sqrtIMYS

sqrtIMYS is a mathematical operator described within the IMYS framework as the square-root transformation of the IMYS function. In this context, IMYS stands for Interpolated Moment Yield Statistic, a hypothetical nonnegative function defined over a given domain to summarize certain moments or yield-like quantities in a dataset. sqrtIMYS(x) is defined as sqrt(IMYS(x)) for inputs x where IMYS(x) is nonnegative.

As a composition, sqrtIMYS inherits properties from both the square root and the underlying IMYS function. If IMYS(x) is nonnegative for all x in its domain, sqrtIMYS(x) is real and nonnegative. If IMYS is monotone increasing on a region, sqrtIMYS remains monotone increasing there. If IMYS is continuous, sqrtIMYS is also continuous; differentiability follows by the chain rule, with sqrtIMYS′(x) = IMYS′(x) / (2 sqrt(IMYS(x))) wherever IMYS(x) > 0, and the derivative may be undefined at points where IMYS(x) = 0 and IMYS′(x) ≠ 0.

Computationally, sqrtIMYS is applied elementwise to vector or matrix inputs, provided IMYS yields nonnegative values. Numerical stability considerations include guarding against division by zero and handling cases where IMYS(x) is exactly zero.

Applications of sqrtIMYS appear in data normalization, variance stabilization in statistical modeling, and signal or image processing workflows that rely on nonnegative feature scaling. The concept is specialized to the IMYS framework and is not a standard standalone function outside that context. See also IMYS and the ordinary square root function for related ideas.