b5c Mon Sep 17 00:00:00 2001
From: cheukhinhojerry <cheukhinhojerry@gmail.com>
Date: Fri, 22 Mar 2024 19:03:44 -0700
Subject: [PATCH 1/2] add trunc_svd svoler

---
 src/solvers.jl             | 37 +++++++++++++++++++++++++++++++++++++
 test/test_linearsolvers.jl |  7 +++++++
 2 files changed, 44 insertions(+)

diff --git a/src/solvers.jl b/src/solvers.jl
index 54ac29c..96f034d 100644
--- a/src/solvers.jl
+++ b/src/solvers.jl
@@ -2,6 +2,7 @@ using LinearAlgebra: qr, I, norm
 using LowRankApprox: pqrfact
 using IterativeSolvers
 using .BayesianLinear
+using LinearAlgebra: SVD, svd
 
 @doc raw"""
 `struct QR` : linear least squares solver, using standard QR factorisation; 
@@ -148,3 +149,39 @@ function SKLEARN_ARD(; n_iter = 300, tol = 1e-3, threshold_lambda = 10000)
 end
 
 # solve(solver::SKLEARN_ARD, ...) is implemented in ext/
+
+@doc raw"""
+`struct Truncated_SVD` : linear least squares solver
+```math 
+ θ = \arg\min \| A \theta - y \|^2 + \lambda \| P \theta \|^2
+```
+Constructor
+```julia
+ACEfit.Truncated_SVD(; lambda = 0.0, P = nothing)
+``` 
+where 
+* `rtol` : relative tolerance
+* `P` : right-preconditioner / tychonov operator
+"""
+struct Truncated_SVD
+    rtol::Number
+    P::Any
+end
+
+Truncated_SVD(; rtol = 1e-9, P = I) = Truncated_SVD(rtol, P)
+
+function trunc_svd(USV::SVD, Y, rtol)
+    U, S, V = USV # svd(A)
+    Ikeep = findall(x -> x > rtol, S ./ maximum(S))
+    U1 = @view U[:, Ikeep]
+    S1 = S[Ikeep]
+    V1 = @view V[:, Ikeep]
+    return V1 * (S1 .\ (U1' * Y))
+end
+
+function solve(solver::Truncated_SVD, A, y)
+    AP = A / solver.P
+    θP = trunc_svd(svd(AP), y, solver.rtol)
+    return Dict{String, Any}("C" => solver.P \ θP)
+end
+
diff --git a/test/test_linearsolvers.jl b/test/test_linearsolvers.jl
index dca778b..fca1b4e 100644
--- a/test/test_linearsolvers.jl
+++ b/test/test_linearsolvers.jl
@@ -79,3 +79,10 @@ results = ACEfit.solve(solver, A, y)
 C = results["C"]
 @show norm(A * C - y)
 @show norm(C)
+
+@info(" ... Truncated_SVD")
+solver = ACEfit.Truncated_SVD()
+results = ACEfit.solve(solver, A, y)
+C = results["C"]
+@show norm(A * C - y)
+@show norm(C)

From e1d674d86a6a808d7d2089d95665c7059552e1ab Mon Sep 17 00:00:00 2001
From: cheukhinhojerry <cheukhinhojerry@gmail.com>
Date: Fri, 22 Mar 2024 19:49:25 -0700
Subject: [PATCH 2/2] update doc

---
 src/solvers.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/solvers.jl b/src/solvers.jl
index 96f034d..11c0f5f 100644
--- a/src/solvers.jl
+++ b/src/solvers.jl
@@ -153,7 +153,7 @@ end
 @doc raw"""
 `struct Truncated_SVD` : linear least squares solver
 ```math 
- θ = \arg\min \| A \theta - y \|^2 + \lambda \| P \theta \|^2
+ θ = \arg\min \| A P^{-1} \theta - y \|^2 
 ```
 Constructor
 ```julia