InterpolatingSpline

Interpolating spline on one-dimensional samples or rectilinear grids.

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Declaration

classdef InterpolatingSpline < TensorSpline

Overview

InterpolatingSpline is the exact-fit counterpart to ConstrainedSpline. Use InterpolatingSpline.fromGriddedValues(...) when your samples live on a one-dimensional grid or a rectilinear tensor grid and should be reproduced exactly. The low-level InterpolatingSpline(...) constructor is the cheap solved-state constructor used for persisted restart and other direct bootstrap paths.

Supported construction forms: spline = InterpolatingSpline.fromGriddedValues(x, V) spline = InterpolatingSpline.fromGriddedValues({x, y, …}, V) spline = InterpolatingSpline(S=S, knotAxes=…, xi=…, gridAxes=…)

If \(\mathbf{B}\) is the tensor-product basis matrix on the supplied grid and \(\tilde{y}\) is the normalized data vector, the stored coefficients are chosen so that

\[\mathbf{B}\xi = \tilde{y}, \qquad \tilde{y} = \frac{y - \bar{y}}{s_y},\]

where \(xMean = \bar{y}\) and \(xStd = s_y\) are stored so later evaluation returns values on the original scale.

Basic usage

x = linspace(0,1,8)';
y = linspace(-1,1,9)';
[X,Y] = ndgrid(x, y);
F = sin(2*pi*X).*cos(pi*Y);
spline = InterpolatingSpline.fromGriddedValues({x, y}, F, S=[3 3]);
Fq = spline(X, Y);

Topics

• Create an interpolating spline
  • InterpolatingSpline Create an interpolating spline from canonical solved state.
  • fromGriddedValues Create an interpolating spline from values on a rectilinear grid.
• Inspect interpolation grids
  • gridAxes Grid-axis objects used to define the interpolation lattice.
  • gridVectors Grid vectors used to define the interpolation lattice.

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