# Ramp

Ramp[x]

gives x if x0 and 0 otherwise.

# Details

• Ramp automatically threads over lists. »

# Examples

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## Basic Examples(3)

Evaluate numerically:

Plot over a subset of the reals:

Ramp is a piecewise function:

## Scope(32)

### Numerical Evaluation(6)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate efficiently at high precision:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix Ramp function using MatrixFunction:

### Specific Values(5)

Values of Ramp at fixed points:

Value at zero:

Values at infinity:

Evaluate symbolically:

Find a value of x for which Ramp[x]1:

### Visualization(4)

Plot the Ramp function:

Visualize shifted Ramp functions:

Visualize the composition of Ramp with a periodic function:

Plot Ramp in three dimensions:

### Function Properties(9)

Ramp is defined for all real numbers:

It is restricted to real inputs:

Function range of Ramp:

Ramp is equivalent to the average of a number with its RealAbs:

Ramp is not an analytic function:

It has singularities, but no discontinuities:

Ramp is nondecreasing:

Ramp is not injective:

Ramp is not surjective:

Ramp is non-negative:

Ramp is convex:

### Differentiation and Integration(4)

First derivative with respect to x:

Except for the singular point , this derivative is UnitStep:

Second derivative with respect to x:

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

### Integral Transforms(4)

The convolution of UnitStep with itself is equal to Ramp:

The convolution of Ramp and UnitStep gives a quadratic on the non-negative reals:

The convolution of Ramp with itself gives a cubic on the non-negative reals:

## Applications(3)

Integrate a piecewise function involving Ramp symbolically and numerically:

Solve a differential equation involving Ramp:

Plot the solution for different values of a:

Create a convolutional classification net to use the subimage extracted by the localization net:

## Properties & Relations(1)

Ramp is related to UnitStep:

Wolfram Research (2016), Ramp, Wolfram Language function, https://reference.wolfram.com/language/ref/Ramp.html.

#### Text

Wolfram Research (2016), Ramp, Wolfram Language function, https://reference.wolfram.com/language/ref/Ramp.html.

#### CMS

Wolfram Language. 2016. "Ramp." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Ramp.html.

#### APA

Wolfram Language. (2016). Ramp. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Ramp.html

#### BibTeX

@misc{reference.wolfram_2024_ramp, author="Wolfram Research", title="{Ramp}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/Ramp.html}", note=[Accessed: 13-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_ramp, organization={Wolfram Research}, title={Ramp}, year={2016}, url={https://reference.wolfram.com/language/ref/Ramp.html}, note=[Accessed: 13-August-2024 ]}