all

Determine if all array elements are nonzero or true

Syntax

B = all(A)

B = all(A,'all')

B = all(A,dim)

B = all(A,vecdim)

Description

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 matrix, then all(A) treats the columns of A as vectors and returns a row vector of logical 1s and 0s.

• 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.

B = all(A,'all') tests over all elements of A. This syntax is valid for MATLAB^® versions R2018b and later.

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

B = all(A,vecdim) tests elements based on the dimensions specified in the vector vecdim. For example, if A is a matrix, then all(A,[1 2]) tests over all elements in A, since every element of a matrix is contained in the array slice defined by dimensions 1 and 2.

Examples

Test Matrix Columns

Create a 3-by-3 matrix, and then test each column for all nonzero elements.

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

A = 3×3

     0     0     3
     0     0     3
     0     0     3

B = all(A)

B = 1x3 logical array

   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 = 1x7 logical array

   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 = logical
   0

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

B = all(A(:) > 0)

B = logical
   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 = 3×3

     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 = 3x1 logical array

   0
   0
   0

Nonzero Elements in Array Page

Create a 3-D array and determine if all elements in each page of data (rows and columns) are zero.

A(:,:,1) = [2 1; 3 5];
A(:,:,2) = [0 0; 0 0];
A(:,:,3) = [-2 9; 4 1];
B = all(A,[1 2])

B = 1x1x3 logical array
B(:,:,1) =

   1


B(:,:,2) =

   0


B(:,:,3) =

   1

Input Arguments

A — Input Array

scalar | 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 along

positive 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

vecdim — Vector of dimensions

vector of positive integers

Vector of dimensions, specified as a vector of positive integers. Each element represents a dimension of the input array. The lengths of the output in the specified operating dimensions are 1, while the others remain the same.

Consider a 2-by-3-by-3 input array, A. Then all(A,[1 2]) returns a 1-by-1-by-3 array whose elements indicate nonzero values for each page of A.

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

Output Arguments

B — Logical array

scalar | 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.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• See Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder).

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).