diff --git a/src/perform_step/linear_perform_step.jl b/src/perform_step/linear_perform_step.jl index 295c337b5e..613b77e941 100644 --- a/src/perform_step/linear_perform_step.jl +++ b/src/perform_step/linear_perform_step.jl @@ -23,7 +23,7 @@ function perform_step!(integrator, cache::MagnusMidpointCache, repeat_step = fal u .= expv(dt, L, u; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else - A = Matrix(L) #size(L) == () ? convert(Number, L) : convert(AbstractMatrix, L) + A = convert(AbstractMatrix, L) u .= exponential!(dt * A, exp_method, exp_cache) * u end @@ -52,24 +52,19 @@ function perform_step!(integrator, cache::LieRK4Cache, repeat_step = false) Y1 = uprev update_coefficients!(L, Y1, p, t) - A = Matrix(deepcopy(L)) - k1 = dt * A + k1 = dt * convert(AbstractMatrix, L) Y2 = exponential!(k1 / 2, exp_method, exp_cache) * uprev update_coefficients!(L, Y2, p, t) - B = Matrix(deepcopy(L)) - - k2 = dt * B + k2 = dt * convert(AbstractMatrix, L) Y3 = exponential!(k2 / 2, exp_method, exp_cache) * uprev update_coefficients!(L, Y3, p, t) - C = Matrix(deepcopy(L)) - k3 = dt * C + k3 = dt * convert(AbstractMatrix, L) Y4 = exponential!(k3 - k1 / 2, exp_method, exp_cache) * Y2 update_coefficients!(L, Y4, p, t) - D = Matrix(deepcopy(L)) - k4 = dt * D + k4 = dt * convert(AbstractMatrix, L) y1_2 = exponential!((3 * k1 + 2 * k2 + 2 * k3 - k4) / 12, exp_method, exp_cache) * uprev @@ -108,20 +103,16 @@ function perform_step!(integrator, cache::RKMK4Cache, repeat_step = false) L = integrator.f.f update_coefficients!(L, uprev, p, t) - A = Matrix(deepcopy(L)) - k1 = dt * A + k1 = dt * convert(AbstractMatrix, L) update_coefficients!(L, exponential!(k1 / 2, exp_method, exp_cache) * uprev, p, t) - B = Matrix(deepcopy(L)) - k2 = dt * B + k2 = dt * convert(AbstractMatrix, L) update_coefficients!(L, exponential!(k1 / 2 - (k1 * k2 - k2 * k1) / 8, exp_method, exp_cache) * uprev, p, t) - C = Matrix(deepcopy(L)) - k3 = dt * C + k3 = dt * convert(AbstractMatrix, L) update_coefficients!(L, exponential!(k3, exp_method, exp_cache) * uprev, p, t) - D = Matrix(deepcopy(L)) - k4 = dt * D + k4 = dt * convert(AbstractMatrix, L) if alg.krylov u .= expv(1 / 6, (k1 + 2 * k2 + 2 * k3 + k4 - (k1 * k4 - k4 * k1) / 2), uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, @@ -156,11 +147,9 @@ function perform_step!(integrator, cache::RKMK2Cache, repeat_step = false) L = integrator.f.f update_coefficients!(L, uprev, p, t) - A = Matrix(deepcopy(L)) - k1 = dt * A + k1 = dt * convert(AbstractMatrix, L) update_coefficients!(L, exponential!(k1, exp_method, exp_cache) * uprev, p, t) - B = Matrix(deepcopy(L)) - k2 = dt * B + k2 = dt * convert(AbstractMatrix, L) if alg.krylov u .= expv(1 / 2, (k1 + k2), uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) @@ -191,14 +180,14 @@ function perform_step!(integrator, cache::CG3Cache, repeat_step = false) L = integrator.f.f update_coefficients!(L, uprev, p, t) - A = Matrix(deepcopy(L)) + A = deepcopy(convert(AbstractMatrix, L)) v2 = exponential!((3 / 4) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v2, p, t + (3 * dt / 4)) - B = Matrix(deepcopy(L)) + B = deepcopy(convert(AbstractMatrix, L)) v3 = exponential!((119 / 216) * dt * B, exp_method, exp_cache) * exponential!((17 / 108) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v3, p, t + (17 * dt / 24)) - C = Matrix(deepcopy(L)) + C = convert(AbstractMatrix, L) u .= (exponential!(dt * (24 / 17) * C, exp_method, exp_cache) * exponential!