# 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.

- 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.

- sorted vector of
- 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"`

)

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.

### 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) 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) 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 — extracts (and sorts) distinct elements, rows or columns of a matrix
- union — Set of all elements, rows, or columns of two arrays, without duplicates
- members — count (and locate) in an array each element or row or column of another array
- vectorfind — locates occurences of a (wildcarded) vector in a matrix or hypermatrix

### History

Version | Description |

< 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. |

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