How to interpolate one-dimensional data with SciPy

Measurements often arrive at fewer positions than downstream calculations require. A shape-preserving interpolator estimates values inside the measured interval without treating the original samples as noisy observations to be fitted.

SciPy's PchipInterpolator uses a monotone piecewise cubic curve and does not overshoot when the input data is not smooth. This makes it a better fit than an ordinary cubic spline for a signal whose increases or decreases must remain intact between samples.

The measured x values must be strictly increasing and contain no duplicates, while the matching y array must use the same length along the interpolation axis. Setting extrapolate=False keeps the script from extending the curve beyond its evidence and returns NaN for out-of-range queries.

1. Create interpolate_1d.py with the SciPy import and measured signal arrays.

   interpolate_1d.py

   import numpy as np
   from scipy.interpolate import PchipInterpolator
    
   x_measured = np.array([0.0, 10.0, 20.0, 30.0, 40.0])
   y_measured = np.array([0.2, 1.1, 1.8, 2.4, 2.7])

2. Add the shape-preserving interpolator below the measured arrays.

   interpolator = PchipInterpolator(
       x_measured,
       y_measured,
       extrapolate=False,
   )

3. Add the query-point evaluation below the interpolator definition.

   x_query = np.array([5.0, 15.0, 25.0, 35.0])
   y_interpolated = interpolator(x_query)

4. Add the formatted signal output below the query evaluation.

   print("Interpolated signal:")
   for x_value, y_value in zip(x_query, y_interpolated):
       print(f"x={x_value:4.1f} -> y={y_value:.3f}")

5. Add the validation block at the end of the script.

   samples_preserved = np.allclose(
       interpolator(x_measured),
       y_measured,
   )
   outside_values = interpolator(np.array([-5.0, 45.0]))
   outside_blocked = np.isnan(outside_values).all()
    
   print()
   print("Known samples preserved:", samples_preserved)
   print("Outside range returns NaN:", outside_blocked)
    
   if not (samples_preserved and outside_blocked):
       raise RuntimeError("Interpolation checks failed")

6. Run the completed script to verify its interpolation behavior.

   $ python3 interpolate_1d.py
   Interpolated signal:
   x= 5.0 -> y=0.677
   x=15.0 -> y=1.468
   x=25.0 -> y=2.131
   x=35.0 -> y=2.581
   
   Known samples preserved: True
   Outside range returns NaN: True