Interpolating Vector Functions Using NumPy / SciPy

Question

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

There are many suggestions that work on scalar functions, and I assume that I can use one of them to evaluate each component of the vector separately, but is there a way to do this more efficiently?

To develop, I have a function f(x) = V , where x is a 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 with vector-valued data for interpolation (but not for vector argument values). Thus, as long as x is scalar, you can use it directly.

The following code is a small extension of the example provided in the meager 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 , so there is an interpolation error for the first component in y in this example.