view diracDiscr.m @ 653:2351a7690e8a feature/d1_staggered

Clean up and improve comments in StaggeredVariable
author Martin Almquist <malmquist@stanford.edu>
date Mon, 04 Dec 2017 11:18:13 -0800
parents 4ee7d15bd8e6
children 5264ce57b573
line wrap: on
line source

function ret = diracDiscr(x_0in , x , m_order, s_order, H)

m = length(x);

% Return zeros if x0 is outside grid
if(x_0in < x(1) || x_0in > x(end) )

    ret = zeros(size(x));

else

    fnorm = diag(H);
    eta = abs(x-x_0in);
    h = x(2)-x(1);
    tot = m_order+s_order;
    S = [];
    M = [];
    poss = find(tot*h/2 >= eta);
    
    % Ensure that poss is not too long
    if length(poss) == (tot + 2)
        poss = poss(2:end-1);
    elseif length(poss) == (tot + 1)
        poss = poss(1:end-1);
    end

    % Use first tot grid points
    if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h;
        index=1:tot;
        pol=(x(1:tot)-x(1))/(x(tot)-x(1));
        x_0=(x_0in-x(1))/(x(tot)-x(1));
        norm=fnorm(1:tot)/h;

    % Use last tot grid points
    elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h;
        index = length(x)-tot+1:length(x);
        pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1));
        norm = fnorm(end-tot+1:end)/h;
        x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1));

    % Interior, compensate for round-off errors.
    elseif length(poss) < tot
        if poss(end)<m
            poss = [poss; poss(end)+1];
        else
            poss = [poss(1)-1; poss];
        end
        pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
        x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
        norm = fnorm(poss)/h;
        index = poss;
        
    % Interior
    else    
        pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1)));
        x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1)));
        norm = fnorm(poss)/h;
        index = poss;
    end

    h_pol = pol(2)-pol(1);
    b = zeros(m_order+s_order,1);

    for i = 1:m_order
        b(i,1) = x_0^(i-1);
    end

    for i = 1:(m_order+s_order)
        for j = 1:m_order
            M(j,i) = pol(i)^(j-1)*h_pol*norm(i);
        end
    end

    for i = 1:(m_order+s_order)
        for j = 1:s_order
            S(j,i) = (-1)^(i-1)*pol(i)^(j-1);
        end
    end

    A = [M;S];

    d = A\b;
    ret = x*0;
    ret(index) = d/h*h_pol;
end

end