Made jacobian more optimal; other

Note: the jacobian is dense for all non-trivial inputs. for the initial condition it might seem like the jacobian is sparse, but this is a red herring. The jacobian is dense, and the way in which it is computed in this code is as efficient as I dare make it.

Author: AndreyAPopov

src/+otp/+kuramotosivashinsky/KuramotoSivashinskyProblem.m

@@ -24,20 +24,17 @@ function onSettingsChanged(obj)
 
             L = obj.Parameters.L;
 
-            N = numel(obj.Y0);
+            N = obj.NumVars;
 
             div = L/(2*pi);
 
             k = (1i*[0:(N/2 - 1), 0, (-N/2 + 1):-1].'/div);
             k2 = k.^2;
             k4 = k.^4;
-            
-            Dfft = dftmtx(N);
-            Difft = conj(Dfft)/N;
 
             obj.Rhs = otp.Rhs(@(t, u) otp.kuramotosivashinsky.f(t, u, k, k2, k4), ...
                 otp.Rhs.FieldNames.Jacobian, ...
-                @(t, u) otp.kuramotosivashinsky.jac(t,u, k, k2, k4, Dfft, Difft), ...
+                @(t, u) otp.kuramotosivashinsky.jac(t,u, k, k2, k4), ...
                 otp.Rhs.FieldNames.JacobianVectorProduct, ...
                 @(t, u, v) otp.kuramotosivashinsky.jvp(t,u, k, k2, k4, v));
 

src/+otp/+kuramotosivashinsky/jac.m

@@ -1,5 +1,5 @@
-function j = jac(~, u, k, k2, k4, Dfft, Difft)
+function j = jac(~, u, k, k2, k4)
 
-j = -diag(k2) - diag(k4) - diag(k)*Dfft*diag(ifft(u))*Difft;
+j = -diag(k2) - diag(k4) - diag(k)*ifft(fft(diag(ifft(u))).').';
 
 end