xStd

Multiplicative scale applied to spline evaluations.

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Type

• Class: double
• Size: (1,1)

Description

Real valued property with no dimensions and no units.

Discussion

xStd is the multiplicative scaling in

\[f(t) = x_{\mathrm{Mean}} + x_{\mathrm{Std}} \sum_{j=1}^{M} \xi_j B_{j,S}(t;\tau).\]

It exists for the same numerical reason as xMean: when the output amplitude is large or very small, solving for a normalized coefficient vector xi is often better conditioned than solving directly in physical units. Unlike xMean, xStd multiplies both the spline values and all derivatives.

  spline = BSpline(S=3, knotPoints=knotPoints, xi=xi, xMean=12.4, xStd=0.8);
  d2values = spline.valueAtPoints(tQuery, D=2);