{
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"cell_type": "code",
"source": [
"using Revise\n",
"using PseudoArcLengthContinuation, LinearAlgebra, Plots, SparseArrays;\n",
"const Cont = PseudoArcLengthContinuation\n"
],
"outputs": [
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"PseudoArcLengthContinuation"
]
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"source": [
"f1(u, v) = u^2*v\n",
"\n",
"function F_bru(x, α, β; D1 = 0.008, D2 = 0.004, l = 1.0)\n",
"\tn = div(length(x), 2)\n",
"\th = 1.0 / (n+1); h2 = h*h\n",
"\n",
"\tu = @view x[1:n]\n",
"\tv = @view x[n+1:2n]\n",
"\n",
"\t# output\n",
"\tf = similar(x)\n",
"\n",
"\tf[1] = u[1] - α\n",
"\tf[n] = u[n] - α\n",
"\tfor i=2:n-1\n",
"\t\tf[i] = D1/l^2 * (u[i-1] - 2u[i] + u[i+1]) / h2 - (β + 1) * u[i] + α + f1(u[i], v[i])\n",
"\tend\n",
"\n\n",
"\tf[n+1] = v[1] - β / α\n",
"\tf[end] = v[n] - β / α;\n",
"\tfor i=2:n-1\n",
"\t\tf[n+i] = D2/l^2 * (v[i-1] - 2v[i] + v[i+1]) / h2 + β * u[i] - f1(u[i], v[i])\n",
"\tend\n",
"\n",
"\treturn f\n",
"end\n",
"\n",
"function Jac_mat(x, α, β; D1 = 0.008, D2 = 0.004, l = 1.0)\n",
"\tn = div(length(x), 2)\n",
"\th = 1.0 / (n+1); hh = h*h\n",
"\n",
"\tJ = zeros(2n, 2n)\n",
"\n",
"\tJ[1, 1] = 1.0\n",
"\tfor i=2:n-1\n",
"\t\tJ[i, i-1] = D1 / hh/l^2\n",
"\t\tJ[i, i] = -2D1 / hh/l^2 - (β + 1) + 2x[i] * x[i+n]\n",
"\t\tJ[i, i+1] = D1 / hh/l^2\n",
"\t\tJ[i, i+n] = x[i]^2\n",
"\tend\n",
"\tJ[n, n] = 1.0\n",
"\n",
"\tJ[n+1, n+1] = 1.0\n",
"\tfor i=n+2:2n-1\n",
"\t\tJ[i, i-n] = β - 2x[i-n] * x[i]\n",
"\t\tJ[i, i-1] = D2 / hh/l^2\n",
"\t\tJ[i, i] = -2D2 / hh/l^2 - x[i-n]^2\n",
"\t\tJ[i, i+1] = D2 / hh/l^2\n",
"\tend\n",
"\tJ[2n, 2n] = 1.0\n",
"\treturn J\n",
"end\n",
"\n",
"function Jac_sp(x, α, β; D1 = 0.008, D2 = 0.004, l = 1.0)\n",
"\t# compute the Jacobian using a sparse representation\n",
"\tn = div(length(x), 2)\n",
"\th = 1.0 / (n+1); hh = h*h\n",
"\n",
"\tdiag = zeros(2n)\n",
"\tdiagp1 = zeros(2n-1)\n",
"\tdiagm1 = zeros(2n-1)\n",
"\n",
"\tdiagpn = zeros(n)\n",
"\tdiagmn = zeros(n)\n",
"\n",
"\tdiag[1] = 1.0\n",
"\tdiag[n] = 1.0\n",
"\tdiag[n + 1] = 1.0\n",
"\tdiag[end] = 1.0\n",
"\n",
"\tfor i=2:n-1\n",
"\t\tdiagm1[i-1] = D1 / hh/l^2\n",
"\t\tdiag[i] = -2D1 / hh/l^2 - (β + 1) + 2x[i] * x[i+n]\n",
"\t\tdiagp1[i] = D1 / hh/l^2\n",
"\t\tdiagpn[i] = x[i]^2\n",
"\tend\n",
"\n",
"\tfor i=n+2:2n-1\n",
"\t\tdiagmn[i-n] = β - 2x[i-n] * x[i]\n",
"\t\tdiagm1[i-1] = D2 / hh/l^2\n",
"\t\tdiag[i] = -2D2 / hh/l^2 - x[i-n]^2\n",
"\t\tdiagp1[i] = D2 / hh/l^2\n",
"\tend\n",
"\treturn spdiagm(0 => diag, 1 => diagp1, -1 => diagm1, n => diagpn, -n => diagmn)\n",
"end\n",
"\n\n\n",
"function finalise_solution(z, tau, step, contResult)\n",
"\tn = div(length(z), 2)\n",
"\tprintstyled(color=:red, \"--> Solution constante = \", norm(diff(z[1:n])), \" - \", norm(diff(z[n+1:2n])), \"\\n\")\n",
"end"
],
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"finalise_solution (generic function with 1 method)"
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"source": [
"n = 101\n",
"# const Δ = spdiagm(0=>2ones(N), -1=>0ones(N-1), 1=>-ones(N-1))\n",
"Jac_fd(u0, α, β, l = l) = Cont.finiteDifferences(u->F_bru(u, α, β, l=l), u0)\n",
"\n",
"a = 2.\n",
"b = 5.45\n",
"sol0 = vcat(a*ones(n), b/a*ones(n))\n",
"\n",
"opt_newton = Cont.NewtonPar(tol = 1e-11, verbose = true)\n",
"\t# ca fait dans les 60.2k Allocations\n",
"\tout, hist, flag = @time Cont.newton(\n",
"\t\tx -> F_bru(x, a, b),\n",
"\t\tx -> Jac_mat(x, a, b),\n",
"\t\tsol0,\n",
"\t\topt_newton)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 0.0000e+00 0\n",
" 0.137356 seconds (406.39 k allocations: 19.447 MiB, 7.24% gc time)\n"
]
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"source": [
"opts_br0 = ContinuationPar(dsmin = 0.001, dsmax = 0.0061, ds= 0.0051, pMax = 1.2, save = false, theta = 0.01, detect_fold = true, detect_bifurcation = true, nev = 16, plot_every_n_steps = 50)\n",
"\topts_br0.newtonOptions.maxIter = 20\n",
"\topts_br0.newtonOptions.tol = 1e-8\n",
"\topts_br0.maxSteps = 130\n",
"\n",
