gh, "Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation", 1970. Examples -------- To produce a polynomial that is zero at 0 and 1 and has derivative 2 at 0, call >>> from scipy.interpolate import KroghInterpolator >>> KroghInterpolator([0,0,1],[0,2,0]) This constructs the quadratic 2*X**2-2*X. The derivative condition is indicated by the repeated zero in the xi array; the corresponding yi values are 0, the function value, and 2, the derivative value. For another example, given xi, yi, and a derivative ypi for each point, appropriate arrays can be constructed as: >>> import numpy as np >>> rng = np.random.default_rng() >>> xi = np.linspace(0, 1, 5) >>> yi, ypi = rng.random((2, 5)) >>> xi_k, yi_k = np.repeat(xi, 2), np.ravel(np.dstack((yi,ypi))) >>> KroghInterpolator(xi_k, yi_k) To produce a vector-valued polynomial, supply a higher-dimensional array for yi: >>> KroghInterpolator([0,1],[[2,3],[4,5]]) This constructs a linear polynomial giving (2,3) at 0 and (4,5) at 1. r