(dt * (-2 / 3) * B, exp_method, exp_cache) * exponential!(dt * (13 / 51) * A, exp_method, exp_cache)) * @@ -227,11 +216,9 @@ function perform_step!(integrator, cache::CG2Cache, repeat_step = false) L = integrator.f.f update_coefficients!(L, uprev, p, t) - A = Matrix(deepcopy(L)) - k1 = dt * A + k1 = dt * convert(AbstractMatrix, L) update_coefficients!(L, exponential!(k1, exp_method, exp_cache) * uprev, p, t) - B = Matrix(deepcopy(L)) - k2 = dt * B + k2 = dt * convert(AbstractMatrix, L) u .= (exponential!((1 / 2) * (k1), exp_method, exp_cache) * (exponential!((1 / 2) * k2, exp_method, exp_cache))) * uprev @@ -258,25 +245,25 @@ function perform_step!(integrator, cache::CG4aCache, repeat_step = false) L = integrator.f.f update_coefficients!(L, uprev, p, t) - A = Matrix(deepcopy(L)) + A = deepcopy(convert(AbstractMatrix, L)) v2 = exponential!((0.8177227988124852) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v2, p, t + (0.8177227988124852 * dt)) - B = Matrix(deepcopy(L)) + B = deepcopy(convert(AbstractMatrix, L)) v3 = exponential!((0.3199876375476427) * dt * B, exp_method, exp_cache) * exponential!((0.0659864263556022) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v3, p, t + (0.3859740639032449 * dt)) - C = Matrix(deepcopy(L)) + C = deepcopy(convert(AbstractMatrix, L)) v4 = exponential!((0.9214417194464946) * dt * C, exp_method, exp_cache) * exponential!((0.4997857776773573) * dt * B, exp_method, exp_cache) * exponential!((-1.0969984448371582) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v4, p, t + (0.3242290522866937 * dt)) - D = Matrix(deepcopy(L)) + D = deepcopy(convert(AbstractMatrix, L)) v5 = exponential!((0.3552358559023322) * dt * D, exp_method, exp_cache) * exponential!((0.2390958372307326) * dt * C, exp_method, exp_cache) * exponential!((1.3918565724203246) * dt * B, exp_method, exp_cache) * exponential!((-1.1092979392113465) * dt * A, exp_method, exp_cache) * uprev update_coefficients!(L, v5, p, t + (0.8768903263420429 * dt)) - E = Matrix(deepcopy(L)) + E = convert(AbstractMatrix, L) u .= (exponential!(dt * (0.3322195591068374) * E, exp_method, exp_cache) * exponential!(dt * (-0.1907142565505889) * D, exp_method, exp_cache) * exponential!(dt * (0.7397813985370780) * C, exp_method, exp_cache) * @@ -304,40 +291,40 @@ function perform_step!(integrator, cache::MagnusAdapt4Cache, repeat_step = false mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L = deepcopy(integrator.f.f) + L = integrator.f.f update_coefficients!(L, uprev, p, t) - A0 = Matrix(L) + A0 = deepcopy(convert(AbstractMatrix, L)) k1 = dt * A0 Q1 = k1 y2 = (1 / 2) * Q1 update_coefficients!(L, exponential!(y2, exp_method, exp_cache) * uprev, p, t + dt / 2) - A1 = Matrix(L) + A1 = deepcopy(convert(AbstractMatrix, L)) k2 = dt * A1 Q2 = k2 - k1 y3 = (1 / 2) * Q1 + (1 / 4) * Q2 update_coefficients!(L, exponential!(y3, exp_method, exp_cache) * uprev, p, t + dt / 2) - A2 = Matrix(L) + A2 = deepcopy(convert(AbstractMatrix, L)) k3 = dt * A2 Q3 = k3 - k2 y4 = Q1 + Q2 update_coefficients!(L, exponential!(y4, exp_method, exp_cache) * uprev, p, t + dt) - A3 = Matrix(L) + A3 = deepcopy(convert(AbstractMatrix, L)) k4 = dt * A3 Q4 = k4 - 2 * k2 + k1 y5 = (1 / 2) * Q1 + (1 / 4) * Q2 + (1 / 3) * Q3 - (1 / 24) * Q4 - (1 / 48) * (Q1 * Q2 - Q2 * Q1) update_coefficients!(L, exponential!(y5, exp_method, exp_cache) * uprev, p, t + dt / 2) - A4 = Matrix(L) + A4 = deepcopy(convert(AbstractMatrix, L)) k5 = dt * A4 Q5 = k5 - k2 y6 = Q1 + Q2 + (2 / 3) * Q3 + (1 / 6) * Q4 - (1 / 6) * (Q1 * Q2 - Q2 * Q1) update_coefficients!