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BiLQR & TriLQR #159

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merged 13 commits into from
Dec 18, 2019
Merged

BiLQR & TriLQR #159

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fc0e34d
BiLQR & TriLQR
amontoison Nov 14, 2019
8125fbc
Improve verbose mode of BiLQR and TriLQR
amontoison Nov 16, 2019
3ab0924
Improve BiLQR and TriLQR statuses
amontoison Nov 16, 2019
8ce1134
Update QMR residual estimate in BiLQR
amontoison Nov 16, 2019
62d3d03
Add ODEs and PDEs adjoint systems
amontoison Nov 16, 2019
ca7ab79
Allows inconsistent dual system in TriLQR
amontoison Nov 16, 2019
f9b6d33
Minor modifications in allocation and multi-precision tests
amontoison Nov 17, 2019
3464945
Correct initial USYMLQ residual norm in TriLQR
amontoison Nov 17, 2019
2fe2b6d
Remove A.tprod syntax in BiLQR and TriLQR
amontoison Nov 21, 2019
35ac5e0
Corrections of BiLQR and TriLQR
Dec 12, 2019
e6ad9cc
Improve the description of BiLQ / BiCG and USYMLQ / USYMCG transfers
amontoison Dec 13, 2019
cadcfbc
Correct norm estimates in BiLQR
amontoison Dec 15, 2019
e7af47e
Update statuses in BiLQR and TriLQR
amontoison Dec 18, 2019
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1 change: 1 addition & 0 deletions docs/src/api.md
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Expand Up @@ -5,6 +5,7 @@ Krylov.KrylovStats
Krylov.SimpleStats
Krylov.LanczosStats
Krylov.SymmlqStats
Krylov.AdjointStats
```

## Utilities
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1 change: 1 addition & 0 deletions docs/src/index.md
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Expand Up @@ -41,6 +41,7 @@ Given a linear operator ``A`` and a right-hand side ``b``, solve ``Ax = b``, whi
Krylov can be installed and tested through the Julia package manager:

```julia
julia> import Pkg
julia> Pkg.add("Krylov")
julia> Pkg.test("Krylov")
```
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2 changes: 2 additions & 0 deletions docs/src/solvers.md
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Expand Up @@ -17,9 +17,11 @@ diom
dqgmres
usymlq
usymqr
trilqr
bilq
cgs
qmr
bilqr
cgls
crls
cgne
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21 changes: 21 additions & 0 deletions src/Krylov.jl
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Expand Up @@ -36,6 +36,15 @@ mutable struct SymmlqStats{T} <: KrylovStats{T}
status :: String
end

"Type for statistics returned by adjoint systems solvers"
mutable struct AdjointStats{T} <: KrylovStats{T}
solved_primal :: Bool
solved_dual :: Bool
residuals_primal :: Vector{T}
residuals_dual :: Vector{T}
status :: String
end

import Base.show

function show(io :: IO, stats :: SimpleStats)
Expand Down Expand Up @@ -72,6 +81,16 @@ function show(io :: IO, stats :: SymmlqStats)
print(io, s)
end

function show(io :: IO, stats :: AdjointStats)
s = "\nAdjoint stats\n"
s *= @sprintf(" solved primal: %s\n", stats.solved_primal)
s *= @sprintf(" solved dual: %s\n", stats.solved_dual)
s *= @sprintf(" residuals primal: %s\n", vec2str(stats.residuals_primal))
s *= @sprintf(" residuals dual: %s\n", vec2str(stats.residuals_dual))
s *= @sprintf(" status: %s\n", stats.status)
print(io, s)
end

include("krylov_aux.jl")
include("krylov_utils.jl")

Expand All @@ -88,10 +107,12 @@ include("diom.jl")

include("usymlq.jl")
include("usymqr.jl")
include("trilqr.jl")

include("bilq.jl")
include("cgs.jl")
include("qmr.jl")
include("bilqr.jl")

include("cgls.jl")
include("crls.jl")
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6 changes: 3 additions & 3 deletions src/bilq.jl
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Expand Up @@ -63,7 +63,7 @@ function bilq(A :: AbstractLinearOperator{T}, b :: AbstractVector{T}; c :: Abstr
d̅ = zeros(T, n) # Last column of D̅ₖ = Vₖ(Qₖ)ᵀ
ζₖ₋₁ = ζbarₖ = zero(T) # ζₖ₋₁ and ζbarₖ are the last components of z̅ₖ = (L̅ₖ)⁻¹β₁e₁
ζₖ₋₂ = ηₖ = zero(T) # ζₖ₋₂ and ηₖ are used to update ζₖ₋₁ and ζbarₖ
δbarₖ₋₁ = δbarₖ = zero(T) # Coefficients of Lₖ₋₁ and L̅ₖ modified during two iterations
δbarₖ₋₁ = δbarₖ = zero(T) # Coefficients of Lₖ₋₁ and L̅ₖ modified over the course of two iterations
norm_vₖ = bNorm / βₖ # ‖vₖ‖ is used for residual norm estimates

# Stopping criterion.
Expand Down Expand Up @@ -178,7 +178,7 @@ function bilq(A :: AbstractLinearOperator{T}, b :: AbstractVector{T}; c :: Abstr
end

# Compute ⟨vₖ,vₖ₊₁⟩ and ‖vₖ₊₁‖
dot_vₖ_vₖ₊₁ = @kdot(n, vₖ₋₁, vₖ)
vₖᵀvₖ₊₁ = @kdot(n, vₖ₋₁, vₖ)
norm_vₖ₊₁ = @knrm2(n, vₖ)

# Compute BiLQ residual norm
Expand All @@ -188,7 +188,7 @@ function bilq(A :: AbstractLinearOperator{T}, b :: AbstractVector{T}; c :: Abstr
else
μₖ = βₖ * (sₖ₋₁ * ζₖ₋₂ - cₖ₋₁ * cₖ * ζₖ₋₁) + αₖ * sₖ * ζₖ₋₁
ωₖ = βₖ₊₁ * sₖ * ζₖ₋₁
rNorm_lq = sqrt(μₖ^2 * norm_vₖ^2 + ωₖ^2 * norm_vₖ₊₁^2 + 2 * μₖ * ωₖ * dot_vₖ_vₖ₊₁)
rNorm_lq = sqrt(μₖ^2 * norm_vₖ^2 + ωₖ^2 * norm_vₖ₊₁^2 + 2 * μₖ * ωₖ * vₖᵀvₖ₊₁)
end
push!(rNorms, rNorm_lq)

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