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I have a set of solutions to an equation, which are all very similar to spherical harmonics. The solutions are discretised on a regular 3d grid. I would like to label them with which spherical harmonic they are most like, so the $l$ and $m$ values for each one.

Theoretically this is just selecting the largest coefficient from a decomposition of each solution vector onto the spherical harmonic space, or a transform of some kind.

Is there a cheap/simple way to calculate which harmonic each solution is nearest?

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    When you say that a function on a regular three-dimensional grid is very similar to a spherical harmonic, do you mean that it's similar to the product of a radial function and a spherical harmonic? Since spherical harmonics are defined on the angular variables, a three-dimensional function can't literally be similar to a spherical harmonic.2011-08-01
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    Well, keeping the radial function constant, i.e. f(r,theta,phi) ~ A.R.Y, so if R=R(r)=1, then f(x,y,z) ~ A.Y2011-08-01
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    A problem could arise if some solutions actually are linear combinations of spherical harmonics. In this case decomposition in the basis of spherical harmonics via scalar product could be of help here.2011-08-01

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