## ALL All True Function

Section: Elementary Functions

### Usage

Reduces a logical array along a given dimension by testing for all logical 1s. The general syntax for its use is

      y = all(x,d)

where `x` is an `n`-dimensions array of `logical` type. The output is of `logical` type. The argument `d` is optional, and denotes the dimension along which to operate. The output `y` is the same size as `x`, except that it is singular along the operated direction. So, for example, if `x` is a `3 x 3 x 4` array, and we `all` operation along dimension `d=2`, then the output is of size `3 x 1 x 4`.

### Function Internals

The output is computed via

If `d` is omitted, then the minimum is taken over all elements of `x`.

### Example

The following piece of code demonstrates various uses of the `all` function

    --> A = [1,0,0;1,0,0;0,0,1]

    A =

     1 0 0
     1 0 0
     0 0 1

We start by calling `all` without a dimension argument, in which case it defaults to testing all values of `A`

    --> all(A)

    ans =

     0

The `all` function is useful in expressions also.

    --> all(A>=0)

    ans =

     1

Next, we apply the `all` operation along the rows.

    --> all(A,2)

    ans =

     1 0 0
     1 0 0
     0 0 1