"\tbr, u1 = @time Cont.continuation(\n",
"\t\t(x, p) -> F_bru(x, a, b, l = p),\n",
"\t\t(x, p) -> Jac_mat(x, a, b, l = p),\n",
"\t\tout,\n",
"\t\t0.3,\n",
"\t\topts_br0,\n",
"\t\tplot = true,\n",
"\t\tplotsolution = (x;kwargs...)->(N = div(length(x), 2);plot!(x[1:N], subplot=4, label=\"\");plot!(x[N+1:2N], subplot=4, label=\"\")),\n",
"\t\tfinaliseSolution = finalise_solution,\n",
"\t\tprintsolution = x->norm(x, Inf64), verbosity = 0)\n"
],
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"text": [
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n"
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"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
"\u001b[31m--> Solution constante = 0.0 - 0.0\u001b[39m\n",
" 6.448177 seconds (12.56 M allocations: 702.959 MiB, 2.79% gc time)\n"
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"(PseudoArcLengthContinuation.ContResult{Float64,Array{Float64,1},Array{Complex{Float64},2}}\n",
" branch: RecursiveArrayTools.VectorOfArray{Float64,2,Array{Array{Float64,1},1}}\n",
" eig: Array{Tuple{Array{Complex{Float64},1},Array{Complex{Float64},2},Int64}}((131,))\n",
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"On affine la bifurcation de Hopf trouvee dans la cellule precedente"
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"ind_hopf = 1\n",
"\thopfpt = Cont.HopfPoint(br, ind_hopf)\n",
"\n",
"\touthopf, hist, flag = @time Cont.newtonHopf((x, p) -> F_bru(x, a, b, l = p),\n",
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"\t\t\t\tbr, ind_hopf,\n",
"\t\t\t\tNewtonPar(verbose = true))\n",
"\tflag && printstyled(color=:red, \"--> We found a Hopf Point at l = \", outhopf[end-1], \", ω = \", outhopf[end], \" from \",hopfpt[end-1] ,\"\\n\")\n"
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"--> Newton Hopf, the eigenvalue considered here is 0.0021967094536775172 - 2.138088375397315im\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.4633e-03 0\n",
" 1 2 2.2351e-05 2\n",
" 2 3 1.4071e-09 2\n",
" 3 4 3.3500e-14 2\n",
" 0.456584 seconds (312.23 k allocations: 431.424 MiB, 19.50% gc time)\n",
"\u001b[31m--> We found a Hopf Point at l = 0.5232588119304792, ω = 2.1395092895335197 from 0.5258319970887445\u001b[39m\n"
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"br_hopf, u1_hopf = @time Cont.continuationHopf(\n",
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"\t\t\t(x, p, β) -> Jac_mat(x, a, β, l = p),\n",
"\t\t\tbr, ind_hopf,\n",
"\t\t\tb,\n",
"\t\t\tContinuationPar(dsmin = 0.001, dsmax = 0.05, ds= 0.01, pMax = 6.5, pMin = 0.0, a = 2., theta = 0.4, newtonOptions = NewtonPar(verbose=true)))"
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"┌ Warning: Bad way it creates a struct for every p2\n",
"└ @ PseudoArcLengthContinuation /Users/rveltz/work/prog_gd/julia/dev/PseudoArcLengthContinuation/src/HopfCont.jl:185\n"
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"\u001b[31m\u001b[1m##################################################\u001b[22m\u001b[39m\n",
"\u001b[31m\u001b[1m*********** ArcLengthContinuationNewton *************\u001b[22m\u001b[39m\n",
"\n",
"\u001b[35m\u001b[1m*********** CONVERGE INITIAL GUESS *************\u001b[22m\u001b[39m\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.4633e-03 0\n",
" 1 2 2.2351e-05 2\n",
" 2 3 1.4071e-09 2\n",
" 3 4 3.3500e-14 2\n",
"\n",
"--> convergence of initial guess = \u001b[32mOK\u001b[39m\n",
"--> p = 5.45, initial step\n",
"\n",
"\u001b[35m\u001b[1m*********** COMPUTING TANGENTS *************\u001b[22m\u001b[39m\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.6314e-03 0\n",
" 1 2 4.5770e-08 2\n",
" 2 3 4.4247e-14 2\n",
"\n",
"--> convergence of initial guess = \u001b[32mOK\u001b[39m\n",
"\n",
"--> p = 5.450200000000001, initial step (bis)\n",
"--> Start continuation from p = 5.45\n",
"########################################################################\n",
"Start of Continuation Step 0 : Parameter: p1 = 5.4624e+00 from 5.4500e+00\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.6310e-03 0\n",
