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expv error estimate: hermitian only #165

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Feb 14, 2024
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expv error estimate: hermitian only #165

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28 changes: 14 additions & 14 deletions src/krylov_phiv.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -43,27 +43,27 @@ function expv(t, A, b; mode = :happy_breakdown, kwargs...)
end
end
function _expv_hb(t::Tt, A, b;
expmethod = ExpMethodHigham2005Base(),
cache = nothing, kwargs_arnoldi...) where {Tt}
expmethod = ExpMethodHigham2005Base(),
cache = nothing, kwargs_arnoldi...) where {Tt}
# Happy-breakdown mode: first construct Krylov subspace then expv!
Ks = arnoldi(A, b; kwargs_arnoldi...)
w = similar(b, promote_type(Tt, eltype(A), eltype(b)))
expv!(w, t, Ks; cache = cache, expmethod = expmethod)
end
function _expv_ee(t::Tt, A, b; m = min(30, size(A, 1)), tol = 1e-7, rtol = √(tol),
ishermitian::Bool = LinearAlgebra.ishermitian(A),
expmethod = ExpMethodHigham2005Base()) where {Tt}
ishermitian::Bool = LinearAlgebra.ishermitian(A),
expmethod = ExpMethodHigham2005Base()) where {Tt}
# Error-estimate mode: construction of Krylov subspace and expv! at the same time
n = size(A, 1)
T = promote_type(typeof(t), eltype(A), eltype(b))
U = ishermitian ? real(T) : T
Ks = KrylovSubspace{T, U}(n, m)
w = similar(b, promote_type(Tt, eltype(A), eltype(b)))
expv!(w, t, A, b, Ks, get_subspace_cache(Ks); atol = tol, rtol = rtol,
expmethod = expmethod)
ishermitian = ishermitian, expmethod = expmethod)
end
function expv(t::Tt, Ks::KrylovSubspace{T, U}; expmethod = ExpMethodHigham2005(),
kwargs...) where {Tt, T, U}
kwargs...) where {Tt, T, U}
n = size(getV(Ks), 1)
w = Vector{promote_type(Tt, T)}(undef, n)
expv!(w, t, Ks; kwargs...)
Expand All @@ -74,7 +74,7 @@ end
Non-allocating version of `expv` that uses precomputed Krylov subspace `Ks`.
"""
function expv!(w::AbstractVector{Tw}, t::Real, Ks::KrylovSubspace{T, U};
cache = nothing, expmethod = ExpMethodHigham2005Base()) where {Tw, T, U}
cache = nothing, expmethod = ExpMethodHigham2005Base()) where {Tw, T, U}
m, beta, V, H = Ks.m, Ks.beta, getV(Ks), getH(Ks)
@assert length(w)==size(V, 1) "Dimension mismatch"
if cache == nothing
Expand Down Expand Up @@ -102,7 +102,7 @@ end
# or Tw can be Float64, while t is ComplexF32 and T is Float64
# thus they can not share the same TypeVar.
function expv!(w::AbstractVector{Complex{Tw}}, t::Complex{Tt}, Ks::KrylovSubspace{T, U};
cache = nothing, expmethod = ExpMethodHigham2005Base()) where {Tw, Tt, T, U}
cache = nothing, expmethod = ExpMethodHigham2005Base()) where {Tw, Tt, T, U}
m, beta, V, H = Ks.m, Ks.beta, getV(Ks), getH(Ks)
@assert length(w)==size(V, 1) "Dimension mismatch"
if cache === nothing
Expand Down Expand Up @@ -130,9 +130,9 @@ function expv!(w::AbstractVector{Complex{Tw}}, t::Complex{Tt}, Ks::KrylovSubspac
end