(L, exponential!(y6, exp_method, exp_cache) * uprev, p, t + dt) - A5 = Matrix(L) + A5 = convert(AbstractMatrix, L) k6 = dt * A5 Q6 = k6 - 2 * k2 + k1 @@ -374,22 +361,22 @@ function perform_step!(integrator, cache::MagnusNC8Cache, repeat_step = false) mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L1 = deepcopy(integrator.f.f) - - update_coefficients!(L1, u, p, t) - A0 = Matrix(L1) - update_coefficients!(L1, u, p, t + dt / 6) - A1 = Matrix(L1) - update_coefficients!(L1, u, p, t + 2 * dt / 6) - A2 = Matrix(L1) - update_coefficients!(L1, u, p, t + 3 * dt / 6) - A3 = Matrix(L1) - update_coefficients!(L1, u, p, t + 4 * dt / 6) - A4 = Matrix(L1) - update_coefficients!(L1, u, p, t + 5 * dt / 6) - A5 = Matrix(L1) - update_coefficients!(L1, u, p, t + dt) - A6 = Matrix(L1) + L = integrator.f.f + + update_coefficients!(L, u, p, t) + A0 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + dt / 6) + A1 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + 2 * dt / 6) + A2 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + 3 * dt / 6) + A3 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + 4 * dt / 6) + A4 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + 5 * dt / 6) + A5 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, u, p, t + dt) + A6 = convert(AbstractMatrix, L) S1 = A0 + A6 S2 = A1 + A5 @@ -423,7 +410,7 @@ function perform_step!(integrator, cache::MagnusNC8Cache, repeat_step = false) Ω2 = (dt^2) * (Q1 + Q2) Ω3_4_5_6 = (dt^3) * (Q3 + Q4) + (dt^4) * (Q5 + Q6) + (dt^5) * Q7 if alg.krylov - u .= expv(1.0, Ω1 + Ω2 + Ω3_4_5_6, uprev; m = min(alg.m, size(L1, 1)), + u .= expv(1.0, Ω1 + Ω2 + Ω3_4_5_6, uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!(Ω1 + Ω2 + Ω3_4_5_6, exp_method, exp_cache) * uprev @@ -450,16 +437,16 @@ function perform_step!(integrator, cache::MagnusGL4Cache, repeat_step = false) mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L1 = deepcopy(integrator.f.f) - update_coefficients!(L1, uprev, p, t + dt * (1 / 2 - sqrt(3) / 6)) - A1 = Matrix(L1) - update_coefficients!(L1, uprev, p, t + dt * (1 / 2 + sqrt(3) / 6)) - A2 = Matrix(L1) + L = integrator.f.f + update_coefficients!(L, uprev, p, t + dt * (1 / 2 - sqrt(3) / 6)) + A1 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt * (1 / 2 + sqrt(3) / 6)) + A2 = convert(AbstractMatrix, L) Ω = (dt / 2) * (A1 + A2) - (dt^2) * (sqrt(3) / 12) * (A1 * A2 - A2 * A1) if alg.krylov - u .= expv(1.0, Ω, uprev; m = min(alg.m, size(L1, 1)), + u .= expv(1.0, Ω, uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!(Ω, exp_method, exp_cache) * uprev @@ -486,20 +473,17 @@ function perform_step!(integrator, cache::MagnusGL8Cache, repeat_step = false) mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L1 = deepcopy(integrator.f.f) - L2 = deepcopy(integrator.f.f) - L3 = deepcopy(integrator.f.f) - L4 = deepcopy(integrator.f.f) + L = integrator.f.f v1 = (1 / 2) * sqrt((3 + 2 * sqrt(6 / 5)) / 7) v2 = (1 / 2) * sqrt((3 - 2 * sqrt(6 / 5)) / 7) - update_coefficients!(L1, uprev, p, t - dt * v1 + dt / 2) - A1 = Matrix(L1) - update_coefficients!(L4, uprev, p, t + dt * v1 + dt / 2) - A4 = Matrix(L4) - update_coefficients!(L2, uprev, p, t - dt * v2 + dt / 2) - A2 = Matrix(L2) - update_coefficients!(L3, uprev, p, t + dt * v2 + dt / 2) - A3 = Matrix(L3) + update_coefficients!