python - Evaluate the output from scipy 2D interpolation along a curve

Question

I have data z sampled from a 2D function f at grid points x, y, as in z = f(x, y).

It is easy to interpolate f with scipy.interp2d via f = interp2d(x, y, z).

However, evaluating f(x, y) returns an entire 2D grid as if I had done

xx, yy = np.meshgrid(x, y)
f(xx, yy)

The behaviour I want is to simply return the values [f(x[i], y[i]) for i in range(len(x))], which I believe is the behaviour for pretty much any other method in numpy.

The reason I want this behaviour is that I'm looking for the path traced out along the surface of f over "time" by the pair (t, u(t)).

It is also surprising that np.diag(f(t, u(t))) differs from np.array([f(ti, u(ti)) for ti in t]), so It's not clear to me how to get at the path f(t, u(t)) from what is returned via interp2d.

EDIT: About diag, I just thought it seemed we should have np.diag(f(t, u(t))) == np.array([f(ti, u(ti)) for ti in t]), but that isn't the case.

Complete example:

def f(t, u):
    return (t**2) * np.exp((u**2) / (1 + u**2))

x = np.linspace(0, 1, 250)
xx, yy = np.meshgrid(x, x)

z = f(xx, yy)
f = scipy.interpolate.interp2d(x, y, z)

print(f(x, y))
print(np.array([f(xi, yi)[0] for xi, yi in zip(x, y)]))

I would like the output of both print statements to be the same.

Answer 1

The method interp2d returns an object whose call method expects the x, y vectors to be coordinates of a rectangular grid. And the reason you don't get the desired values from the diagonal of the returned array is that it sorts x, y first.

But there is a workaround, which I also used in Querying multiple points on a bivariate spline in the B-spline basis. After executing

import scipy.interpolate as si
f = si.interp2d(x, y, z)

evaluate f not by calling it, but by passing its tck properties, followed by your x, y coordinates, to internal bispeu method. Like this:

print(si.dfitpack.bispeu(f.tck[0], f.tck[1], f.tck[2], f.tck[3], f.tck[4], x, y)[0])

The above returns the same as the slow loop

print(np.array([f(xi, yi)[0] for xi, yi in zip(x, y)]))

Explanation

The object f is secretly a B-spline of order 1. The spline parameters (knots, coefficients, order) are contained in its tck property and can be used directly by lower-order routines to the desired effect.

(Ideally, the call method of f would have a Boolean parameter grid which we'd set to False to let it know we don't want grid evaluation. Alas, it's not implemented.)