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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

Indeed

so I need to rotate each pair of data (from the data set from the montcarlo output)

data=augment(hv,R)

(where hv is the variable and R1 the output of the montcarlo)

if Rz is the rotation matrix (anticlockwise)

datarotate=(Rz(-beta)*data^T)^T

 

where beta is the angle for the major axis

Cannot plot this ! so must work on each set of data

Working on a cut-down version of the test sheet to post

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

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