" 1 1 2.1484e-07 ( 2, 2)\n"
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.6152e-02 0\n",
" 1 1 5.8455e-06 ( 2, 2)\n",
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"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 2 : Parameter: p1 = 5.5597e+00 from 5.4977e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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" 3 1 1.1325e-13 ( 2, 2)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 4 : Parameter: p1 = 5.6837e+00 from 5.6217e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 7.1007e-03 0\n",
" 1 1 8.9484e-05 ( 2, 2)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 2.7672\n",
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"Start of Continuation Step 5 : Parameter: p1 = 5.7458e+00 from 5.6837e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 6.3397e-03 0\n",
" 1 1 6.6431e-05 ( 2, 2)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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" 3 1 1.4672e-13 ( 2, 2)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 2.7672\n",
"########################################################################\n",
"Start of Continuation Step 7 : Parameter: p1 = 5.8698e+00 from 5.8078e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.2141e-03 0\n",
" 1 1 3.9305e-05 ( 2, 2)\n",
" 2 1 2.2842e-09 ( 2, 2)\n",
" 3 1 7.3495e-14 ( 2, 2)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 2.7672\n",
"########################################################################\n",
"Start of Continuation Step 8 : Parameter: p1 = 5.9318e+00 from 5.8698e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.7863e-03 0\n",
" 1 1 3.1215e-05 ( 2, 2)\n",
" 2 1 1.3083e-09 ( 2, 2)\n",
" 3 1 1.2024e-13 ( 2, 2)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 2.7672\n",
"########################################################################\n",
"Start of Continuation Step 9 : Parameter: p1 = 5.9939e+00 from 5.9318e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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"Start of Continuation Step 10 : Parameter: p1 = 6.0559e+00 from 5.9939e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.1078e-03 0\n",
" 1 1 2.0648e-05 ( 2, 2)\n",
" 2 1 5.2915e-10 ( 2, 2)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 11 : Parameter: p1 = 6.1179e+00 from 6.0559e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 3.8342e-03 0\n",
" 1 1 1.7112e-05 ( 2, 2)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 12 : Parameter: p1 = 6.1800e+00 from 6.1179e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 3.5938e-03 0\n",
" 1 1 1.4357e-05 ( 2, 2)\n",
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"Start of Continuation Step 13 : Parameter: p1 = 6.2420e+00 from 6.1800e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"\n",
" Newton Iterations \n",
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"\n",
" Newton Iterations \n",
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"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
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"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
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" Newton Iterations \n",
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" 2 1 2.2932e-11 ( 2, 2)\n",
"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 2.8432\n",
" 14.569767 seconds (9.82 M allocations: 14.934 GiB, 18.78% gc time)\n"
]
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"text/plain": [
"(PseudoArcLengthContinuation.ContResult{Float64,Array{Float64,1},Array{Complex{Float64},2}}\n",
" branch: RecursiveArrayTools.VectorOfArray{Float64,2,Array{Array{Float64,1},1}}\n",
" eig: Array{Tuple{Array{Complex{Float64},1},Array{Complex{Float64},2},Int64}}((1,))\n",
" bifpoint: Array{Tuple{Symbol,Int64,Float64,Float64,Array{Float64,1},Array{Float64,1},Int64}}((0,))\n",
" stability: Array{Bool}((1,)) Bool[false]\n",
" n_imag: Array{Int64}((1,)) [0]\n",
" n_unstable: Array{Int64}((1,)) [0]\n",
