07a55317-1e04-428a-acb9-ee1e7ae85fdd 12 6 9 decimal

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vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

ODR fit Circle/Ellipse

1: fit circle

XY 118.13 - 108.90 - 115.69 - 109.63 - 113.58 - 104.58 - 119.73 - 114.83 - 42 mat :

Given an array of measured vectorsin Cartesian coodinates: How do I calculate and plot a 1 sigma error ellipse for any possible number of vectors ? Anonymous from Mathsoft Collaboratory ODR => Orthogonal Distance Radius

Plot an ellipse that shows the standard deviation in X and Y

X XY 1 col : Y XY 2 col : 21 line

Xmean X Mean : Ymean Y Mean : 21 line

Xσ X StdDev : Yσ Y StdDev : 21 line

Xmean Ymean 21 mat 116.7825 - 109.485 - 21 mat

Xσ Yσ 21 mat 2.705123 4.202828 21 mat

x f Xσ x cos * Xmean + :

y g Yσ y sin * Ymean + :

x y Fit x f y g * :

data X Y . 15 red plotG :

Circle x π - π π - 0.025 + (range : i 1 x rows range f i el x i el f : g i el x i el g : 21 line for f g augment 31 line :

Circle XY 2 1 sys

ODR fit to cicle

Circle data XY 3 1 sys

2: fit ellipse

Magnitude i 1 X rows range m i el X i el (2^Y i el (2^+ sqrt : for m 21 line :

Angle j 1 X rows range a j el X j el Y j el i * + arg : for a 21 line :

Magnitude 160.667 159.383 154.394 165.895 41 mat

Angle 2.397 - 2.383 - 2.397 - 2.377 - 41 mat

Mmean Magnitude Mean : Amean Angle Mean : 21 line

Mmean Amean 21 mat 160.085 2.389 - 21 mat

Mσ Magnitude StdDev : Aσ Angle StdDev : 21 line

Mσ Aσ 21 mat 4.725 6.386 21 mat

<= error in Aσ

sanity MCD 11 Aσ 0.010144 :

t m Mσ t cos * Mmean + :

t a Aσ t sin * Amean + :

t xmag t m t a cos * :

t ymag t m t a sin * :

Ellipse x π - π π - 0.025 + (range : i 1 x rows range ff i el x i el xmag : gg i el x i el ymag : 21 line for ff gg augment 31 line :

ODR fit to ellipse

Ellipse data XY 3 1 sys Ellipse XY 2 1 sys

ODR is juat to give a name. Read more jargon from literature.