How to code a multivalued sign function

Hello all Please could you help me i want to code a multivalued signum function that is defined by

Let x ∈ R. The multivalued signum function Sgn: R ⇒ R is defined as:

sgn(x) ={ 1 if x > 0 −1 if x < 0 [−1, 1] if x = 0.

If x ∈ R^n then the multivalued signum function Sgn: R^n⇒R^n

is defined as: Sgn(x) : = (Sgn(x1), . . . , Sgn(xn))^T

Thank you so much for your help Best regards

Answer 1

[Stephen23]

Based on the explanation given "Can we program the same function but when x=0 the output sgn(0) is to take any value in the range [-1,1]?", then this fully vectorized code will achieve this:

function Y = msgn(X)
% Multivalued sign function
Y = sign(X);
Z = Y==0;
Y(Z) = 1-2*rand(1,sum(Z(:)));
end

And then we can test it:

>> msgn(5)
ans =
     1
>> msgn(-5)
ans =
    -1
>> msgn(0)
ans =
   -0.6294
>> msgn([-5,0,0,0,5])
ans =
   -1.0000   -0.8116    0.7460   -0.8268    1.0000

Note that I used rand, which provides uniformly distributed values. If you want another random distribution, then you can simply change this function to another, such as randn.

Note also that the function accepts and returns arrays of any size, just like sign does.

[lady bird]

Thank you so much Mr Stephen Cobeldick Best regards

Answer 2

[Stephen23]

Two simple versions: the first assumes that the input is a scalar numeric:

function v = sgn(x)
assert(isscalar(x),'input must be scalar')
a = [-1,1];
v = a([x<=0,x>=0]);
end

>> sgn(-5)
ans = -1
>> sgn(0)
ans = [-1,1]
>> sgn(5)
ans = 1

The second allows a vector input:

function v = sgn(x)
assert(isvector(x),'input must be vector')
a = [-1;1];
u = arrayfun(@(n)a([n<=0,n>=0]),x(:),'UniformOutput',false);
v = reshape(cell2mat(u),1:isrow(x),1:iscolumn(x));
end

>> sgn([-5,0,5])
ans =  -1   -1    1    1