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Clip [x]

gives x clipped to be between and .

Clip [x,{min,max}]

gives x for minxmax, min for x<min and max for x>max.

Clip [x,{min,max},{vmin,vmax}]

gives vmin for x<min and vmax for x>max.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Specific Values  
Visualization  
Function Properties  
Differentiation and Integration  
Applications  
Possible Issues  
See Also
Tech Notes
Related Guides
History
Cite this Page

Clip [x]

gives x clipped to be between and .

Clip [x,{min,max}]

gives x for minxmax, min for x<min and max for x>max.

Clip [x,{min,max},{vmin,vmax}]

gives vmin for x<min and vmax for x>max.

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

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Basic Examples  (3)

Evaluate numerically:

Plot the unit clip function over a subset of the reals:

Use different clip levels:

Scope  (28)

Numerical Evaluation  (5)

Evaluate numerically:

Evaluate to high precision:

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

Evaluate efficiently at high precision:

Clip threads over lists in its first argument:

Compute average-case statistical intervals using Around :

Specific Values  (5)

Values of Clip at fixed points:

Value at zero:

Value at infinity:

Evaluate symbolically:

Find a value of x for which the Clip [x,{-2,2}]=1:

Visualization  (3)

Visualize the three-argument form of Clip :

Plot the composition of Clip with a periodic function:

Plot Clip in three dimensions:

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:

See Also

RealSign   Piecewise   Min   Rescale   Round   Chop   Tanh   Unitize   Threshold

Function Repository: GeneralizedSmoothStep   AggregateSmallest

History

Introduced in 2004 (5.1)

Wolfram Research (2004), Clip, Wolfram Language function, https://reference.wolfram.com/language/ref/Clip.html.

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]}

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