--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/ode/private/integrate_const.m	Thu Sep 24 12:58:46 2015 +0200
@@ -0,0 +1,289 @@
+## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it>
+## OdePkg - A package for solving ordinary differential equations and more
+##
+## This program is free software; you can redistribute it and/or modify
+## it under the terms of the GNU General Public License as published by
+## the Free Software Foundation; either version 2 of the License, or
+## (at your option) any later version.
+##
+## This program is distributed in the hope that it will be useful,
+## but WITHOUT ANY WARRANTY; without even the implied warranty of
+## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+## GNU General Public License for more details.
+##
+## You should have received a copy of the GNU General Public License
+## along with this program; If not, see <http://www.gnu.org/licenses/>.
+
+
+## -*- texinfo -*-
+## @deftypefn {Command} {[@var{t}, @var{y}] =} integrate_const (@var{@@stepper},
+## @var{@@fun}, @var{tspan}, @var{x0}, @var{dt}, @var{options})
+##
+## This function file can be called by an ODE solver function in order to
+## integrate the set of ODEs on the interval @var{[t0,t1]} with a
+## constant timestep @var{dt}.
+##
+## This function must be called with two output arguments: @var{t} and @var{y}.
+## Variable @var{t} is a column vector and contains the time stamps,
+## instead @var{y} is a matrix in which each column refers to a different
+## unknown of the problem and the rows number is the same of @var{t} rows
+## number so that each row of @var{y} contains the values of all unknowns at
+## the time value contained in the corresponding row in @var{t}.
+##
+## The first input argument must be a function_handle or an inline function
+## representing the stepper, that is the function responsible for step-by-step
+## integration. This function discriminates one method from the others.
+##
+## The second input argument is the order of the stepper. It is needed to
+## compute the adaptive timesteps.
+##
+## The third input argument is a function_handle or an inline function
+## that defines the set of ODE:
+##
+## @ifhtml
+## @example
+## @math{y' = f(t,y)}
+## @end example
+## @end ifhtml
+## @ifnothtml
+## @math{y' = f(t,y)}.
+## @end ifnothtml
+##
+## The third input argument is the time vector which defines integration
+## interval, that is @var{[tspan(1),tspan(end)]} and all the intermediate
+## elements are taken as times at which the solution is required.
+##
+## The fourth argument contains the initial conditions for the ODEs.
+##
+## The fifth input argument represents the fixed timestep and the last input
+## argument contains some options that may be needed for the stepper.
+## @end deftypefn
+##
+## @seealso{integrate_adaptive, integrate_n_steps}
+
+function solution = integrate_const (stepper, func, tspan, x0, dt, options)
+
+  solution = struct;
+
+  ## first values for time and solution
+  t = tspan(1);
+  x = x0(:);
+
+  vdirection = odeget (options, "vdirection", [], "fast");
+  if (sign (dt) != vdirection)
+    error ("OdePkg:InvalidArgument",
+           "option ''InitialStep'' has a wrong sign");
+  endif
+
+  ## setting parameters
+  k = length (tspan);
+  counter = 2;
+  comp = 0.0;
+  tk = tspan(1);
+  options.comp = comp;
+  
+  ## Initialize the OutputFcn
+  if (options.vhaveoutputfunction)
+    if (options.vhaveoutputselection)
+      solution.vretout = x(options.OutputSel,end);
+    else 
+      solution.vretout = x;
+    endif
+    feval (options.OutputFcn, tspan, solution.vretout, "init",
+           options.vfunarguments{:});
+  endif
+
+  ## Initialize the EventFcn
+  if (options.vhaveeventfunction)
+    odepkg_event_handle (options.Events, t(end), x, "init",
+                         options.vfunarguments{:});
+  endif
+  
+  solution.vcntloop = 2;
+  solution.vcntcycles = 1;
+  #vu = vinit;
+  #vk = vu.' * zeros(1,6);
+  vcntiter = 0;
+  solution.vunhandledtermination = true;
+  solution.vcntsave = 2;
+  
+  z = t;
+  u = x;
+  k_vals = feval (func, t , x, options.vfunarguments{:});
+
+  while (counter <= k)
+    ## computing the integration step from t to t+dt
+    [s, y, ~, k_vals] = stepper (func, z(end), u(:,end), dt, options, k_vals);
+
+    [tk, comp] = kahan (tk,comp, dt);
+    options.comp = comp;
+    s(end) = tk;
+    
+    if (options.vhavenonnegative)
+      x(options.NonNegative,end) = abs (x(options.NonNegative,end));
+      y(options.NonNegative,end) = abs (y(options.NonNegative,end));
+      y_est(options.NonNegative,end) = abs (y_est(options.NonNegative,end));
+    endif
+    
+    if (options.vhaveoutputfunction && options.vhaverefine)
+      vSaveVUForRefine = u(:,end);
+    endif
+
+    ## values on this interval for time and solution
+    z = [t(end);s];
+    u = [x(:,end),y];
+
+    ## if next tspan value is caught, update counter
+    if ((z(end) == tspan(counter))
+        || (abs (z(end) - tspan(counter)) /
+            (max(abs (z(end)), abs(tspan(counter)))) < 8*eps) )
+      counter++;
+
+    ## if there is an element in time vector at which the solution is required
+    ## the program must compute this solution before going on with next steps
+    elseif (vdirection * z(end) > vdirection * tspan(counter) )
+      ## initializing counter for the following cycle
+      i = 2;
+      while (i <= length (z))
+
+        ## if next tspan value is caught, update counter
+        if ((counter <= k)
+            && (((z(i) == tspan(counter))
+                 || (abs (z(i) - tspan(counter)) /
+                     (max(abs (z(i)), abs (tspan(counter)))) < 8*eps))) )
+          counter++;
+        endif
+        ## else, loop until there are requested values inside this subinterval
+        while ((counter <= k)
+               && vdirection * z(i) > vdirection * tspan(counter) )
+          ## add the interpolated value of the solution
+          u = [u(:,1:i-1),u(:,i-1) + (tspan(counter)-z(i-1))/(z(i)-z(i-1))* ...
