(sw-uniquetol)=

# sw_uniquetol

## Syntax
  
`[Mu, firstIdx] = sw_uniquetol(M,tol)`
  
## Description
  
`[Mu, firstIdx] = sw_uniquetol(m,tol)` returns unique column vectors
within the given `tol` tolerance. Two column vectors are considered
unequal, if the distance between them is larger than the tolerance
($\delta$):
 
$$\sqrt{\sum_i (V_i-U_i)^2} < \delta$$
  
## Input Arguments
  
`M`
: Matrix that contains column vectors.
  
`tol`
: Distance tolerance, default value is $10^{-5}$.
  
## Output Arguments
  
`Mu`
: Matrix that contains the unique column vectors.
 
`firstIdx`
: Indices pointing to the first occurence of the unique element.
 
This function is similar to the Matlab built-in
`unique(M,'rows','first')`, but with controllable tolerance.
 
## See Also
 
[unique](https://ch.mathworks.com/help/matlab/ref/unique.html)