Plot an implicit function containing the correlation of two vectors

Question

I am trying to do something like this:

ContourPlot3D[
 Expand[Correlation[{0, 1, 2}, {b1, b2, b3}] == .5], {b1, -5, 
  5}, {b2, -5, 5}, {b3, -10, 10}]

But apparently this make the computer freeze.

It works fine for me; it might be faster to plot expr = Re[Correlation[{0, 1, 2}, {b1, b2, b3}]] though. — b.gates.you.know.what, Sep 01 '13 at 15:37
@b.gatessucks Could you please type out the whole command here? Thanks! — qed, Sep 01 '13 at 15:40
ContourPlot3D[ expr == .5], {b1, -5, 5}, {b2, -5, 5}, {b3, -10, 10}]. — b.gates.you.know.what, Sep 01 '13 at 15:52
I found your solution faster than the one proposed in the answer. Could you please post it as an answer? — qed, Sep 01 '13 at 18:55

score 6 · Answer 1 · answered Sep 01 '13 at 18:01

First simplify your function:

f[b1_, b2_, b3_] = FullSimplify[Correlation[{0, 1, 2}, {b1, b2, b3}], 
  Assumptions -> {b1, b2, b3} \[Element] Reals]

enter image description here

The plot. Teared edge is where singularity happens. Stripes help you to see where the slope is steeper.

ContourPlot3D[
 f[b1, b2, b3] == .5, {b1, -5, 5}, {b2, -5, 5}, {b3, -10, 10}, 
 MeshFunctions -> {#3 &}, MeshShading -> {Red, Automatic}, 
 ContourStyle -> Directive[Opacity[0.5], Yellow]]

enter image description here

Plot an implicit function containing the correlation of two vectors

1 Answers1