# Find approximate match between 2 matrices.

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Aristo on 31 Oct 2017
Edited: Rik on 2 Nov 2017
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 on 31 Oct 2017
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.

Rik on 2 Nov 2017
Edited: Rik on 2 Nov 2017
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.