remove update_minaug_every_step = 1

docs/src/tutorials/ode/lorenz84-PO.md

@@ -50,9 +50,9 @@ prob = BK.BifurcationProblem(Lor, z0, parlor, (@lens _.F);
 	record_from_solution = (x, p) -> (X = x[1], Y = x[2], Z = x[3], U = x[4]),)
 
 opts_br = ContinuationPar(p_min = -1.5, p_max = 3.0, ds = 0.002, dsmax = 0.05, n_inversion = 6, detect_bifurcation = 3, max_bisection_steps = 25, nev = 4, max_steps = 200, plot_every_step = 30)
-	@set! opts_br.newton_options.verbose = false
-	@set! opts_br.newton_options.tol = 1e-12
-	br = @time continuation(re_make(prob, params = setproperties(parlor;T=0.04,F=3.)),
+@set! opts_br.newton_options.verbose = false
+@set! opts_br.newton_options.tol = 1e-12
+br = @time continuation(re_make(prob, params = setproperties(parlor;T=0.04,F=3.)),
 	 	PALC(), opts_br;
 		normC = norminf, bothside = true)
 
@@ -64,19 +64,16 @@ scene = plot(br, plotfold=false, markersize=4, legend=:topleft)
 We follow the Fold points in the parameter plane $(T,F)$. We tell the solver to consider `br.specialpoint[5]` and continue it.
 
 ```@example LORENZ84V2
-sn_codim2 = continuation(br, 5, (@lens _.T), ContinuationPar(opts_br, p_max = 3.2, p_min = -0.1, detect_bifurcation = 1, dsmin=1e-5, ds = -0.001, dsmax = 0.005, n_inversion = 10, save_sol_every_step = 1, max_steps = 130, max_bisection_steps = 55) ; plot = true,
+sn_codim2 = continuation(br, 5, (@lens _.T), ContinuationPar(opts_br, p_max = 3.2, p_min = -0.1, detect_bifurcation = 1, dsmin=1e-5, ds = -0.001, dsmax = 0.005, n_inversion = 10, max_steps = 130, max_bisection_steps = 55) ; plot = true,
 	normC = norminf,
 	detect_codim2_bifurcation = 2,
-	update_minaug_every_step = 1,
 	start_with_eigen = false,
 	bothside = false,
 	)
 
 hp_codim2_1 = continuation(br, 3, (@lens _.T), ContinuationPar(opts_br, ds = -0.001, dsmax = 0.02, dsmin = 1e-4, n_inversion = 8, save_sol_every_step = 1, detect_bifurcation = 1) ; plot = false, verbosity = 0,
 	normC = norminf,
-	# tangentAlgo = BorderedPred(),
 	detect_codim2_bifurcation = 2,
-	update_minaug_every_step = 1,
 	start_with_eigen = true,
 	bothside = true,
 	)
@@ -122,7 +119,6 @@ ns_po1 = continuation(hp_codim2_1, 4, opts_ns_po,
 		# which of the 2 NS curves should we compute?
 		whichns = 1,
 		jacobian_ma = :minaug,
-		verbosity = 3,
 		)
 plot!(ns_po1, vars=(:F, :T), branchlabel = "NS1")
 ```

docs/src/tutorials/ode/lorenz84.md

@@ -96,8 +96,6 @@ We follow the Fold points in the parameter plane $(T,F)$. We tell the solver to
 sn_codim2 = continuation(br, 5, (@lens _.T), ContinuationPar(opts_br, p_max = 3.2, p_min = -0.1, dsmin=1e-5, ds = -0.001, dsmax = 0.005, n_inversion = 10) ; normC = norminf,
 	# detection of codim 2 bifurcations with bisection
 	detect_codim2_bifurcation = 2,
-	# we update the Fold problem at every continuation step
-	update_minaug_every_step = 1,
 	start_with_eigen = false,
 	# we save the different components for plotting
 	record_from_solution = recordFromSolutionLor,
@@ -126,8 +124,6 @@ We follow the Hopf points in the parameter plane $(T,F)$. We tell the solver to
 hp_codim2_1 = continuation(br, 3, (@lens _.T), ContinuationPar(opts_br, ds = -0.001, dsmax = 0.02, dsmin = 1e-4, n_inversion = 6) ; normC = norminf,
 	# detection of codim 2 bifurcations with bisection
 	detect_codim2_bifurcation = 2,
-	# we update the Fold problem at every continuation step
-	update_minaug_every_step = 1,
 	# we save the different components for plotting
 	record_from_solution = recordFromSolutionLor,
 	# compute both sides of the initial condition
@@ -158,8 +154,6 @@ hp_from_bt = continuation(sn_codim2, 4, ContinuationPar(opts_br, ds = -0.001, ds
 	n_inversion = 6, detect_bifurcation = 1) ; normC = norminf,
 	# detection of codim 2 bifurcations with bisection
 	detect_codim2_bifurcation = 2,
-	# we update the Fold problem at every continuation step
-	update_minaug_every_step = 1,
 	# we save the different components for plotting
 	record_from_solution = recordFromSolutionLor,
 	)
@@ -184,7 +178,6 @@ When we computed the curve of Fold points, we detected a Zero-Hopf bifurcation.
 hp_from_zh = continuation(sn_codim2, 2, ContinuationPar(opts_br, ds = 0.001, dsmax = 0.02, n_inversion = 6, detect_bifurcation = 1, max_steps = 150) ;
 	normC = norminf,
 	detect_codim2_bifurcation = 2,
-	update_minaug_every_step = 1,
 	start_with_eigen = true,
 	record_from_solution = recordFromSolutionLor,
 	bothside = false,

