Clip

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  (21)

Numerical Evaluation  (4)

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:

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  (3)

Function domain of Clip:

It is restricted to real inputs:

Function range of Clip:

The single-argument form of Clip is an odd function:

This is not true, in general, of the two- and three-argument forms:

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:

Introduced in 2004
 (5.1)