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# and

logical AND between the elements of a boolean or numerical array

### Syntax

b = and(A) b = and(A, 'r') b = and(A, 'c') b = and(A, n)

### Arguments

- A
vector, matrix, or hypermatrix of booleans, encoded integers (of any inttype), real, or complex numbers.

`A`

may be sparse-encoded.A number is considered as %F (false) if it is 0 or 0+0i. Otherwise (including %nan), it is equivalent to %T (true).

Special`A`

:`and([])`

returns`%T`

.`and(%nan)`

returns`%T`

.

- b
boolean scalar, if

`and(A)`

is used without any option`"r", "c", n`

. Then`and(A)`

sets`b`

to- %F, if at least one of
`A`

's components is %F or zero. - %T, otherwise: All
`A`

components are %T or non zero or %nan.

Otherwise: boolean vector, matrix or hypermatrix. See

`n`

below.When

`A`

is sparse-encoded,`b`

is so as well.- %F, if at least one of
- n
Index <= ndims(A) of the dimension along which

`and()`

is applied / projected. By default,`and()`

is applied between all`A`

's elements. Otherwise:- n = 1 | "r" :
`and()`

is applied row-wise. If`A`

is a matrix, the result`b`

is a**r**ow, with`b(j) = and(A(:,j))`

- n = 2 | "c" :
`and()`

is applied column-wise. If`A`

is a matrix, the result`b`

is a**c**olumn, with`b(i) = and(A(i,:))`

- n > 2 : If
`A`

is an hypermatrix with at least`n`

dimensions,`and()`

is applied accross the n^{th}dimension.Example: If

`ndims(A)==3`

and`n=3`

,`b`

is a boolean matrix of size size(A)([1 2]), with`b(i,j) = and(A(i,j,:))`

- n = 1 | "r" :

### Description

`and()`

computes a logical AND between
the components of the single input `A`

.

To compute AND in an element-wise way between two arrays
`C`

and `D`

of same sizes, please
use the `&`

operator instead.

Why is `and([])`

set to `%T`

?
Whatever are compatible `B`

and `C`

,
`and([B C])==(and(B) & and(C))`

.
Now, for `B = []`

, `and([B C])==and(C)`

.
To have always `(and([]) & and(C))==and(C)`

,
`and([])`

must be `%T`

.

### Examples

and([]) and(0) and(0+0*%i) and(%eps) and(%i) and(%nan) // Projection accross a dimension / along a direction: A = rand(2,5)<0.5 and(A) and(A, "r") // and(A, 1) does the same and(A, "c") // and(A, 2) does the same // Equivalent application to encoded integers: A = int16(grand(3,5,"uin",-10,10)); A(abs(A)<3) = 0 and(A) and(A,1) // With an hypermatrix of decimal numbers: A = rand(3,4,2); A(A<0.2) = 0 and(A,3) // With a sparse matrix: A = sprand(70,100, 0.001) and(A, "r") and(A, "c")

--> and([]) ans = T --> and(0) ans = F --> and(0+0*%i) ans = F --> and(%eps) ans = T --> and(%i) ans = T --> and(%nan) ans = T --> // Projection accross a dimension / along a direction: --> A = rand(2,5)<0.5 A = T T F F F F T F F T --> and(A) ans = F --> and(A, "r") // and(A, 1) does the same ans = F T F F F --> and(A, "c") // and(A, 2) does the same ans = F F --> // Equivalent application to encoded integers: --> A = int16(grand(3,5,"uin",-10,10)); --> A(abs(A)<3) = 0 A = 0 0 -8 -6 8 -10 6 -5 3 -10 0 3 -10 7 10 --> and(A) ans = F --> and(A,1) ans = F F T T T --> // With an hypermatrix of decimal numbers: --> A = rand(3,4,2); --> A(A<0.2) = 0 A = (:,:,1) 0.4052 0.4819 0.2806 0.2119 0.9185 0.264 0. 0. 0. 0.4148 0.7783 0.6857 (:,:,2) 0. 0.4062 0. 0.5896 0.6971 0.4095 0. 0.6854 0.8416 0.8784 0.5619 0.8906 --> and(A,3) ans = F T F T T T F F F T T T --> // With a sparse matrix: --> A = sprand(70,100, 0.001) A = ( 70, 100) sparse matrix ( 4, 87) 0.6463 ( 5, 39) 0.4898 ( 7, 92) 0.7094 ( 29, 87) 0.794 ( 33, 1) 0.4087 ( 36, 79) 0.4876 ( 54, 65) 0.4456 ( 67, 45) 0.458 --> and(A, "r") ans = ( 1, 100)False sparse matrix --> and(A, "c") ans = ( 70, 1)False sparse matrix

### See also

- & (element-wise) — Binary AND between integers. Logical AND over/between booleans and numbers
- or — logical OR over the elements of a boolean or numerical array
- not — (~) 論理否定

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