function [found z3 i3] = gradAlg(x1o, x2o, x1f, x2f)
% Step 1: Estimate a set of control variable histories, u(t)
found = 0;
amplitude = 50;
resolution = 1;
lenStim = 30;
totalLength = 100;
W = 2;
epsilon = 0.5;
iterations = 1000;
zt = linspace(0, lenStim, lenStim * resolution + 1);
z = 2 * rand(1, lenStim * resolution + 1) * amplitude - amplitude;
i3 = 0;
finalSize = 10000;
iTemp = zeros(iterations, 1);
dist = zeros(iterations, 1);
ap = zeros(iterations, 1);
lengthStorage = zeros(finalSize, iterations);
zt3 = linspace(0, totalLength, finalSize);
for counter = 1:iterations
% counter
% Step 2: Integrate system equations forward with specified
% initial conditions x(t0) and control variable histories.
% Record x, u, psi(x(tf))
% x1o = 0.95836586; x2o = -0.322958325;
% x1f = 0.891; x2f = -0.4063;
% x1f = -1.667; x2f = 0.4908;
z2 = [z 0 0];
zt2 = [zt lenStim + 0.000001 totalLength];
[Tx X] = ode45(@(t, y) fhn(t, y, zt2, z2), [0 100], [x1o x2o]);
X30 = interp1(Tx, X, 30);
psi = (X30 - [x1f x2f])';
lengthStorage(:, counter) = interp1(zt2, z2, zt3);
figure (1);
subplot(2, 2, 1); plot(zt, z); xlabel('Time'); ylabel('Stimulus Current');
subplot(2, 2, 2); plot(X(:, 1), X(:, 2)); hold on; plot(X30(1), X30(2), 'r.'); plot(x1f, x2f, 'g.'); hold off; xlabel('X1'); ylabel('X2');
subplot(2, 2, 3); plot(iTemp); xlabel('Iteration'); ylabel('L2-Norm');
subplot(2, 2, 4); plot(dist); xlabel('Iteration'); ylabel('Error in Terminal Condition');
% Step 3: Determine n-vector p(t), and matrix R(t) by backward integration
% of the influence equations using x(tf) obtained in step 2 to determine
% boundary conditions
[Tp p] = ode45(@(t, y) pInfluence(t, y, Tx, X), [lenStim 0], [0 0]);
[TR R] = ode45(@(t, y) RInfluence(t, y, Tx, X), [lenStim 0], [1 0 0 1]);
% consolidating all the time stamps
t1 = union(TR, zt);
t = union(Tp, t1);
iz = interp1(zt, z, t);
ip = interp1(Tp, p, t);
iR = interp1(TR, R, t);
% Step 4: Compute Ipp, Ijp, Ijj integrals
Ipp = zeros(2, 2);
Ipp(1, 1) = (1 / W) * trapz(t, iR(:, 1) .^ 2);
Ipp(1, 2) = (1 / W) * trapz(t, iR(:, 1) .* iR(:, 2));
Ipp(2, 1) = (1 / W) * trapz(t, iR(:, 1) .* iR(:, 2));
Ipp(2, 2) = (1 / W) * trapz(t, iR(:, 2) .^ 2);
Ijp = zeros(1, 2);
Ijp(1, 1) = (1 / W) * trapz(t, (ip(:, 1) + 2 * iz) .* iR(:, 1));
Ijp(1, 2) = (1 / W) * trapz(t, (ip(:, 1) + 2 * iz) .* iR(:, 2));
Ijj = (1 / W) * trapz(t, (ip(:, 1) + 2 * iz) .* (ip(:, 1) + 2 * iz));
% Step 5: Choose values of dPsi, then determine v
dPsi = -epsilon * psi;
v = -inv(Ipp) * (dPsi + Ijp');
iTemp(counter) = Ijj - Ijp / Ipp * Ijp';
iTemp2(counter) = trapz(zt2, z2 .^ 2);
dist(counter) = sqrt(psi(1) ^ 2 + psi(2) ^ 2);
ap(counter) = max(X(ceil(0.80*length(X)):length(X), 1) - min(X(ceil(0.80*length(X)):length(X), 1)));
% Step 6: Improve estimate of z(t)
dZ = -(1 / W) * (2 * iz + ip(:, 1) + iR(:, 1) * v(1) + iR(:, 2) * v(2));
z = iz + dZ;
% zt = t;
zt = linspace(0, 30, 1001);
za = interp1(t, z, zt);
z = za;
% [counter iTemp(counter) * 1000 dist(counter)]
end
index = find(ap > 3.5);
iTemp2 = iTemp(index);
lnStorage = lengthStorage(:, index);
[x i] = min(iTemp2);
z3 = lnStorage(:, i);