function [dbx,dby] = bound_spec(dbp,x,y,dbtype,nbr);

% function [dbx,dby] = bound_spec(dbp,x,y,dbtype,nbr);

% dbDN, D = x,y is the domain on which the decision bound function is
% defined, so if D = x, it serves primarily to divide the 'upper'
% region from the 'lower' region, whereas if D = y, it serves to divide
% the 'left' from the 'right'.

lenx = length(x);
leny = length(y);

if strcmp(dbtype,'linear')
    
    dbx(1,:) = dbp(1,1)*( x + dbp(1,5) ).^3 + dbp(1,2)*( x + dbp(1,5) ).^2 + dbp(1,3)*( x + dbp(1,5) ) + dbp(1,4);
    dby(1,:) = dbp(2,1)*( y + dbp(2,5) ).^3 + dbp(2,2)*( y + dbp(2,5) ).^2 + dbp(2,3)*( y + dbp(2,5) ) + dbp(2,4);
    
    if nbr == 5
        dbx(2,:) = dbp(1,1)*( x + dbp(1,5) ).^3 + dbp(1,2)*( x + dbp(1,5) ).^2 + dbp(3,3)*( x + dbp(1,5) ) + dbp(3,4);
        dbx(3,:) = dbp(1,1)*( x + dbp(1,5) ).^3 + dbp(1,2)*( x + dbp(1,5) ).^2 + dbp(5,3)*( x + dbp(1,5) ) + dbp(5,4);
        dby(2,:) = dbp(2,1)*( y + dbp(2,5) ).^3 + dbp(2,2)*( y + dbp(2,5) ).^2 + dbp(6,3)*( y + dbp(2,5) ) + dbp(6,4);
        dby(3,:) = dbp(2,1)*( y + dbp(2,5) ).^3 + dbp(2,2)*( y + dbp(2,5) ).^2 + dbp(4,3)*( y + dbp(2,5) ) + dbp(4,4);
    end

elseif strcmp(dbtype,'piecewise')

    if nbr == 1
        dbx = ones(1,lenx);
        dby = ones(1,leny);
        miny3p = length( x( x < min( dbp(2,3:4) ) ) );
        maxy3p = lenx - length( x( x > max( dbp(2,3:4) ) ) );
        minx3p = length( y( y < min( dbp(1,3:4) ) ) );
        maxx3p = leny - length( y( y > max( dbp(1,3:4) ) ) );
    elseif nbr == 5
        dbx = ones(3,lenx);
        dby = ones(3,leny);
        miny3p = length( x( x < min( dbp(6,3:4) ) ) );
        maxy3p = lenx - length( x( x > max( dbp(6,3:4) ) ) );
        minx3p = length( y( y < min( dbp(3,3:4) ) ) );
        maxx3p = leny - length( y( y > max( dbp(3,3:4) ) ) );
    end

    % dbx1
    cx = dbp(1,3);
    dx = dbp(1,4);
    dbx(1,1:miny3p) = dbx(1,1:miny3p) * cx;
    dbx(1,maxy3p:lenx) = dbx(1,maxy3p:lenx) * dx;
    % changes made 4/10/08 to take care of 'divide by zero' problem
    slope_num = dx-cx;
    slope_den = (x(maxy3p)-x(miny3p));
    if slope_den == 0
        slope = 0;
    else
        slope = slope_num/slope_den;
    end
    itcpt = dx - slope * x(maxy3p);
    dbx(1,miny3p+1:maxy3p-1) = slope * x(miny3p+1:maxy3p-1) + itcpt;

