misc.solveGenericBvpFirstOrder: catch the case that jordan form is not...

misc.solveGenericBvpFirstOrder: catch the case that jordan form is not recognized due to numerical uncertainty -> round()

+misc/solveGenericBvpFirstOrder.m

@@ -53,6 +53,11 @@ E1 = I(:, diag(L0)>0);
 E2 = I(:, diag(L0)<0);
 % get jordan chains
 [V, J, lengthJb] = misc.jordan_complete(S);
+if abs(det(V)) < 1e-12
+	% in some badly scaled cases, the jordan blocks of S are not calculated correctly, which leads
+	% to badly scaled modal matrices V. Hence, better results are obtained after round().
+	[V, J, lengthJb] = misc.jordan_complete(round(S, 15));
+end
 mu = diag(J);
 numJb = numel(lengthJb);
 Linv = inv(L);
@@ -106,6 +111,9 @@ for it = 1 : numJb
 	end % for kt = 1 : lenghtJb(it)
 end  % for it = 1 : numJb
 X = horzcat(X_ik{:}) / V;
+assert(MAX(abs(imag(X))) < 1e-6, "there is a imaginary part with a max abs value of " ...
+	+ num2str(MAX(abs(imag(X)))) + " in the solution");
+X = real(X);
 if calculateW
 	W = horzcat(W_ik{:}) / V;
 else