sign

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 = 1×5

    -1     0     1     1   NaN

Find the sign function of the values of a matrix.

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

ans = 3×3

     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 $$-3<x<-3$$ and $$-3<y<3$$.

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')