--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/diracDiscrTest.m	Wed Nov 20 22:24:06 2019 +0000
@@ -0,0 +1,415 @@
+function tests = diracDiscrTest()
+	    tests = functiontests(localfunctions);
+end
+
+%TODO:
+%   1.  Test discretizing with smoothness conditions.
+%       Only discretization with moment conditions currently tested.
+%   2.  Test using other types of grids. Only equidistant grids currently used.
+
+function testLeftRandom(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+    rng(1) % Set seed
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup1D(order, mom_cond);
+        xl = g.lim{1}{1};
+        h = g.scaling();
+        x = g.x{1};
+
+        % Test random points near left boundary
+        x0s = xl + 2*h*rand(1,10);
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - f(x0));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testRightRandom(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+    rng(1) % Set seed
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup1D(order, mom_cond);
+        xr = g.lim{1}{2};
+        h = g.scaling();
+        x = g.x{1};
+
+        % Test random points near right boundary
+        x0s = xr - 2*h*rand(1,10);
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - f(x0));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testInteriorRandom(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+    rng(1) % Set seed
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup1D(order, mom_cond);
+        xl = g.lim{1}{1};
+        xr = g.lim{1}{2};
+        h = g.scaling();
+        x = g.x{1};
+
+        % Test random points in interior
+        x0s = (xl+2*h) + (xr-xl-4*h)*rand(1,20);
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - f(x0));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+% x0 outside grid should yield 0 integral!
+function testX0OutsideGrid(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup1D(order, mom_cond);
+        xl = g.lim{1}{1};
+        xr = g.lim{1}{2};
+        h = g.scaling();
+        x = g.x{1};
+
+        % Test points outisde grid
+        x0s = [xl-1.1*h, xr+1.1*h];
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - 0);
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testAllGP(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+       [g, H, fs] = setup1D(order, mom_cond);
+        x = g.x{1};
+
+        % Test all grid points
+        x0s = x;
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - f(x0));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testHalfGP(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup1D(order, mom_cond);
+        x = g.x{1};
+
+        % Test halfway between all grid points
+        x0s = 1/2*(x(2:end)+x(1:end-1));
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(x);
+            for i = 1:length(x0s)
+                x0 = x0s(i);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H*fx;
+                err = abs(integral - f(x0));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+%=============== 2D tests ==============================
+function testAllGP2D(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup2D(order, mom_cond);
+        H_global = kron(H{1}, H{2});
+        X = g.points();
+        % Test all grid points
+        x0s = X;
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(X(:,1), X(:,2));
+            for i = 1:length(x0s)
+                x0 = x0s(i,:);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H_global*fx;
+                err = abs(integral - f(x0(1), x0(2)));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testAllRandom2D(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+    rng(1) % Set seed
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup2D(order, mom_cond);
+        H_global = kron(H{1}, H{2});
+        X = g.points();
+        xl = g.lim{1}{1};
+        xr = g.lim{1}{2};
+        yl = g.lim{2}{1};
+        yr = g.lim{2}{2};
+        h = g.scaling();
+
+
+        % Test random points, even outside grid
+        Npoints = 100;
+        x0s = [(xl-3*h(1)) + (xr-xl+6*h(1))*rand(Npoints,1), ...
+               (yl-3*h(2)) + (yr-yl+6*h(2))*rand(Npoints,1) ];
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(X(:,1), X(:,2));
+            for i = 1:length(x0s)
+                x0 = x0s(i,:);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H_global*fx;
+
+                % Integral should be 0 if point is outside grid
+                if x0(1) < xl || x0(1) > xr || x0(2) < yl || x0(2) > yr
+                    err = abs(integral - 0);
+                else
+                    err = abs(integral - f(x0(1), x0(2)));
+                end
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+%=============== 3D tests ==============================
+function testAllGP3D(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup3D(order, mom_cond);
+        H_global = kron(kron(H{1}, H{2}), H{3});
+        X = g.points();
+        % Test all grid points
+        x0s = X;
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(X(:,1), X(:,2), X(:,3));
+            for i = 1:length(x0s)
+                x0 = x0s(i,:);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H_global*fx;
+                err = abs(integral - f(x0(1), x0(2), x0(3)));
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+function testAllRandom3D(testCase)
+
+    orders = [2, 4, 6];
+    mom_conds = orders;
+    rng(1) % Set seed
+
+    for o = 1:length(orders)
+        order = orders(o);
+        mom_cond = mom_conds(o);
+        [g, H, fs] = setup3D(order, mom_cond);
+        H_global = kron(kron(H{1}, H{2}), H{3});
+        X = g.points();
+        xl = g.lim{1}{1};
+        xr = g.lim{1}{2};
+        yl = g.lim{2}{1};
+        yr = g.lim{2}{2};
+        zl = g.lim{3}{1};
+        zr = g.lim{3}{2};
+        h = g.scaling();
+
+        % Test random points, even outside grid
+        Npoints = 200;
+        x0s = [(xl-3*h(1)) + (xr-xl+6*h(1))*rand(Npoints,1), ...
