# find

Find indices and values of nonzero elements

## Syntax

• ``k = find(X)``
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• ``k = find(X,n)``
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• ``k = find(X,n,direction)``
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• ``````[row,col] = find(___)``````
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• ``````[row,col,v] = find(___)``````
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## Description

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````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.If `X` contains no nonzero elements or is empty, then `find` returns an empty array.```

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

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

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``````[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.```

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

## Examples

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### Zero and Nonzero Elements in Matrix

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

```X = [1 0 2; 0 1 1; 0 0 4] ```
```X = 1 0 2 0 1 1 0 0 4 ```
```k = find(X) ```
```k = 1 5 7 8 9 ```

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

```k2 = find(~X) ```
```k2 = 2 3 4 6 ```

### Elements Satisfying a Condition

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

```X = magic(4) ```
```X = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1 ```
```k = find(X<10,5) ```
```k = 2 3 4 5 7 ```

View the corresponding elements of `X`.

```X(k) ```
```ans = 5 9 4 2 7 ```

### Elements Equal to Specific Values

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 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 = Columns 1 through 7 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 Columns 8 through 11 0.7000 0.8000 0.9000 1.0000 ```
```k = find(y==0.3) ```
```k = Empty matrix: 1-by-0 ```
```k = find(abs(y-0.3) < 0.001) ```
```k = 4 ```

### Last Several Nonzero Elements

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 = 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 = 30 32 34 36 ```

### Elements Satisfying Multiple Conditions

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 = 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 = 2 3 4 col = 1 1 1 ```

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

### Subscripts and Values for Nonzero Elements

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 2 0 -5 0 7 0 0 1 ```
```[row,col,v] = find(X) ```
```row = 1 2 1 2 3 col = 1 1 2 3 3 v = 3 -5 2 7 1 ```

### Subscripts of Multidimensional Array

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(:,:,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 = 1 4 3 1 col = 1 3 5 6 ```

## Input Arguments

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### `X` — Input arrayscalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array. If `X` is an empty array or has no nonzero elements, then `k` is an empty array.

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

### `n` — Number of nonzeros to findpositive integer scalar

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`.

### `direction` — Search direction`'first'` (default) | `'last'`

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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### `k` — Indices to nonzero elementsvector

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 array when `X` is an empty array or has no nonzero elements.

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

### `row` — Row subscriptsvector

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

### `col` — Column subscriptsvector

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)`.

### `v` — Nonzero elements of `X`vector

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)```.