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Use 5-arguments mul! in BILQ and QMR #356

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Jun 25, 2021
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Use 5-arguments mul! in BILQ and QMR #356

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36 changes: 17 additions & 19 deletions src/bilq.jl
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Expand Up @@ -52,7 +52,7 @@ function bilq!(solver :: BilqSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstra
Aᵀ = A'

# Set up workspace.
uₖ₋₁, uₖ, q, vₖ₋₁, vₖ, p, x, d̅ = solver.uₖ₋₁, solver.uₖ, solver.q, solver.vₖ₋₁, solver.vₖ, solver.p, solver.x, solver.d̅
uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, d̅ = solver.uₖ₋₁, solver.uₖ, solver.vₖ₋₁, solver.vₖ, solver.x, solver.d̅

# Initial solution x₀ and residual norm ‖r₀‖.
x .= zero(T)
Expand Down Expand Up @@ -100,20 +100,23 @@ function bilq!(solver :: BilqSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstra
# AVₖ = VₖTₖ + βₖ₊₁vₖ₊₁(eₖ)ᵀ = Vₖ₊₁Tₖ₊₁.ₖ
# AᵀUₖ = Uₖ(Tₖ)ᵀ + γₖ₊₁uₖ₊₁(eₖ)ᵀ = Uₖ₊₁(Tₖ.ₖ₊₁)ᵀ

mul!(q, A , vₖ) # Forms vₖ₊₁ : q ← Avₖ
mul!(p, Aᵀ, uₖ) # Forms uₖ₊₁ : p ← Aᵀuₖ
mul!(vₖ₋₁, A , vₖ, one(T), -γₖ) # Forms vₖ₊₁ : vₖ₋₁ ← Avₖ - γₖvₖ₋₁
mul!(uₖ₋₁, Aᵀ, uₖ, one(T), -βₖ) # Forms uₖ₊₁ : uₖ₋₁ ← Aᵀuₖ - βₖuₖ₋₁

@kaxpy!(n, -γₖ, vₖ₋₁, q) # q ← q - γₖ * vₖ₋₁
@kaxpy!(n, -βₖ, uₖ₋₁, p) # p ← p - βₖ * uₖ₋₁
αₖ = @kdot(n, vₖ₋₁, uₖ) # αₖ = (Avₖ- γₖvₖ₋₁)ᵀuₖ

αₖ = @kdot(n, q, uₖ) # αₖ = qᵀuₖ
@kaxpy!(n, -αₖ, vₖ, vₖ₋₁) # vₖ₋₁ ← vₖ₋₁ - αₖ * vₖ
@kaxpy!(n, -αₖ, uₖ, uₖ₋₁) # uₖ₋₁ ← uₖ₋₁ - αₖ * uₖ

@kaxpy!(n, -αₖ, vₖ, q) # q ← q - αₖ * vₖ
@kaxpy!(n, -αₖ, uₖ, p) # p ← p - αₖ * uₖ
qᵗp = @kdot(n, uₖ₋₁, vₖ₋₁) # qᵗp = ⟨Avₖ - γₖvₖ₋₁ - αₖvₖ, Aᵀuₖ - βₖuₖ₋₁ -αₖuₖ⟩
βₖ₊₁ = √(abs(qᵗp)) # βₖ₊₁ = √(|qᵗp|)
γₖ₊₁ = qᵗp / βₖ₊₁ # γₖ₊₁ = qᵗp / βₖ₊₁

qᵗp = @kdot(n, p, q) # qᵗp = ⟨q,p⟩
βₖ₊₁ = √(abs(qᵗp)) # βₖ₊₁ = √(|qᵗp|)
γₖ₊₁ = qᵗp / βₖ₊₁ # γₖ₊₁ = qᵗp / βₖ₊₁
# Compute vₖ₊₁ and uₖ₊₁.
if qᵗp ≠ zero(T)
@. vₖ₋₁ = vₖ₋₁ / βₖ₊₁ # βₖ₊₁vₖ₊₁ = Avₖ - γₖvₖ₋₁ - αₖvₖ
@. uₖ₋₁ = uₖ₋₁ / γₖ₊₁ # γₖ₊₁uₖ₊₁ = Aᵀuₖ - βₖuₖ₋₁ - αₖuₖ
end

# Update the LQ factorization of Tₖ = L̅ₖQₖ.
# [ α₁ γ₂ 0 • • • 0 ] [ δ₁ 0 • • • • 0 ]
Expand Down Expand Up @@ -187,14 +190,9 @@ function bilq!(solver :: BilqSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstra
@kaxpby!(n, -cₖ, vₖ, sₖ, d̅)
end

