gerlero/pchipinterpolation.jl

Monotonic cubic interpolation in Julia

pchipinterpolation.jl's Issues

Broken code sample in README.md

The first code snippet in the README file was broken by the changes in 316c1af. xs and ys ought to be 1D (column) vectors instead of row vectors.

BoundsError sometimes when evaluating at rightmost point

using PCHIPInterpolation

x = collect(range(0, stop=1, length=199))
itp = Interpolator(x, x)
itp(1) # Uses linear search (length < 200): OK

x = collect(range(0, stop=1, length=200))
itp = Interpolator(x, x)
itp(1) # Uses bisection: BoundsError: attempt to access 200-element Vector{Float64} at index [201]

x = collect(range(0, stop=1, length=1000))
itp = Interpolator(x, x)
itp(1) # Also uses bisection: but OK

Interpolator susceptible to input array mutations after construction

Would be better to make defensive copies of the input vectors.

Bug in definition of wl and wr terms

I believe there may be an bug in the following lines:

PCHIPInterpolation.jl/src/PCHIPInterpolation.jl

Lines 39 to 40 in cfc4287

	wl = 2hl + hr
	wr = hl + 2hr

Based on the scipy/Matlab implementations of the derivative function the wl and wr terms should be swapped so that:

wl = hl + 2hr
wr = 2hl + hr

See https://github.com/scipy/scipy/blob/main/scipy/interpolate/_cubic.py#L285 for the corresponding scipy version.

Due to this issue, the current Julia version gives subtly different results to both Matlab and scipy.

For example, the Python scipy version:

import numpy as np
import scipy.interpolate

xs = np.array([0.0,  1.2,  2.0,  5.0, 10.0, 11.0])
ys = np.array([2.0,  2.1,  1.0,  0.0,  0.0,  3.0])
yp = scipy.interpolate.pchip_interpolate(xs, ys, 2.5)

gives yp=0.714763623953731

The Matlab version:

xs = [0.0,  1.2,  2.0,  5.0, 10.0, 11.0]
ys = [2.0,  2.1,  1.0,  0.0,  0.0,  3.0]
yp = pchip(x, y, 2.5)

also gives yp=0.714763623953731

The current Julia version:

xs = [0.0,  1.2,  2.0,  5.0, 10.0, 11.0]
ys = [2.0,  2.1,  1.0,  0.0,  0.0,  3.0]
itp = Interpolator(xs, ys)
yp = itp(2.5)

gives yp=0.7592273552265896

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