", PseudoArcLengthContinuation.BorderedVector{Array{Float64,1},Float64}([2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0 … 3.2761, 3.2761, 3.2761, 3.2761, 3.2761, 3.2761, 3.2761, 3.2761, 0.281741, 2.40871], 6.552192506676094), PseudoArcLengthContinuation.BorderedVector{Array{Float64,1},Float64}([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.620359, 0.620359, 0.620359, 0.620359, 0.620359, 0.620359, 0.620359, 0.620359, -0.116094, 0.257022], 1.2407185524290318))"
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{
"cell_type": "markdown",
"source": [
"On essaie de trouver une orbite periodique proche de la bifurcation de Hopf"
],
"metadata": {}
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"cell_type": "code",
"source": [
"function plotPeriodic(outpof,n,M)\n",
"\toutpo = reshape(outpof[1:end-1], 2n, M)\n",
"\tplot(heatmap(outpo[1:n,:], ylabel=\"Time\"),\n",
"\t\t\theatmap(outpo[n+2:end,:]))\n",
"end\n",
"\n",
"ind_hopf = 1\n",
"hopfpt = Cont.HopfPoint(br, ind_hopf)\n",
"\n",
"l_hopf = hopfpt[end-1]\n",
"ωH = hopfpt[end] |> abs\n",
"M = 50\n",
"\n\n",
"orbitguess = zeros(2n, M)\n",
"plot([0, 1], [0, 0])\n",
"\tphase = []; scalphase = []\n",
"\tvec_hopf = br.eig[br.bifpoint[ind_hopf][2]][2][:, br.bifpoint[ind_hopf][end]-1]\n",
"\tfor ii=1:M\n",
"\tt = (ii-1)/(M-1)\n",
"\torbitguess[:, ii] .= real.(hopfpt[1:2n] +\n",
"\t\t\t\t\t\t26*0.1 * vec_hopf * exp(2pi * complex(0, 1) * (t - 0.279))) #k=1\n",
"\tpush!(phase, t);push!(scalphase, dot(orbitguess[:, ii]- hopfpt[1:2n], real.(vec_hopf)))\n",
"end\n",
"\tplot!(phase, scalphase) |> display\n",
"orbitguess_f = vcat(vec(orbitguess), 2pi/ωH) |> vec;"
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{
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"source": [
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"metadata": {
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{
"cell_type": "code",
"source": [
"opt_po = Cont.NewtonPar(tol = 1e-8, verbose = true, maxIter = 50)\n",
"\toutpo_f, hist, flag = @time Cont.newton(\n",
"\t\t\t\t\t\tx -> poTrap(l_hopf + 0.01)(x),\n",
"\t\t\t\t\t\tx -> poTrap(l_hopf + 0.01)(x, :jacsparse),\n",
"\t\t\t\t\t\torbitguess_f,\n",
"\t\t\t\t\t\topt_po)\n",
"\tprintln(\"--> T = \", outpo_f[end])\n",
"\tplotPeriodic(outpo_f,n,M)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.3832e-01 0\n",
" 1 2 6.2039e-03 1\n",
" 2 3 2.3989e-02 1\n",
" 3 4 1.9345e-03 1\n",
" 4 5 4.2416e-05 1\n",
" 5 6 1.6252e-08 1\n",
" 6 7 2.5161e-13 1\n",
" 16.885581 seconds (155.59 k allocations: 4.864 GiB, 5.55% gc time)\n",
"--> T = 3.025391601509498\n"
]
},
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"execution_count": 37,
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"execution_count": 37,
"metadata": {
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{
"cell_type": "code",
"source": [
"opts_po_cont = ContinuationPar(dsmin = 0.0001, dsmax = 0.05, ds= 0.001, pMax = 2.3, maxSteps = 400, secant = true, theta=0.1, plot_every_n_steps = 3, newtonOptions = NewtonPar(verbose = true))\n",
"\tbr_pok2, upo , _= @time Cont.continuation(\n",
"\t\t\t\t\t\t\t(x, p) -> poTrap(p)(x),\n",
"\t\t\t\t\t\t\t(x, p) -> poTrap(p)(x, :jacsparse),\n",
"\t\t\t\t\t\t\toutpo_f, l_hopf + 0.01,\n",
"\t\t\t\t\t\t\topts_po_cont,\n",
"\t\t\t\t\t\t\tplot = true,\n",
"\t\t\t\t\t\t\tplotsolution = (x;kwargs...)->heatmap!(reshape(x[1:end-1], 2*n, M)', subplot=4, ylabel=\"time\"),\n",
"\t\t\t\t\t\t\tprintsolution = u -> u[end])"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\u001b[31m\u001b[1m##################################################\u001b[22m\u001b[39m\n",
"\u001b[31m\u001b[1m*********** ArcLengthContinuationNewton *************\u001b[22m\u001b[39m\n",
"\n",
"\u001b[35m\u001b[1m*********** CONVERGE INITIAL GUESS *************\u001b[22m\u001b[39m\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.5161e-13 0\n",
"\n",
"--> convergence of initial guess = \u001b[32mOK\u001b[39m\n",
"--> p = 0.5358319970887445, initial step\n",
"\n",
