numpy vectorize multidimensional function

As mentioned in the notes for vectorize:

The vectorize function is provided primarily for convenience, not for performance. The implementation is essentially a for loop.

So while vectorizing your code may be a good idea via numpy types and functions, you probably shouldn't do this using numpy.vectorize.

For the example you gave, your cost might be simply and efficiently calculated as a function operating on a numpy array:

def cost(x):    # Create the empty output     output = np.empty(x.shape)    # Select the first group using a boolean array    group1 = (0 < x) & (x < 15)     output[group1] = np.sin(x[group1])*x[group1]    # Select second group as inverse (logical not) of group1     output[~group1] = 15 + np.min(        [np.abs(x[~group1]-0), np.abs(x[~group1]-15)],        axis=0)    return output

np.vectorize feeds scalars to your function. For example:

In [1090]: def _cost(u):      ...:     return u*2In [1092]: cost=np.vectorize(_cost)In [1093]: cost(np.arange(10)      ...: )Out[1093]: array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])In [1094]: cost(np.ones((3,4)))Out[1094]: array([[ 2.,  2.,  2.,  2.],       [ 2.,  2.,  2.,  2.],       [ 2.,  2.,  2.,  2.]])

But your function acts as though it is getting a list or array with 2 values. What were you intending?

A function with 2 scalars:

In [1095]: def _cost(u,v):      ...:     return u+v      ...:           ...: In [1096]: cost=np.vectorize(_cost)In [1098]: cost(np.arange(3),np.arange(3,6))Out[1098]: array([3, 5, 7])In [1099]: cost([[1],[2]],np.arange(3,6))Out[1099]: array([[4, 5, 6],       [5, 6, 7]])

Or with your 2 column x:

In [1103]: cost(x[:,0],x[:,1])Out[1103]: array([-1.7291913 , -0.46343403,  0.61574928,  0.9864683 , -1.22373097,        1.01970917,  0.22862683, -0.11653917, -1.18319723, -3.39580376])

which is the same as doing an array sum on axis 1

In [1104]: x.sum(axis=1)Out[1104]: array([-1.7291913 , -0.46343403,  0.61574928,  0.9864683 , -1.22373097,        1.01970917,  0.22862683, -0.11653917, -1.18319723, -3.39580376])