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Scilab Help >> Elementary Functions > Set operations > intersect

# 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.

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.
```

• members — count (and locate) in an array each element or row or column of another array
• unique — extracts (and sorts) distinct elements, rows or columns of a matrix
• gsort — sorts boolean, numerical and string arrays
• union — Set of all elements, rows, or columns of two arrays, without duplicates

### History

 Version Description 6.1.0 Complex numbers are now accepted. 6.1.1 Sparse matrices are now accepted (numbers or booleans).