How can I give specific x values to `scipy.interpolate.splev`?

Question

How can I interpolate a hysteresis loop at specific x points? Multiple related questions/answers are available on SOF regarding B-spline interpolation using scipy.interpolate.splprep (other questions here or here). However, I have hundreds of hysteresis loops at very similar (but not exactly same) x positions and I would like to perform B-spline interpolation on all of them at specific x coordinates.

Taking a previous example:

import numpy as np
from scipy import interpolate
from matplotlib import pyplot as plt

x = np.array([23, 24, 24, 25, 25])
y = np.array([13, 12, 13, 12, 13])

# append the starting x,y coordinates
x = np.r_[x, x[0]]
y = np.r_[y, y[0]]

# fit splines to x=f(u) and y=g(u), treating both as periodic. also note that s=0
# is needed in order to force the spline fit to pass through all the input points.
tck, u = interpolate.splprep([x, y], s=0, per=True)

# evaluate the spline fits for 1000 evenly spaced distance values
xi, yi = interpolate.splev(np.linspace(0, 1, 1000), tck)

# plot the result
fig, ax = plt.subplots(1, 1)
ax.plot(x, y, 'or')
ax.plot(xi, yi, '-b')
plt.show()

Is it possible to provide specific x values to interpolate.splev? I get unexpected results:

x2, y2 = interpolate.splev(np.linspace(start=23, stop=25, num=30), tck)

fig, ax = plt.subplots(1, 1)
ax.plot(x, y, 'or')
ax.plot(x2, y2, '-b')
plt.show()

Answer 1

The b-spline gives x and y positions for a given u (between 0 and 1). Getting y positions for a given x position involves solving for the inverse. As there can be many y's corresponding to one x (in the given example there are places with 4 y's, for example at x=24).

A simple way to get a list of (x,y)'s for x between two limits, is to create a filter:

import numpy as np
from scipy import interpolate
from matplotlib import pyplot as plt

x = np.array([23, 24, 24, 25, 25])
y = np.array([13, 12, 13, 12, 13])

# append the starting x,y coordinates
x = np.r_[x, x[0]]
y = np.r_[y, y[0]]

tck, u = interpolate.splprep([x, y], s=0, per=True)

# evaluate the spline fits for 1000 evenly spaced distance values
xi, yi = interpolate.splev(np.linspace(0, 1, 1000), tck)

# plot the result
fig, ax = plt.subplots(1, 1)
ax.plot(x, y, 'or')
ax.plot(xi, yi, '-b')

filter = (xi >= 24) & (xi <= 25)
x2 = xi[filter]
y2 = yi[filter]
ax.scatter(x2, y2, color='c')

plt.show()