# true

Logical 1 (true)

## Description

example

true is shorthand for logical(1).

example

T = true(n) is an n-by-n matrix of logical ones.

example

T = true(sz) is an array of logical ones where the size vector, sz, defines size(T). For example, true([2 3]) returns a 2-by-3 array of logical ones.

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T = true(sz1,...,szN) is a sz1-by-...-by-szN array of logical ones where sz1,...,szN indicates the size of each dimension. For example, true(2,3) returns a 2-by-3 array of logical ones.

example

T = true(___,'like',p) returns an array of logical ones of the same sparsity as the logical variable p using any of the previous size syntaxes.

## Examples

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### Generate Square Matrix of Logical Ones

Use true to generate a 3-by-3 square matrix of logical ones.

A = true(3)
class(A)
A =
1     1     1
1     1     1
1     1     1
ans =
logical

The result is of class logical.

### Generate Array of Logical Ones with Arbitrary Dimensions

Use true to generate a 3-by-2-by-2 matrix of logical ones.

true(3,2,2)
ans(:,:,1) =
1     1
1     1
1     1

ans(:,:,2) =
1     1
1     1
1     1

Alternatively, you can use a size vector to specify the size of the matrix.

true([3,2,2])
ans(:,:,1) =
1     1
1     1
1     1

ans(:,:,2) =
1     1
1     1
1     1

Note that specifying multiple vector inputs returns an error.

### Execute Logic Statement

true along with false can be used to execute logic statements.

Test the logical statement $~\left(A\text{\hspace{0.17em}}\text{​}and\text{\hspace{0.17em}}B\right)\equiv \left(~A\right)or\left(~B\right)$ for A = logical true and B = logical false.

~(true & false) == (~true) | (~false)
ans =
1

The result is logical 1 (true), since the logical statements on both sides of the equation are equivalent. This logical statement is an instance of De Morgan's Law.

### Generate Logical Array of Selected Sparsity

Generate a logical array of the same sparsity as the selected array.

A = logical(sparse(5,3));
whos A
T = true(4,'like',A);
whos T
Name      Size            Bytes  Class      Attributes
A         5x3                41  logical    sparse
Name      Size            Bytes  Class      Attributes
T         4x4               184  logical    sparse

The output array T has the same sparse attribute and data-type as the specified array A.

## Input Arguments

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### n — Size of square matrixinteger

Size of square matrix, specified as an integer. n sets the output array size to n-by-n. For example, true(3) returns a 3-by-3 array of logical ones.

• If n is 0, then T is an empty matrix.

• If n is negative, then it is treated as 0.

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

### sz — Size vectorrow vector of integers

Size vector, specified as a row vector of integers. For example, true([2 3]) returns a 2-by-3 array of logical ones.

• If the size of any dimension is 0, then T is an empty array.

• If the size of any dimension is negative, then it is treated as 0.

• If any trailing dimensions greater than 2 have a size of 1, then the output, T, does not include those dimensions.

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

### sz1,...,szN — Size inputscomma-separated list of integers

Size inputs, specified by a comma-separated list of integers. For example, true(2,3) returns a 2-by-3 array of logical ones.

• If the size of any dimension is 0, then T is an empty array.

• If the size of any dimension is negative, then it is treated as 0.

• If any trailing dimensions greater than 2 have a size of 1, then the output, T, does not include those dimensions.

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

### p — Prototypelogical variable

Prototype, specified as a logical variable.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

## Output Arguments

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### T — Output of logical onesscalar | vector | matrix | N-D array

Output of logical ones, returned as a scalar, vector, matrix, or N-D array.

Data Types: logical

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### Tips

• true(n) is much faster and more memory efficient than logical(true(n)).