Trust region solver: recompute Jacobian only when necessary

Previously, the solver would recompute the Jacobian at every iteration. But, if
an iteration fails, the current point is not moved (only the radius of the
trust region changes), hence it is not necessary to recompute the Jacobian in
that case. This commit implements this optimization.

matlab/trust_region.m

@@ -25,7 +25,7 @@ function [x,check,info] = trust_region(fcn,x0,j1,j2,jacobian_flag,gstep,tolf,tol
 %    none
 
 % Copyright (C) 2008-2012 VZLU Prague, a.s.
-% Copyright (C) 2014-2017 Dynare Team
+% Copyright (C) 2014-2019 Dynare Team
 %
 % This file is part of Dynare.
 %
@@ -65,24 +65,27 @@ info = 0;
 fvec = fcn (x, varargin{:});
 fvec = fvec(j1);
 fn = norm (fvec);
+recompute_jacobian = true;
 
 % Outer loop.
 while (niter < maxiter && ~info)
 
-    % Calculate function value and Jacobian (possibly via FD).
-    if jacobian_flag
-        [fvec, fjac] = fcn (x, varargin{:});
-        fvec = fvec(j1);
-        fjac = fjac(j1,j2);
-    else
-        dh = max(abs(x(j2)),gstep(1)*ones(n,1))*eps^(1/3);
+    % Calculate Jacobian (possibly via FD).
+    if recompute_jacobian
+        if jacobian_flag
+            [~, fjac] = fcn (x, varargin{:});
+            fjac = fjac(j1,j2);
+        else
+            dh = max(abs(x(j2)),gstep(1)*ones(n,1))*eps^(1/3);
 
-        for j = 1:n
-            xdh = x ;
-            xdh(j2(j)) = xdh(j2(j))+dh(j) ;
-            t = fcn(xdh,varargin{:});
-            fjac(:,j) = (t(j1) - fvec)./dh(j) ;
+            for j = 1:n
+                xdh = x ;
+                xdh(j2(j)) = xdh(j2(j))+dh(j) ;
+                t = fcn(xdh,varargin{:});
+                fjac(:,j) = (t(j1) - fvec)./dh(j) ;
+            end
         end
+        recompute_jacobian = false;
     end
 
     % Get column norms, use them as scaling factors.
@@ -164,20 +167,13 @@ while (niter < maxiter && ~info)
         xn = norm (dg .* x(j2));
         fvec = fvec1;
         fn = fn1;
+        recompute_jacobian = true;
     end
 
     niter = niter + 1;
 
 
-    % Tests for termination conditions. A mysterious place, anything
-    % can happen if you change something here...
-
-    % The rule of thumb (which I'm not sure M*b is quite following)
-    % is that for a tolerance that depends on scaling, only 0 makes
-    % sense as a default value. But 0 usually means uselessly long
-    % iterations, so we need scaling-independent tolerances wherever
-    % possible.
-
+    % Tests for termination condition
     if (fn <= tolf)
         info = 1;
     end