Clip
Details
- Clip [x] is effectively equivalent to Piecewise [{{-1,x<-1},{+1,x>+1}},x].
- The vi, as well as other arguments of Clip , need not be numbers.
- For exact numeric quantities, Clip internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision .
Examples
open all close allBasic Examples (3)
Evaluate numerically:
Plot the unit clip function over a subset of the reals:
Use different clip levels:
Scope (28)
Numerical Evaluation (5)
Specific Values (5)
Visualization (3)
Function Properties (9)
Clip is defined for all real inputs:
It is restricted to real inputs:
Function range of Clip [x]:
Range of Clip [x,{min,max},{vmin,vmax}]:
The single-argument form of Clip is an odd function:
This is not true, in general, of the two- and three-argument forms:
Clip is not an analytic function:
Clip [x] has singularities but no discontinuities:
The three-argument form may have discontinuities:
Clip [x] is nondecreasing:
Clip [x] is not injective:
Clip [x] is not surjective:
Clip [x] is neither non-negative nor non-positive:
Clip [x] is neither convex nor concave:
Differentiation and Integration (6)
First derivative with respect to x:
First and second derivatives with respect to x:
Formula for the ^(th) derivative with respect to x:
Compute the indefinite integral using Integrate :
Verify the anti-derivative:
Definite integral:
More integrals:
Applications (1)
A clipped or saturated sinusoid:
Possible Issues (1)
Clip is not defined for complex values:
Clip the real and imaginary parts separately:
Tech Notes
History
Introduced in 2004 (5.1)
Text
Wolfram Research (2004), Clip, Wolfram Language function, https://reference.wolfram.com/language/ref/Clip.html.
CMS
Wolfram Language. 2004. "Clip." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Clip.html.
APA
Wolfram Language. (2004). Clip. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Clip.html
BibTeX
@misc{reference.wolfram_2025_clip, author="Wolfram Research", title="{Clip}", year="2004", howpublished="\url{https://reference.wolfram.com/language/ref/Clip.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_clip, organization={Wolfram Research}, title={Clip}, year={2004}, url={https://reference.wolfram.com/language/ref/Clip.html}, note=[Accessed: 16-November-2025]}