TopolearnResampling signals, filling grids and building smooth curves from measurements all need interpolation.
Interpolation builds a function that passes through known points so you can evaluate it in between.
For 1-D data the main options are:
np.interp(x_new, x, y): piecewise linear, fast, fine for many purposes.interpolate.CubicSpline(x, y): smooth (continuous second derivative), can overshoot between points;bc_typecontrols the ends, and the object has.derivative()and.integrate(a, b).interpolate.PchipInterpolator(x, y)andAkima1DInterpolator: smooth but shape-preserving, no overshoot. Use them for monotonic data such as cumulative curves or concentrations that cannot go negative.interpolate.make_interp_spline(x, y, k=3): a B-spline of chosen degree.
These objects are callable: cs(x_new). The older interp1d class is legacy and should not be used in new code.
Interpolation is not smoothing. With noisy data an interpolant reproduces the noise; use a smoothing spline such as make_smoothing_spline(x, y) instead.
Beyond 1-D: RegularGridInterpolator for data on a grid, griddata or RBFInterpolator for scattered points.
Extrapolation outside the data range is risky: splines extrapolate their last polynomial piece, which can go wild. Prefer extrapolate=False (returns NaN) unless you have a reason.
Example
import numpy as np
from scipy import interpolate
x = np.array([0, 1, 2, 3, 4], dtype=float)
y = np.array([0, 0, 1, 1, 1], dtype=float) # a step-like, monotonic curve
cs = interpolate.CubicSpline(x, y)
pc = interpolate.PchipInterpolator(x, y)
xs = np.array([0.5, 2.5])
print(cs(xs).round(3)) # [-0.297 1.109] (overshoots below 0 and above 1)
print(pc(xs).round(3)) # [0. 1.] (stays within the data range)
print(np.interp(xs, x, y)) # [0. 1.]
print(round(float(cs.integrate(0, 4)), 3)) # 2.333 (area under the spline)
print(pc(5.0), interpolate.PchipInterpolator(x, y, extrapolate=False)(5.0)) # 1.0 nanRemember
- Use
CubicSplinefor smooth curves,PchipInterpolatorto avoid overshoot - Interpolants are callable and support derivatives and integrals
- Use smoothing splines for noisy data; avoid extrapolating
Watch out for
- Using the legacy
interp1din new code.