Quadratic Spline Interpolation Code

What is the MATLAB code for quadratic splines? As linear uses interp1 linear and cubic splines uses interp1 spline. What is the corresponding interp1 coding for quadratic splines?

[darova]

Matlab has no quadratic spline

Try FILEEXCHANGE

Answer 1

[Ameer Hamza]

You can write your own quadratic spline function

function yq = quadSpline(x, y, xq)    
    X = [x(:).^2 x(:) ones(size(x(:)))];
    coff = X\y(:);
    yq = [xq(:).^2 xq(:) ones(size(xq(:)))]*coff;
end

Example

x = 1:10;
y = x.^2 + 5 + rand(size(x))*10;

xq = linspace(0,10);
yq = quadSpline(x, y, xq);

plot(x, y, 'r+', 'MarkerSize', 10, 'LineWidth', 2);
hold on
plot(xq, yq, 'b-');

[Enes Senel]

this is not quadratic spline

[Rik]

Can you show what is wrong with his function? Can you provide a suggestion to fix it?

[Enes Senel]

splines should pass from data points. This seems like polynomial regression

[John D'Errico]

The comments are correct. This is NOT a quadratic spline tool. All that is given in this answer is a quadratic polynomial regression. That is not a spline. The comment about a spline passing through the data points is not always correct though. An INTERPOLATING spline passes through the data points. However, regression or smoothing splines need not do so. But as said, this still is not a spline, in the sense that a spline is a piecewise function.

Answer 2

[Bruno Luong]

My toolbox provide any order (1D) spline, including quadratic

https://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation