%
% @file pde2d_sym_pardiso.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='pde2d_sym_pardiso.h5';
%
%     Get data from data sets
%
r=hdf5read(file,'/xgrid');
t=hdf5read(file,'/ygrid');
sol=hdf5read(file,'/sol')';
solexact=hdf5read(file,'/solana')';
err=hdf5read(file,'/errors')';
solr=hdf5read(file,'/derivx')';
solt=hdf5read(file,'/derivy')';
%
%     Attributes
%
if verLessThan('matlab', '7.9');
    NR=hdf5read(file,'/NX'); NTH=hdf5read(file,'/NY');
    NIDBAS1=hdf5read(file,'/NIDBAS1');
    NIDBAS2=hdf5read(file,'/NIDBAS2');
    MBESS=hdf5read(file,'/MBESS');
    EPSI=hdf5read(file,'/EPSI');
    attr=hdf5read(file,'/xgrid/title'); x_ann=attr.Data;
    attr=hdf5read(file,'/ygrid/title'); y_ann=attr.Data;
    attr=hdf5read(file,'/sol/title'); sol_ann=attr.Data;
    attr=hdf5read(file,'/solana/title'); solexact_ann=attr.Data;
    attr=hdf5read(file,'/errors/title');err_ann=attr.Data;
else
    NR=hdf5read(file,'/','NX'); NTH=hdf5read(file,'/','NY');
    NIDBAS1=hdf5read(file,'/','NIDBAS1');
    NIDBAS2=hdf5read(file,'/','NIDBAS2');
    MBESS=hdf5read(file,'/','MBESS');
    EPSI=hdf5read(file,'/','EPSI');
    attr=hdf5read(file,'/xgrid/','title'); x_ann=attr.Data;
    attr=hdf5read(file,'/ygrid/','title'); y_ann=attr.Data;
    attr=hdf5read(file,'/sol/','title'); sol_ann=attr.Data;
    attr=hdf5read(file,'/solana/','title'); solexact_ann=attr.Data;
    attr=hdf5read(file,'/errors/','title');err_ann=attr.Data;
end
LABEL=sprintf('nr = %d, ntheta = %d, nidbas = (%d,%d), mbess = %d, epsi = %3.2f', ...
              NR, NTH, NIDBAS1, NIDBAS2, MBESS, EPSI);


[R,T]=meshgrid(r,t);
x = R.*cos(T); y= R.*sin(T);
solx = cos(T).*solr - sin(T)./R.*solt;
soly = sin(T).*solr + cos(T)./R.*solt;

figure
subplot(221)
pcolor(double(r),double(t),double(sol));
shading interp
hold on, quiver(r,t,solr,solt)
xlabel(x_ann); ylabel(y_ann)
title(LABEL)
colorbar

subplot(222)
pcolor(double(x),double(y),double(sol))
shading interp
hold on, quiver(x,y,solx,soly)
hold off, axis image
xlabel('X'); ylabel('Y')
title('X-Y plane')
colorbar

subplot(223)
surfc(double(x),double(y),double(sol))
xlabel('X'); ylabel('Y');
title(sol_ann)

subplot(224)
surfc(double(x),double(y),double(err))
xlabel('X'); ylabel('Y');
title(err_ann)



if verLessThan('matlab', '7.9');
    n = hdf5read(file,'/MAT/RANK');
    nnz = hdf5read(file,'/MAT/NNZ');
    nlsym = hdf5read(file,'/MAT/NLSYM');
else
    n = hdf5read(file,'/MAT/', 'RANK');
    nnz = hdf5read(file,'/MAT/', 'NNZ');
    nlsym = hdf5read(file,'/MAT/', 'NLSYM');
end

cols=hdf5read(file, '/MAT/cols');
irow=hdf5read(file, '/MAT/irow');
val=hdf5read(file, '/MAT/val');
perm=hdf5read(file, '/MAT/perm');

rows = zeros(nnz,1);
cols=double(cols);
irow=double(irow);
perm=double(perm);

for i=1:n
    s = irow(i);
    e = irow(i+1)-1;
    rows(s:e) = i;    
end

mat = sparse(rows,cols,val);
figure
   subplot(121)
   spy(mat)
   title('Original Matrix structure')
   subplot(122)
   spy(mat(perm,perm))
   title('Permuted Matrix structure')