Hi everyone, how to use pchip and csape together for data smoothing?

Hi everyone, how to use pchip and csape together for data smoothing?

Answer 1

[Gautam]

Hello Ayisha,

I am not sure of your specific use case, but, in general, you can use both "pchip" and "csape" together for data smoothing, in the following way:

1. Use "pchip" for Initial Smoothing: Apply "pchip" to your data to create a smooth curve that respects the shape of your data points. This is particularly useful if you want to avoid overshooting and maintain monotonicity.
2. Refine with "csape": Use "csape" to further refine the curve, especially if you need to impose specific boundary conditions or require a smoother result.

You can follow something similar to this script

% Sample data
x = 0:10;
y = [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100];

% Generate more points for smooth plotting
xq = linspace(min(x), max(x), 100);

% Step 1: Initial smoothing with pchip
y_pchip = pchip(x, y, xq);

% Step 2: Further smoothing with csape
% 'variational' boundary condition minimizes the second derivative at boundaries
y_csape = fnval(csape(x, y, 'variational'), xq);

% Plotting
figure;
plot(x, y, 'o', 'MarkerFaceColor', 'r'); % Original data points
hold on;
plot(xq, y_pchip, '-b', 'LineWidth', 1.5); % pchip interpolation
plot(xq, y_csape, '--g', 'LineWidth', 1.5); % csape interpolation
legend('Data Points', 'pchip', 'csape');
xlabel('x');
ylabel('y');