# Documentation

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# sign

Sign function (signum function)

## Description

example

Y = sign(x) returns an array Y the same size as x, where each element of Y is:

• 1 if the corresponding element of x is greater than 0.

• 0 if the corresponding element of x equals 0.

• -1 if the corresponding element of x is less than 0.

• x./abs(x) if x is complex.

## Examples

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Find the sign function of a number.

sign(2)
ans =

1

Find the sign function of the values of a vector.

V = [-11 0 1.5 Inf NaN];
sign(V)
ans =

-1     0     1     1   NaN

Find the sign function of the values of a matrix.

M = magic(3) - 5;
sign(M)
ans =

1    -1     1
-1     0     1
-1     1    -1

Find the sign function of a complex number.

z = 4 - 3*i;
sign(z)
ans =

0.8000 - 0.6000i

Plot the sign function and show its behavior at the zero-crossing. Use eps to represent values just above and below 0.

x = [-5 -eps(1) 0 eps(1) 5];
y = sign(x);
plot(x,y)
ylim([-2 2])
grid on

Plot real and imaginary parts of the sign function over and .

First, create a mesh of values over -3 < x < 3 and -3 < y < 3 using meshgrid. Then create complex numbers from these values using z = x + 1i*y.

v = -3:0.1:3;
[x, y] = meshgrid(v);
z = x + 1i*y;

Find the real and imaginary parts of the sign function of z.

s = sign(z);
re = real(s);
im = imag(s);

Plot the real and imaginary parts.

surf(x,y,re)
title('Real part of sign function')
xlabel('x')
ylabel('y')
figure(2)
surf(x,y,im)
title('Imaginary part of sign function')
xlabel('x')
ylabel('y')

## Input Arguments

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Input, specified as a number, vector, matrix, or multidimensional array.

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

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### Sign Function

The value of the sign function, sign(x), for:

• x > 0 is 1.

• x = 0 is 0.

• x < 0 is -1.

• complex x is x/|x|.

### Tall Array Support

This function fully supports tall arrays. For more information, see Tall Arrays.