Skip to main content
J
JBlackhole16-Pearl
16-Pearl
September 20, 2018
Solved

Creating the “enveloping” ellipse for a Monte Carlo plot?

  • September 20, 2018
  • 2 replies
  • 6108 views

To all

 I am doing my 1st step with the montecarlo() function in mcad 15. I copied the example and put my own function and it seems to work fine.

Does anyone know if there is a way of getting/creating the “enveloping” ellipse one often sees on a Monte Carlo plot? I attached one on which I drew the ellipse

 

I think the length of the minor and major axis have a meaning (in the Mont Carlo world) byut can’t quite remember what it is!

Best answer by JBlackhole

Get the mean data X0 =(x0,y0)

Get pts

1: X1=(x1,y1) x1=min(x), y(x1)

2: X2=(x2,y2) x2=max(x), y(x2)

 

Centre of the ellipse is X0

Major axis a =|| X2-X1||

Rotation angle of the ellipse atan(|X2|/|X1|)

Search minor axis (b) to envelope all the pts

Plot ellipse translated by X0 and rotated by alpha

2 replies

J
JBlackhole16-PearlAuthorAnswer
16-Pearl
September 25, 2018

Get the mean data X0 =(x0,y0)

Get pts

1: X1=(x1,y1) x1=min(x), y(x1)

2: X2=(x2,y2) x2=max(x), y(x2)

 

Centre of the ellipse is X0

Major axis a =|| X2-X1||

Rotation angle of the ellipse atan(|X2|/|X1|)

Search minor axis (b) to envelope all the pts

Plot ellipse translated by X0 and rotated by alpha

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
September 25, 2018

And the minor axis is?

J
JBlackhole16-PearlAuthor
16-Pearl
September 25, 2018

Thanks

Why is there no way of rotating the "scatter" data M(x,y) using a rotation matrix?

Mrot(x',y') = R(alpha).M(x',y')

D
DJF16-Pearl
16-Pearl
September 26, 2018

Here's a solution that uses Minimize to make an ellipse of minimum area that includes all the points.  Seems to work.

 

2018-09-26_16-58-04.jpg

 

4.0/pdf attached

    J
    JBlackhole16-PearlAuthor
    16-Pearl
    September 27, 2018

    Thanks for that.

    Thanks to Fred and yourself for the input. Really appreciated

    Terms & ConditionsCookie settingsAccessibility statement