(L, uprev, p, t - dt * v1 + dt / 2) + A1 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt * v1 + dt / 2) + A4 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t - dt * v2 + dt / 2) + A2 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt * v2 + dt / 2) + A3 = convert(AbstractMatrix, L) w1 = (1 / 2) - (1 / 6) * sqrt(5 / 6) w2 = (1 / 2) + (1 / 6) * sqrt(5 / 6) S1 = A1 + A4 @@ -530,7 +514,7 @@ function perform_step!(integrator, cache::MagnusGL8Cache, repeat_step = false) Ω2 = (dt^2) * (Q1 + Q2) Ω3_4_5_6 = (dt^3) * (Q3 + Q4) + (dt^4) * (Q5 + Q6) + (dt^5) * Q7 if alg.krylov - u .= expv(1.0, Ω1 + Ω2 + Ω3_4_5_6, uprev; m = min(alg.m, size(L1, 1)), + u .= expv(1.0, Ω1 + Ω2 + Ω3_4_5_6, uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!(Ω1 + Ω2 + Ω3_4_5_6, exp_method, exp_cache) * uprev @@ -557,21 +541,17 @@ function perform_step!(integrator, cache::MagnusNC6Cache, repeat_step = false) mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L0 = deepcopy(integrator.f.f) - L1 = deepcopy(integrator.f.f) - L2 = deepcopy(integrator.f.f) - L3 = deepcopy(integrator.f.f) - L4 = deepcopy(integrator.f.f) - update_coefficients!(L0, uprev, p, t) - A0 = Matrix(L0) - update_coefficients!(L1, uprev, p, t + dt / 4) - A1 = Matrix(L1) - update_coefficients!(L2, uprev, p, t + dt / 2) - A2 = Matrix(L2) - update_coefficients!(L3, uprev, p, t + 3 * dt / 4) - A3 = Matrix(L3) - update_coefficients!(L4, uprev, p, t + dt) - A4 = Matrix(L4) + L = integrator.f.f + update_coefficients!(L, uprev, p, t) + A0 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt / 4) + A1 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt / 2) + A2 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + 3 * dt / 4) + A3 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt) + A4 = convert(AbstractMatrix, L) B0 = (1 / 90) * (7 * (A0 + A4) + 32 * (A1 + A3) + 12 * (A2)) B1 = (1 / 90) * ((7 / 2) * (A4 - A0) + 8 * (A3 - A1)) B2 = (1 / 90) * ((7 / 4) * (A0 + A4) + 2 * (A1 + A3)) @@ -582,7 +562,7 @@ function perform_step!(integrator, cache::MagnusNC6Cache, repeat_step = false) (B0 * (dt * B2 / 2 - Ω2 / 60) - (dt * B2 / 2 - Ω2 / 60) * B0) * B0) + (3 * dt / 5) * (B1 * Ω2 - Ω2 * B1) if alg.krylov - u .= expv(1.0, Ω1 + Ω2 + Ω3_4, uprev; m = min(alg.m, size(L1, 1)), + u .= expv(1.0, Ω1 + Ω2 + Ω3_4, uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!(Ω1 + Ω2 + Ω3_4, exp_method, exp_cache) * uprev @@ -609,15 +589,13 @@ function perform_step!(integrator, cache::MagnusGL6Cache, repeat_step = false) mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L1 = deepcopy(integrator.f.f) - L2 = deepcopy(integrator.f.f) - L3 = deepcopy(integrator.f.f) - update_coefficients!(L1, uprev, p, t - dt * (sqrt(3 / 20)) + dt / 2) - A1 = Matrix(L1) - update_coefficients!(L2, uprev, p, t + dt / 2) - A2 = Matrix(L2) - update_coefficients!(L3, uprev, p, t + dt * (sqrt(3 / 20)) + dt / 2) - A3 = Matrix(L3) + L = integrator.f.f + update_coefficients!(L, uprev, p, t - dt * (sqrt(3 / 20)) + dt / 2) + A1 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt / 2) + A2 = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt * (sqrt(3 / 20)) + dt / 2) + A3 = convert(AbstractMatrix, L) B0 = (1 / 18) * (5 * (A1 + A3) + 8 * A2) B1 = (sqrt(15) / 36) * (A3 - A1) B2 = (1 / 24) * (A1 + A3) @@ -628,7 +606,7 @@ function perform_step!(integrator, cache::MagnusGL6Cache, repeat_step = false) (B0 * (dt * B2 / 2 - Ω2 / 60) - (dt * B2 / 2 - Ω2 / 60) * B0) * B0) + (3 * dt / 5) * (B1 * Ω2 - Ω2 * B1) if alg.krylov - u .= expv(1.0, Ω1 + Ω2 + Ω3_4, uprev; m = min(alg.m, size(L1, 1)), + u .