Special name for a function

Question

Suppose we define the function $L(x)$ as follows: $$\begin{equation} L(x)= \begin{cases} 0, & \text{if}\ x<0 \\ x, & \text{if}\ 0<x<1 \\ 1, & \text{otherwise}. \end{cases} \end{equation}$$

For example, suppose we have $x_i(t+1)=x_i(t)+1$, then we can write $x_i(t+1)=L[y_i(t)]$, where $y_i(t)=x_i(t)+1$.

Does the function $L(x)$ have a special name? Is it similar to an operator?

Thank you for any help.

This is an important special case of the function asked about in MSE question 1336636 "Is 'clamp' a formally recognized mathematical function?" — Somos, Sep 17 '18 at 03:47

score 3 · Accepted Answer · answered Sep 17 '18 at 02:48

3

$L$ is the CDF of the uniform distribution.

When you limit yourself to $(0,1)$, it is the identity function.

answered Sep 17 '18 at 02:48

gt6989b

54,422

score 0 · Answer 2 · answered Sep 22 '18 at 08:34

0

I call $L(x)$ a ramp function, based on the picture it produces. It's not really that special of a name.

answered Sep 22 '18 at 08:34

Sean Roberson

9,110

But the $x$ in $L(x)$ could also be a function. Actually in the case I am studying the term $x$ always represents a function of $x$ (i.e. $L[y(x)]$). I think by definition a ramp function simply maps real numbers to non-negative real numbers, right? – johnny09 Sep 23 '18 at 13:28

Special name for a function

2 Answers2