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ListInterpolation

Usage

ListInterpolation[array] 构造一个InterpolatingFunction对象,表示对给定数组进行插值的近似函数。
ListInterpolation[array,   xmin, xmax ,  ymin, ymax , ...  ] 指定array 中的值来自的格点的域。


Notes

• 可以用格线位置的确切列表代替  xmin, xmax 等。格线假设是等间距。
ListInterpolation[array] 假设格线在每个方向的整数位置。
array 可以是任何维数的数组,相应于有任何嵌套层数的列表。
ListInterpolation[array, domain] 产生一个InterpolatingFunction对象,该对象返回和在  array, domain 中有相同精度的值。
• 参见注释 Interpolation.
• 参见 Mathematica 全书: 3.8.2.
Further Examples

ListInterpolation is similar to Interpolation, but provides a more convenient interface for data that does not include coordinates and for multidimensional data.

Here is a table of values of a function on a regular three dimensional grid.

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This constructs an approximate function that represents these values. There is not enough data in the z direction (only z = 0 and z = 1) for a higher order approximation, so the order in that direction is reduced automatically. (The order can be reduced manually; in this case by setting the option InterpolationOrder to {3,3,1}.)

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The approximation reproduces the values at each of the points in the table.

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You can get approximate values at other points. In this case, the interpolation is a fairly good approximation to the function.

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Here values and derivatives specified at the points  ,  ,  and  . There is not enough data to construct a third order (cubic) polynomial in either the x or the y direction, so the (default) interpolation order of  is reduced automatically.

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Again, the given values are represented by the approximate function.

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The given derivatives are also represented.

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Where the derivative was given by Automatic, it is computed automatically by the interpolation.

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You can also get approximate values at other points.

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Let's clean up by getting rid of the symbols defined in these examples.

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