"\u001b[35m\u001b[1m*********** COMPUTING TANGENTS *************\u001b[22m\u001b[39m\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.4668e-05 0\n",
" 1 2 2.1042e-07 1\n",
" 2 3 3.6092e-13 1\n",
"\n",
"--> convergence of initial guess = \u001b[32mOK\u001b[39m\n",
"\n",
"--> p = 0.5358519970887445, initial step (bis)\n",
"--> Start continuation from p = 0.5358319970887445\n",
"########################################################################\n",
"Start of Continuation Step 0 : Parameter: p1 = 5.3632e-01 from 5.3583e-01\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.3011e-04 0\n",
" 1 1 1.6952e-08 ( 1, 1)\n"
]
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"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4607999999999999\n",
"########################################################################\n",
"Start of Continuation Step 1 : Parameter: p1 = 5.3707e-01 from 5.3634e-01\n",
"Current step size = 1.4608e-03 Previous step size = 1.0000e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.3265e-04 0\n",
" 1 1 2.0301e-08 ( 1, 1)\n",
" 2 1 2.5308e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4607999999999999\n",
"########################################################################\n",
"Start of Continuation Step 2 : Parameter: p1 = 5.3813e-01 from 5.3706e-01\n",
"Current step size = 2.1339e-03 Previous step size = 1.0000e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 9.3565e-04 0\n",
" 1 1 7.0354e-08 ( 1, 1)\n",
" 2 1 2.6061e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4607999999999999\n",
"########################################################################\n",
"Start of Continuation Step 3 : Parameter: p1 = 5.3975e-01 from 5.3816e-01\n",
"Current step size = 3.1173e-03 Previous step size = 1.4608e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.9761e-03 0\n",
" 1 1 3.1539e-07 ( 1, 1)\n",
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" 2 1 4.6547e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4607999999999999\n",
"########################################################################\n",
"Start of Continuation Step 4 : Parameter: p1 = 5.4223e-01 from 5.3981e-01\n",
"Current step size = 4.5537e-03 Previous step size = 2.1339e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.1522e-03 0\n",
" 1 1 1.4031e-06 ( 1, 1)\n",
" 2 1 5.9161e-12 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 2 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4607999999999999\n",
"########################################################################\n",
"Start of Continuation Step 5 : Parameter: p1 = 5.4607e-01 from 5.4236e-01\n",
"Current step size = 6.6520e-03 Previous step size = 3.1173e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 8.6571e-03 0\n",
" 1 1 6.1684e-06 ( 1, 1)\n",
" 2 1 1.1191e-10 ( 1, 1)\n",
" 3 1 2.4186e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 6 : Parameter: p1 = 5.5202e-01 from 5.4632e-01\n",
"Current step size = 9.5909e-03 Previous step size = 4.5537e-03\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.7464e-02 0\n",
" 1 1 2.5536e-05 ( 1, 1)\n",
" 2 1 1.8711e-09 ( 1, 1)\n"
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 7 : Parameter: p1 = 5.6139e-01 from 5.5250e-01\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 3.4402e-02 0\n",
" 1 1 1.0139e-04 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 8 : Parameter: p1 = 5.7628e-01 from 5.6226e-01\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 6.5906e-02 0\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 9 : Parameter: p1 = 5.9999e-01 from 5.7776e-01\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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" 3 1 1.1244e-11 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 10 : Parameter: p1 = 6.3742e-01 from 6.0230e-01\n",
"Current step size = 4.1446e-02 Previous step size = 1.9937e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.0903e-01 0\n",
" 1 1 4.0590e-03 ( 1, 1)\n",
" 2 1 2.4998e-05 ( 1, 1)\n",
" 3 1 3.7728e-10 ( 1, 1)\n",
