function driver
% Driver for the code rowmap with example Bruss2D
clc;
fclose('all');

% -------------------------------------------------------------------------

iAv    = 1;          % number for the computation of Jac*v
i_meth = 1;          % number of the scheme
atol   = 10.^-(2:6); % tolerances AbsTol = RelTol

% -------------------------------------------------------------------------

ex         = 'Bruss_2D';        % name of the example

flagAv     = {'DQ','Jac'};      % computation of Jac*v by DQ or exact

rm_methods = {'GRK4T' ,4        % available methods
              'LSTAB' ,4
              'RODAS' ,6
              'RODASP',6 };

% -------------------------------------------------------------------------

[meth s] = rm_methods{i_meth,:};

% reading the important data for this example
[fh,u0,u_ref,tspan,aut] = Bruss2D_init();

% set the opts for rowmap
opts = struct('Scheme',meth,...
              'AbsTol',[],...    % will be set in function loops_tols_write
              'RelTol',[],...    % will be set in function loops_tols_write
              'Autonomous',aut,...
              's',s);

% set the function_handles for the rigtht-hand side and may be for the
% jacobian-vector product
if (strcmpi(flagAv{iAv},'Jac')) && (length(fh)>1)
        rhs = fh{1};   opts.Jacv = fh{2};
else    rhs = fh{1};   
end

% call the function which calls rowmap and writes the statistics in a file
loop_tols_write(atol,ex,rhs,tspan,u0,u_ref,opts)
end
% -------------------------------------------------------------------------
% ---------------------------- loop for atol ------------------------------
% -------------------------------------------------------------------------
function loop_tols_write(atol,ex,rhs,tspan,u0,u_ref,opts)

% initialise writing file 
fid = write_in_file([],ex,opts);
          
for i = 1:length(atol)
    
    % set the tolerances
    opts.AbsTol = atol(i);
    opts.RelTol = atol(i);
    
    % calling the integrator ROWMAP
    [ t_m, u, stats ] = rowmap(rhs,tspan,u0,opts);
    
    % computing the relative error
    stats.Err = 1/sqrt(length(u0))*norm(u - u_ref);
    
    stats.ex = ex;      % name of the example
    stats.opts = opts;  % options used from rowmap
    
    % write results in file
    write_in_file(stats,fid)
    
end

% close writing file
write_in_file(fid)
end

% -------------------------------------------------------------------------
% --------------------------- writing function ----------------------------
% -------------------------------------------------------------------------
function varargout = write_in_file(in1,in2,in3)
% write results in a file

% -------------------------------------------------------------------------
if nargin == 3  % initialisation
    
    ex = in2;   
    opts = in3;
    
    % get the actual date and time
    dt = {datestr(now,'yyyy.mm.dd'),datestr(now,13)};
    
    % filename
%     [gamma, c] = feval(opts.scheme);
%     s = length(c);
    if ~isdir('results'); mkdir('results');end
    folder = ['results',filesep,dt{1}];
    if ~isdir(folder); mkdir(folder);end
    folder = [folder,filesep];    
    % fn = ['res_',ex,'_',opts.peerVers,'_',num2str(s),'.txt'];
    if isfield(opts,'Vers')
         Vers = opts.Vers;
    else Vers = 'rowmap';
    end
    fn = ['res_',ex,'_',Vers,'_',opts.Scheme,'.txt'];
        
    % open file with name fn for writing
    fid = fopen([folder,fn],'a');
    
    % headlines
    hl1 = sprintf('# %s, %s, %s, %s, %s', ex, Vers, ...
                 opts.Scheme, dt{1}, dt{2});
%     if strcmpi(opts.SolverLinSys,'MAP')
%        Iter = sprintf('%i-',opts.kd);
%        Iter = Iter(1:end-1);
%     else
    if isfield(opts,'MaxIter')
         Iter = sprintf('%i',opts.MaxIter);
    else Iter = '63';
    end
%     end             
    
    if isfield(opts,'KryTol')
         KryTol = opts.KryTol;
    else KryTol = 0.1;
    end
    
    if isfield(opts,'Jacv') && isa(opts.Jacv,'function_handle')
         flagAv = 'Jac';
    else flagAv = 'DQ';
    end
    
    hl2 = sprintf('# linSys %s(%s,%6.1e,%s)','MAP', ...
                  flagAv,KryTol,Iter);
             
