# intersect

elements or rows or columns met in both input arrays, without duplicates

### Syntax

M = intersect(a, b) M = intersect(a, b, orient) [M, ka] = intersect(..) [M, ka, kb] = intersect(..)

### Arguments

- a, b
- vectors, matrices or hypermatrices of booleans, encoded integers, real or
complex numbers, or text.
`a`

and`b`

must have the same datatype. For text inputs, UTF characters are accepted. Sparse numeric or boolean matrices are accepted : Either`a`

or`b`

or both`a`

and`b`

may be sparse. - orient
- flag with possible values : 1 or "r", 2 or "c". Can't be used if
`a`

or/and`b`

is an hypermatrix. - M
matrix of the same datatype as

`a`

and`b`

.- Without
`orient`

:`M`

is a row vector. - With
`orient="r"|1`

:`M`

is a matrix stacking the common rows of`a`

and`b`

. - With
`orient="c"|2`

:`M`

is a matrix stacking the common columns of`a`

and`b`

.

`M`

is sparse as soon as either`a`

or`b`

is sparse and none is empty.- Without
- ka
- Dense row vector of indices in
`a`

. - kb
- Dense row vector of indices in
`b`

.

### Description

`intersect(a,b)`

returns a row vector of unique values
present in both `a`

and `b`

arrays. Values are
sorted in increasing order

- for complex numbers : par increasing magnitudes, then by increasing phases
- for text : in alphabetical order.

Two NaN elements are always considered as different. So NaN or rows or columns having
NaN will never be in the result `M` . |

`[M, ka, kb] = intersect(a,b)`

additionally returns the vectors
`ka`

and `kb`

of indices in `a`

and `b`

of selected components firstly met, such that
`M=a(ka)`

and `M=b(kb)`

.

##### Common rows or columns

When the `orient`

argument is provided, the comparison is performed
between the rows of `a`

and `b`

-- each one being
considered as a whole --, or between their columns.

`intersect(a,b,"r")`

or `intersect(a,b,1)`

will return
the matrix of stacked unduplicated rows met in both `a`

and
`b`

, sorted in lexicographic ascending order.
If `a`

and `b`

don't have the same number of columns,
[] is returned without comparing the values.

`[M,ka,kb] = intersect(a,b,"r")`

additionally returns the vectors
`ka`

and `kb`

of the minimal indices of common rows,
respectively in `a`

and `b`

,
such that `M=a(ka,:)`

and `M=b(kb,:)`

.

`intersect(a,b,"c")`

or `intersect(a,b,2)`

does
the same for columns.

### Examples

A = grand(3, 3, "uin", 0, 9) B = grand(2, 4, "uin", 0, 9) intersect(A, B) [N, ka, kb] = intersect(A,B); ka, kb

--> A = grand(3, 3, "uin", 0, 9) A = 0. 6. 4. 6. 6. 6. 2. 7. 9. --> B = grand(2, 4, "uin", 0, 9) B = 1. 8. 0. 2. 6. 2. 2. 1. --> intersect(A, B) ans = 0. 2. 6. --> [N, ka, kb] = intersect(A,B); --> ka, kb ka = 1. 3. 2. kb = 5. 4. 2.

In the above example, note that 6 is met four times in A, at indices [2 4 5 8]. Only the minimal index 2 is returned in ka. Same situation for 2 in B.

NaN values can never be in the result:

%nan == %nan intersect([1 -2 %nan 3 6], [%nan 1:3])

--> %nan == %nan ans = F --> intersect([1 -2 %nan 3 6], [%nan 1:3]) ans = 1. 3.

intersect() can also process some characters or some texts. Since Scilab is great with UTF characters, here is an example with some Arabic contents, getting characters present in both sentences:

A = strsplit("هو برنامج علمي كبير ""Scilab""")' B = strsplit("فهو حر ومفتوح")' intersect(A,B)

--> A = strsplit("هو برنامج علمي كبير ""Scilab""")' A = !ه و ب ر ن ا م ج ع ل م ي ك ب ي ر " S c i l a b " ! --> B = strsplit("فهو حر ومفتوح")' B = !ف ه و ح ر و م ف ت و ح ! --> intersect(A,B) ans = ! ر م ه و !

Column-wise or Row-wise processing of two matrices: Here we process 2 matrices of signed 1-byte integers, and get the common columns:

A = int8(grand(3,5,"uin",0,1)) B = int8(grand(3,9,"uin",0,1)) [M,ka,kb] = intersect(A, B, "c"); M, ka, kb

--> A = int8(grand(3,5,"uin",0,1)) A = 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 --> B = int8(grand(3,9,"uin",0,1)) B = 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 --> [M,ka,kb] = intersect(A, B, "c"); --> M, ka, kb M = 0 1 1 0 0 1 0 1 0 ka = 1. 5. 3. kb = 2. 3. 4.

`intersect()`

for booleans is mainly useful with the "r" or "c" option.
Here is an example with a sparse boolean matrix:

[F, T] = (%f, %t); A = [F F T F T F ; T F F T T T ; T T F T F F] B = [F T F T F F ; T F F F T F ; F T F F T F] [M,ka,kb] = intersect(A, sparse(B), "c"); issparse(M), full(M), ka, kb

--> A = [F F T F T F ; T F F T T T ; T T F T F F] A = F F T F T F T F F T T T T T F T F F --> B = [F T F T F F ; T F F F T F ; F T F F T F] B = F T F T F F T F F F T F F T F F T F --> [M,ka,kb] = intersect(A, sparse(B), "c"); --> issparse(M), full(M), ka, kb ans = T ans = F F T T T F F T F ka = 6. 1. 3. kb = 1. 5. 4.

### See also

### History

Version | Description |

6.1.0 | Complex numbers are now accepted. |

6.1.1 | Sparse matrices are now accepted (numbers or booleans). |

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