+               (yl-3*h(2)) + (yr-yl+6*h(2))*rand(Npoints,1), ...
+               (zl-3*h(3)) + (zr-zl+6*h(3))*rand(Npoints,1) ];
+
+        for j = 1:length(fs)
+                f = fs{j};
+                fx = f(X(:,1), X(:,2), X(:,3));
+            for i = 1:length(x0s)
+                x0 = x0s(i,:);
+                delta = diracDiscr(g, x0, mom_cond, 0, H);
+                integral = delta'*H_global*fx;
+
+                % Integral should be 0 if point is outside grid
+                if x0(1) < xl || x0(1) > xr || x0(2) < yl || x0(2) > yr || x0(3) < zl || x0(3) > zr
+                    err = abs(integral - 0);
+                else
+                    err = abs(integral - f(x0(1), x0(2), x0(3)));
+                end
+                testCase.verifyLessThan(err, 1e-12);
+            end
+        end
+    end
+end
+
+
+% ======================================================
+% ============== Setup functions =======================
+% ======================================================
+function [g, H, fs] = setup1D(order, mom_cond)
+
+    % Grid
+    xl = -3;
+    xr = 900;
+    L = xr-xl;
+    m = 101;
+    g = grid.equidistant(m, {xl, xr});
+
+    % Quadrature
+    ops = sbp.D2Standard(m, {xl, xr}, order);
+    H = ops.H;
+
+    % Moment conditions
+    fs = cell(mom_cond,1);
+    for p = 0:mom_cond-1
+        fs{p+1} = @(x) (x/L).^p;
+    end
+
+end
+
+function [g, H, fs] = setup2D(order, mom_cond)
+
+    % Grid
+    xlims = {-3, 20};
+    ylims = {-11,5};
+    Lx = xlims{2} - xlims{1};
+    Ly = ylims{2} - ylims{1};
+    m = [15, 16];
+    g = grid.equidistant(m, xlims, ylims);
+
+    % Quadrature
+    opsx = sbp.D2Standard(m(1), xlims, order);
+    opsy = sbp.D2Standard(m(2), ylims, order);
+    Hx = opsx.H;
+    Hy = opsy.H;
+    H = {Hx, Hy};
+
+    % Moment conditions
+    fs = cell(mom_cond,1);
+    for p = 0:mom_cond-1
+        fs{p+1} = @(x,y) (x/Lx + y/Ly).^p;
+    end
+end
+
+function [g, H, fs] = setup3D(order, mom_cond)
+
+    % Grid
+    xlims = {-3, 20};
+    ylims = {-11,5};
+    zlims = {2,4};
+    Lx = xlims{2} - xlims{1};
+    Ly = ylims{2} - ylims{1};
+    Lz = zlims{2} - zlims{1};
+    m = [13, 14, 15];
+    g = grid.equidistant(m, xlims, ylims, zlims);
+
+    % Quadrature
+    opsx = sbp.D2Standard(m(1), xlims, order);
+    opsy = sbp.D2Standard(m(2), ylims, order);
+    opsz = sbp.D2Standard(m(3), zlims, order);
+    Hx = opsx.H;
+    Hy = opsy.H;
+    Hz = opsz.H;
+    H = {Hx, Hy, Hz};
+
+    % Moment conditions
+    fs = cell(mom_cond,1);
+    for p = 0:mom_cond-1
+        fs{p+1} = @(x,y,z) (x/Lx + y/Ly + z/Lz).^p;
+    end
+end