# all

Determine if all array elements are nonzero or `true`

## Description

example

````B = all(A)` tests along the first array dimension of `A` whose size does not equal 1, and determines if the elements are all nonzero or logical `1` (`true`). In practice, `all` is a natural extension of the logical AND operator.If `A` is a vector, then `all(A)` returns logical `1` (`true`) if all the elements are nonzero and returns logical `0` (`false`) if one or more elements are zero.If `A` is a nonempty, nonvector matrix, then `all(A)` treats the columns of `A` as vectors and returns a row vector of logical `1`s and `0`s.If `A` is an empty 0-by-0 matrix, then `all(A)` returns logical `1` (`true`).If `A` is a multidimensional array, then `all(A)` acts along the first array dimension whose size does not equal 1 and returns an array of logical values. The size of this dimension becomes `1`, while the sizes of all other dimensions remain the same.```

example

````B = all(A,dim)` tests elements along dimension `dim`. The `dim` input is a positive integer scalar.```

## Examples

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### Test Matrix Columns

Create a 3-by-3 matrix.

```A = [0 0 3;0 0 3;0 0 3] ```
```A = 0 0 3 0 0 3 0 0 3```

Test each column for all nonzero elements.

`B = all(A)`
```B = 0 0 1 ```

### Reduce a Logical Vector to a Single Condition

Create a vector of decimal values and test which values are less than 0.5.

```A = [0.53 0.67 0.01 0.38 0.07 0.42 0.69]; B = (A < 0.5) ```
```B = 0 0 1 1 1 1 0```

The output is a vector of logical values. The `all` function reduces such a vector of logical values to a single condition. In this case, `B = all(A < 0.5)` yields logical `0`.

This makes `all` particularly useful in `if` statements.

```if all(A < 0.5) %do something else %do something else end```

The code is executed depending on a single condition, rather than a vector of possibly conflicting conditions.

### Test Arrays of Any Dimension

Create a 3-by-7-by-5 multidimensional array and test to see if all of its elements are less than 3.

```A = rand(3,7,5) * 5; B = all(A(:) < 3) ```
```B = 0```

You can also test the array for elements that are greater than zero.

```B = all(A(:) > 0) ```
```B = 1```

The syntax `A(:)` turns the elements of `A` into a single column vector, so you can use this type of statement on an array of any size.

### Test Matrix Rows

Create a 3-by-3 matrix.

```A = [0 0 3;0 0 3;0 0 3] ```
```A = 0 0 3 0 0 3 0 0 3```

Test the rows of `A` for all nonzero elements by specifying `dim = 2`.

`B = all(A,2)`
```B = 0 0 0 ```

## Input Arguments

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### `A` — Input Arrayscalar | vector | matrix | multidimensional array

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

### `dim` — Dimension to operate alongpositive integer scalar

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

Consider a two-dimensional input array, `A`:

• `all(A,1)` works on successive elements in the columns of `A` and returns a row vector of logical values.

• `all(A,2)` works on successive elements in the rows of `A` and returns a column vector of logical values.

Data Types: `double` | `single` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

## Output Arguments

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### `B` — Logical arrayscalar | vector | matrix | multidimensional array

Logical array, returned as a scalar, vector, matrix, or multidimensional array. The dimension of `A` acted on by `all` has size `1` in `B`.

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