% Setup the forcing function for the given boundary conditions and data.
% Each bc is a struct with the fields
%  * type     -- Type of boundary condition
%  * boundary -- Boundary identifier
%  * data     -- A function_handle for a function which provides boundary data.(see below)
% S_sign allows changing the sign of the function to put on different sides in the system of ODEs.
%   default is 1, which the same side as the diffOp.
% Returns a forcing function S.
%
% The boundary data function can either be a function of time or a function of time and space coordinates.
% In the case where it only depends on time it should return the data as grid function for the boundary.
% In the case where it also takes space coordinates the number of space coordinates should match the number of dimensions of the problem domain.
% For example in the 2D case: f(t,x,y).

function S = forcingSetup(diffOp, penalties, bcs, S_sign)
    default_arg('S_sign', 1);

    assertType(bcs, 'cell');
    assertIsMember(S_sign, [1, -1]);

    scheme.bc.verifyFormat(bcs, diffOp);

    [gridData, symbolicData] = parseAndSortData(bcs, penalties, diffOp);

    if length(gridData) + length(symbolicData) == 0
        S = [];
    else
        % Setup penalty function
        O = spzeros(size(diffOp),1);
        S = @S_fun;
    end

    function v = S_fun(t)
        v = O;
        for i = 1:length(gridData)
            v = v + gridData{i}.penalty*gridData{i}.func(t);
        end

        for i = 1:length(symbolicData)
            v = v + symbolicData{i}.penalty*symbolicData{i}.func(t, symbolicData{i}.coords{:});
        end

        v = S_sign * v;
    end
end

% Go through a cell array of boundary condition specifications and return cell arrays
% of structs for grid and symbolic data.
function [gridData, symbolicData] = parseAndSortData(bcs, penalties, diffOp)
    gridData = {};
    symbolicData = {};
    for i = 1:length(bcs)
        [ok, isSymbolic, data] = parseData(bcs{i}, penalties{i}, diffOp.grid);

        if ~ok
            continue % There was no data
        end

        if isSymbolic
            symbolicData{end+1} = data;
        else
            gridData{end+1} = data;
        end
    end
end

function [ok, isSymbolic, dataStruct] = parseData(bc, penalty, grid)
    if ~isfield(bc,'data') || isempty(bc.data)
        isSymbolic = [];
        dataStruct = struct();
        ok = false;
        return
    end
    ok = true;

    nArg = nargin(bc.data);

    if nArg > 1
        % Symbolic data
        isSymbolic = true;
        coord = grid.getBoundary(bc.boundary);
        dataStruct.penalty = penalty;
        dataStruct.func = bc.data;
        dataStruct.coords = num2cell(coord, 1);
    else
        % Grid data
        isSymbolic = false;
        dataStruct.penalty = penalty;
        dataStruct.func = bc.data;
    end
end