Find approximate match between 2 matrices.

Hi all,

I have 2 matrices of 10000 x 3 and 15000 x 3 of floating numbers. where in for example

A=[x1,y1,z1] and B=[x2,y2,z2]

A=[22.35 55.36  110.72          &   B=[12.65  15.36  22.36 
   21.48 -54.35 -35.65                  22.35 54.36  113.36
   32.64  65.35 -110.35                 15.36  175.23 23.65
   23.35  54.36  112                     6.56  18.56 -72.36
   6.35  -90.35 -156.36                  7.35 -92.32 -153.72
   19.36 -12.36  176.53                  18.72 -10.36 176.78
   22.36 15.36   22.36]                  23.36 17.36   19.88]

I want to approximate match x1 to x2,y1 to y2, and z1 to z2 with tolerance of +/- 1.0000 for x, +/- 2.0000 for y and +/- 3.000 for z matching. If I find approximate match, I want to make a separate matrix of of A1 and B1.

A1=[x11,y11,z11] and B1=[x21,y21,z21]
A1=[23.35 55.36 110.72  &            B1=[22.35 54.36 113.36
    22.35 54.36  112                     22.35 54.36 113.36
   6.35  -90.35 -156.36                  7.35 -92.32 -153.72
   19.36 -12.36  176.53                  18.72 -10.36 176.78
   22.36 15.36   22.36]                  23.36 17.36   19.88]
Where A1 is the values of A coinciding with B and B1 is the coinciding values of A with B. Such that size of A1 and B1 are same.

[Rik]

What have you tried? Do you have a small example you could show input and output for? Have a read here and here. It will greatly improve your chances of getting an answer.

Answer 1

[Rik]

You can try pdist2 with a custom distance function: a function that returns only true or false. Your custom function needs to return a numeric array, and logical apparently doesn't count. 15k by 15k might not fit in memory (1 800 000 000 bytes=225MB for double, 1/8 for logical, uint8 or int8).

DISTFUN=@(ZI,ZJ) uint8(...
  abs(ZJ(:,1)-ZI(1))<=1 ...
  & abs(ZJ(:,2)-ZI(2))<=2 ...
  & abs(ZJ(:,3)-ZI(3))<=3);
within_tolerance=pdist2(A,B,DISTFUN);

With that matrix you can generate A1 and B1 with the sort you need.