Module Owl_maths_interpolate

polint xs ys x performs polynomial interpolation of the given arrays xs and ys. Given arrays xs[0..(n-1)] and ys[0..(n-1)], and a value x, the function returns a value y, and an error estimate dy. If P(x) is the polynomial of degree N − 1 such that P(xs[i]) = ys[i] for i = 0,...,n-1,

Parameters: * xs: an array of input x values of P(x). * ys: an array of corresponding y values of P(x). * x: value to interpolate.

Returns: * (y, dy) wherein y is the returned value y = P(x), and dy is the estimated error.

ratint xs ys x performs rational function interpolation on the data points given by xs and ys, and returns the interpolated value at the point x, along with an estimate of the error.

This function fits a rational function (a ratio of two polynomials) to the provided data points. It is particularly useful when the data exhibits behavior that might be better captured by such a function, especially in cases where the data might have singularities or steep gradients.

The function raises an exception if the lengths of xs and ys do not match, or if a pole is encountered during the interpolation process.

Parameters:

• parameter xs

  An array of x-values (the independent variable).

• parameter ys

  An array of y-values (the dependent variable) corresponding to xs.

• parameter x

  The point at which the interpolated value is to be calculated.

  Returns:

• returns

  A tuple (y, dy), where y is the interpolated value at x, and dy is an estimate of the error in the interpolation.