docs/src/tutorials/ode/steinmetz.md

@@ -84,26 +84,28 @@ opts_po_cont = ContinuationPar(p_min = 0., p_max = 20.0, ds = 0.002, dsmax = 0.0
 @set! opts_po_cont.newton_options.verbose = false
 @set! opts_po_cont.newton_options.max_iterations = 10
 br_sh = continuation(deepcopy(probsh), cish, PALC(tangent = Bordered()), opts_po_cont;
-	#verbosity = 3, plot = true,
+	# verbosity = 3, plot = true,
 	callback_newton = BK.cbMaxNorm(10),
 	argspo...)
+scene = plot(br_sh)
 ```
 
 ### Curve of Fold points of periodic orbits
 
 ```@example STEINMETZ
 opts_posh_fold = ContinuationPar(br_sh.contparams, detect_bifurcation = 2, max_steps = 35, p_max = 1.9, plot_every_step = 10, dsmax = 4e-2, ds = 1e-2)
 @set! opts_posh_fold.newton_options.tol = 1e-12
-@set! opts_posh_fold.newton_options.verbose = true
-fold_po_sh = @time continuation(br_sh, 2, (@lens _.k7), opts_posh_fold;
-		#verbosity = 3, plot = true,
-		detect_codim2_bifurcation = 2,
-		start_with_eigen = false,
+# @set! opts_posh_fold.newton_options.verbose = true
+fold_po_sh = @time continuation(deepcopy(br_sh), 2, (@lens _.k7), opts_posh_fold;
+		# verbosity = 2, plot = true,
+		detect_codim2_bifurcation = 0,
+		update_minaug_every_step = 1,
+		start_with_eigen = true,
 		usehessian = false,
 		jacobian_ma = :minaug,
 		normC = norminf,
 		callback_newton = BK.cbMaxNorm(1e1),
-		bdlinsolver = BorderingBLS(solver = DefaultLS(), check_precision = false),
+		# bdlinsolver = BorderingBLS(solver = DefaultLS(), check_precision = false),
 		)
 plot(fold_po_sh)
 ```
@@ -112,11 +114,12 @@ plot(fold_po_sh)
 ```@example STEINMETZ
 opts_posh_ns = ContinuationPar(br_sh.contparams, detect_bifurcation = 0, max_steps = 35, p_max = 1.9, plot_every_step = 10, dsmax = 4e-2, ds = 1e-2)
 @set! opts_posh_ns.newton_options.tol = 1e-12
-ns_po_sh = continuation(br_sh, 1, (@lens _.k7), opts_posh_ns;
-		verbosity = 2, plot = false,
+# @set! opts_posh_ns.newton_options.verbose = true
+ns_po_sh = continuation(deepcopy(br_sh), 1, (@lens _.k7), opts_posh_ns;
+		# verbosity = 2, plot = true,
 		detect_codim2_bifurcation = 2,
+		update_minaug_every_step = 1,
 		start_with_eigen = false,
-		usehessian = false,
 		jacobian_ma = :minaug,
 		normC = norminf,
 		callback_newton = BK.cbMaxNorm(1e1),
@@ -127,3 +130,54 @@ ns_po_sh = continuation(br_sh, 1, (@lens _.k7), opts_posh_ns;
 plot(ns_po_sh, fold_po_sh, branchlabel = ["NS","Fold"])
 ```
 
+## Computation with collocation
+
+```@example STEINMETZ
+probcoll, cicoll = generate_ci_problem( PeriodicOrbitOCollProblem(50, 4), prob, sol, 16.)
+
+opts_po_cont = ContinuationPar(p_min = 0., p_max = 2.0, 
+	ds = 0.002, dsmax = 0.05, 
+	# n_inversion = 6,
+	nev = 4,
+	max_steps = 50, 
+	tol_stability = 1e-5)
+br_coll = continuation(probcoll, cicoll, PALC(tangent = Bordered()), opts_po_cont;
+    # verbosity = 3, plot = true,
+    callback_newton = BK.cbMaxNorm(10),
+    argspo...)
+```
+
+### Curve of Fold points of periodic orbits
+
+```@example STEINMETZ
+opts_pocl_fold = ContinuationPar(br_coll.contparams, detect_bifurcation = 1, plot_every_step = 10, dsmax = 4e-2)
+fold_po_cl = @time continuation(br_coll, 2, (@lens _.k7), opts_pocl_fold;
+        # verbosity = 3, plot = true,
+        detect_codim2_bifurcation = 2,
+        update_minaug_every_step = 1,
+        start_with_eigen = false,
+        usehessian = true,
+        jacobian_ma = :minaug,
+        normC = norminf,
+        callback_newton = BK.cbMaxNorm(1e1),
+        )
+```
+
+### Curve of NS points of periodic orbits
+
+```@example STEINMETZ
