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Octave has a number of functions for managing sets of data. A set is defined
as a collection of unique elements and is typically represented by a vector of
numbers sorted in ascending order. Any vector or matrix can be converted to a
set by removing duplicates through the use of the `unique`

function.
However, it isn’t necessary to explicitly create a set as all of the functions
which operate on sets will convert their input to a set before proceeding.

- :
`y`=**unique***(*¶`x`) - :
`y`=**unique***(*¶`x`, "rows") - :
`y`=**unique***(…, "sorted")*¶ - :
`y`=**unique***(…, "stable")*¶ - :
*[*`y`,`i`,`j`] =**unique***(…)*¶ - :
*[*`y`,`i`,`j`] =**unique***(…, "first")*¶ - :
*[*`y`,`i`,`j`] =**unique***(…, "last")*¶ - :
*[*`y`,`i`,`j`] =**unique***(…, "legacy")*¶ Return the unique elements of

`x`.If the input

`x`is a column vector then return a column vector; Otherwise, return a row vector.`x`may also be a cell array of strings.If the optional argument

`"rows"`

is given then return the unique rows of`x`. The input must be a 2-D numeric matrix to use this option.The optional argument

`"sorted"`

/`"stable"`

controls the order in which unique values appear in the output. The default is`"sorted"`

and values in the output are placed in ascending order. The alternative`"stable"`

preserves the order found in the input`x`.If requested, return column index vectors

`i`and`j`such that

and`y`=`x`(`i`)

.`x`=`y`(`j`)Additionally, if

`i`is a requested output then one of the flags`"first"`

or`"last"`

may be given. If`"last"`

is specified, return the highest possible indices in`i`, otherwise, if`"first"`

is specified, return the lowest. The default is`"first"`

.Example 1 : sort order

unique ([3, 1, 1, 2]) ⇒ [1, 2, 3] unique ([3, 1, 1, 2], "stable") ⇒ [3, 1, 2]

Example 2 : index selection

[~,

`i`] = unique ([3, 1, 1, 2], "first") ⇒`i`= [2; 4; 1] [~,`i`] = unique ([3, 1, 1, 2], "last") ⇒`i`= [3; 4; 1]Programming Notes: The input flag

`"legacy"`

changes the algorithm to be compatible with MATLAB releases prior to R2012b. Specifically, The index ordering flag is changed to`"last"`

, and the shape of the outputs`i`,`j`will follow the shape of the input`x`rather than always being column vectors.The third output,

`j`, has not been implemented yet when the sort order is`"stable"`

.

- :
`c`=**uniquetol***(*¶`A`) - :
`c`=**uniquetol***(*¶`A`,`tol`) - :
`c`=**uniquetol***(…,*¶`property`,`value`) - :
*[*`c`,`ia`,`ic`] =**uniquetol***(…)*¶ Return the unique elements of

`A`within tolerance`tol`.Two values,

`x`and`y`, are within relative tolerance if`abs (`

.`x`-`y`) <=`tol`* max (abs (`A`(:)))The input

`A`must be a real (non-complex) floating point type (double or single).If

`tol`is unspecified, the default tolerance is 1e-12 for double precision input or 1e-6 for single precision input.The function may also be called with the following optional property/value pairs. Property/value pairs must be passed after other input arguments:

`"ByRows"`

(default:`false`

)When true, return the unique rows of

`A`.`A`must be a 2-D array to use this option. For rows, the criteria for uniqueness is changed to`all (abs (`

which compares each column component of a row against a column-specific tolerance.`x`-`y`) <=`tol`*max (abs (`A`),[],1))`"DataScale"`

The tolerance test is changed to

`abs (`

where`x`-`y`) <=`tol`*`DS``DS`is a scalar unless the property`"ByRows"`

is true. In that case,`DS`can either be a scalar or a vector with a length equal to the number of columns in`A`. Using a value of`1.0`

for`DS`will change the tolerance from a relative one to an absolute tolerance. Using a value of`Inf`

will disable testing.`"OutputAllIndices"`

(default:`false`

)When true,

`ia`is a cell array (not a vector) that contains the indices for*all*elements in`A`that are within tolerance of a value in`C`. That is, each cell in`ia`corresponds to a single unique value in`C`, and the values in each cell correspond to locations in`A`.

The output

`c`is a row vector if the input`A`is a row vector. For all other cases, a column vector is returned.The optional output

`ia`is a column index vector such that

. If the`c`=`A`(`ia`)`"ByRows"`

property is true, the condition is

. If the`c`=`A`(`ia`, :)`"OutputAllIndices"`

property is true, then the values

are all within tolerance of the unique value`A`(`ia`{`i`})

.`c`(`i`)The optional output

`ic`is a column index vector such that

when`A`=`c`(`ic`)`A`is a vector. When`A`is a matrix,

. If the`A`(:) =`c`(`ic`)`"ByRows"`

property is true then

.`A`=`c`(`ic`,:)Example: small round-off errors require

`uniquetol`

, not`unique`

x = [1:5]; ## Inverse_Function (Function (x)) should return exactly x y = exp (log (x)); D = unique ([x, y]) ⇒ [1 2 3 3 4 5 5] C = uniquetol ([x, y]) ⇒ [1 2 3 4 5]

**See also:**unique, union, intersect, setdiff, setxor, ismember.

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