PSPLINE

PSPLINE -- a collection of Spline and Hermite interpolation tools for 1D, 2D, and 3D datasets on rectilinear grids. Spline routines give full control over boundary conditions -- the user may specify ”periodic”, ”not a knot”, 1st derivative match, 2nd derivative match, or divided difference based boundary conditions on either end of each grid dimension. Hermite routines take as input the function value and derivatives at each grid point, giving back a representation of the function between grid points. Routines are provided for creating Hermite datasets, with appropriate boundary conditions applied. The 1D spline and Hermite routines are based on standard methods; the 2D and 3D spline or Hermite interpolation functions are constructed from 1D spline or Hermite interpolation functions in a straightforward manner. The splines are continuously twice differentiable in all directions across all grid cell boundaries and over the entire grid domain; Hermite functions are continuously once differentiable in all directions over the entire grid domain. For a representation of dimensionality N, an N-dimensional spline or Hermite function requires 2**N*(nx1*nx2*...*nxN) memory words. There is also an ”explicit spline” representation requiring 4**N*(nx1*nx2*...*nxN) memory words: much more memory but somewhat faster computationally. Spline and Hermite interpolation functions are often much faster to evaluate than other representations using e.g. Fourier series or otherwise involving transcendental functions.

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