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

[JBlackhole]

To all

 I am doing my 1^st 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!

[JBlackhole · Accepted solution]

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

[Fred_Kohlhepp]

And the minor axis is?

[JBlackhole]

Haven’t quite work this out in detail – I thought I had something !

I know that it is a vector normal to a =|| X2-X1|| and must be of such length as to enclosed all (most) of the points

Some of steps work fine in a stand-alone example but not when I try to integrate it to the monte-carlo plot

So kind of a step back !

[Fred_Kohlhepp]

How about this?

You've calculated the angle for the major axis.  (I liked what you've got so far.

Now

    Rotate all of the data so that the major axis is parallel to the x axis.

    Then the length of the minor axis is max(y)-min(y).  And the minor axis is normal to the major axis, so you know the whole ellipse.

[JBlackhole]

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

[Fred_Kohlhepp]

a poor example (created in 4.0 express)

[JBlackhole]

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')

[Fred_Kohlhepp]

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@JBlackhole wrote:

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')

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There is; you'd need to have the data paired (x,y) rather than two separate vectors.

[DJF]

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

4.0/pdf attached

[JBlackhole]

Thanks for that.

Thanks to Fred and yourself for the input. Really appreciated

[Fred_Kohlhepp]

VERY NICE!!