" 4 1 1.7953e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 4 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4232\n",
"########################################################################\n",
"Start of Continuation Step 11 : Parameter: p1 = 6.8651e-01 from 6.4065e-01\n",
"Current step size = 5.0000e-02 Previous step size = 2.8746e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.4842e-01 0\n",
" 1 1 6.5633e-03 ( 1, 1)\n",
" 2 1 4.4919e-05 ( 1, 1)\n",
" 3 1 8.6777e-10 ( 1, 1)\n",
" 4 1 1.5847e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 4 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4232\n",
"########################################################################\n",
"Start of Continuation Step 12 : Parameter: p1 = 7.3805e-01 from 6.8954e-01\n",
"Current step size = 5.0000e-02 Previous step size = 4.1446e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.8823e-01 0\n",
" 1 1 5.0369e-03 ( 1, 1)\n",
" 2 1 1.6777e-05 ( 1, 1)\n"
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 13 : Parameter: p1 = 7.9002e-01 from 7.3990e-01\n",
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"\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 14 : Parameter: p1 = 8.4210e-01 from 7.9107e-01\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 15 : Parameter: p1 = 8.9430e-01 from 8.4272e-01\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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" 3 1 1.2538e-13 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 16 : Parameter: p1 = 9.4658e-01 from 8.9468e-01\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.4308e-02 0\n",
" 1 1 1.3395e-03 ( 1, 1)\n",
" 2 1 2.5313e-07 ( 1, 1)\n",
" 3 1 9.4771e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 17 : Parameter: p1 = 9.9891e-01 from 9.4681e-01\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.7096e-02 0\n",
" 1 1 1.1123e-03 ( 1, 1)\n",
" 2 1 1.3974e-07 ( 1, 1)\n",
" 3 1 8.5336e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 18 : Parameter: p1 = 1.0513e+00 from 9.9905e-01\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.4186e-02 0\n",
" 1 1 9.6321e-04 ( 1, 1)\n",
" 2 1 8.8951e-08 ( 1, 1)\n"
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" 3 1 7.6920e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 19 : Parameter: p1 = 1.1036e+00 from 1.0513e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.4002e-02 0\n",
" 1 1 8.6063e-04 ( 1, 1)\n",
" 2 1 6.2937e-08 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"########################################################################\n",
"Start of Continuation Step 20 : Parameter: p1 = 1.1559e+00 from 1.1036e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.5499e-02 0\n",
" 1 1 7.8606e-04 ( 1, 1)\n",
" 2 1 4.7949e-08 ( 1, 1)\n",
" 3 1 6.6152e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 21 : Parameter: p1 = 1.2082e+00 from 1.1559e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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" 1 1 7.2815e-04 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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" 0 1 5.1038e-02 0\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 23 : Parameter: p1 = 1.3126e+00 from 1.2604e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.4216e-02 0\n",
" 1 1 6.3163e-04 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 24 : Parameter: p1 = 1.3648e+00 from 1.3126e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 25 : Parameter: p1 = 1.4169e+00 from 1.3647e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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" 1 1 5.2490e-04 ( 1, 1)\n",
" 2 1 1.8723e-08 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 26 : Parameter: p1 = 1.4689e+00 from 1.4168e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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" 1 1 4.6104e-04 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 27 : Parameter: p1 = 1.5209e+00 from 1.4689e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 28 : Parameter: p1 = 1.5729e+00 from 1.5209e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.9994e-02 0\n",
