Quadratic Interpolation given median information
[m21,m22,m23, a,b,c] = QuadMedRef(m1, m2, m3)
medians of the desired quadratic polynomial on [0,1], [1,2] and [2,3] respectively
interval to impute to: default, impute to [1,2] option='Left' => impute to [0,1] , option='Right => impute to [2,3]
medians of the computed quadratic polynomial on [1,4/3], [4/3,5/3], [5/3,2] respectively
coef. of the interpolating quadratic polynomial, p(x) = a + bx + cx^2, Median{p(x) | [0,1]} = m1, Median{p(x) | [1,2]} = m2, and Median{p(x) | [2,3]} = m3.
Warning: This is an old and slower implementation. When this code was developed, the author hadn't developed the closed form formulae for directly calculating the medians from one scale to the other. Instead, he had only formulae that calculate the median interpolant and (consequently) median refinement was done by two separate steps: median interpolation followed by median imputation, as in the definition. He later developed the formulae that combines the two steps into one single step; and he reimplemented this code in mex. This code, however, is useful by itself because it gives also the median interpolant.