BUILT-IN MATHEMATICA SYMBOL

InterpolatingFunction

represents an approximate function whose values are found by interpolation.

MORE INFORMATION

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

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Basic 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:

Plot the function and its derivative:

Find the indefinite integral of the solution:

Make an InterpolatingFunction object that will go through the given points:

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Only the domain is shown in standard output format:

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Evaluate the function at a point in the domain:

In[3]:=

Out[3]=

Plot the function over its domain, showing the interpolation points:

In[4]:=

Out[4]=

Get an InterpolatingFunction object approximating the solution of a differential equation:

In[1]:=

Out[1]=

Plot the function and its derivative:

In[2]:=

Out[2]=

Find the indefinite integral of the solution:

In[3]:=

Out[3]=

In[4]:=

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Scope (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:

Integrate it across the first and last dimensions:

Properties & Relations (1)

InterpolatingFunction does a Piecewise polynomial interpolation: