Skip to content

LSMR: return x = 0 instead of NaN when Aᴴb = 0 #169

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
Jutho merged 2 commits into from
Sep 24, 2026
Merged

LSMR: return x = 0 instead of NaN when Aᴴb = 0 #169

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
2c4e81a
LSMR: return x = 0 when Aᴴb = 0 instead of NaN
ParadaCarleton Sep 24, 2026
0653cfc
Update src/lssolve/lsmr.jl
ParadaCarleton Sep 24, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
33 changes: 18 additions & 15 deletions src/lssolve/lsmr.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,24 @@ function lssolve(operator, b, alg::LSMR, λ_::Real = 0)
v = scale(v₀, one(T))
β = norm(u)
S = typeof(β)
tol::S = alg.tol

# Check for early return, before normalising: ‖Aᴴb‖ = α * β vanishes whenever
# `b` or `Aᴴb` does, and then `x = 0` solves the (damped) least-squares problem
absζ̄ = norm(v)
if absζ̄ <= tol
if alg.verbosity > STARTSTOP_LEVEL
@info """LSMR lssolve converged without any iterations:
* ‖b - A * x ‖ = $(normres2string(β))
* ‖[b - A * x; λ * x] ‖ = $(normres2string(β))
* ‖ Aᴴ(b - A x) - λ^2 x ‖ = $(normres2string(absζ̄))
* number of operations = 1"""
end
return (zerovector(v), ConvergenceInfo(1, u, absζ̄, 0, 1))
elseif alg.verbosity >= STARTSTOP_LEVEL
@info "LSMR lssolve starts with convergence measure ‖ Aᴴ(b - A x) - λ^2 x ‖ = $(normres2string(absζ̄))"
end

u = scale!!(u, 1 / β)
v = scale!!(v, 1 / β)
α = norm(v)
Expand Down Expand Up @@ -41,23 +59,8 @@ function lssolve(operator, b, alg::LSMR, λ_::Real = 0)
numiter = 0
numops = 1 # One (adjoint) function application for v
maxiter = alg.maxiter
tol::S = alg.tol
λ::S = convert(S, λ_)

# Check for early return
if absζ̄ < tol
if alg.verbosity > STARTSTOP_LEVEL
@info """LSMR lssolve converged without any iterations:
* ‖b - A * x ‖ = $(normres2string(β))
* ‖[b - A * x; λ * x] ‖ = $(normres2string(β))
* ‖ Aᴴ(b - A x) - λ^2 x ‖ = $(normres2string(absζ̄))
* number of operations = $numops"""
end
return (x, ConvergenceInfo(1, r, absζ̄, numiter, numops))
elseif alg.verbosity >= STARTSTOP_LEVEL
@info "LSMR lssolve starts with convergence measure ‖ Aᴴ(b - A x) - λ^2 x ‖ = $(normres2string(absζ̄))"
end

while true
numiter += 1
Av = apply_normal(operator, v)
Expand Down
20 changes: 20 additions & 0 deletions test/lssolve.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -111,3 +111,23 @@ end
end
end
end
@testset "LSMR with Aᴴb = 0 ($mode)" for mode in (:vector, :inplace, :outplace, :mixed)
scalartypes = mode === :vector ? (Float32, Float64, ComplexF32, ComplexF64) :
(ComplexF64,)
@testset for T in scalartypes
# the last n rows of A vanish, so both b = 0 and b supported on them give Aᴴb = 0
A = vcat(rand(T, (n, n)), zeros(T, (n, n)))
for b in (zeros(T, 2 * n), vcat(zeros(T, n), rand(T, n))), tol in (0, 1.0e-8)
for λ in (0, rand(real(T)))
x, info = @constinferred lssolve(
wrapop(A, Val(mode)), wrapvec(b, Val(mode)),
LSMR(; tol, verbosity = SILENT_LEVEL), λ
)
@test iszero(unwrapvec(x))
@test unwrapvec(info.residual) == b
@test info.converged == 1
@test info.numops == 1
end
end
end
end
Loading