FIND Find Non-zero Elements of An Array

Usage

Returns a vector that contains the indicies of all non-zero elements in an array. The usage is

   y = find(x)

The indices returned are generalized column indices, meaning that if the array x is of size [d1,d2,...,dn], and the element x(i1,i2,...,in) is nonzero, then y will contain the integer

$$i_1 + (i_2-1) d_1 + (i_3-1) d_1 d_2 + \dots$$

The second syntax for the find command is

   [r,c] = find(x)

which returns the row and column index of the nonzero entries of x. The third syntax for the find command also returns the values

   [r,c,v] = find(x).

This form is particularly useful for converting sparse matrices into IJV form.

Example

Some simple examples of its usage, and some common uses of find in FreeMat programs.

--> a = [1,2,5,2,4];
--> find(a==2)
ans = 
  <uint32>  - size: [2 1]
 
Columns 1 to 1
            2  
            4

Here is an example of using find to replace elements of A that are 0 with the number 5.

--> A = [1,0,3;0,2,1;3,0,0]
A = 
  <int32>  - size: [3 3]
 
Columns 1 to 3
             1              0              3  
             0              2              1  
             3              0              0  
--> n = find(A==0)
n = 
  <uint32>  - size: [4 1]
 
Columns 1 to 1
            2  
            4  
            6  
            9  
--> A(n) = 5
A = 
  <int32>  - size: [3 3]
 
Columns 1 to 3
             1              5              3  
             5              2              1  
             3              5              5

Incidentally, a better way to achieve the same concept is:

--> A = [1,0,3;0,2,1;3,0,0]
A = 
  <int32>  - size: [3 3]
 
Columns 1 to 3
             1              0              3  
             0              2              1  
             3              0              0  
--> A(A==0) = 5
A = 
  <int32>  - size: [3 3]
 
Columns 1 to 3
             1              5              3  
             5              2              1  
             3              5              5

Now, we can also return the indices as row and column indices using the two argument form of find:

--> A = [1,0,3;0,2,1;3,0,0]
A = 
  <int32>  - size: [3 3]
 
Columns 1 to 3
             1              0              3  
             0              2              1  
             3              0              0  
--> [r,c] = find(A)
r = 
  <uint32>  - size: [5 1]
 
Columns 1 to 1
            1  
            3  
            2  
            1  
            2  
c = 
  <uint32>  - size: [5 1]
 
Columns 1 to 1
            1  
            1  
            2  
            3  
            3

Or the three argument form of find, which returns the value also:

--> [r,c,v] = find(A)
r = 
  <uint32>  - size: [5 1]
 
Columns 1 to 1
            1  
            3  
            2  
            1  
            2  
c = 
  <uint32>  - size: [5 1]
 
Columns 1 to 1
            1  
            1  
            2  
            3  
            3  
v = 
  <int32>  - size: [5 1]
 
Columns 1 to 1
             1  
             3  
             2  
             3  
             1