" 1 1 3.3781e-04 ( 1, 1)\n",
" 2 1 2.1204e-08 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
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"Start of Continuation Step 29 : Parameter: p1 = 1.6249e+00 from 1.5729e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.6768e-02 0\n",
" 1 1 3.2215e-04 ( 1, 1)\n",
" 2 1 3.0598e-08 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 30 : Parameter: p1 = 1.6768e+00 from 1.6249e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 5.1548e-02 0\n",
" 1 1 3.6760e-04 ( 1, 1)\n",
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" 3 1 3.4444e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"########################################################################\n",
"Start of Continuation Step 31 : Parameter: p1 = 1.7288e+00 from 1.6768e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 4.4558e-02 0\n",
" 1 1 4.6661e-04 ( 1, 1)\n",
" 2 1 7.3095e-08 ( 1, 1)\n",
" 3 1 3.3558e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 32 : Parameter: p1 = 1.7808e+00 from 1.7288e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 3.6590e-02 0\n",
" 1 1 5.7885e-04 ( 1, 1)\n",
" 2 1 1.3453e-07 ( 1, 1)\n",
" 3 1 3.2502e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 33 : Parameter: p1 = 1.8329e+00 from 1.7809e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.8967e-02 0\n",
" 1 1 6.1794e-04 ( 1, 1)\n",
" 2 1 2.2004e-07 ( 1, 1)\n"
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"text": [
" 3 1 3.1204e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 34 : Parameter: p1 = 1.8851e+00 from 1.8330e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 2.2835e-02 0\n",
" 1 1 5.2271e-04 ( 1, 1)\n",
" 2 1 2.0618e-07 ( 1, 1)\n",
" 3 1 3.0281e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 35 : Parameter: p1 = 1.9374e+00 from 1.8852e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.8364e-02 0\n",
" 1 1 3.5272e-04 ( 1, 1)\n",
" 2 1 1.2122e-07 ( 1, 1)\n",
" 3 1 2.8854e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"########################################################################\n",
"Start of Continuation Step 36 : Parameter: p1 = 1.9897e+00 from 1.9375e+00\n",
"Current step size = 5.0000e-02 Previous step size = 5.0000e-02\n",
"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.5064e-02 0\n",
" 1 1 2.1037e-04 ( 1, 1)\n",
" 2 1 5.6889e-08 ( 1, 1)\n"
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 37 : Parameter: p1 = 2.0421e+00 from 1.9898e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.2557e-02 0\n",
" 1 1 1.2855e-04 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 38 : Parameter: p1 = 2.0946e+00 from 2.0422e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
" 0 1 1.0676e-02 0\n",
" 1 1 8.6031e-05 ( 1, 1)\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 39 : Parameter: p1 = 2.1470e+00 from 2.0946e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
"\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
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"Start of Continuation Step 40 : Parameter: p1 = 2.1995e+00 from 2.1471e+00\n",
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"\n",
" Newton Iterations \n",
" Iterations Func-count f(x) Linear-Iterations\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"Start of Continuation Step 41 : Parameter: p1 = 2.2520e+00 from 2.1996e+00\n",
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"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
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"\n",
" Newton Iterations \n",
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" 3 1 2.4307e-14 ( 1, 1)\n",
"\u001b[32m--> Step Converged in 3 Nonlinear Solver Iterations!\u001b[39m\n",
"--> predictor = Secant\n",
"1 + contparams.a * factor ^ 2 = 1.4418\n",
"389.917333 seconds (22.41 M allocations: 108.193 GiB, 6.11% gc time)\n"
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