+opts_pocl_ns = ContinuationPar(br_coll.contparams, detect_bifurcation = 1, plot_every_step = 10, dsmax = 4e-2)
+ns_po_cl = continuation(br_coll, 1, (@lens _.k7), opts_pocl_ns;
+        # verbosity = 3, plot = true,
+        detect_codim2_bifurcation = 2,
+        update_minaug_every_step = 1,
+        start_with_eigen = false,
+        jacobian_ma = :minaug,
+        normC = norminf,
+        callback_newton = BK.cbMaxNorm(1e1),
+        )
+```
+
+```@example STEINMETZ
+plot(ns_po_cl, fold_po_cl, branchlabel = ["NS","Fold"])
+```

docs/src/tutorials/ode/tutorialCO.md

@@ -81,8 +81,6 @@ sn_codim2 = continuation(br, 2, (@lens _.k),
 	bothside = true,
 	# detection of codim 2 bifurcations
 	detect_codim2_bifurcation = 2,
-	# update the Fold problem at every continuation step
-	update_minaug_every_step = 1,
 	)
 
 scene = plot(sn_codim2, vars = (:q2, :x), branchlabel = "Fold")
@@ -99,9 +97,6 @@ hp_codim2 = continuation(br, 1, (@lens _.k),
 	normC = norminf,
 	# detection of codim 2 bifurcations
 	detect_codim2_bifurcation = 2,
-	# tell to start the Hopf problem using eigen elements: compute left eigenvector
-	# we update the Hopf problem at every continuation step
-	update_minaug_every_step = 1,
 	# compute both sides of the initial condition
 	bothside = true,
 	)

docs/src/tutorials/ode/tutorialsCodim2PO.md

@@ -42,7 +42,7 @@ z0 = [0.1,0.1,1,0]
 prob = BifurcationProblem(Pop!, z0, par_pop, (@lens _.b0);
 	record_from_solution = (x, p) -> (x = x[1], y = x[2], u = x[3]))
 
-opts_br = ContinuationPar(p_min = 0., p_max = 20.0, ds = 0.002, dsmax = 0.01, n_inversion = 6, detect_bifurcation = 3, max_bisection_steps = 25, nev = 4, max_steps = 20000)
+opts_br = ContinuationPar(p_min = 0., p_max = 20.0, ds = 0.002, dsmax = 0.01, n_inversion = 6, nev = 4)
 
 nothing #hide
 ```
@@ -104,7 +104,6 @@ We continue w.r.t. to $\epsilon$ and find a period-doubling bifurcation.
 ```@example TUTPPREY
 prob2 = @set probtrap.prob_vf.lens = @lens _.ϵ
 brpo_pd = continuation(prob2, ci, PALC(), opts_po_cont;
-	verbosity = 3, plot = true,
 	argspo...
 	)
 scene = plot(brpo_pd)
@@ -120,7 +119,6 @@ probsh, cish = generate_ci_problem( ShootingProblem(M=3),
 
 opts_po_cont = setproperties(opts_br, max_steps = 50, tol_stability = 1e-3)
 br_fold_sh = continuation(probsh, cish, PALC(tangent = Bordered()), opts_po_cont;
-	verbosity = 3, plot = true,
 	argspo...
 )
 
@@ -132,7 +130,6 @@ We continue w.r.t. to $\epsilon$ and find a period-doubling bifurcation.
 ```@example TUTPPREY
 probsh2 = @set probsh.lens = @lens _.ϵ
 brpo_pd_sh = continuation(probsh2, cish, PALC(), opts_po_cont;
-	verbosity = 3, plot = true,
 	argspo...
 	)
 scene = plot(brpo_pd_sh)
@@ -144,12 +141,11 @@ We do the same as in the previous section but using orthogonal collocation. This
 
 ```@example TUTPPREY
 # this is the function which builds probcoll from sol
-probcoll, ci = generate_ci_problem(PeriodicOrbitOCollProblem(26, 3; update_section_every_step = 0),
+probcoll, ci = generate_ci_problem(PeriodicOrbitOCollProblem(26, 3),
 	prob, sol, 2.)
 
 opts_po_cont = setproperties(opts_br, max_steps = 50, tol_stability = 1e-8)
 brpo_fold = continuation(probcoll, ci, PALC(), opts_po_cont;
-	verbosity = 3, plot = true,
 	argspo...
 	)
 scene = plot(brpo_fold)
@@ -160,7 +156,6 @@ We continue w.r.t. to $\epsilon$ and find a period-doubling bifurcation.
 ```@example TUTPPREY
 prob2 = @set probcoll.prob_vf.lens = @lens _.ϵ
 brpo_pd = continuation(prob2, ci, PALC(), ContinuationPar(opts_po_cont, dsmax = 5e-3);
-	verbosity = 3, plot = true,
 	argspo...
 	)
 
