Distance Matrix

fast, vectorized distance matrix calculation

Description

Returns the point-to-point distance between all pairs of points (similar to PDIST in the Statistics Toolbox, for those without it)
 
DMAT = DISTMAT(XY) Calculates the distance matrix using an automatic option
DMAT = DISTMAT(XY,OPT) Uses the specified option to compute the distance matrix
[DMAT,OPT] = DISTMAT(XY) Also returns the automatic option used by the function
 
Inputs:
XY is an NxP matrix of coordinates for N points in P dimensions
OPT (optional) is an integer between 1 and 4 representing the chosen method for computing the distance matrix (see note below)
 
Outputs:
DMAT is an NxN matrix, where the value of DMAT(i,j) corresponds to the distance from XY(i,:) to XY(j,:)
OPT (optional) is an integer between 1 and 4 representing the method used to compute the distance matrix (see note below)
 
Note:
DISTMAT contains 4 methods for computing the distance matrix
 OPT=1 Usually fastest for small inputs. Takes advantage of the symmetric property of distance matrices to perform half as many calculations
 OPT=2 Usually fastest for medium inputs. Uses a fully vectorized method
 OPT=3 Usually fastest for large inputs. Uses a partially vectorized method with relatively small memory requirement
 OPT=4 Another compact calculation, but usually slower than the others

• Acknowledgements: This submission has inspired the following:; IPDM: Inter-Point Distance Matrix
• MATLAB release: MATLAB 7.4 (R2007a)

[Siyi Deng]

Good implementation. Nice examples and screen shots.

[Jon Dattorro]

For more methods of fast computation of distance matrices, see the book:
Convex Optimization & Euclidean Distance Geometry, Dattorro
http://convexoptimization.com

[Nina Hendrarini]