clc; clear all; close all;
% Initialization
iter = 1;
x = [0 0.25 0.5 0.75 1];
y = [5 6 3 2 8];
% Prepare X1 and Y1 matrices
X1 = zeros(4,4);
x1 = [x(3) x(4) x(5)];
x2 = [x(3) x(4) x(5)];
x3 = [x(1) x(2) x(3)];
x4 = [x(1) x(2) x(3) x(4)];
r = [length(x1) length(x2) length(x3) length(x4)];
X1(1,1:r(1)) = x1;
X1(2,1:r(2)) = x2;
X1(3,1:r(3)) = x3;
X1(4,1:r(4)) = x4;
Y1 = zeros(4,4);
y1 = [y(3) y(4) y(5)];
y2 = [y(3) y(4) y(5)];
y3 = [y(1) y(2) y(3)];
y4 = [y(1) y(2) y(3) y(4)];
r = [length(y1) length(y2) length(y3) length(y4)];
Y1(1,1:r(1)) = y1;
Y1(2,1:r(2)) = y2;
Y1(3,1:r(3)) = y3;
Y1(4,1:r(4)) = y4;
alpha = [-0.8 0.7 0.7 -0.8];
N = length(x);
% Initialize d and d1
d = zeros(1, N-1); % Adjust the size as needed
d1 = zeros(4, 4); % Adjust the size as needed
% Computation of a, b, and q values
for i = 1:N-1
a(i) = (x(i+1) - x(i)) / (X1(i, r(i)) - X1(i, 1));
b(i) = (X1(i, r(i)) * x(i) - X1(i, 1) * x(i+1)) / (X1(i, r(i)) - X1(i, 1));
% Calculating q(i) with careful attention to parentheses
term1 = (y(i) - alpha(i) * Y1(i, 1)) * (1 - (x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))).^3;
term2 = (y(i+1) - alpha(i) * Y1(i, r(i))) * ((x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))).^3;
term3 = (r(i) * (y(i) - alpha(i) * Y1(i, 1)) + (x(i+1) - x(i)) * d(i) - alpha(i) * d1(i, 1) * (X1(i, r(i)) - X1(i, 1))) * ...
(1 - (x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))).^2 * (x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1));
term4 = (r(i) * (y(i+1) - alpha(i) * Y1(i, r(i))) - (x(i+1) - x(i)) * d(i+1) + alpha(i) * d1(i, r(i)) * (x1(i, r(i)) - x1(i, 1))) * ...
(1 - (x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))) * ((x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))).^2;
numerator = term1 + term2 + term3 + term4;
denominator = 1 + (r(i) - 3) * (1 - (x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1))) * ((x(i) - X1(i, 1)) / (X1(i, r(i)) - X1(i, 1)));
q(i) = numerator / denominator;
end
abq_values = [a' b' q'];
L = []; L1 = []; X = []; Y = [];
p = N;
for k = 1:iter
fprintf("ITERATION=%d\n", k)
for i = 1:N-1
for j = 1:p-2
if(k == 1) % First iteration
% Input data is (x,y) or given data
L(i,j) = a(i) * X(i,j) + b(i);
L1(i,j) = alpha(i) * Y1(i,j) + (q(i) * X1(i,j));
else % More than one iteration
% Input data is (X1, Y1) OR output after the first iteration
L(i,j) = a(i) * X(i,j) + b(i);
L1(i,j) = alpha(i) * Y(i,j) + (q(i) * X1(i,j));
end
end
X = [X L(i,:)];
Y = [Y L1(i,:)];
end
X1 = X;
Y1 = Y;
X = [];
Y = [];
g = [X1' Y1'];
g = str2num(num2str(g,10));
g = unique(g, 'rows');
X1 = g(:, 1);
Y1 = g(:, 2);
p = length(X1);
end
plot(x, y, '.k', 'markersize', 80);
hold on;
plot(X1, Y1, 'b-');
Index exceeds the number of array elements. Index must not exceed 4. Please give me correct program