    % head of the table
    
    % string for iteracc and iterall
    % siter = repmat(' ',1,ceil((opts.s*11-5)/2)); 
    % string for iterall only
%     siter = repmat(' ',1,ceil((opts.s*5-5)/2)); 
    
    th = sprintf(['#   TOL     err      time steps   rej   fcn     Av',...
                  '    jac   Iter']);
    
    % values for dashed line
    a  = '-';
    % length of the dashed line
    na = max([length(hl1),length(hl2),length(th)]) + 3;
    dl = sprintf('#%s',a(ones(na-1,1))); 
    
    % write head of the table in the file
    fprintf(fid,'%s\n',hl1,hl2,dl,th,dl);
    
    varargout = {fid};
% -------------------------------------------------------------------------
elseif nargin == 2 % write results in the file
    s = in1;    fid = in2;
    
    % insert values in the tabel
    for i = 1:length(s)
        
        x = s(i);
        
        % iter = sprintf('%4.1f(%4.1f) ',[x.Ave_iter_all;x.Ave_iter_acc]);
        iter = sprintf('%4.1f ', x.Ave_iter);
        
        if isfield(x.opts,'Jacv') && isa(x.opts.Jacv,'function_handle')
             njac = x.nsteps-x.nrej;
        else njac = 0;            
        end
        
        fprintf(fid,['  %6.0E %6.1E %7.2f %5i %5i %5i ',...
                     '%6i %6i   %s\n'],...  
                    x.AbsTol, x.Err, x.Time, x.nsteps, x.nrej, x.FCN,...
                    x.nJacv, njac,iter(1:end-1));
    end
    
    % save the iteration-statistic if x.opts.IterStat == true
    if isfield(x.opts,'IterStat')
         iIterStat = x.opts.IterStat;
    else iIterStat = false;
    end
    if iIterStat
        fn = fopen(fid);
        fn = [fn(1:end-4),'_IterStat_',num2str(s.opts.AbsTol,'%6.0e')];
        IterStat = s.IterStat;
        save(fn,'IterStat');
    end
% -------------------------------------------------------------------------
elseif nargin == 1 % close file
    fid = in1;    
    fprintf(fid,'\n\n');
    fclose(fid);
end
end
% -------------------------------------------------------------------------
% --------------------- initial values and parameter ----------------------
% -------------------------------------------------------------------------
function [fh,u0,u_ref,tspan,aut,S] = Bruss2D_init

aut   = true;      % the problem ist autonomous
tspan = [0 1];     % time vector [t0 tfinal]

% some parameters
alpha = 2e-2;      % controls the stiffness of the problem (default 1/50)
A  = 1;     
B  = 3;     
B1 = B + 1;
N  = 100;
N2 = N*N;

% Indices, important for many computions in this example
BRUSS_I1 =      1 : N2;
BRUSS_I2 = N2 + 1 : 2*N2;

% initial value
InitialValue = 'planes'; % 'peaks';
u0       = zeros(2*N2,1); 
switch InitialValue
    case 'peaks'
        u0(BRUSS_I1,1) = reshape(peaks(N),N2,1);
        u0(BRUSS_I2,1) = zeros(N2,1);        
    case 'planes'
        [X,Y] = meshgrid(linspace(0,1,N),linspace(0,1,N));
        u0(BRUSS_I1,1) = 0.5 + Y(:);
        u0(BRUSS_I2,1) = 1 + 5*X(:);        
    otherwise
        error('Bruss2D_Init:Inival',['Unknown Initial conditions ',...
              'requested: %s'],InitialValue);
end

T = spdiags([-ones(N,1),2*ones(N,1),-ones(N,1)],-1:1,N,N);
T(1,2) = -2;  T(N,N-1) = -2;
c = alpha * (N-1)^2;

BRUSS_JAC = c*(kron(T,speye(N,N)) + kron(speye(N,N),T));

% parameter
t_last = tspan(1)-1;
par = {N,N2,A,B,B1,BRUSS_I1,BRUSS_I2,BRUSS_JAC,t_last,[]};

% reading the reference solution
u_ref = Bruss2D_ref();

% function_handles for the right handside and the Jacobian
fh = {@(t,u)Bruss2D(t,u,par) ,...
      @(rhs,t_m,u_m,norm_u_m,f_m,v)Jacv(rhs,t_m,u_m,norm_u_m,f_m,v,par)};

