%
% @file poisson_fe.m
%
% @brief
%
% @copyright
% Copyright (©) 2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
% SPC (Swiss Plasma Center)
%
% SPClibs is free software: you can redistribute it and/or modify it under
% the terms of the GNU Lesser General Public License as published by the Free
% Software Foundation, either version 3 of the License, or (at your option)
% any later version.
%
% SPClibs 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 Lesser General Public License
% along with this program. If not, see <https://www.gnu.org/licenses/>.
%
% @author
% (in alphabetical order)
% @author Trach-Minh Tran <trach-minh.tran@epfl.ch>
%
file='poisson_fe.h5';
%
nx=h5readatt(file,'/','NX');
ny=h5readatt(file,'/','NY');
kx=h5readatt(file,'/','KX');
ky=h5readatt(file,'/','KY');
nidbas1=h5readatt(file,'/','NIDBAS1');
nidbas2=h5readatt(file,'/','NIDBAS2');
relax=h5readatt(file,'/','RELAX');
nlevels=h5readatt(file,'/','LEVELS');
nu1=h5readatt(file,'/','NU1');
nu2=h5readatt(file,'/','NU2');
mu=h5readatt(file,'/','MU');
title_str=sprintf(['N=(%d,%d), NIDBAS=(%d,%d), relax=%s, nu1=%d, ' ...
                   'nu2=%d, mu=%d, LEVELS=%d, KX=%d, KY=%d'], ...
                  nx,ny,nidbas1,nidbas2,relax,nu1,nu2,mu,nlevels,kx,ky);


%
%   Prolongation matrices at the coarsest grid
%
levels=nlevels;
mglevel=sprintf('/mglevels/level.%.2d', levels);
dset=strcat(mglevel,'/matpx');
matpx=h5read(file,dset);
dset=strcat(mglevel,'/matpy');
matpy=h5read(file,dset);

%
%   FE matrix at the finest grid
%
levels=1;
mglevel=sprintf('/mglevels/level.%.2d', levels);
dset=strcat(mglevel,'/mata');
[mata,diag]=csr_mat(file,dset);

f=h5read(file,strcat(mglevel,'/f'));
v=h5read(file,strcat(mglevel,'/v'));
f1d=h5read(file,strcat(mglevel,'/f1d'));
v1d=h5read(file,strcat(mglevel,'/v1d'));
% $$$ figure
% $$$ spy(mata)

%
%    Solutions at the finest grid
%
x=h5read(file,'/solutions/xg');
y=h5read(file,'/solutions/yg');
dense=h5read(file,'/solutions/dense');
sol_anal=h5read(file,'/solutions/anal');
sol_calc=h5read(file,'/solutions/calc');
sol_direct=h5read(file,'/solutions/direct');
nx=int32(size(x,1));
ny=int32(size(y,1));

figure
surf(x,y,sol_direct'-sol_anal')
xlabel('X'); ylabel('Y');
title('Error on the finest grid')

figure
subplot(211)
[yy,iy] = max(abs(sol_anal),[],2);
[xx,ix] = max(yy);
iy0=iy(ix);
str=sprintf('Solution at y = %.4f', y(iy0));
plot(x, sol_anal(:,iy0),x, sol_direct(:,iy0),'o')
xlabel('x'); ylabel(str);
grid on
legend('Analytic Solution', 'Direct Solution')
title(title_str)
subplot(212)
[xx,ix] = max(abs(sol_anal));
[yy,iy] = max(xx);
ix0=ix(iy);
str=sprintf('Solution at x = %.4f', x(ix0));
plot(y, sol_anal(ix0,:),y, sol_direct(ix0,:),'o')
xlabel('y'); ylabel(str);
grid on
title(title_str)

%
%   Iterations
%
dset='/Iterations/';
disc_err=h5read(file, strcat(dset,'disc_errors'));
resid=h5read(file, strcat(dset,'residues'));
its=0:1:size(resid,1)-1;
figure
subplot(211)
semilogy(its,resid,'o-')
grid on
xlabel('Iterations'); ylabel('Norm of residue');
title(title_str);
subplot(212)
semilogy(its,disc_err,'h-')
grid on
xlabel('Iterations'); ylabel('Norm of error');