Difference between revisions of "CubicInterp"
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[[Category:Doc Status D]] <!-- For Lumina use, do not change --> | [[Category:Doc Status D]] <!-- For Lumina use, do not change --> | ||
| − | = CubicInterp(d,r,x,I) = | + | == CubicInterp(d,r,x,I) == |
Returns the natural cubic spline interpolated values of ''r'' along ''d'', interpolating for values of X. The points ''(r,d)'' that get interpolated are indexed by ''I''. The values of ''d'' must be ascending. | Returns the natural cubic spline interpolated values of ''r'' along ''d'', interpolating for values of X. The points ''(r,d)'' that get interpolated are indexed by ''I''. The values of ''d'' must be ascending. | ||
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A cubic interpolation can vary wildly from the actual values of the data points. In the above graph, all the ''r'' values are positive, yet the interpolation is as small as -22.5 around x=33. Even if the ''r'' values are monotonically increasing, this does not mean that the cubic interpolation will be monotonically increasing. The [[MonoCubicInterp]] function is a variation that provides a guarantee of monotonicity. | A cubic interpolation can vary wildly from the actual values of the data points. In the above graph, all the ''r'' values are positive, yet the interpolation is as small as -22.5 around x=33. Even if the ''r'' values are monotonically increasing, this does not mean that the cubic interpolation will be monotonically increasing. The [[MonoCubicInterp]] function is a variation that provides a guarantee of monotonicity. | ||
| − | = Library = | + | == Library == |
Array functions | Array functions | ||
| − | = See also = | + | == See also == |
* [[MonoCubicInterp]] | * [[MonoCubicInterp]] | ||
* [[LinearInterp]] | * [[LinearInterp]] | ||
* [[StepInterp]] | * [[StepInterp]] | ||
| + | |||
| + | =User Guide= | ||
| + | Returns the natural cubic spline interpolated values of y along x, interpolating for values of v. x and y must both be indexed by i, and x must be increasing along i. | ||
| + | |||
| + | For each value of v, Cubicinterp() finds the nearest values from x, and using a natural cubic spline between the corresponding values of y, computes the interpolated value. If v is less than the minimum value in x, it returns the first value in y; if v is greater than the maximum value in x, it returns the last value for y. | ||
| + | |||
| + | ==Library== | ||
| + | Array | ||
| + | |||
| + | ==Example== | ||
| + | Cubicinterp(Index_b, Array_a, 1.5, Index_b) → | ||
| + | Index_a > | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | ! scope="col"| a | ||
| + | ! scope="col"| b | ||
| + | ! scope="col"| c | ||
| + | |- | ||
| + | | 0.6875 | ||
| + | | -2.875 | ||
| + | | 2.219 | ||
| + | |} | ||
Revision as of 19:54, 30 July 2015
CubicInterp(d,r,x,I)
Returns the natural cubic spline interpolated values of r along d, interpolating for values of X. The points (r,d) that get interpolated are indexed by I. The values of d must be ascending. The index I is optional when d and r have only one index is common; however, it is recommended that you explicitly specify I, since this will enable your expression to array-abstract if any dimension is ever added to d and r in the future.
Null values are allowed in d and r only in releases later than 4.1.1 (not including 4.1.1). Points having either d or r equal to null are ignored. When x is null, the result is null.
A cubic interpolation can vary wildly from the actual values of the data points. In the above graph, all the r values are positive, yet the interpolation is as small as -22.5 around x=33. Even if the r values are monotonically increasing, this does not mean that the cubic interpolation will be monotonically increasing. The MonoCubicInterp function is a variation that provides a guarantee of monotonicity.
Library
Array functions
See also
User Guide
Returns the natural cubic spline interpolated values of y along x, interpolating for values of v. x and y must both be indexed by i, and x must be increasing along i.
For each value of v, Cubicinterp() finds the nearest values from x, and using a natural cubic spline between the corresponding values of y, computes the interpolated value. If v is less than the minimum value in x, it returns the first value in y; if v is greater than the maximum value in x, it returns the last value for y.
Library
Array
Example
Cubicinterp(Index_b, Array_a, 1.5, Index_b) → Index_a >
| a | b | c |
|---|---|---|
| 0.6875 | -2.875 | 2.219 |
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