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CSPLINE

Creates an interpolated curve from input points with a specified number of values. Interpolates using the cubic splines.
The algorithm that fits the cubic spline is from Computer Methods for Mathematical Computations by Forsythe, Malcolm and Moler (1977, Prentice-Hall: Englewood Cliffs, NJ). The INTEGR function uses the same algorithm.
The length of the Independent Data array must be equal to the Dependent Data array.

Format

CSPLINE (Independent Data, Dependent Data, Number of Output Values)

Arguments

 
Independent Data
A 1xN array of x values for the curve to be interpolated. These x values must be in ascending order, and the length of the array must be greater than or equal to 4.
Dependent Data
A 1xN array of y values for the curve to be interpolated.
Number of Output Values
The number of values to be generated in the output array.

Example

The following function interpolates a set of four points with ordinal values from 1 to 4 and abscissal values as shown, into a series of 10 abscissal values:
 
Function
CSPLINE({1, 2, 3, 4}, {0, 2, 1, 3}, 10)
Result
{0.0, 0.936, 1.704, 2.0, 1.741, 1.259, 1.0, 1.296, 2.037, 3.0}
To compute the ordinal values for these splined values, you can use the SERIES2 function as follows:
 
Function
SERIES2(1, 4, 10)
Result
{1.0, 1.333, 1.667, 2.0, 2.333, 2.667, 3.0, 3.333, 3.667, 4.0}
 
Note:  
This design function do not exactly represent Solver CUBSPL. The interpolation follows CUBIC method (closely matches) but extrapolation follows 'linear' of 'cubic' based on type of spline specified (based on option extrapolate_linear=yes/no).
Learn more about matrix/array functions.