Index exceeds the number of array elements. Index must not exceed 1.
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Hy. I'm trying to code a Hermite interpolation function in MATLAB. However , i'm getting an error of "Index exceeds the number of array elements. Index must not exceed 1." Below is my code . I need to run it using the codes commented at the end of the function. Your suggestions are highly appreciated.
%%-----------------------------------------------------------------------------------------
% Example usage. Please run in command window or new editor
Np=10;
x_j = 0.5 + (1./pi).*asin((2.*(0:Np)./Np)-1);
f_j = 1./ (1+ (x_j.*x_j));
f_prime_j =-(2*x_j)/(x_j.^2 + 1).^2;
% Generate points for interpolation
x_values = linspace(min(x_j), max(x_j), 1000);
% Perform Hermite interpolation
interpolated_values = hermite_interpolation2(x_values, x_j, f_j, f_prime_j);
% Plot the results
figure;
plot(x_j, f_j, 'o', 'MarkerSize', 10, 'DisplayName', 'Data Points');
hold on;
plot(x_values, interpolated_values, '-', 'LineWidth', 2, 'DisplayName', 'Hermite Interpolation');
xlabel('x');
ylabel('f(x)');
legend('Location', 'Best');
title('Hermite Interpolation');
grid on;
function interpolated_values = hermite_interpolation2(x, x_j, f_j, f_prime_j)
n = length(f_j) - 1; % Degree of the polynomial
% Initialize the interpolated values
interpolated_values = zeros(size(x));
for j = 1:n+1
% Compute Lagrange polynomial and its derivative
L = 1;
L_prime = 0;
for i = 1:n+1
if i ~= j
L = L .* (x - x_j(i)) / (x_j(j) - x_j(i));
L_prime = L_prime + 1 / (x_j(j) - x_j(i));
end
end
% Compute Hermite polynomials
H = (1 - 2 * L_prime * (x - x_j(j))) .* L.^2;
tilde_H = (x - x_j(j)) .* L.^2;
% Add contributions to the interpolated values
interpolated_values = interpolated_values + f_j(j) * H + f_prime_j(j) * tilde_H;
end
end
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采纳的回答
Dyuman Joshi
2023-11-29
There was a missing element-wise division sign in the definition of f_prime_j, causing the said variable to be defined as a scalar.
When you called the function, it tried to access the data in f_prime_j via indices for which values did not exist, thus you got the error.
See the correction below -
% Example usage. Please run in command window or new editor
Np=10;
x_j = 0.5 + (1./pi).*asin((2.*(0:Np)./Np)-1);
f_j = 1./ (1+ (x_j.*x_j));
%% Missing sign
%% v
f_prime_j =-(2*x_j)./(x_j.^2 + 1).^2;
% Generate points for interpolation
x_values = linspace(min(x_j), max(x_j), 1000);
% Perform Hermite interpolation
interpolated_values = hermite_interpolation2(x_values, x_j, f_j, f_prime_j);
% Plot the results
figure;
plot(x_j, f_j, 'o', 'MarkerSize', 10, 'DisplayName', 'Data Points');
hold on;
plot(x_values, interpolated_values, '-', 'LineWidth', 2, 'DisplayName', 'Hermite Interpolation');
xlabel('x');
ylabel('f(x)');
legend('Location', 'Best');
title('Hermite Interpolation');
grid on;
function interpolated_values = hermite_interpolation2(x, x_j, f_j, f_prime_j)
n = length(f_j) - 1; % Degree of the polynomial
% Initialize the interpolated values
interpolated_values = zeros(size(x));
for j = 1:n+1
% Compute Lagrange polynomial and its derivative
L = 1;
L_prime = 0;
for i = 1:n+1
if i ~= j
L = L .* (x - x_j(i)) / (x_j(j) - x_j(i));
L_prime = L_prime + 1 / (x_j(j) - x_j(i));
end
end
% Compute Hermite polynomials
H = (1 - 2 * L_prime * (x - x_j(j))) .* L.^2;
tilde_H = (x - x_j(j)) .* L.^2;
% Add contributions to the interpolated values
interpolated_values = interpolated_values + f_j(j) * H + f_prime_j(j) * tilde_H;
end
end
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