% jpattern matrix S for sparse option in ODE15s or for the numerical
% computation of the jacobian with numjac
S11 = spdiags(ones(N,3), -1:1 ,N,N);
S12 = spdiags(ones(N,2),[-1,1],N,N);

S1 = kron(speye(N,N),S11) + kron(S12,speye(N,N));
S2 = speye(N2,N2);

S = [S1,S2;S2,S1];
% -------------------------------------------------------------------------
% ------------------------------- Jacobian --------------------------------
% -------------------------------------------------------------------------
    function Av = Jacv(rhs,t_m,u_m,norm_u_m,f_m,v,par)
        if t_m ~= par{1,9}
            % computes the jacobian of this problem
            N2 = par{1,2};           B = par{1,4};           B1 = par{1,5};
            BRUSS_I1 = par{1,6};    BRUSS_I2 = par{1,7};    BRUSS_JAC = par{1,8};
            
            tmp = 2*u_m(BRUSS_I1).*u_m(BRUSS_I2);
            J11 = -BRUSS_JAC + spdiags( tmp - B1      , 0, N2, N2);
            J12 =              spdiags( u_m(BRUSS_I1).^2, 0, N2, N2);
            J22 = -BRUSS_JAC - J12;
            J21 =              spdiags( B - tmp       , 0, N2, N2);
            Jac = [J11 J12; J21 J22];
            par{1,10} = Jac;
        end
        Av = par{1,10}*v;   
    end
end
% -------------------------------------------------------------------------
% ------------------------------- Bruss2D ---------------------------------
% -------------------------------------------------------------------------
function fw = Bruss2D(t,y,par)
% The Brusselator example in 2D.
%   t: time.
%   y: space vector.
%   n: sets the dimension of the problem.
%   alpha: optional, controls the stiffness of the problem (default 1/50).
%   InitialValue: is either the string 'peaks' or 'planes'.
%
% This is a modified form of the Brusselator equation found in:
% E. Hairer and G. Wanner, Solving Ordinary Differential Equations II,
% Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin,
% 1991, pp. 5-8.
%
% Example: Solve the equation
%
%   du                               / d^2u   d^2u \
%   -- = A + u^2*v - (B+1)*u + alpha*| ---- + ---- |
%   dt                               \ dx^2   dy^2 /
%
%   dv                       / d^2v   d^2v \
%   -- = B*u - u^2*v + alpha*| ---- + ---- |
%   dt                       \ dx^2   dy^2 /
%
% with 0 <= x,y <= 1, A = 1, B = 3.4, alpha = 0.02 (default) and
% Neumann boundary conditions and initial conditions
%   u(x,y,0) = peaks(x,y), v(x,y,0) = 0
% for 0 <= t <= 5.
% Compute the solution on the time grid
% t = 5*(exp(linspace(0,1,50).^2)-1)/(exp(1)-1).
%
% The spatial derivatives are replaced by finite difference on a grid
% with N^2 mesh points, this gives for N = 100 a system of ODEs of
% dimension 2*N^2 = 2000.


       A = par{1,3};          B = par{1,4};          B1 = par{1,5};
BRUSS_I1 = par{1,6};   BRUSS_I2 = par{1,7};   BRUSS_JAC = par{1,8};

y            = y(:);
dy           = zeros(size(y));
dy(BRUSS_I1) = -(BRUSS_JAC*y(BRUSS_I1));
dy(BRUSS_I2) = -(BRUSS_JAC*y(BRUSS_I2));
tmp          = (y(BRUSS_I1).^2).*y(BRUSS_I2);
dy(BRUSS_I1) = A + dy(BRUSS_I1) + tmp - B1*y(BRUSS_I1);
dy(BRUSS_I2) =     dy(BRUSS_I2) + B*y(BRUSS_I1) - tmp;
fw           = dy(:);
end


