InterpolatingFunction
✖
InterpolatingFunction
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.
Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Make an InterpolatingFunction object that will go through the given points:
https://wolfram.com/xid/0puyxkkvpu-c313f7
Only the domain is shown in standard output format:
https://wolfram.com/xid/0puyxkkvpu-iyz16
Evaluate the function at a point in the domain:
https://wolfram.com/xid/0puyxkkvpu-g2n0ir
Plot the function over its domain, showing the interpolation points:
https://wolfram.com/xid/0puyxkkvpu-kr5ox7
Get an InterpolatingFunction object approximating the solution of a differential equation:
https://wolfram.com/xid/0puyxkkvpu-msej96
Plot the function and its derivative:
https://wolfram.com/xid/0puyxkkvpu-gav3qe
Find the indefinite integral of the solution:
https://wolfram.com/xid/0puyxkkvpu-dmhkod
https://wolfram.com/xid/0puyxkkvpu-hh08k1
Scope (5)Survey of the scope of standard use cases
Make an InterpolatingFunction with exact data:
https://wolfram.com/xid/0puyxkkvpu-lel9yy
Compute the value using exact arithmetic:
https://wolfram.com/xid/0puyxkkvpu-p73fw
Compute using machine-number arithmetic:
https://wolfram.com/xid/0puyxkkvpu-hq64l
Compute using arbitrary-precision arithmetic:
https://wolfram.com/xid/0puyxkkvpu-b29n82
Make a new InterpolatingFunction with numerical values of all the data:
https://wolfram.com/xid/0puyxkkvpu-fbtv7n
With this InterpolatingFunction values are computed using machine arithmetic:
https://wolfram.com/xid/0puyxkkvpu-cwl7i
Integrate an InterpolatingFunction:
https://wolfram.com/xid/0puyxkkvpu-hm02db
https://wolfram.com/xid/0puyxkkvpu-eyalbm
Make a new InterpolatingFunction that is the indefinite integral:
https://wolfram.com/xid/0puyxkkvpu-dwspnx
https://wolfram.com/xid/0puyxkkvpu-i8plw2
The derivative of an InterpolatingFunction is another InterpolatingFunction:
https://wolfram.com/xid/0puyxkkvpu-j689ft
https://wolfram.com/xid/0puyxkkvpu-efc15m
https://wolfram.com/xid/0puyxkkvpu-k2gyn4
Use partial derivatives of an InterpolatingFunction to check the residual for a PDE:
https://wolfram.com/xid/0puyxkkvpu-fxqdhh
https://wolfram.com/xid/0puyxkkvpu-b6awi4
Make an InterpolatingFunction that takes 4 arguments:
https://wolfram.com/xid/0puyxkkvpu-2y3o7
Integrate it across the first and last dimensions:
https://wolfram.com/xid/0puyxkkvpu-twrxt
https://wolfram.com/xid/0puyxkkvpu-l1kcn
Properties & Relations (1)Properties of the function, and connections to other functions
InterpolatingFunction does a Piecewise polynomial interpolation:
https://wolfram.com/xid/0puyxkkvpu-kc48s
https://wolfram.com/xid/0puyxkkvpu-beygk7
https://wolfram.com/xid/0puyxkkvpu-cm1rmm
Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).
Text
Wolfram Research (1991), InterpolatingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/InterpolatingFunction.html (updated 1996).
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.
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
Wolfram Language. (1991). InterpolatingFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InterpolatingFunction.html
BibTeX
@misc{reference.wolfram_2024_interpolatingfunction, author="Wolfram Research", title="{InterpolatingFunction}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/InterpolatingFunction.html}", note=[Accessed: 21-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_interpolatingfunction, organization={Wolfram Research}, title={InterpolatingFunction}, year={1996}, url={https://reference.wolfram.com/language/ref/InterpolatingFunction.html}, note=[Accessed: 21-January-2025
]}