= expv(1.0, Ω1 + Ω2 + Ω3_4, uprev; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!(Ω1 + Ω2 + Ω3_4, exp_method, exp_cache) * uprev @@ -655,15 +633,14 @@ function perform_step!(integrator, cache::MagnusGauss4Cache, repeat_step = false mass_matrix = integrator.f.mass_matrix exp_method = ExpMethodGeneric() - L1 = deepcopy(integrator.f.f) - L2 = deepcopy(integrator.f.f) - update_coefficients!(L1, uprev, p, t + dt * (1 / 2 + sqrt(3) / 6)) - A = Matrix(L1) - update_coefficients!(L2, uprev, p, t + dt * (1 / 2 - sqrt(3) / 6)) - B = Matrix(L2) + L = integrator.f.f + update_coefficients!(L, uprev, p, t + dt * (1 / 2 + sqrt(3) / 6)) + A = deepcopy(convert(AbstractMatrix, L)) + update_coefficients!(L, uprev, p, t + dt * (1 / 2 - sqrt(3) / 6)) + B = convert(AbstractMatrix, L) if alg.krylov u .= expv(dt, (A + B) ./ 2 + (dt * sqrt(3)) .* (B * A - A * B) ./ 12, u; - m = min(alg.m, size(L1, 1)), opnorm = integrator.opts.internalopnorm, + m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else u .= exponential!((dt / 2) .* (A + B) + @@ -700,8 +677,7 @@ function perform_step!(integrator, cache::LieEulerCache, repeat_step = false) u .= expv(dt, L, u; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else - A = Matrix(L) #size(L) == () ? convert(Number, L) : convert(AbstractMatrix, L) - u .= exponential!(dt * A, exp_method, exp_cache) * u + u .= exponential!(dt * convert(AbstractMatrix, L), exp_method, exp_cache) * u end integrator.f(integrator.fsallast, u, p, t + dt) @@ -734,7 +710,7 @@ function perform_step!(integrator, cache::MagnusLeapfrogCache, repeat_step = fal u .= expv(dt, L, u; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else - A = Matrix(L) #size(L) == () ? convert(Number, L) : convert(AbstractMatrix, L) + A = convert(AbstractMatrix, L) u .= exponential!(dt * A, exp_method, exp_cache) * u end @@ -748,7 +724,7 @@ function perform_step!(integrator, cache::MagnusLeapfrogCache, repeat_step = fal u .= expv(2 * dt, L, uprev2; m = min(alg.m, size(L, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) else - A = Matrix(L) #size(L) == () ? convert(Number, L) : convert(AbstractMatrix, L) + A = convert(AbstractMatrix, L) u .= exponential!(2 * dt * A, exp_method, exp_cache) * uprev2 end uprev = u @@ -774,10 +750,10 @@ function perform_step!(integrator, cache::LinearExponentialConstantCache, repeat_step = false) @unpack t, dt, uprev, f, p = integrator alg = unwrap_alg(integrator, nothing) - A = f.f # assume f to be an ODEFunction wrapped around a linear operator + A = convert(AbstractMatrix, f.f) # assume f to be an ODEFunction wrapped around a linear operator if alg.krylov == :off - u = exp(dt * Matrix(f)) * integrator.u + u = exponential!(dt * A, ExpMethodGeneric()) * integrator.u elseif alg.krylov == :simple u = expv(dt, A, integrator.u; m = min(alg.m, size(A, 1)), opnorm = integrator.opts.internalopnorm, iop = alg.iop) @@ -814,10 +790,10 @@ function perform_step!(integrator, cache::LinearExponentialCache, repeat_step = @unpack tmp, KsCache, exp_cache = cache alg = unwrap_alg(integrator, nothing) exp_method = ExpMethodGeneric() - A = f.f # assume f to be an ODEFunction wrapped around a linear operator + A = convert(AbstractMatrix, f.f) # assume f to be an ODEFunction wrapped around a linear operator if alg.krylov == :off - E = exponential!(dt * Matrix(A), exp_method, exp_cache) + E = exponential!(dt * A, exp_method, exp_cache) mul!(tmp, E, u) elseif alg.krylov == :simple Ks, expv_cache = KsCache