interpVariance

fiducia.stats.interpVariance(x, xp, fpUnc, leftVar=None, rightVar=None, period=None)

Propagate uncertainty for linear interpolation.

Parameters

• x (numpy.ndarray, list) – The x-coordinates at which to evaluate the interpolated values.

• xp (numpy.ndarray, list) – The 1D x-coordinates of the data points, must be increasing order

• fpUnc (numpy.ndarray, list) – The uncertainty in the y-coordinates of the data points, same length as xp.

• leftVar (float, optional) – Variance to return for x < xp[0]. If not given, the first yUnc element will be used. Default is None

• rightVar (float, optional) – Variance to return for x > xp[-1]. If not given, the last yUnc element will be used. Default is None

Returns

yVar – 1D array containing the variance for each interpolated x.

Return type

numpy.ndarray

Notes

Variance of interpolated point, assuming no uncertainty in x and xp, and no covariance between y-coordinates, is given by

\[\operatorname{Var}(y) = \frac{1}{(x_1 - x_0)^2} ( (x_1 - x)^2 \sigma_{y_0}^2 + (x-x_0)^2 \sigma_{y_1}^2 )\]

Examples