    % dby2
    cy = dbp(2,3);
    dy = dbp(2,4);
    dby(1,1:minx3p) = dby(1,1:minx3p) * cy;
    dby(1,maxx3p:leny) = dby(1,maxx3p:leny) * dy;
    % slope = (dy-cy)/(y(maxx3p)-y(minx3p));
    % changes made 4/10/08 to take care of 'divide by zero' problem
    slope_num = dy-cy;
    slope_den = (y(maxx3p)-y(minx3p));
    if slope_den == 0
        slope = 0;
    else
        slope = slope_num/slope_den;
    end
    itcpt = dy - slope * y(maxx3p);
    dby(1,minx3p+1:maxx3p-1) = slope * y(minx3p+1:maxx3p-1) + itcpt;
    
    if nbr == 5
        
        % dbx3
        cx = dbp(3,3);
        dx = dbp(3,4);
        dbx(2,1:miny3p) = dbx(2,1:miny3p) * cx;
        dbx(2,maxy3p:lenx) = dbx(2,maxy3p:lenx) * dx;
        % slope = (dx-cx)/(x(maxy3p)-x(miny3p));
        % changes made 4/10/08 to take care of 'divide by zero' problem
        slope_num = dx-cx;
        slope_den = (x(maxy3p)-x(miny3p));
        if slope_den == 0
            slope = 0;
        else
            slope = slope_num/slope_den;
        end
        itcpt = dx - slope * x(maxy3p);
        dbx(2,miny3p+1:maxy3p-1) = slope * x(miny3p+1:maxy3p-1) + itcpt;

        % dbx5
        cx = dbp(5,3);
        dx = dbp(5,4);
        dbx(3,1:miny3p) = dbx(3,1:miny3p) * cx;
        dbx(3,maxy3p:lenx) = dbx(3,maxy3p:lenx) * dx;
        % slope = (dx-cx)/(x(maxy3p)-x(miny3p));
        % changes made 4/10/08 to take care of 'divide by zero' problem
        slope_num = dx-cx;
        slope_den = (x(maxy3p)-x(miny3p));
        if slope_den == 0
            slope = 0;
        else
            slope = slope_num/slope_den;
        end
        itcpt = dx - slope * x(maxy3p);
        dbx(3,miny3p+1:maxy3p-1) = slope * x(miny3p+1:maxy3p-1) + itcpt;

        % dby3
        cy = dbp(6,3);
        dy = dbp(6,4);
        dby(2,1:minx3p) = dby(2,1:minx3p) * cy;
        dby(2,maxx3p:leny) = dby(2,maxx3p:leny) * dy;
        % slope = (dy-cy)/(y(maxx3p)-y(minx3p));
        % changes made 4/10/08 to take care of 'divide by zero' problem
        slope_num = dy-cy;
        slope_den = (y(maxx3p)-y(minx3p));
        if slope_den == 0
            slope = 0;
        else
            slope = slope_num/slope_den;
        end
        itcpt = dy - slope * y(maxx3p);
        dby(2,minx3p+1:maxx3p-1) = slope * y(minx3p+1:maxx3p-1) + itcpt;

        % dby4
        cy = dbp(4,3);
        dy = dbp(4,4);
        dby(3,1:minx3p) = dby(3,1:minx3p) * cy;
        dby(3,maxx3p:leny) = dby(3,maxx3p:leny) * dy;
        % slope = (dy-cy)/(y(maxx3p)-y(minx3p));
        % changes made 4/10/08 to take care of 'divide by zero' problem
        slope_num = dy-cy;
        slope_den = (y(maxx3p)-y(minx3p));
        if slope_den == 0
            slope = 0;
        else
            slope = slope_num/slope_den;
        end
        itcpt = dy - slope * y(maxx3p);
        dby(3,minx3p+1:maxx3p-1) = slope * y(minx3p+1:maxx3p-1) + itcpt;

    end

elseif strcmp(dbtype,'maxpost')

    % these bounds are a function of the distributions, so there.
    %
    % given the need to plot these bastards, it would probably be a
    % good idea to go ahead and figure out how to derive the bounds
    % in terms of weighted piecewise quadratic functions based on
    % pairs of densities

else
    error('dbtype is misspecified: it must be "linear", "piecewise", or "maxpost"')
end