heaviside

Heaviside step function

Syntax

heaviside(x)

Description

heaviside(x) returns the value 0 for x < 0, 1 for x > 0, and 1/2 for x = 0.

Examples

Evaluate Heaviside Function for Numeric and Symbolic Arguments

Depending on the argument value, heaviside returns one of these values: 0, 1, or 1/2. If the argument is a floating-point number (not a symbolic object), then heaviside returns floating-point results.

For x < 0, the function heaviside(x) returns 0:

heaviside(sym(-3))

ans =
0

For x > 0, the function heaviside(x) returns 1:

heaviside(sym(3))

ans =
1

For x = 0, the function heaviside(x) returns 1/2:

heaviside(sym(0))

ans =
1/2

For numeric x = 0, the function heaviside(x) returns the numeric result:

heaviside(0)

ans =
    0.5000

Use Assumptions on Variables

heaviside takes into account assumptions on variables.

syms x
assume(x < 0)
heaviside(x)

ans =
0

For further computations, clear the assumptions on x by recreating it using syms:

syms x

Plot Heaviside Function

Plot the Heaviside step function for x and x - 1.

syms x
fplot(heaviside(x), [-2, 2])

fplot(heaviside(x - 1), [-2, 2])

Evaluate Heaviside Function for Symbolic Matrix

Call heaviside for this symbolic matrix. When the input argument is a matrix, heaviside computes the Heaviside function for each element.

syms x
heaviside(sym([-1 0; 1/2 x]))

ans =
[ 0,          1/2]
[ 1, heaviside(x)]

Differentiate and Integrate Expressions Involving Heaviside Function

Compute derivatives and integrals of expressions involving the Heaviside function.

Find the first derivative of the Heaviside function. The first derivative of the Heaviside function is the Dirac delta function.

syms x
diff(heaviside(x), x)

ans =
dirac(x)

Find the integral of the expression involving the Heaviside function:

syms x
int(exp(-x)*heaviside(x), x, -Inf, Inf)

ans =
1

Change Value of Heaviside Function at Origin

heaviside assumes that the value of the Heaviside function at the origin is 1/2.

heaviside(sym(0))

ans =
1/2

Other common values for the Heaviside function at the origin are 0 and 1. To change the value of heaviside at the origin, use the 'HeavisideAtOrigin' preference of sympref. Store the previous parameter value returned by sympref, so that you can restore it later.

oldparam = sympref('HeavisideAtOrigin',1);

Check the new value of heaviside at 0.

heaviside(sym(0))

ans =
1

The preferences set by sympref persist throughout your current and future MATLAB^® sessions. To restore the previous value of heaviside at the origin, use the value stored in oldparam.

sympref('HeavisideAtOrigin',oldparam);

Alternatively, you can restore the default value of 'HeavisideAtOrigin' by using the 'default' setting.

sympref('HeavisideAtOrigin','default');

Input Arguments

x — Input

symbolic number | symbolic variable | symbolic expression | symbolic function | symbolic vector | symbolic matrix

Input, specified as a symbolic number, variable, expression, function, vector, or matrix.