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Unique values within tolerance

`C = uniquetol(A,tol)`

`C = uniquetol(A)`

```
[C,IA,IC]
= uniquetol(___)
```

`[___] = uniquetol(___,Name,Value)`

returns
the unique elements in `C`

= uniquetol(`A`

,`tol`

)`A`

using tolerance `tol`

.
Two values, `u`

and `v`

, are within
tolerance if

`abs(u-v) <= tol*max(abs(A(:)))`

That is, `uniquetol`

scales the `tol`

input
based on the magnitude of the data.

`uniquetol`

is similar to `unique`

.
Whereas `unique`

performs exact comparisons, `uniquetol`

performs
comparisons using a tolerance.

`[___] = uniquetol(___,`

uses
additional options specified by one or more Name-Value pair arguments
using any of the input or output argument combinations in previous
syntaxes. For example, `Name,Value`

)`uniquetol(A,'ByRows',true)`

determines
the unique rows in `A`

.

There can be multiple valid

`C`

outputs that satisfy the condition,*no two elements in*. The`C`

are within tolerance of each other`uniquetol`

function just returns one of the valid outputs.`uniquetol`

sorts the input lexicographically, and then starts at the lowest value to find unique values within tolerance. As a result, changing the sorting of the input could change the output. For example,`uniquetol(-A)`

might not give the same results as`-uniquetol(A)`

.