# Compute vₖ₊₁ and uₖ₊₁.
@. vₖ₋₁ = vₖ # vₖ₋₁ ← vₖ
@. uₖ₋₁ = uₖ # uₖ₋₁ ← uₖ

if qᵗp ≠ 0
@. vₖ = q / βₖ₊₁ # βₖ₊₁vₖ₊₁ = q
@. uₖ = p / γₖ₊₁ # γₖ₊₁uₖ₊₁ = p
end
# Update uₖ₋₁, vₖ₋₁, uₖ and vₖ.
@kswap(uₖ₋₁, uₖ)
@kswap(vₖ₋₁, vₖ)

# Compute ⟨vₖ,vₖ₊₁⟩ and ‖vₖ₊₁‖
vₖᵀvₖ₊₁ = @kdot(n, vₖ₋₁, vₖ)
Expand Down
12 changes: 2 additions & 10 deletions src/krylov_solvers.jl
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Expand Up @@ -708,24 +708,20 @@ may be used in order to create these vectors.
mutable struct BilqSolver{T,S} <: KrylovSolver{T,S}
uₖ₋₁ :: S
uₖ :: S
q :: S
vₖ₋₁ :: S
vₖ :: S
p :: S
x :: S
d̅ :: S

function BilqSolver(n, m, S)
T = eltype(S)
uₖ₋₁ = S(undef, n)
uₖ = S(undef, n)
q = S(undef, n)
vₖ₋₁ = S(undef, n)
vₖ = S(undef, n)
p = S(undef, n)
x = S(undef, n)
d̅ = S(undef, n)
solver = new{T,S}(uₖ₋₁, uₖ, q, vₖ₋₁, vₖ, p, x, d̅)
solver = new{T,S}(uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, d̅)
return solver
end

Expand All @@ -749,10 +745,8 @@ may be used in order to create these vectors.
mutable struct QmrSolver{T,S} <: KrylovSolver{T,S}
uₖ₋₁ :: S
uₖ :: S
q :: S
vₖ₋₁ :: S
vₖ :: S
p :: S
x :: S
wₖ₋₂ :: S
wₖ₋₁ :: S
Expand All @@ -761,14 +755,12 @@ mutable struct QmrSolver{T,S} <: KrylovSolver{T,S}
T = eltype(S)
uₖ₋₁ = S(undef, n)
uₖ = S(undef, n)
q = S(undef, n)
vₖ₋₁ = S(undef, n)
vₖ = S(undef, n)
p = S(undef, n)
x = S(undef, n)
wₖ₋₂ = S(undef, n)
wₖ₋₁ = S(undef, n)
solver = new{T,S}(uₖ₋₁, uₖ, q, vₖ₋₁, vₖ, p, x, wₖ₋₂, wₖ₋₁)
solver = new{T,S}(uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, wₖ₋₂, wₖ₋₁)
return solver
end

Expand Down
36 changes: 17 additions & 19 deletions src/qmr.jl
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Expand Up @@ -59,7 +59,7 @@ function qmr!(solver :: QmrSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstract
Aᵀ = A'

# Set up workspace.
uₖ₋₁, uₖ, q, vₖ₋₁, vₖ, p, x, wₖ₋₂, wₖ₋₁ = solver.uₖ₋₁, solver.uₖ, solver.q, solver.vₖ₋₁, solver.vₖ, solver.p, solver.x, solver.wₖ₋₂, solver.wₖ₋₁
uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, wₖ₋₂, wₖ₋₁ = solver.uₖ₋₁, solver.uₖ, solver.vₖ₋₁, solver.vₖ, solver.x, solver.wₖ₋₂, solver.wₖ₋₁

# Initial solution x₀ and residual norm ‖r₀‖.
x .= zero(T)
Expand Down Expand Up @@ -105,20 +105,23 @@ function qmr!(solver :: QmrSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstract
# AVₖ = VₖTₖ + βₖ₊₁vₖ₊₁(eₖ)ᵀ = Vₖ₊₁Tₖ₊₁.ₖ
# AᵀUₖ = Uₖ(Tₖ)ᵀ + γₖ₊₁uₖ₊₁(eₖ)ᵀ = Uₖ₊₁(Tₖ.ₖ₊₁)ᵀ

mul!(q, A , vₖ) # Forms vₖ₊₁ : q ← Avₖ
mul!(p, Aᵀ, uₖ) # Forms uₖ₊₁ : p ← Aᵀuₖ
mul!(vₖ₋₁, A , vₖ, one(T), -γₖ) # Forms vₖ₊₁ : vₖ₋₁ ← Avₖ - γₖvₖ₋₁
mul!(uₖ₋₁, Aᵀ, uₖ, one(T), -βₖ) # Forms uₖ₊₁ : uₖ₋₁ ← Aᵀuₖ - βₖuₖ₋₁

@kaxpy!(n, -γₖ, vₖ₋₁, q) # q ← q - γₖ * vₖ₋₁
@kaxpy!(n, -βₖ, uₖ₋₁, p) # p ← p - βₖ * uₖ₋₁
αₖ = @kdot(n, vₖ₋₁, uₖ) # αₖ = (Avₖ- γₖvₖ₋₁)ᵀuₖ

