lin_evol_gen_reduced_data_primal_dual.m

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function reduced_data = lin_evol_gen_reduced_data_primal_dual(model, detailed_data)
%reduced_data = lin_evol_gen_reduced_data_primal_dual(model, detailed_data)
%
% method which produces reduced_data, which is the data, that will be passed to
% an online-algorithm. Therefore, no quantities dependent on the high-dimension
% H may be included here. Neither may online-data include parameter-dependent
% mu-quantities. So no complete grid or detailed solutions or reduced basis
% vectors may be stored here. So online data is produced in the offline stage,
% but may be used in online-stages. So the computation time may depend on H,
% but the results may not depend on this complexity.
%    
% allowed dependency of generated data: Nmax
% not allowed dependency of data: H
% allowed dependency of computation: Nmax, H
% Unknown at this stage: mu, N
%
% Bernard Haasdonk 16.5.2007
%
% extended to primal/dual formulaton by Dominik Garmatter:
%
% the following cases are possible:
% - model.want_improved_output = 0 and model.want_dual = 1 or 0:
% => lin_evol_gen_reduced_data_primal_dual(model, detailed_data) with
% detailed_data including the primal or dual detailed data. Simply produced
% reduced_data for a primal or a dual problem. In the dual case a
% functional has to be specified via model.name_output_functional.
%
%- model.want_improved_output = 1 and model.want_dual = 0:
% => lin_evol_gen_reduced_data_primal_dual(model, detailed_data) with
% detailed_data including both the primal and dual detailed_data!
% See (and use) lin_evol_primal_dual_gen_detailed_data,
% lin_evol_primal_dual_gen_reduced_data and
% lin_evol_primal_dual_rb_simulation for this case.
%
% In all the cases it is possible to enable the SCM via model.use_scm = 1 to
% compute scm_offline_data for a lower bound to the infsup or a coercivity
% constant in the rb_simulation. Only makes sense in the above second case
% or if you set model.error_norm = 'energy' for the future rb_simulation.
% See scm_offline for a description on the required scm quantities.
%
% special Note: in the european_option_pricing model a functional named
% 'theta' includes a partial timederivative and therefore produces a
% slightly different dual problem. Therefore the 'theta'-case is sometimes
% treated differently. Don't care about this case if you don't use the
% european_option_pricing model.

% Dominik Garmatter 20.07 2012

if ~isfield(model, 'want_dual')
    model.want_dual = 0;
end
if ~isfield(model, 'want_improved_output')
    model.want_improved_output = 0;
end
if ~isfield(model, 'use_scm')
    model.use_scm = 0;        
end

model.decomp_mode = 1; % always components

if model.want_dual % dual
  if strcmp(model.name_output_functional, 'theta') == 1 % theta
    if model.use_scm % with scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, reduced_data.K_IdId, reduced_data.K_IdE, ~, ~, ~, reduced_data.scm_offline_data] = rb_operators(model, detailed_data);
    else % without scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, reduced_data.K_IdId, reduced_data.K_IdE, ~, ~, ~] = rb_operators(model, detailed_data);
    end
  else % dual without theta
    if model.use_scm % with scm
      [reduced_data.LL_I, reduced_data.LL_E, ~, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      ~, ~, ~, reduced_data.K_IdId, reduced_data.K_IdE, ~, ~, ~, reduced_data.scm_offline_data] = rb_operators(model, detailed_data);
    else % without scm
      [reduced_data.LL_I, reduced_data.LL_E, ~, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      ~, ~, ~, reduced_data.K_IdId, reduced_data.K_IdE, ~, ~, ~] = rb_operators(model, detailed_data);
    end
  end
elseif model.want_improved_output && model.want_dual == 0 % primal with improved output
    if model.use_scm % with scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, ~, ~, reduced_data.LL_I_correct, reduced_data.LL_E_correct, ...
      reduced_data.bb_correct, reduced_data.scm_offline_data] = rb_operators(model, detailed_data);
    else % without scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, ~, ~, ...
      reduced_data.LL_I_correct, reduced_data.LL_E_correct, reduced_data.bb_correct] = rb_operators(model, detailed_data);
    end
else % primal without improved output
    if model.use_scm % with scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, ~, ~, ~, ~, ~, reduced_data.scm_offline_data] = rb_operators(model, detailed_data);
    else % without scm
      [reduced_data.LL_I, reduced_data.LL_E, reduced_data.bb, ...
      reduced_data.K_II, reduced_data.K_IE, reduced_data.K_EE, ... 
      reduced_data.m_I, reduced_data.m_E, reduced_data.m, ~, ~, ~, ~, ~] = rb_operators(model, detailed_data);
    end
end
% Note by Dominik Garmatter 20.09 2012 regarding a problem with this
% implementation:
% It makes sense to compute the scm_offline_data in gen_reduced_data, but
% when generating a reduced basis there might be a call of gen_reduced_data
% in every step of the basis generation. This will result in multiple
% generations of scm_offline_data but scm_offline_data is not dependant on
% the reduced basis and therefore it would be sufficient to compute it only
% once. But there is no real solution to this problem yet, because one
% might need the SCM while basis generation (i.e. to compute the error
% indicators). Otherwise one could disable the SCM while basis generation
% (model.use_scm = 0) and enable it after basis generation.

reduced_data.N = model.get_rb_size(model, detailed_data);
reduced_data.a0 = rb_init_values(model, detailed_data);

% only in the primal case an output makes sense
if isfield(model,'name_output_functional') && model.want_dual == 0
% initialise s_RB = v'*\Phi, with \Phi being the reduced basis
% later in the rb_simulation it will be s_N = s_RB * a, with a being the rb_coefficients.
    s_RB = zeros(1,size(detailed_data.RB,2));
    % get v the riesz-representant and l the continuousity constant of the respective functional
    if model.want_improved_output % no l is required here
        [v,~] = model.operators_output(model,detailed_data);
    else 
        [v, l] = model.operators_output(model,detailed_data);
        reduced_data.s_l2norm = l;
    end
    for n = 1 : size(detailed_data.RB,2)
      s_RB(1,n) = (v(:)')*detailed_data.RB(:,n);
    end
    reduced_data.s_RB = s_RB;
end