Creates an interpolated curve from input points with a specified number of values. Interpolates using linear interpolation.
The length of the Independent Data array must be the same as the Dependent Data array.
The algorithm that fits the linear spline is from Digital Computation and Numerical Methods, chapter 8.1.2 (Southworth, 1965).
Format
LINEAR_SPLINE (Independent Data, Dependent Data, Number of Output Values)
Arguments
Independent Data | A 1xN array of x values for the curve to be interpolated. The 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 | LINEAR_SPLINE({1, 2, 3, 4}, {0, 2, 1, 3}, 10) |
Result | {0.0, .667, 1.333, 2.0, 1.667, 1.333, 1.0, 1.667, 2.333, 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} |