αₖ = @kdot(n, q, uₖ) # αₖ = qᵀuₖ
@kaxpy!(n, -αₖ, vₖ, vₖ₋₁) # vₖ₋₁ ← vₖ₋₁ - αₖ * vₖ
@kaxpy!(n, -αₖ, uₖ, uₖ₋₁) # uₖ₋₁ ← uₖ₋₁ - αₖ * uₖ

@kaxpy!(n, -αₖ, vₖ, q) # q ← q - αₖ * vₖ
@kaxpy!(n, -αₖ, uₖ, p) # p ← p - αₖ * uₖ
qᵗp = @kdot(n, uₖ₋₁, vₖ₋₁) # qᵗp = ⟨Avₖ - γₖvₖ₋₁ - αₖvₖ, Aᵀuₖ - βₖuₖ₋₁ -αₖuₖ⟩
βₖ₊₁ = √(abs(qᵗp)) # βₖ₊₁ = √(|qᵗp|)
γₖ₊₁ = qᵗp / βₖ₊₁ # γₖ₊₁ = qᵗp / βₖ₊₁

qᵗp = @kdot(n, p, q) # qᵗp = ⟨q,p⟩
βₖ₊₁ = √(abs(qᵗp)) # βₖ₊₁ = √(|qᵗp|)
γₖ₊₁ = qᵗp / βₖ₊₁ # γₖ₊₁ = qᵗp / βₖ₊₁
# Compute vₖ₊₁ and uₖ₊₁.
if qᵗp ≠ zero(T)
@. vₖ₋₁ = vₖ₋₁ / βₖ₊₁ # βₖ₊₁vₖ₊₁ = Avₖ - γₖvₖ₋₁ - αₖvₖ
@. uₖ₋₁ = uₖ₋₁ / γₖ₊₁ # γₖ₊₁uₖ₊₁ = Aᵀuₖ - βₖuₖ₋₁ - αₖuₖ
end

# Update the QR factorization of Tₖ₊₁.ₖ = Qₖ [ Rₖ ].
# [ Oᵀ ]
Expand Down Expand Up @@ -201,14 +204,9 @@ function qmr!(solver :: QmrSolver{T,S}, A, b :: AbstractVector{T}; c :: Abstract
# xₖ ← xₖ₋₁ + ζₖ * wₖ
@kaxpy!(n, ζₖ, wₖ, x)

# Compute vₖ₊₁ and uₖ₊₁.
@. vₖ₋₁ = vₖ # vₖ₋₁ ← vₖ
@. uₖ₋₁ = uₖ # uₖ₋₁ ← uₖ

if qᵗp ≠ zero(T)
@. vₖ = q / βₖ₊₁ # βₖ₊₁vₖ₊₁ = q
@. uₖ = p / γₖ₊₁ # γₖ₊₁uₖ₊₁ = p
end
# Update uₖ₋₁, vₖ₋₁, uₖ and vₖ.
@kswap(uₖ₋₁, uₖ)
@kswap(vₖ₋₁, vₖ)

# Compute τₖ₊₁ = τₖ + ‖vₖ₊₁‖²
τₖ₊₁ = τₖ + @kdot(n, vₖ, vₖ)
Expand Down
8 changes: 4 additions & 4 deletions test/test_alloc.jl
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Expand Up @@ -364,8 +364,8 @@ function test_alloc()
@test (VERSION < v"1.5") || (inplace_trilqr_bytes == 208)

# BILQ needs:
# - 8 n-vectors: uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, d̅, p, q
storage_bilq(n) = 8 * n
# - 6 n-vectors: uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, d̅
storage_bilq(n) = 6 * n
storage_bilq_bytes(n) = 8 * storage_bilq(n)

expected_bilq_bytes = storage_bilq_bytes(n)
Expand Down Expand Up @@ -409,8 +409,8 @@ function test_alloc()
@test (VERSION < v"1.5") || (inplace_minres_qlp_bytes == 208)

# QMR needs:
# - 9 n-vectors: uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, wₖ₋₁, wₖ, p, q
storage_qmr(n) = 9 * n
# - 7 n-vectors: uₖ₋₁, uₖ, vₖ₋₁, vₖ, x, wₖ₋₁, wₖ
storage_qmr(n) = 7 * n
storage_qmr_bytes(n) = 8 * storage_qmr(n)

expected_qmr_bytes = storage_qmr_bytes(n)
Expand Down
2 changes: 1 addition & 1 deletion test/test_show.jl
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@@ -1,4 +1,4 @@
@testset "Increase coverage of show" begin
@testset "show" begin
solver = Krylov.SimpleStats(true, true, Float64[], Float64[], "t")
io = IOBuffer()
show(io, solver)
Expand Down