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MATCHALL_ND

MATCHALL_ND

## Purpose

Determines which of a set of coordinates of arbitratry dimension are a
given distance from each of a vector of points. Based on JD's MATCH_2D
and my MATCHALL_SPH.

Astro

## Calling Sequence

Result = MATCHALL_ND(P1, P2, MaxDistance, Nwithin)

## Inputs

P1: N1xD array of D-dimensional coordinates.
P2: N2xD array of D-dimensional coordinates.
MaxDistance: Maximum D-dimensional distance.

## Outputs

The function returns the list of indices of P2 that lie within
Distance of each point in P1. The format of the returned array is
similar to the REVERSE_INDICES array from HISTOGRAM: the indices
into P2 that are close enough to element i of P1 are
contained in Result[Result[i]:Result[i+1]-1] (note, however, that
these indices are not guaranteed to be sorted). If there are no matches,
then Result[i] eq Result[i+1].

## Optional Outputs

Nwithin: A vector containing the number of matches for each entry in P1.

## Keyword Parameters

DISTANCE: Optional output containing the distances between each pair.
The distances are stored in the same order as the Result
array but starting at 0, i.e. if j is match number k to
element i then
j = Result[Result[i]+k]
and the distance between points i and j is
DISTANCE[Result[i]+k-Result]

## Example

Generates Gaussian 3D clouds around each of several locations and colours
the points in the cloud that lie within the Gaussian dispersion of any
location.
na = 10
nbpera = 1000
a = randomn(seed, na, 3)
b = 0.1*randomn(seed, na*nbpera, 3)
b += rebin(a, na*nbpera, 3, /sample)
result = matchall_nd(a, b, 0.1)
matches = result[na+1:*]
iplot, /scatter, /iso, b[*,0], b[*,1], b[*,2]
iplot, /overplot, /scatter, sym_color=[255,0,0], b[matches,0], \$
b[matches,1], b[matches,2]
iplot, /overplot, sym_index=1, sym_color=[0,0,255], linestyle=6, a[*,0], \$
a[*,1], a[*,2]

## Modification History

Written by: Jeremy Bailin
10 June 2008 Public release in JBIU as WITHINSPHRAD
24 April 2009 Vectorized as WITHINSPHRAD_VEC
25 April 2009 Polished to improve memory use
heavily from JD Smith's MATCH_2D
13 May 2009 Removed * from LHS index in final remapping for speed
6 May 2010 Changed to MATCHALL_2D and just using Euclidean 2D
coordinates (add a bunch of stuff back in from MATCH_2D and
take out a bunch of angle stuff)
25 May 2010 Bug fix to allow X2 and Y2 to have any dimension.
23 August 2010 Generalized to an arbitrary number of dimensions and
to use the manifold-mapping technique from WITHINSPHRAD_VEC3D
if the space is sparse enough as MATCHALL_ND.
9 Feb 2010 Added DISTANCE output keyword.

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