# 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

open allclose all

## Basic Examples(3)

Evaluate numerically:

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

Use different clip levels:

## Scope(27)

### 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(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  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: