logical AND between the elements of a boolean or numerical array
b = and(A) b = and(A, 'r') b = and(A, 'c') b = and(A, n)
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 :
|
boolean scalar, if and(A)
is used without any option "r", "c", n
.
Then and(A)
sets b
to
A
's
components is %F or zero.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.
Index <= ndims(A) of the dimension along which
and()
is applied / projected.
By default, and()
is applied between
all A
's elements. Otherwise:
and()
is
applied row-wise. If A
is a matrix, the result b
is a
row, with
b(j) = and(A(:,j))
and()
is applied column-wise.
If A
is a matrix, the result b
is a
column, with
b(i) = and(A(i,:))
A
is an
hypermatrix with at least n
dimensions, and()
is applied
accross the nth 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,:))
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
.
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