InterpolatingFunction
InterpolatingFunction[domain,table]
represents an approximate function whose values are found by interpolation.
Details
- InterpolatingFunction works like Function.
- InterpolatingFunction[…][x] finds the value of an approximate function with a particular argument x.
- In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <>. »
- domain specifies the domain of the data from which the InterpolatingFunction was constructed.
- If you supply arguments outside of the domain, a warning is generated, and then an extrapolated value is returned.
- InterpolatingFunction objects that take any number of real arguments may be constructed.
- You can take derivatives of InterpolatingFunction objects using D and Derivative.
- NDSolve returns its results in terms of InterpolatingFunction objects.
- InterpolatingFunction[…][prop] gives the property prop of the InterpolatingFunction object. The following properties may be given:
-
"Coordinates" grid coordinates for each tensor product dimension "DerivativeOrder" what derivative of the interpolated function will be computed upon evaluation "Domain" the bounding box of domain of the InterpolatingFunction "ElementMesh" the spatial mesh if one is present "InterpolationMethod" the method used for interpolation "InterpolationOrder" the degree of polynomials used for computing interpolated values "Periodicity" whether the interpolating function is periodic in the respective dimensions "QuantityUnits" the quantity units associated with abscissa and ordinates "ValuesOnGrid" gives the function values at each mesh coordinate
Examples
open all close allBasic Examples (2)
Make an InterpolatingFunction object that will go through the given points:
Only the domain is shown in standard output format:
Evaluate the function at a point in the domain:
Plot the function over its domain, showing the interpolation points:
Get an InterpolatingFunction object approximating the solution of a differential equation:
Scope (5)
Basic Uses (5)
Make an InterpolatingFunction with exact data:
Compute the value using exact arithmetic:
Compute using machine-number arithmetic:
Compute using arbitrary-precision arithmetic:
Make a new InterpolatingFunction with numerical values of all the data:
With this InterpolatingFunction values are computed using machine arithmetic:
Integrate an InterpolatingFunction:
Make a new InterpolatingFunction that is the indefinite integral:
The derivative of an InterpolatingFunction is another InterpolatingFunction:
Use partial derivatives of an InterpolatingFunction to check the residual for a PDE:
Make an InterpolatingFunction that takes 4 arguments:
Properties & Relations (1)
InterpolatingFunction does a Piecewise polynomial interpolation:
Text
Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).
CMS
Wolfram Language. 1991. "InterpolatingFunction." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/InterpolatingFunction.html.
APA
Wolfram Language. (1991). InterpolatingFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InterpolatingFunction.html