setdiff returns elements that are in a set but not in another one.

## Syntax

                v = setdiff(a, b)
                v = setdiff(a, b, orien)
                [v, ka] = setdiff(..)

## Arguments

a

  a set of elements

b

  elements to remove from `a`.

orien
  oriented processing:
  - `"r"`: rows of `a` are searched among `b` ones.
  - `"c"`: columns of `a` are searched among `b` ones.
  - no orien: elements of `a` are searched among `b` ones.

If the option `orien="r"` is used, `a` and `b` must have the same number of columns. If the `orien="c"` is used, they must have the same number of rows.

v
  Array with `a`'s data type and encoding:
  - sorted vector of `a`'s components that are not in `b`.
  - `orien="r"`: matrix of rows of `a` that are not in `b`, sorted in lexicographic order.
  - `orien="c"`: matrix of columns of `a` that are not in `b`, sorted in lexicographic order.
ka

  vector of linear indices of selected `a`'s components, rows, or columns, such that

  - `v = a(ka)`, or
  - `v = a(ka,:)` (`orien="r"`), or
  - `v = a(:,ka)` (`orien="c"`)

## Description

`setdiff(a, b,..)` computes and returns the elements or rows or columns of `a` that are not in `b`.

All duplicates (elements or rows or columns) are removed from `a` and from `b` before processing.

Both `a` and `b` must have the same data type (and integer type), but may mix dense and sparse encoding. It can be vectors, matrices or hypermatrices of real or complex numbers, encoded integers, booleans, or strings. Sparse-encoded inputs are also accepted.

If `a` is an hypermatrix and the `"r"` option is used, `a` is replaced with the matrix of all its rows over all its higher dimensions, before processing. Same thing if `b` is an hypermatrix. If the `"c"` option is used, `a` or/and `"b"` are replaced with the respective matrices of all their columns.

The format of results is presented in the following table, according to the shape of `a` and the `orien` option. In all cases, if all entities of `a` are in `b`, `[]` is returned for `v` as for `ka`:

orien → | none | "r" | "c"
a ↓ | v | ka | v | ka | v | ka
--- | --- | --- | --- | --- | --- | ---
row | row | row | row | scal | row | row
column | col | col | col | col | col | scal
matrix | col | col | mat | col | mat | row
hypermatrix | col | col | mat | col | mat | row
scalar | scal | scal | scal | scal | scal | scal

`v` and `ka` become empty if `a` is empty (whatever is `b`), or if all `a` elements are in `b`.

For booleans, `setdiff(…)` is useful mainly with the "r" or "c" options.

## Examples

Example #1:

    a = grand(1, 10,"uin", 0, 9)
    b = grand(2, 4, "uin", 0, 9)
    [d, k] = setdiff(a, b);
    d, k

    --> a = grand(1, 10,"uin", 0, 9)
     a  =
       2.   2.   4.   5.   4.   1.   9.   5.   8.   3.

    --> b = grand(2, 4, "uin", 0, 9)
     b  =
       5.   0.   9.   9.
       5.   6.   0.   4.

    --> [d, k] = setdiff(a, b);
    --> d, k
     d  =
       1.   2.   3.   8.

     k  =
       6.   1.   10.   9.

Example #2: column-wise processing

    a = grand(2, 7,"uin", 0, 3)
    b = grand(2, 10, "uin", 0, 3)
    [d, k] = setdiff(a, b, "c");
    d, k

    --> a = grand(2, 7,"uin", 0, 3)
     a  =
       0.   1.   0.   2.   3.   0.   2.
       2.   2.   2.   1.   0.   1.   2.

    --> b = grand(2, 10, "uin", 0, 3)
     b  =
       1.   1.   3.   1.   1.   1.   3.   0.   2.   0.
       3.   3.   2.   2.   0.   0.   1.   0.   1.   0.

    --> [d, k] = setdiff(a, b, "c");
    --> d, k
     d  =
       0.   0.   2.   3.
       1.   2.   2.   0.

     k  =
       6.   1.   7.   5.

Example #3: with some text

    v1 = tokens("ab  ca  ba  bb  ca  cb  ba  aa  cc  bc  ac  aa")'
    v2 = tokens("cc  ac  ca  bb  ac  bc  ab")'
    [r, k] = setdiff(v1, v2);
    r, k

    --> v1 = tokens("ab  ca  ba  bb  ca  cb  ba  aa  cc  bc  ac  aa")'
     v1  =
    !ab  ca  ac  bb  ca  cb  ba  aa  cc  bc  ac  aa  !

    --> v2 = tokens("cc  ac  ca  bb  ac  bc  ab")'
     v2  =
    !cc  ac  ca  bb  ac  bc  ab  !

    --> [r, k] = setdiff(v1, v2);
    --> r, k
     r  =
    !aa  ba  cb  !

     k  =
       8.   3.   6.

## See also

- unique
- union
- members
- vectorfind

## History

< 5.0 Function introduced.
6.0.2 Option "r" | "c" added, including for hypermatrices.
6.1.0 Extension to complex numbers.
6.1.1 Boolean inputs and sparse inputs (boolean or numeric) are now accepted.