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).

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

• 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