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InterpolatingFunction

  • InterpolatingFunction[ domain , table ] represents an approximate function whose values are found by interpolation.
  • 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.
  • See the Mathematica book: Section 1.6.4, Section 2.2.8Section 3.8.2.
  • See also Implementation NotesA.9.44.25MainBookLinkOldButtonDataA.9.44.25.
  • See also: CompiledFunction, FunctionInterpolation.
  • Related package: NumericalMath`SplineFit`.

    Further Examples

    Here is a table of values of the reciprocal function and an InterpolatingFunction object that represents the data.

    In[1]:=

    Out[1]=

    In[2]:=

    Out[2]=

    An InterpolatingFunction object can be evaluated just like any other Mathematica function. The approximate function reproduces the values given at the data points and it gives approximate values in between.

    In[3]:=

    Out[3]=

    The approximate function is close to the original reciprocal function for most values in the domain.

    Evaluate the cell to see the graphic.

    In[4]:=

    In[5]:=