How can I parametrize a cosine to become asymmetric?

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lzeeysjp
lzeeysjp 2017-5-30
评论： lzeeysjp 2017-5-30
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
  2 个评论
Jan
Jan 2017-5-30
编辑：Jan 2017-5-30
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
lzeeysjp 2017-5-30
编辑：lzeeysjp 2017-5-30
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]

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Stephen23
Stephen23 2017-5-30
编辑：Stephen23 2017-5-30
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)
  1 个评论
lzeeysjp
lzeeysjp 2017-5-30
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.

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