function ExponentialUtilities.expv!(w::GPUArraysCore.AbstractGPUVector{Tw},
t::Real, Ks::KrylovSubspace{T, U};
cache = nothing,
expmethod = ExpMethodHigham2005Base()) where {Tw, T, U}
t::Real, Ks::KrylovSubspace{T, U};
cache = nothing,
expmethod = ExpMethodHigham2005Base()) where {Tw, T, U}
m, beta, V, H = Ks.m, Ks.beta, getV(Ks), getH(Ks)
@assert length(w)==size(V, 1) "Dimension mismatch"
if cache === nothing
Expand Down Expand Up @@ -238,7 +238,7 @@ Compute the matrix-phi-vector products using a pre-constructed Krylov subspace.
Formula (10).
"""
function phiv(t, A, b, k; cache = nothing, correct = false, errest = false,
kwargs_arnoldi...)
kwargs_arnoldi...)
Ks = arnoldi(A, b; kwargs_arnoldi...)
w = Matrix{eltype(b)}(undef, length(b), k + 1)
phiv!(w, t, Ks, k; cache = cache, correct = correct, errest = errest)
Expand All @@ -254,8 +254,8 @@ end
Non-allocating version of 'phiv' that uses precomputed Krylov subspace `Ks`.
"""
function phiv!(w::AbstractMatrix, t::Number, Ks::KrylovSubspace{T, U}, k::Integer;
cache = nothing, correct = false,
errest = false) where {T <: Number, U <: Number}
cache = nothing, correct = false,
errest = false) where {T <: Number, U <: Number}
m, beta, V, H = Ks.m, Ks.beta, getV(Ks), getH(Ks)
@assert size(w, 1)==size(V, 1) "Dimension mismatch"
@assert size(w, 2)==k + 1 "Dimension mismatch"
Expand Down
25 changes: 16 additions & 9 deletions src/krylov_phiv_error_estimate.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@
super-/subdiagonal, diagonalizing via `stegr!`.
"""
function expT!(α::AbstractVector{R}, β::AbstractVector{R}, t::Number,
cache::StegrCache{T, R}) where {T, R <: Real}
cache::StegrCache{T, R}) where {T, R <: Real}
LAPACK.stegr!(α, β, cache.sw)
sel = 1:length(α)
@inbounds for i in sel
Expand Down Expand Up @@ -55,12 +55,19 @@
exponential.
"""
function expv!(w::AbstractVector{T}, t::Number, A, b::AbstractVector{T},
Ks::KrylovSubspace{T, B, B}, cache::HSC;
atol::B = 1.0e-8, rtol::B = 1.0e-4,
m = min(Ks.maxiter, size(A, 1)),
verbose::Bool = false,
expmethod = ExpMethodHigham2005Base()) where {B, T <: Number,
HSC <: HermitianSubspaceCache}
Ks::KrylovSubspace{T, B, B}, cache::HSC;
atol::B = 1.0e-8, rtol::B = 1.0e-4,
m = min(Ks.maxiter, size(A, 1)),
ishermitian::Bool = LinearAlgebra.ishermitian(A),
verbose::Bool = false,
expmethod = ExpMethodHigham2005Base()) where {B, T <: Number,
HSC <: HermitianSubspaceCache}
# TODO: this only implements the Lanczos algorithm for Hermitian matrices
# ks.H is tridiagonal, required for the expT! function above to call stegr!()
if !ishermitian
error("Error estimation not yet available for non-Hermitian matrices.")

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end

if m > Ks.maxiter
resize!(Ks, m)
else
Expand All @@ -77,7 +84,7 @@
@. V[:, 1] = b / Ks.beta

ε = atol + rtol * Ks.beta
verbose && @printf("Initial norm: β₀ %e, stopping threshold: %e\n", Ks.beta, ε)
verbose && @printf("Initial norm: β₀ %e, stopping threshold: %e\n", Ks.beta,ε)

α = @diagview(H)
β = @diagview(H, -1)
Expand All @@ -92,7 +99,7 @@
# Saad, Y. (1992). Analysis of some Krylov subspace
# approximations. SIAM Journal on Numerical Analysis.
σ = β[j] * Ks.beta * abs(cache.v[j])
verbose && @printf("iter %d, α[%d] %e, β[%d] %e, σ %e\n", j, j, α[j], j, β[j], σ)
verbose && @printf("iter %d, α[%d] %e, β[%d] %e, σ %e\n", j, j, α[j], j, β[j],σ)
if σ < ε
Ks.m = j
break
Expand Down
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