# find

Find indices and values of nonzero elements

## Description

example

k = find(X) returns a vector containing the linear indices of each nonzero element in array X.

• If X is a vector, then find returns a vector with the same orientation as X.

• If X is a multidimensional array, then find returns a column vector of the linear indices of the result.

example

k = find(X,n) returns the first n indices corresponding to the nonzero elements in X.

example

k = find(X,n,direction), where direction is 'last', finds the last n indices corresponding to nonzero elements in X. The default for direction is 'first', which finds the first n indices corresponding to nonzero elements.

example

[row,col] = find(___) returns the row and column subscripts of each nonzero element in array X using any of the input arguments in previous syntaxes.

example

[row,col,v] = find(___) also returns vector v, which contains the nonzero elements of X.

## Examples

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Find the nonzero elements in a 3-by-3 matrix.

X = [1 0 2; 0 1 1; 0 0 4]
X = 3×3

1     0     2
0     1     1
0     0     4

k = find(X)
k = 5×1

1
5
7
8
9

Use the logical not operator on X to locate the zeros.

k2 = find(~X)
k2 = 4×1

2
3
4
6

Find the first five elements that are less than 10 in a 4-by-4 magic square matrix.

X = magic(4)
X = 4×4

16     2     3    13
5    11    10     8
9     7     6    12
4    14    15     1

k = find(X<10,5)
k = 5×1

2
3
4
5
7

View the corresponding elements of X.

X(k)
ans = 5×1

5
9
4
2
7

To find a specific integer value, use the == operator. For instance, find the element equal to 13 in a 1-by-10 vector of odd integers.

x = 1:2:20
x = 1×10

1     3     5     7     9    11    13    15    17    19

k = find(x==13)
k = 7

To find a noninteger value, use a tolerance value based on your data. Otherwise, the result is sometimes an empty matrix due to floating-point roundoff error.

y = 0:0.1:1
y = 1×11

0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000    0.8000    0.9000    1.0000

k = find(y==0.3)
k =

1x0 empty double row vector
k = find(abs(y-0.3) < 0.001)
k = 4

Create a 6-by-6 magic square matrix with all of the odd-indexed elements equal to zero.

X = magic(6);
X(1:2:end) = 0
X = 6×6

0     0     0     0     0     0
3    32     7    21    23    25
0     0     0     0     0     0
8    28    33    17    10    15
0     0     0     0     0     0
4    36    29    13    18    11

Locate the last four nonzeros.

k = find(X,4,'last')
k = 4×1

30
32
34
36

Find the first three elements in a 4-by-4 matrix that are greater than 0 and less than 10. Specify two outputs to return the row and column subscripts to the elements.

X = [18 3 1 11; 8 10 11 3; 9 14 6 1; 4 3 15 21]
X = 4×4

18     3     1    11
8    10    11     3
9    14     6     1
4     3    15    21

[row,col] = find(X>0 & X<10,3)
row = 3×1

2
3
4

col = 3×1

1
1
1

The first instance is X(2,1), which is 8.

Find the nonzero elements in a 3-by-3 matrix. Specify three outputs to return the row subscripts, column subscripts, and element values.

X = [3 2 0; -5 0 7; 0 0 1]
X = 3×3

3     2     0
-5     0     7
0     0     1

[row,col,v] = find(X)
row = 5×1

1
2
1
2
3

col = 5×1

1
1
2
3
3

v = 5×1

3
-5
2
7
1

Find the nonzero elements in a 4-by-2-by-3 array. Specify two outputs, row and col, to return the row and column subscripts of the nonzero elements. When the input is a multidimensional array (N > 2), find returns col as a linear index over the N-1 trailing dimensions of X.

X = zeros(4,2,3);
X([1 12 19 21]) = 1
X =
X(:,:,1) =

1     0
0     0
0     0
0     0

X(:,:,2) =

0     0
0     0
0     0
1     0

X(:,:,3) =

0     1
0     0
1     0
0     0

[row,col] = find(X)
row = 4×1

1
4
3
1

col = 4×1

1
3
5
6

## Input Arguments

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Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char
Complex Number Support: Yes

Number of nonzeros to find, specified as a positive integer scalar. By default, find(X,n) looks for the first n nonzero elements in X.

Search direction, specified as the string 'first' or 'last'. Look for the last n nonzero elements in X using find(X,n,'last').

## Output Arguments

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Indices to nonzero elements, returned as a vector.

• If X is a row vector, then k is also a row vector. Otherwise, k is a column vector.

• k is an empty row vector or empty column vector when X is an empty array or has no nonzero elements.

• find uses the convention that k is an empty matrix [] when X is an empty matrix [].

You can return the nonzero values in X using X(k).

Row subscripts, returned as a vector. Together, row and col specify the X(row,col) subscripts corresponding to the nonzero elements in X.

Column subscripts, returned as a vector. Together, row and col specify the X(row,col) subscripts corresponding to the nonzero elements in X.

If X is a multidimensional array with N > 2, then col is a linear index over the N-1 trailing dimensions of X. This preserves the relation X(row(i),col(i)) == v(i).

Nonzero elements of X, returned as a vector.

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### Linear Indices

A linear index allows use of a single subscript to index into an array, such as A(k). MATLAB® treats the array as a single column vector with each column appended to the bottom of the previous column. Thus, linear indexing numbers the elements in the columns from top to bottom, left to right.

For example, consider a 3-by-3 matrix. You can reference the A(2,2) element with A(5), and the A(2,3) element with A(8). The linear index changes depending on the size of the array; A(5) returns a differently located element for a 3-by-3 matrix than it does for a 4-by-4 matrix.

The sub2ind and ind2sub functions are useful in converting between subscripts and linear indices.

## Tips

• To find array elements that meet a condition, use find in conjunction with a relational expression. For example, find(X<5) returns the linear indices to the elements in X that are less than 5.

• To directly find the elements in X that satisfy the condition X<5, use X(X<5). Avoid function calls like X(find(X<5)), which unnecessarily use find on a logical matrix.

• When you execute find with a relational operation like X>1, it is important to remember that the result of the relational operation is a logical matrix of ones and zeros. For example, the command [row,col,v] = find(X>1) returns a column vector of logical 1 (true) values for v.

• The row and column subscripts, row and col, are related to the linear indices in k by k = sub2ind(size(X),row,col).

## Version History

Introduced before R2006a