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 = 1×3 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 = 1×7 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 = 3×1 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 = 1×1×3 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 you do not specify the dimension, 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.

The all 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:

• For input argument A:

  • If you do not specify a dimension, the code generator operates along the first dimension of the input array that is variable size or whose size does not equal 1. If this dimension is variable size at code generation time and is 1 at run time, a run-time error can occur. To avoid this error, specify the dimension.

  • If all dimensions of the input array are variable size at code generation time, this array cannot be empty at run time.

• If used, the dim argument must be a constant at code generation time.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Double data types are not supported.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

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

The all function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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).

Version History

Introduced before R2006a