Vector-valued function interpolation using NumPy/SciPy

Question

Is there a way to interpolate a vector-valued function using NumPy/SciPy?

There are plenty of offerings that work on scalar-valued functions, and I guess I can use one of those to estimate each component of the vector separately, but is there a way to do it more efficiently?

To elaborate, I have a function f(x) = V, where x is scalar and V is a vector. I also have a collection of xs and their corresponding Vs. I would like to use it to interpolate and estimate V for an arbitrary x.

Answer 1

The interpolation function scipy.interpolate.interp1d also works on vector-valued data for the interpolant (not for vector-valued argument data though). Thus, as long as x is scalar, you can use it directly.

The following code is a slight extension of the example given in the scipy documentation:

>>> from scipy.interpolate import interp1d
>>> x = np.linspace(0, 10, 10)
>>> y = np.array([np.exp(-x/3.0), 2*x])
>>> f = interp1d(x, y)
>>> f(2)
array([ 0.51950421,  4.        ])
>>> np.array([np.exp(-2/3.0), 2*2])
array([ 0.51341712,  4.        ])

Note that 2 is not in the argument vector x, thus the interpolation error for the first component in y in this example.