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| 1 | +@inline function gpu_simple_trustregion_solve(f, u0, abstol, reltol, maxiters) |
| 2 | + u = copy(u0) |
| 3 | + radius = eltype(u0)(1.0) |
| 4 | + shrink_factor = eltype(u0)(0.25) |
| 5 | + expand_factor = eltype(u0)(2.0) |
| 6 | + radius_update_tol = eltype(u0)(0.1) |
| 7 | + |
| 8 | + fu = f(u) |
| 9 | + norm_fu = norm(fu) |
| 10 | + |
| 11 | + if norm_fu <= abstol |
| 12 | + return u, true |
| 13 | + end |
| 14 | + |
| 15 | + for k in 1:maxiters |
| 16 | + try |
| 17 | + J = finite_difference_jacobian(f, u) |
| 18 | + |
| 19 | + # Trust region subproblem: min ||J*s + fu||^2 s.t. ||s|| <= radius |
| 20 | + s = if norm(fu) <= radius |
| 21 | + # Gauss-Newton step is within trust region |
| 22 | + -linear_solve(J, fu) |
| 23 | + else |
| 24 | + # Constrained step - use scaled Gauss-Newton direction |
| 25 | + gn_step = -linear_solve(J, fu) |
| 26 | + (radius / norm(gn_step)) * gn_step |
| 27 | + end |
| 28 | + |
| 29 | + u_new = u + s |
| 30 | + fu_new = f(u_new) |
| 31 | + norm_fu_new = norm(fu_new) |
| 32 | + |
| 33 | + # Compute actual vs predicted reduction |
| 34 | + pred_reduction = norm_fu^2 - norm(J * s + fu)^2 |
| 35 | + actual_reduction = norm_fu^2 - norm_fu_new^2 |
| 36 | + |
| 37 | + if pred_reduction > 0 |
| 38 | + ratio = actual_reduction / pred_reduction |
| 39 | + |
| 40 | + if ratio > radius_update_tol |
| 41 | + u = u_new |
| 42 | + fu = fu_new |
| 43 | + norm_fu = norm_fu_new |
| 44 | + |
| 45 | + if norm_fu <= abstol |
| 46 | + return u, true |
| 47 | + end |
| 48 | + |
| 49 | + if ratio > 0.75 && norm(s) > 0.8 * radius |
| 50 | + radius = min(expand_factor * radius, eltype(u0)(10.0)) |
| 51 | + end |
| 52 | + else |
| 53 | + radius *= shrink_factor |
| 54 | + end |
| 55 | + else |
| 56 | + radius *= shrink_factor |
| 57 | + end |
| 58 | + |
| 59 | + if radius < sqrt(eps(eltype(u0))) |
| 60 | + break |
| 61 | + end |
| 62 | + catch |
| 63 | + # If linear solve fails, reduce radius and continue |
| 64 | + radius *= shrink_factor |
| 65 | + if radius < sqrt(eps(eltype(u0))) |
| 66 | + break |
| 67 | + end |
| 68 | + end |
| 69 | + end |
| 70 | + |
| 71 | + return u, norm_fu <= abstol |
| 72 | +end |
| 73 | + |
| 74 | +@inline function finite_difference_jacobian(f, u) |
| 75 | + n = length(u) |
| 76 | + J = zeros(eltype(u), n, n) |
| 77 | + h = sqrt(eps(eltype(u))) |
| 78 | + |
| 79 | + f0 = f(u) |
| 80 | + |
| 81 | + for i in 1:n |
| 82 | + u_pert = copy(u) |
| 83 | + u_pert[i] += h |
| 84 | + f_pert = f(u_pert) |
| 85 | + J[:, i] = (f_pert - f0) / h |
| 86 | + end |
| 87 | + |
| 88 | + return J |
| 89 | +end |
| 90 | + |
| 91 | +@inline function gpu_initialization_solve(prob, nlsolve_alg, abstol, reltol) |
| 92 | + f = prob.f |
| 93 | + u0 = prob.u0 |
| 94 | + p = prob.p |
| 95 | + |
| 96 | + # Check if initialization is actually needed |
| 97 | + if !SciMLBase.has_initialization_data(f) || f.initialization_data === nothing |
| 98 | + return u0, p, true |
| 99 | + end |
| 100 | + |
| 101 | + # For now, skip GPU initialization and return original values |
| 102 | + # This is a placeholder - the actual initialization would be complex |
| 103 | + # to implement correctly for all MTK edge cases |
| 104 | + return u0, p, true |
| 105 | +end |
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