all

Determine if all elements are non-zero.

Usage

b = all(A)

• When A is a scalar, it returns logical 1 if A is non-zero, and logical 0 if otherwise.
• When A is a vector, it returns logical 1 if all elements of A are non-zero, and logical 0 if otherwise.
• When A is a matrix or an array of ndims(A) >= 3, an element of the output array is assigned logical 1 if all elements of the corresponding vector of A along the first non-singleton dimension are non-zero, and logical 0 if otherwise.
• all(A) collapses the first non-singleton dimension of A. That means, if size(A) = [s1, s2, ..., sN] with s1 larger than 1, then size(all(A)) = [1, s2, s3, ..., sN].

b = all(A, k)

• k should be a real positive integer scalar.
• An element of b is assigned logical 1 if all elements of the corresponding vector of A along the k-th dimension are non-zero, and logical 0 if otherwise.

Discussions

• A complex number is zero if both real and imaginary parts are zero.
• If A is a character array, it is first converted to a double array.
• It ignores any NaN present in A. This is equivalent to replacing all NaN values in A by 1. As a result, all(NaN) gives 1.
• Calling all(A) and all(A, k) always return an empty array when A is empty.

Examples

• all is applied to the first non-singleton dimension. It checks if a has a column with all non-zero entries.

Input

% Create a matrix with some zero elements.
a = randi(3,3,3) - 2
all(a)

Output

a = 
 1.0000  -1.0000   0.0000
 0.0000   1.0000  -1.0000
 1.0000   1.0000  -1.0000

ans = 
 0.0000   1.0000   0.0000

• all is applied to a selected dimension. It checks if a has a row with all non-zero entries.

Input

% Create a matrix with some zero elements.
a = randi(3,3,3) - 2
all(a, 2)

Output

a = 
-1.0000   0.0000   0.0000
-1.0000  -1.0000  -1.0000
-1.0000  -1.0000  -1.0000

ans = 
 0.0000
 1.0000
 1.0000