% -------------------------------------------------------------------------
% --------------------------- reference  solution -------------------------
% -------------------------------------------------------------------------
function u_ref = Bruss2D_ref
u_ref = [
  0.3441803268967372  0.3444953073944410  0.3454438445461025  0.3470369353079685  0.3492936252074115  0.3522421468820455  0.3559216466574768  0.3603846497624396  0.3657004856699949  0.3719599907139541  0.3792819353613052  0.3878218003504041  0.3977837629042440  0.4094370639460491  0.4231383146066651  0.4393617480440028  0.4587398617685408  0.4821171504580208  0.5106193210382652  0.5457387793554064  0.5894330017827482  0.6442236727293854  0.7132686601527126  0.8003541176948303  0.9097222999378858  1.0456246890348619  1.2115012511045500  1.4087851515577900  1.6355554327628310  1.8855551704753040  2.1482463742443771  2.4103038534599261  2.6582335854205619  2.8810995526077008  3.0722624005440222  3.2296518577467008  3.3548673230600188  3.4517794369627208  3.5252156392874121  3.5800174634378021  3.6205042372813550  3.6502517290509822  3.6720683976920339  3.6880737304204771  3.6998159196252902  3.7083935478718648  3.7145642570751489  3.7188339558160441  3.7215254745410040  3.7228278301141620  2.6704286168432150  2.6738606489595238  2.6841108100708899  2.7010422311520670  2.7244298349096372  2.7539645986022059  2.7892589413020712  2.8298526687872898  2.8752187614464289  2.9247681438693069  2.9778524198303491  3.0337633796655190  3.0917278724302890  3.1508963677147128  3.2103232063157461  3.2689361769133991  3.3254927394211751  3.3785201466240289  3.4262373161546802  3.4664583690812720  3.4964826357520091  3.5129856849159422  3.5119430815441190  3.4886448533698209  3.4378914997090941  3.3544882176849660  3.2341399670876370  3.0747446749886631  2.8778480223524872  2.6497168563584661  2.4013291078892331  2.1468546851158208  1.9009398128617121  1.6758344897120390  1.4794987705800740  1.3152022116776940  1.1823419448743531  1.0778078830947211  0.9973013454488862  0.9363049455976228  0.8906565493677104  0.8568101970219817  0.8318965316252899  0.8136761600209226  0.8004482214423726  0.7909498299167845  0.7842640539213576  0.7797435526185345  0.7769515424397379  0.7756193848923099
  0.3442172041180682  0.3445324467288058  0.3454817804762587  0.3470762338453018  0.3493349075101955  0.3522861170247931  0.3559691257342678  0.3604366190693280  0.3657581424856550  0.3720248212084296  0.3793558104169104  0.3879071015366495  0.3978835473722491  0.4095552782723105  0.4232800679615297  0.4395336532579514  0.4589504467724091  0.4823773286453593  0.5109428818971726  0.5461428126398953  0.5899380906260556  0.6448535770921724  0.7140490685240618  0.8013099135685747  0.9108727810798767  1.0469765010278951  1.2130397180150461  1.4104662970114330  1.6373027299185630  1.8872654007487071  2.1498061453761959  2.4116125946245410  2.6592240042865840  2.8817471762360269  3.0725819685111211  3.2296849207876508  3.3546678017312610  3.4514020621369310  3.5247089954921562  3.5794210807464339  3.6198483391149061  3.6495583342699631  3.6713528925648160  3.6873464269595311  3.6990833919582902  3.7076596934208279  3.7138311026728079  3.7181022559287711  3.7207951532860069  3.7220983143365669  2.6704909850249550  2.6739224568318760  2.6841709215372842  2.7010994626245930  2.7244829200370240  2.7540121472802048  2.7892993900612959  2.8298842190008289  2.8752393009197861  2.9247751462579230  2.9778428149944989  3.0337333866023042  3.0916727850260610  3.1508102826705771  3.2101986830283882  3.2687638222838560  3.3252607189291101  3.3782136403789971  3.4258379707197451  3.4659438503287969  3.4958264733685400  3.5121577204621892  3.5109109797204909  3.4873772639851639  3.4363634482751531  3.3526889396453190  3.2320824164636970  3.0724742523810291  2.8754462654383759  2.6472955045141369  2.3990128943129232  2.1447571388311211  1.8991413741238241  1.6743716748155919  1.4783668869172850  1.3143673590918370  1.1817554761117040  1.0774182499466110  0.9970614591160921  0.9361754978352616  0.8906066280316117  0.8568164755110974  0.8319419163049150  0.8137483888927718  0.8005386351174287  0.7910523802517446  0.7843745403667111  0.7798590470960748  0.7770699571201538  0.7757391401592143
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];
u_ref = reshape(u_ref,20000,1);
end
