UnitTriangle
UnitTriangle[x]
represents the unit triangle function on the interval .
UnitTriangle[x1,x2,…]
represents the multidimensional unit triangle function on the interval .
Details
- UnitTriangle[x] is equivalent to Piecewise[{{x+1,-1≤x<0},{1-x,0≤x≤1}}].
- UnitTriangle can be used in integrals and integral transforms.
- UnitTriangle has attribute Orderless.
- UnitTriangle automatically threads over lists. »
Examples
open allclose allBasic Examples (4)
UnitTriangle is a piecewise function:
Scope (36)
Numerical Evaluation (7)
For inputs between -1 and 1, the precision of the output tracks the precision of the input:
For inputs outside that range, the result is exact:
Evaluate efficiently at high precision:
UnitTriangle threads over lists:
Compute the elementwise values of an array using automatic threading:
Or compute the matrix UnitTriangle function using MatrixFunction:
Compute average-case statistical intervals using Around:
Specific Values (4)
Values of UnitTriangle at fixed points:
Find a value of x for which UnitTriangle[x]=0.4:
Visualization (4)
Plot the UnitTriangle function:
Visualize scaled UnitTriangle functions:
Visualize the composition of UnitTriangle with a periodic function:
Plot UnitTriangle in three dimensions:
Function Properties (11)
Function domain of UnitTriangle:
It is restricted to real inputs:
Function range of UnitTriangle:
UnitTriangle is an even function:
The area of the UnitTriangle is 1:
UnitTriangle is not an analytic function:
However, it is continuous everywhere:
Verify the claim at one of its singular points:
UnitTriangle is neither nondecreasing nor nonincreasing:
UnitTriangle is not injective:
UnitTriangle is not surjective:
UnitTriangle is non-negative:
UnitTriangle is neither convex nor concave:
TraditionalForm typesetting:
Differentiation and Integration (6)
First derivative with respect to x:
Higher-order derivatives with respect to x:
First derivative with respect to z:
Series expansion at the origin:
Compute the indefinite integral using Integrate:
Integral Transforms (4)
FourierTransform of UnitTriangle is a squared Sinc function:
Find the LaplaceTransform of UnitTriangle:
The convolution of UnitTriangle with itself:
Applications (4)
Integrate a piecewise function involving UnitTriangle symbolically and numerically:
Solve a differential equation involving UnitBox and UnitTriangle:
Visualize discontinuities in the wavelet domain:
Detail coefficients in the region of discontinuities have larger values:
Generate data from some distribution:
Apply mean shift until all data points have converged:
Properties & Relations (4)
The derivative of UnitTriangle is a piecewise function:
The derivative of HeavisideLambda is a distribution:
At higher orders, the DiracDelta distribution appears:
Convert into Piecewise:
Multidimensional unit triangle function equals the product of 1D functions for each argument:
UnitTriangle is a special case of BSplineBasis:
Text
Wolfram Research (2008), UnitTriangle, Wolfram Language function, https://reference.wolfram.com/language/ref/UnitTriangle.html.
CMS
Wolfram Language. 2008. "UnitTriangle." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/UnitTriangle.html.
APA
Wolfram Language. (2008). UnitTriangle. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/UnitTriangle.html