error using spline: The first input must contain unique values.

i am using spline function and its showing error message: The first input must contain unique values.

i am running matlab code for the initial geometry of the semicircular curved beam. When same code is run for quarter circular beam, spline is not showing any error.

How can I proceed ?

%x represents all the gauss quadrature points on the beam which are already calculated.

%initial geometry

th = linspace(pi/2, -pi/2, ng); %semicircle beam

R = 1; % radius

x = R*cos(th) ;

y = R*sin(th)+1;

plot(x,y); axis equal;

theta = spline(x,dd(y),1); %calculating the end point slope of the beam .

% dd function is created for numerical differentiation

I can provide other parts of code if required.

[Bruno Luong]

Frankly your spline usage looks wrong to me for whatever the calculation you are after, regardless it returns an error of duplication data.

[Stefi]

whats looks wrong with the usage ? I am just trying to calculate the slope using spline.

[Bruno Luong]

What is wrong? I keep saying that

• you cannot call spline on x since what ever the second argument i is not a function of x.
• The end points has x = 0 in your example (cos(p/2) and cos(-pi/2), why you call spline with 1 as query point? It is not the end point.
• If you already have dd(y), from your own word it's already a slope, then you already have a slope at all the x points, includng the end point. Whar is the purpose of calluing spline that only make INTERPOLATION of whatever you have provided as second input, meaning dd(y).

Answer 1

[Bruno Luong]

You did not post your spline command, my guess is you do spline(x,y)

Try to remove the last (or the first value of th, then do the rest

th = linspace(pi/2, -pi/2, ng); %semicircle beam
th(end) = [];
% ...

Or better do the before last two commands before callinfg splie(x,y)

This will fix the error but I doubt it will do what you want. Please see mu othe answer

tt = linspace(-pi,pi);
x = cos(tt);
y = sin(tt);


% spline(x,y); % error

[xu,~,J] = unique(x);
yu = accumarray(J(:), y(:), [], @mean);
s = spline(xu, yu);

[Stefi]

theta = spline(x,dd(y),1);

this is my spline command . here dd is a function for differentiation.. basically it is used to calculate slope

[Bruno Luong]

At the glance your math/code looks strange to me.

My comment still applies: you cannot use spline on parametric data by ignoring the parameter (here th). The second argument dd(y) MUST implicitly be a function of the first argument (x).As x turns around each y has 2 branches values for each x. This is NOT a function.

https://en.wikipedia.org/wiki/Function_(mathematics)

Answer 2

[Bruno Luong]

Your spline command wouldn't do what you want, since for every x you have made corresponding two y values. It is NOT a function of x; so it cannot be represented/approximated by spline function/

You better call twice spline! x wrt tt and y wrt to tt.yi

ng = 7;
th = linspace(pi/2, -pi/2, ng); %semicircle beam
R = 1; % radius 
x = R*cos(th) ;
y = R*sin(th)+1;
plot(x,y,'o-.'); axis equal;

ti = linspace(min(th),max(th));
xi = spline(th,x,ti);
yi = spline(th,y,ti);

hold on
plot(xi,yi);
legend('data','spline interpolation')