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Add an implementation of USYMLQR #886

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More debug when I find time...
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amontoison committed Jan 6, 2025
commit e6b1e3436e35e441f1959b7366bca7d7972f2f2c
2 changes: 1 addition & 1 deletion docs/src/examples/usymlqr.md
Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,7 @@ c = -b
# [D A] [x] = [b]
# [Aᴴ 0] [y] [c]
opH = BlockDiagonalOperator(inv(D), eye(n))
(x, y, stats) = usymlqr(A, b, c, M=D, ldiv=true)
(x, y, stats) = usymlqr(A, b, c, M=inv(D))
K = [D A; A' zeros(n,n)]
B = [b; c]
r = B - K * [x; y]
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39 changes: 19 additions & 20 deletions src/usymlqr.jl
Original file line number Diff line number Diff line change
Expand Up @@ -215,8 +215,6 @@ kwargs_usymlqr = (:transfer_to_usymcg, :M, :N, :ldiv, :atol, :rtol, :itmax, :tim
error("c must be nonzero")
end

ε = atol + rtol * rNorm
κ = zero(T)
(verbose > 0) && @printf(iostream, "%4s %7s %7s %7s\n", "k", "αₖ", "βₖ", "γₖ")
kdisplay(iter, verbose) && @printf(iostream, "%4d %7.1e %7.1e %7.1e\n", iter, αₖ, βₖ, γₖ)

Expand All @@ -231,10 +229,13 @@ kwargs_usymlqr = (:transfer_to_usymcg, :M, :N, :ldiv, :atol, :rtol, :itmax, :tim
δbarₖ₋₁ = δbarₖ = zero(FC) # Coefficients of Rₖ₋₁ and Rₖ modified over the course of two iterations

# Stopping criterion.
rNorm_LS = β₁
rNorm_LN = γ₁
solved_LS = rNorm_LS ≤ ε
solved_LN = rNorm_LN ≤ ε
rNorm_LS = βₖ
rNorm_LN = γₖ
ε_LS = atol + rtol * rNorm_LS
ε_LN = atol + rtol * rNorm_LN
κ = zero(T)
solved_LS = rNorm_LS ≤ ε_LS
solved_LN = rNorm_LN ≤ ε_LN
solved = solved_LS && solved_LN
inconsistent = false
tired = iter ≥ itmax
Expand Down Expand Up @@ -265,15 +266,15 @@ kwargs_usymlqr = (:transfer_to_usymcg, :M, :N, :ldiv, :atol, :rtol, :itmax, :tim
kaxpy!(n, -conj(αₖ), N⁻¹vₖ, p) # p ← p - ᾱₖ * N⁻¹vₖ

# Compute vₖ₊₁ and uₖ₊₁
MisI || mulorldiv!(uₖ₊₁, M, q, ldiv) # βₖ₊₁uₖ₊₁ = MAvₖ - γₖuₖ₋₁ - αₖuₖ
NisI || mulorldiv!(vₖ₊₁, N, p, ldiv) # γₖ₊₁vₖ₊₁ = NAᴴuₖ - βₖvₖ₋₁ - ᾱₖvₖ
MisI || mulorldiv!(M⁻¹uₖ, M, q, ldiv) # βₖ₊₁uₖ₊₁ = MAvₖ - γₖuₖ₋₁ - αₖuₖ
NisI || mulorldiv!(N⁻¹vₖ, N, p, ldiv) # γₖ₊₁vₖ₊₁ = NAᴴuₖ - βₖvₖ₋₁ - ᾱₖvₖ

βₖ₊₁ = knorm_elliptic(m, uₖ₊₁, q) # βₖ₊₁ = ‖uₖ₊₁‖_E
γₖ₊₁ = knorm_elliptic(n, vₖ₊₁, p) # γₖ₊₁ = ‖vₖ₊₁‖_F
βₖ₊₁ = knorm_elliptic(m, M⁻¹uₖ, q) # βₖ₊₁ = ‖uₖ₊₁‖_E
γₖ₊₁ = knorm_elliptic(n, N⁻¹vₖ, p) # γₖ₊₁ = ‖vₖ₊₁‖_F

# Update M⁻¹uₖ₋₁ and N⁻¹vₖ₋₁
M⁻¹uₖ₋₁ .= M⁻¹uₖ
N⁻¹vₖ₋₁ .= N⁻¹vₖ
kcopy!(m, M⁻¹uₖ₋₁, M⁻¹uₖ)
kcopy!(n, N⁻¹vₖ₋₁, N⁻¹vₖ)

# Update the QR factorization of Tₖ₊₁.ₖ = Qₖ [ Rₖ ].
# [ Oᵀ ]
Expand Down Expand Up @@ -455,17 +456,15 @@ kwargs_usymlqr = (:transfer_to_usymcg, :M, :N, :ldiv, :atol, :rtol, :itmax, :tim
# δbarₖ₋₁ = δbarₖ

# Update stopping criterion.
ill_cond_lim = one(T) / Acond ≤ ctol
iter == 1 && (κ = atol + rtol * AᴴrNorm)
user_requested_exit = callback(solver) :: Bool
# ill_cond_lim = one(T) / Acond ≤ ctol
ill_cond_mach = one(T) + one(T) / Acond ≤ one(T)
ill_cond = ill_cond_mach || ill_cond_lim
tired = iter ≥ itmax
solved = rNorm ≤ ε_LS
solved_lq = rNorm_lq ≤ ε_LN
solved_cg = transfer_to_usymcg && (abs(δbarₖ) > eps(T)) && (rNorm_cg ≤ ε_LN)
solved = solved_LS && solved_LN

iter == 1 && (κ = atol + rtol * AᴴrNorm)
user_requested_exit = callback(solver) :: Bool
solved = rNorm ≤ ε
solved_lq = rNorm_lq ≤ ε
solved_cg = transfer_to_usymcg && (abs(δbarₖ) > eps(T)) && (rNorm_cg ≤ ε)
inconsistent = !solved && AᴴrNorm ≤ κ
tired = iter ≥ itmax
timer = time_ns() - start_time
Expand Down
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