heaviside
Heaviside step function
Syntax
Description
Examples
Evaluate Heaviside Function for Symbolic and Numeric Arguments
The heaviside
function returns 0, 1/2, or 1 depending on the argument value. If the argument is a floating-point number (not a symbolic object), then heaviside
returns floating-point results.
Evaluate the Heaviside step function for a symbolic input sym(-3)
. The function heaviside(x)
returns 0
for x < 0
.
H = heaviside(sym(-3))
H =
Evaluate the Heaviside step function for a symbolic input sym(3)
. The function heaviside(x)
returns 1
for x > 0
.
H = heaviside(sym(3))
H =
Evaluate the Heaviside step function for a symbolic input sym(0)
. The function heaviside(x)
returns 1/2
for x = 0
.
H = heaviside(sym(0))
H =
For a numeric input x = 0
, the function heaviside(x)
returns floating-point results.
H = heaviside(0)
H = 0.5000
Use Assumptions on Symbolic Variables
heaviside
takes into account assumptions on variables.
Create a symbolic variable x
and assume that it is less than 0.
syms x
assume(x < 0)
Evaluate the Heaviside step function for the symbolic input x
.
H = heaviside(x)
H =
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
Evaluate the Heaviside function for a symbolic matrix. When the input argument is a matrix, heaviside
computes the Heaviside function for each element.
syms x
H = heaviside(sym([-1 0; 1/2 x]))
H =
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_H = diff(heaviside(x),x)
diff_H =
Evaluate the integral .
syms x
int_H = int(exp(-x)*heaviside(x),x,-Inf,Inf)
int_H =
Change Value of Heaviside Function at Origin
The default value of the Heaviside function at the origin is 1/2
.
H = heaviside(sym(0))
H =
Other common values for the Heaviside function at the origin are 0 and 1. To change the value of heaviside
at the origin, use sympref
to set the value of the "HeavisideAtOrigin"
preference. 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
.
H = heaviside(sym(0))
H =
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
number | symbolic number | symbolic variable | symbolic expression | symbolic function | symbolic vector | symbolic matrix
Input, specified as a number, symbolic number, variable, expression, function, vector, or matrix.
Version History
Introduced before R2006a
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