hmf.core._kernels.interpolation

Interpolation kernels: local interpolants on uniform lattices, and frozen splines.

The local interpolants work in a coordinate u in [0, 1] between two adjacent nodes x0 and x0 + h of a uniform lattice, from the values (and derivatives) at a fixed set of nodes. Each result depends only on those nodes and on u, so interpolants on a lazily extended lattice do not change as the lattice grows, and all of them are elementwise (batch-size independent).

• hermite_cubic(): values and first derivatives at the two ends;

• hermite_quintic(): values, first and second derivatives at the two ends;

• lagrange4(): values at four nodes, -1, 0, 1, 2 (in units of h);

• invert_hermite(): the inverse of a decreasing Hermite interpolant.

Tables (of a transfer function, a growth factor, a power spectrum) are interpolated by cubic splines, fitted once and kept as their coefficients:

• FrozenSpline: a scipy.interpolate.CubicSpline’s breakpoints and piecewise-polynomial coefficients, evaluated by scipy.interpolate.PPoly.construct_fast(), so it gives exactly the spline’s values;

• extrapolate_power_law(): a spline of ln y against ln x, continued beyond its ends as straight lines (power laws in y) with its slopes there.

Classes

FrozenSpline(x, c[, extrapolate])

A cubic spline, fitted once and kept as its piecewise-polynomial coefficients.

Functions

extrapolate_power_law(spline, ln_x)	A spline of ln y against ln x, continued as power laws beyond its ends.
hermite_cubic(u, h, y0, y1, d0, d1)	The cubic Hermite interpolant on [x0, x0 + h] at x0 + u h.
hermite_quintic(u, h, y0, y1, d0, d1, c0, c1)	The quintic Hermite interpolant on [x0, x0 + h] at x0 + u h.
invert_hermite(target, h, y0, y1, d0, d1[, ...])	Solve hermite(u) = target for u in [0, 1], for a decreasing interpolant.
lagrange4(u, f_m1, f_0, f_1, f_2)	The 4-point Lagrange interpolant through nodes at -1, 0, 1, 2, evaluated at u.