+              (u(:,i)-u(:,i-1)),u(:,i:end)];
+          ## add the time requested
+          z = [z(1:i-1);tspan(counter);z(i:end)];
+
+          ## update counters
+          counter++;
+          i++;
+        endwhile
+
+        ## if new time requested is not out of this interval
+        if ((counter <= k)
+            && vdirection * z(end) > vdirection * tspan(counter))
+          ## update the counter
+          i++;
+        else
+          ## else, stop the cycle and go on with the next iteration
+          i = length (z)+1;
+        endif
+
+      endwhile
+    endif
+
+    if (mod (solution.vcntloop-1, options.OutputSave) == 0)
+      x = [x,u(:,2:end)];
+      t = [t;z(2:end)];
+      solution.vcntsave = solution.vcntsave + 1;    
+    endif
+    solution.vcntloop = solution.vcntloop + 1;
+    vcntiter = 0;
+      
+    ## Call plot only if a valid result has been found, therefore this
+    ## code fragment has moved here. Stop integration if plot function
+    ## returns false
+    if (options.vhaveoutputfunction)
+      for vcnt = 0:options.Refine # Approximation between told and t
+        if (options.vhaverefine) # Do interpolation
+          vapproxtime = (vcnt + 1) / (options.Refine + 2);
+          vapproxvals = (1 - vapproxtime) * vSaveVUForRefine ...
+                        + (vapproxtime) * y(:,end);
+          vapproxtime = s(end) + vapproxtime*dt;
+        else
+          vapproxvals = x(:,end);
+          vapproxtime = t(end);
+        endif
+        if (options.vhaveoutputselection)
+          vapproxvals = vapproxvals(options.OutputSel);
+        endif
+        vpltret = feval (options.OutputFcn, vapproxtime, vapproxvals, [],
+                         options.vfunarguments{:});
+        if (vpltret) # Leave refinement loop
+          break
+        endif
+      endfor
+      if (vpltret) # Leave main loop
+        solution.vunhandledtermination = false;
+        break
+      endif
+    endif
+      
+    ## Call event only if a valid result has been found, therefore this
+    ## code fragment has moved here. Stop integration if veventbreak is true
+    if (options.vhaveeventfunction)
+      solution.vevent = odepkg_event_handle (options.Events, t(end), x(:,end),
+                                             [], options.vfunarguments{:});
+      if (! isempty (solution.vevent{1})
+          && solution.vevent{1} == 1)
+        t(solution.vcntloop-1,:) = solution.vevent{3}(end,:);
+        x(:,solution.vcntloop-1) = solution.vevent{4}(end,:)';
+        solution.vunhandledtermination = false; 
+        break
+      endif
+    endif
+    
+    ## Update counters that count the number of iteration cycles
+    solution.vcntcycles = solution.vcntcycles + 1; # Needed for cost statistics
+    vcntiter = vcntiter + 1;     # Needed to find iteration problems
+
+    ## Stop solving because the last 1000 steps no successful valid
+    ## value has been found
+    if (vcntiter >= 5000)
+      error (["Solving has not been successful. The iterative",
+              " integration loop exited at time t = %f before endpoint at",
+              " tend = %f was reached. This happened because the iterative",
+              " integration loop does not find a valid solution at this time",
+              " stamp. Try to reduce the value of ''InitialStep'' and/or",
+              " ''MaxStep'' with the command ''odeset''.\n"],
+             s(end), tspan(end));
+    endif
+
+    ## if this is the last iteration, save the length of last interval
+    if (counter > k)
+      j = length (z);
+    endif
+  endwhile
+  
+  ## Check if integration of the ode has been successful
+  if (vdirection * z(end) < vdirection * tspan(end))
+    if (solution.vunhandledtermination == true)
+      error ("OdePkg:InvalidArgument",
+             ["Solving has not been successful. The iterative integration loop",
+              " exited at time t = %f before endpoint at tend = %f was",
+              " reached. This may happen if the stepsize grows smaller than",
+              " defined in vminstepsize. Try to reduce the value of",
+              " ''InitialStep'' and/or ''MaxStep'' with the command",
+              " ''odeset''.\n"], z(end), tspan(end));
+    else
+      warning ("OdePkg:InvalidArgument",
+               ["Solver has been stopped by a call of ''break'' in the main",
+                " iteration loop at time t = %f before endpoint at tend = %f",
+                " was reached. This may happen because the @odeplot function",
+                " returned ''true'' or the @event function returned",
+                " ''true''.\n"],
+               z(end), tspan(end));
+    endif
+  endif
+
+  ## compute how many values are out of time inerval
+  d = vdirection * t((end-(j-1)):end) > vdirection * tspan(end) * ones (j, 1);
+  f = sum (d);
+
+  ## remove not-requested values of time and solution
+  solution.t = t(1:end-f);
+  solution.x = x(:,1:end-f)';
+  
+endfunction
+
+## Local Variables: ***
+## mode: octave ***
+## End: ***