@@ -176,7 +171,7 @@ opts_posh_fold = ContinuationPar(br_fold_sh.contparams, detect_bifurcation = 3,
 @set! opts_posh_fold.newton_options.tol = 1e-12
 
 fold_po_sh2 = continuation(br_fold_sh, 1, (@lens _.ϵ), opts_posh_fold;
-		verbosity = 2, plot = true,
+		# verbosity = 2, plot = true,
 		detect_codim2_bifurcation = 2,
 		jacobian_ma = :minaug,
 		start_with_eigen = false,
@@ -185,7 +180,7 @@ fold_po_sh2 = continuation(br_fold_sh, 1, (@lens _.ϵ), opts_posh_fold;
 		)
 
 fold_po_sh1 = continuation(br_fold_sh, 2, (@lens _.ϵ), opts_posh_fold;
-		verbosity = 2, plot = true,
+		# verbosity = 2, plot = true,
 		detect_codim2_bifurcation = 2,
 		jacobian_ma = :minaug,
 		start_with_eigen = false,
@@ -206,18 +201,17 @@ probshpd, ci = generate_ci_problem(ShootingProblem(M=3), re_make(prob, params =
 
 prob2 = @set probshpd.lens = @lens _.ϵ
 brpo_pd = continuation(prob2, ci, PALC(), ContinuationPar(opts_po_cont, dsmax = 5e-3);
-	verbosity = 3, plot = true,
+	# verbosity = 3, plot = true,
 	argspo...,
 	bothside = true,
 	)
 
-opts_pocoll_pd = ContinuationPar(brpo_pd.contparams, detect_bifurcation = 3, max_steps = 40, p_min = 1.e-2, plot_every_step = 10, dsmax = 1e-2, ds = -1e-3)
+opts_pocoll_pd = ContinuationPar(brpo_pd.contparams, max_steps = 40, p_min = 1.e-2, dsmax = 1e-2, ds = -1e-3)
 @set! opts_pocoll_pd.newton_options.tol = 1e-12
 pd_po_sh2 = continuation(brpo_pd, 2, (@lens _.b0), opts_pocoll_pd;
-		verbosity = 3,
+		# verbosity = 3,
 		detect_codim2_bifurcation = 2,
 		start_with_eigen = false,
-		usehessian = false,
 		jacobian_ma = :minaug,
 		normC = norminf,
 		callback_newton = BK.cbMaxNorm(10),

docs/src/tutorials/ode/tutorialsODE-PD.md

@@ -203,7 +203,7 @@ br_po = continuation(
 scene = plot(br, br_po)
 ```
 
-Two period doubling bifurcations were detected. We shall now compute the branch of periodic orbits from these PD points. We do not provide Automatic Branch Switching as we do not have the PD normal form computed in `BifurcationKit`. Hence, it takes some trial and error to find the `ampfactor` of the PD branch.
+Two period doubling bifurcations were detected. We shall now compute the branch of periodic orbits from these PD points. We do not provide Automatic Branch Switching as we do not have the PD normal form computed for `PeriodicOrbitTrapProblem`. Hence, it takes some trial and error to find the `ampfactor` of the PD branch.
 
 ```@example TUTLURE
 # aBS from PD