# setdiff

returns elements or rows or columns of an array that do not belong to another one

### Syntax

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

### Arguments

- a, b
vectors, matrices or hypermatrices of real or complex numbers, encoded integers, booleans, or strings. Sparse-encoded inputs are accepted. Both

`a`

and`b`

must have the same data type (and integer type), but may mix dense and sparse encoding.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.- 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"`

)

### 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.

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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