How can I parametrize a cosine to become asymmetric?

Hello,

I have a question and hope that you can help me.

I need function that looks like an cosine, but with the turning points at different places. They should shifted towards 0 and 2pi (see image below) depending on some parameter. Ideally the function converges to the cosine for some value.

And no, its no homework :) I need the function for an optimization problem I am trying to solve.

Kind regards, Joe

[Jan]

There is an infinite number of such functions. Do you have any further limitations? The shown curve is still symmetric. Do you mean a symmetry realted to the rotation around the y=0 points?

[lzeeysjp]

No limitation so far. Built-in would be great :)

I meant symmetric at x = Pi when using fliplr.

One possibility I found so far is

• add an offset to the cosine (to stay positive)
• (cos(x) + 2.0)^n, where n is the free parameter
• then map the result to [-1, 1]

Answer 1

[Stephen23]

This is one simple solution, where a p value of 1 returns cos, and other p values change the shape:

fun = @(x,p)2*(((1+cos(x))/2).^p)-1;
X = 0:0.01:2*pi;
Y1 = fun(X,1); % cos
Y2 = fun(X,3); % adjusted
plot(X,Y1,X,Y2)

[lzeeysjp]

Yes that works, too. I guess this is similar to the one I posted in the comment above. By adding +2.0 to the cosine it also seems to work for negative parameters.