function [D1,H,x,h] = D1_minimal_8th_6BP_2shifts(N,L)

% L: Domain length
% N: Number of grid points
if(nargin < 2)
    L = 1;
end

% BP: Number of boundary points
% m:  Number of nonequidistant spacings
% order: Accuracy of interior stencil
BP = 6;
m = 2;
order = 8;

%%%% Non-equidistant grid points %%%%%
x0 =  0.0000000000000e+00;
x1 =  4.9439570885261e-01;
x2 =  1.4051531374839e+00;
x3 =  2.4051531374839e+00;
x4 =  3.4051531374839e+00;
x5 =  4.4051531374839e+00;
x6 =  5.4051531374839e+00;

xb = zeros(m+1,1);
for i = 0:m
    xb(i+1) = eval(['x' num2str(i)]);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%% Compute h %%%%%%%%%%
h = L/(2*xb(end) + N-1-2*m);
%%%%%%%%%%%%%%%%%%%%%%%%%

%%%% Define grid %%%%%%%%
x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
%%%%%%%%%%%%%%%%%%%%%%%%%

%%%% Norm matrix %%%%%%%%
P = zeros(BP,1);
%#ok<*NASGU>
P0 =  1.4523997892351e-01;
P1 =  7.6864793350174e-01;
P2 =  9.9116487068535e-01;
P3 =  9.9992473335107e-01;
P4 =  1.0002097054636e+00;
P5 =  9.9996591555866e-01;

for i = 0:BP-1
    P(i+1) = eval(['P' num2str(i)]);
end

H = ones(N,1);
H(1:BP) = P;
H(end-BP+1:end) = flip(P);
H = spdiags(h*H,0,N,N);
%%%%%%%%%%%%%%%%%%%%%%%%%

%%%% Q matrix %%%%%%%%%%%

% interior stencil
switch order
    case 2
        d = [-1/2,0,1/2];
    case 4
        d = [1/12,-2/3,0,2/3,-1/12];
    case 6
        d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
    case 8
        d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
    case 10
        d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
    case 12
        d = [1/5544,-1/385,1/56,-5/63,15/56,-6/7,0,6/7,-15/56,5/63,-1/56,1/385,-1/5544];
end
d = repmat(d,N,1);
Q = spdiags(d,-order/2:order/2,N,N);

% Boundaries
Q0_0 = -5.0000000000000e-01;
Q0_1 =  6.6697342753834e-01;
Q0_2 = -2.2919342278749e-01;
Q0_3 =  7.4283116457276e-02;
Q0_4 = -1.2020661178873e-02;
Q0_5 = -4.2460029252999e-05;
Q0_6 =  0.0000000000000e+00;
Q0_7 =  0.0000000000000e+00;
Q0_8 =  0.0000000000000e+00;
Q0_9 =  0.0000000000000e+00;
Q1_0 = -6.6697342753834e-01;
Q1_1 =  0.0000000000000e+00;
Q1_2 =  8.8241196934163e-01;
Q1_3 = -2.6653314104602e-01;
Q1_4 =  5.5302527504316e-02;
Q1_5 = -4.2079282615860e-03;
Q1_6 =  0.0000000000000e+00;
Q1_7 =  0.0000000000000e+00;
Q1_8 =  0.0000000000000e+00;
Q1_9 =  0.0000000000000e+00;
Q2_0 =  2.2919342278749e-01;
Q2_1 = -8.8241196934163e-01;
Q2_2 =  0.0000000000000e+00;
Q2_3 =  8.2904844081126e-01;
Q2_4 = -2.1156614214635e-01;
Q2_5 =  3.9307676460659e-02;
Q2_6 = -3.5714285714286e-03;
Q2_7 =  0.0000000000000e+00;
Q2_8 =  0.0000000000000e+00;
Q2_9 =  0.0000000000000e+00;
Q3_0 = -7.4283116457276e-02;
Q3_1 =  2.6653314104602e-01;
Q3_2 = -8.2904844081126e-01;
Q3_3 =  0.0000000000000e+00;
Q3_4 =  8.0305501223679e-01;
Q3_5 = -2.0078040553808e-01;
Q3_6 =  3.8095238095238e-02;
Q3_7 = -3.5714285714286e-03;
Q3_8 =  0.0000000000000e+00;
Q3_9 =  0.0000000000000e+00;
Q4_0 =  1.2020661178873e-02;
Q4_1 = -5.5302527504316e-02;
Q4_2 =  2.1156614214635e-01;
Q4_3 = -8.0305501223679e-01;
Q4_4 =  0.0000000000000e+00;
Q4_5 =  8.0024692689207e-01;
Q4_6 = -2.0000000000000e-01;
Q4_7 =  3.8095238095238e-02;
Q4_8 = -3.5714285714286e-03;
Q4_9 =  0.0000000000000e+00;
Q5_0 =  4.2460029252999e-05;
Q5_1 =  4.2079282615860e-03;
Q5_2 = -3.9307676460659e-02;
Q5_3 =  2.0078040553808e-01;
Q5_4 = -8.0024692689207e-01;
Q5_5 =  0.0000000000000e+00;
Q5_6 =  8.0000000000000e-01;
Q5_7 = -2.0000000000000e-01;
Q5_8 =  3.8095238095238e-02;
Q5_9 = -3.5714285714286e-03;
for i = 1:BP
    for j = 1:BP
        Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
        Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
    end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%% Difference operator %%
D1 = H\Q;
%%%%%%%%%%%%%%%%%%%%%%%%%%%