Rational Interpolation (Not in Base Package)

Interpolates or extrapolates f at x using a rational function. The rational function passes through all the points formed by Y Array and X Array. Details

Y Array is the input array.
X Array If the number of elements in the X Array is different from the number of elements in the Y Array, the VI sets the output interpolation value and interpolation error to NaN and returns an error.
If x value is in the range of X, the VI performs interpolation. Otherwise, the VI performs extrapolation. If x value is too far from the range of X, the extrapolation error may be large. It is not a satisfactory extrapolation.
interpolation value is the interpolation of the function f at x.
interpolation error is an estimate of the error in the interpolation.
error returns any error or warning condition from the VI.

Rational Interpolation Details

The rational function

passes through all the points formed by Y Array and X Array. P and Q are polynomials, and the rational function is unique, given a set of n points , where , f is any function, and given a number x in the range of the values.

This VI calculates the output interpolation value y using

If the number of points is odd, the degrees of freedom of P and Q are using . If the number of points is even, the degrees of freedom of P are , and the degrees of freedom of Q are , where n is the total number of points formed by Y Array and X Array.